CN109804479B - Hot carrier solar cell and method of forming the same - Google Patents

Abstract

Various embodiments may provide a hot carrier solar cell. The solar cell may include a nanocrystal layer including or comprising one or more nanocrystals, each of the one or more nanocrystals including a halide perovskite material. The hot carrier solar cell may further include a first electrode in contact with the first side of the nanocrystal layer. The hot carrier solar cell may further include a second electrode in contact with a second side of the nanocrystal layer, wherein the second side is opposite the first side. The nanocrystal layer may have a thickness of less than 100 nm.

Description

Hot carrier solar cell and method of forming same

related application

This application claims priority from Singapore Patent Application No. 10201606182S filed on 27 July 2016, the contents of which are hereby incorporated by reference in their entirety.

technical field

Various aspects of the present disclosure relate to hot carrier solar cells. Various aspects of the disclosure relate to methods of forming hot carrier solar cells.

Background technique

A feature common to all current solar cells is that solar photons (from ultraviolet to infrared wavelengths) have energies greater than the semiconductor bandgap and can generate free carriers or excitons with excess energy beyond the bandgap; these current carriers Carriers or excitons with a temperature higher than the material lattice temperature are called "hot carriers" or "hot excitons". This excess carrier energy is kinetic free energy and is rapidly (on sub-picosecond timescales) lost by converting the excess kinetic energy into heat through electron-phonon scattering. In 1961, Shockley and Queisser (SQ) calculated the maximum possible thermodynamic efficiency for conversion of solar irradiance to electrical free energy in solar cells based on the assumption that radiative recombination was the only other free energy loss mechanism and complete hot-carrier cooling. This calculation yields a theoretical maximum thermodynamic efficiency of 31–33%, with an optimal bandgap between about 1.1 eV and 1.4 eV.

Thermodynamic calculations in 1982 first showed that if the excess energy of thermally photogenerated carriers is harnessed before cooling to the lattice temperature, the conversion efficiency can reach 66%, thereby surpassing the SQ limit and improving solar cell efficiency. One approach is to transport the hot carriers to a carrier-collecting contact with an appropriate work function before the carriers cool down. These cells are known as hot carrier solar cells. Therefore, the research community is continuously searching for suitable solar cell absorber materials with slow hot-carrier cooling properties.

During the early development of nanotechnology, it was initially thought that quantum confinement in semiconductor nanocrystals (NCs) could slow down the hot-carrier cooling process through the phonon bottleneck effect. However, further investigations revealed that slow hot-carrier cooling in quantum-confined systems remains challenging due to alternative fast relaxation routes that may exceed the phonon bottleneck. Therefore, it is highly desirable to develop new materials with slow hot-carrier cooling properties.

Contents of the invention

Various embodiments may provide hot carrier solar cells. The solar cell may include a layer of nanocrystals comprising or comprising one or more nanocrystals, each of the one or more nanocrystals comprising a halide perovskite material. The hot carrier solar cell can also include a first electrode in contact with the first side of the nanocrystal layer. The hot carrier solar cell can also include a second electrode in contact with a second side of the nanocrystal layer, wherein the second side is opposite the first side. The nanocrystalline layer may have a thickness of less than 100 nm.

Various embodiments may provide methods of forming hot carrier solar cells. The method can include providing or forming a nanocrystal layer comprising one or more nanocrystals (as described herein), each of the one or more nanocrystals comprising a halide perovskite material. The method may also include forming the first electrode such that the first electrode is in contact with the first side of the nanocrystal layer. The method can also include forming a second electrode such that the second electrode is in contact with a second side of the nanocrystal layer, wherein the second side is opposite the first side. The nanocrystalline layer may have a thickness of less than 100 nm.

Description of drawings

The invention may be better understood by reference to the detailed description taken in conjunction with the non-limiting examples and drawings in which:

Figure 1 shows a general illustration of nanocrystals according to various embodiments.

Figure 2 shows a general illustration of a hot carrier solar cell according to various embodiments.

FIG. 3 shows a schematic diagram of a method of forming nanocrystals according to various embodiments.

FIG. 4 shows a schematic diagram of a method of forming a hot carrier solar cell according to various embodiments.

Figure 5 shows a schematic diagram of (a) intra-band Auger energy transfer, (b) phonon bottleneck effect and (c) hot-carrier cooling of inter-band Auger process in semiconductor nanocrystals.

Figure 6 shows the structure of methylamine lead bromide perovskite (MAPbBr ₃ ) nanocrystals (NCs) with relatively (a) small size, (c) medium size and (e) large size, according to various embodiments. Typical transmission electron microscope (TEM) image with corresponding size histograms (b,d,f) on the right. The size distribution can be modeled with a Gaussian distribution.

Figure 7 shows scanning electron microscope (SEM) images of (a) top view and (b) side view of a methylamine lead bromide ( _MAPbBr3 ) bulk film.

Figure 8 shows (a) a graph of photoluminescence (PL) intensity (arbitrary units or au) versus wavelength (nanometers or nm) representing methylamine lead bromide dispersed in toluene according to various embodiments Photoluminescence (PL) spectra of perovskite (MAPbBr ₃ ) nanocrystals (NCs) and their bulk film counterparts; (b) plot of absorbance (arbitrary units or au) versus wavelength (nanometers or nm), indicating dispersion Ultraviolet-visible (UV-vis) absorption spectra of methylamine lead bromide perovskite (MAPbBr ₃ ) nanocrystals (NCs) and bulk film counterparts according to various examples in toluene; (c) 1s Graph of exciton energy E _1s (electron volts or eV) versus nanocrystal mean radius a (nanometers or nm) representing the 1s excitons of methylamine lead bromide perovskite (MAPbBr ₃ ) according to various embodiments and (d) plots of X-ray diffraction (XRD) intensity (arbitrary units or au) versus angle 2θ (in degrees) for three different sizes of formazan according to various embodiments XRD patterns of amine lead bromide perovskite (MAPbBr ₃ ) nanocrystals (NC).

Figure 9A shows a false-color transient absorption (TA) map of medium-sized methylamine lead bromide perovskite nanocrystals ( _MAPbBr3NC ) (radius ~4-5 nm) in solution according to various embodiments ( Upper panel, time (picosecond or ps) vs. energy (electron volts or eV) plot) and normalized transient absorption (TA) spectrum (lower panel, normalized transmittance change ΔT/T vs. energy (electron volts or eV) volts or eV), where at low pump power densities (left graph), the average electron-hole pairs generated per nanocrystal initially are <N ₀ >～0.1 (average current-carrying per nanocrystal volume sub-density n _0avg ～2.6×10 ¹⁷ cm ^-3 ), at high pump power density (right figure) <N ₀ >～2.5 (n _0avg ～6.5×10 ¹⁸ cm ^-3 ).

Figure 9B shows a false-color representation of the bulk film of MAPbBr ₃ (upper panel, time (picosecond or ps) and normalized transient absorption (TA) spectrum (lower panel, normalized transmittance change ΔT/T vs. Energy (electron volts or eV)). At low pump power density (left), the initial carrier density is n ₀ ~ 2.1×10 ¹⁷ cm ³ , and at high pump power density ( Right picture) n ₀ ~ 1.5×10 ¹⁹ cm ³ .

Figure 10 shows a graph of time (picoseconds or ps) versus energy (electron volts or eV) representing (a) small and (b) large size methylammonium bromide in solution according to various embodiments Pbbr perovskite nanocrystal (MAPbBr ₃ NC) pseudocolor transient absorption (TA) spectra (time in picoseconds or ps versus energy in electron volts or eV). After 3.1eV photoexcitation, the initial average electron-hole pairs per nanocrystal are <N ₀ >～0.1 at low pump power density (left figure), and <N at high pump power density (right figure) ₀ > ~ 2.5.

Figure 11 shows (a) a plot of normalized transmittance change ΔT/T versus energy (electron volts or eV) for meso-sized methylamine lead bromide calcium titanium in toluene according to various embodiments Normalized TA spectra of ore nanocrystals (MAPbBr ₃ NC) at different short delay times, the average electron-hole pairs <N ₀ >~0.1 generated per nanocrystal (after 3.1eV photoexcitation); and (b ) Unnormalized transient absorption (TA) spectrum of (a).

Figure 12 shows a graph of carrier temperature (Kelvin or K) versus time (picoseconds or ps), representing meso-sized nanocrystals (NC) and Time evolution of the hot-carrier temperature _Tc of the bulk film: hot-carrier density n ₀ for initial photoexcitation (bulk film) and electron-hole pairs <N ₀ > averagely generated per NC, where <N ₀ >=Jσ, where J is the pump power density, and σ is the absorption cross section.

Figure 13 shows (a) a graph of photoluminescence (PL) intensity (arbitrary units or au) versus time (nanoseconds or ns) for mesoscale methylamine lead bromide perovskites according to various embodiments Pump power density dependence of time-resolved photoluminescence (PL) of ore nanocrystals (MAPbBr ₃ NC) under 3.1eV light excitation; (b) transient photoluminescence (PL) intensity (arbitrary unit or au) on pump Graph of intensity (microjoules/cm2 or μJ cm ⁻² ) representing normalized PL intensity versus pump power density at measurement time Δt=4 ns for three different sizes of MAPbBr ₃ NCs according to various embodiments and (c) a plot of the probability of occupancy (percentage or %) versus the number of electron-hole (eh) pairs per NC according to various embodiments.

In the table shown in Figure 14, the methylamine lead bromide perovskite nanocrystal (MAPbBr ₃ NC) according to various embodiments, the methylamine lead bromide perovskite bulk film and the reported in the literature are compared. properties of other materials.

15 shows the carrier temperature ( _Kelvin or K) Graphs versus time delay (picoseconds or ps), where (a) at low pump power densities (equivalent to <N ₀ > ~ 0.1 in NC, n ₀ ~ 2.1×10 ¹⁷ cm in bulk membranes ³ ), (b) under high pump power density (equivalent to <N ₀ >~2.5 in NC, n ₀ ~1.5×10 ¹⁹ cm ³ in bulk membrane).

Figure 16 shows a graph of normalized transmittance change ΔT/T versus time (picoseconds or ps) for methylamine lead bromide in solution (a) bulk film, (b) according to various Small-sized nanocrystals (NCs) of the embodiments, (c) medium-sized nanocrystals (NCs) according to various embodiments, and (d) large-sized nanocrystals (NCs) according to various embodiments, respectively, at high pump power Density and low pump power density, normalized photobleaching kinetics at band-edge detection; and (e) meso-sized nanocrystals (NC) in solution according to various embodiments and Transient absorption (TA) kinetics comparison of spin-coated nanocrystal (NC) films of Pump power density dependence of probed bleaching kinetics.

Figure 17 shows (a) a plot of energy loss rate (electron volts per picosecond eV ps ^-1 ) versus carrier temperature (Kelvin or K) for methylamine lead calcium bromide according to various embodiments Titanium nanocrystal (MAPbBr ₃ NC) (where <N ₀ >～0.1) and methylamine lead bromide perovskite (MAPbBr ₃ ) bulk film (where n ₀ ～2.1×10 ¹⁷ cm ^-3 ) supported Graph of carrier temperature _Tc versus energy loss rate of hot carriers; (b) graph of normalized transmittance change ΔT/T versus time (picoseconds or ps), representing colloidal Normalized bleaching kinetics of band-edge probing of methylamine lead bromide perovskite nanocrystals (MAPbBr ₃ NC) and bulk films at low carrier densities; and (c) rise time (femtosecond or fs )/confinement energy (electron volts or eV), representing methylamine lead bromide perovskite nanocrystals (MAPbBr ₃ NC) (black solid squares), bulk films (light colored solid squares) (particle sizes given by The size dependence of the rise time of band-edge bleaching in cadmium selenide nanocrystals (CdSe NCs) (closed circles), and the quantum confinement energy in _MAPbBr3 NCs (open squares) and CdSe NCs (open circles) rely.

18 shows a graph of Raman intensity (arbitrary units or au) versus wavenumber (per centimeter or cm ⁻¹ ) for methylamine lead bromide perovskite nanocrystals (MAPbBr _{3 )} prepared according to various embodiments. NC) Room temperature Raman spectra of drop-coating on glass substrates.

Figure 19 shows (a) a plot of normalized transmittance change ΔT/T versus time (picoseconds or ps) for colloidal CdSe NCs with different diameters (indicated in the legend) at low pump power densities Normalized bleaching kinetics for lower band edge detection; and (b) a plot of time (picoseconds or ps) versus energy (electron volts or eV) showing initial generation of <N ₀ >∼0.1 at low pump power densities (left), <N ₀ >~2.5 at high pump power density (right). The photoexcitation energy is 3.1 eV.

20 shows (a) a plot of energy loss rate (electron volts per picosecond or eV ps ⁻¹ ) versus carrier temperature (Kelvin or K) for methylamine lead bromide according to various embodiments. The relationship between energy loss rate and carrier temperature T _c of perovskite nanocrystal MAPbBr ₃ NC (<N ₀ >～2.5) and MAPbBr ₃ bulk film (n ₀ ～1.5×10 ¹⁹ cm ^-3 ); (b ) lifetime (picosecond or ps) versus nanocrystal volume (cubic nanometer or nm ³ ), illustrating perovskite nanocrystal (NC) volume versus Auger recombination lifetime and hot carrier cooling according to various embodiments Dependence of time, and (c) a plot of normalized hot carrier concentration _nhot versus time (picoseconds or ps), showing the normalized heat load at different pump power densities according to various embodiments Flow decay.

Figure 21 is a graph of energy loss rate (electron volts per picosecond or eV ps ^-1 ) versus carrier temperature (Kelvin or K) showing a bulk film of methylamine lead bromide (MAPbBr ₃ ) at low current-carrying Carrier density and hot carrier energy loss rate at high carrier density as a function of carrier temperature _Tc .

Figure 22 shows a graph of photoelectron intensity (counts per second or cts/s) versus energy (electron volts or eV) representing (a) 1,2-ethanedithiol on an indium tin oxide (ITO) substrate (EDT) treated and (b) post-annealed EDT treated methylamine lead bromide (MAPbBr ₃ ) nanocrystalline (NC) films according to various embodiments, and (c) 7-diphenyl-1 , Ultraviolet photoelectron spectroscopy (UPS) of 10-phenanthroline (Bphen) film.

23A is a flat-band energy diagram (vertical axis electron volts or eV) to illustrate thermal electron transfer from perovskite nanocrystals to 7-diphenyl-1,10-phenanthroline (Bphen) according to various embodiments Extraction and competition of thermionic cooling pathways.

Figure 23B shows an atomic force microscope (AFM) image of a 1,2-ethanedithiol (EDT)-treated nanocrystalline (NC) film according to various embodiments.

23C is a scanning electron scan of a 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/7-diphenyl-1,10-phenanthroline (Bphen) bilayer film according to various embodiments Microscope (SEM) images.

FIG. 23D is a graph of normalized transmittance change ΔT/T versus energy (electron volts or eV) with (continuous line)/without (dashed line) 7-diphenyl-1,10 according to various embodiments. -Normalization of about 35 nm thick 1,2-ethanedithiol (EDT)-treated nanocrystalline (NC) films of phenanthroline (Bphen) after 3.1 eV photoexcitation (<N ₀ >about 0.1) Transient Absorption (TA) Spectroscopy.

23E is 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film and 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film/7 according to various embodiments - Plot of hot carrier temperature (Kelvin or K) versus delay time (picoseconds or ps) for biphenyl-1,10-phenanthroline (Bphen) bilayer films at different pump power densities.

23F is a graph of extraction efficiency η _hot (percentage or %) versus hot electron excess energy (electron volts or eV), showing the efficiency of about 35 nm thick 1,2-ethanedithiol (EDT) treatment according to various embodiments. Pump energy dependence of hot electron extraction efficiency in nanocrystalline (NC)/7-diphenyl-1,10-phenanthroline (Bphen) bilayers.

Figure 23G is a graph of extraction efficiency η _hot (percentage or %) versus thickness (nanometers or nm) representing 1,2-ethanedithiol (EDT)-treated nanocrystals (NC)/7 according to various embodiments -Diphenyl-1,10-phenanthroline (Bphen) bilayer film and bulk film/7-diphenyl-1,10-phenanthroline (Bphen) bilayer film excited by 3.1eV pump energy Perovskite film thickness dependence of hot electron extraction efficiency.

Figure 24(a) shows a graph of transmittance (arbitrary units or au) versus wavenumber (per centimeter or cm ^-1 ) for methylamine lead bromide nanocrystals (MAPbBr ₃ NCs), 1,2-ethanedithiol (EDT)-treated nanocrystals (EDT-NC) and 70°C annealed 1,2-ethanedithiol nanocrystals (Ann-EDT-NC) attenuated total reflection- Fourier transform infrared (ATR-FTIR) spectra; and plots of light emission intensity (arbitrary units or au) versus binding energy (electron volts or eV) representing (b) unannealed and (c) according to various embodiments Sulfur (S)2p X-ray photoelectron spectroscopy (XPS) of 1,2-ethanedithiol (EDT)-treated nanocrystal (EDT-NC) films annealed at 70 °C.

Figure 25 shows (a) atomic force microscopy (AFM) images of untreated medium-sized methylamine lead bromide nanocrystal (MAPbBr ₃ NC) films according to various embodiments, and (b) Representative transmission electron microscope (TEM) image of 1,2-ethanedithiol-treated methylamine lead bromide nanocrystals (EDT-treated MAPbBr ₃ NC).

Figure 26 shows (a) medium-sized methylamine lead bromide nanocrystal (MAPbBr ₃ NC) film according to various embodiments, (b) 1,2-ethanedithiol-treated Nanocrystalline (EDT-treated NC) films, and (c) 1,2-ethanedithiol-treated nanocrystalline films/7-diphenyl-1,10-phenanthroline (EDT-treated False-color transients of NC film/Bphen) bilayer film at low pump power density (left picture, <N ₀ >～0.1) and high pump power density (right picture, <N ₀ >～2.5) Absorption (TA) Spectrum.

Figure 27 shows an energy graph (y-axis: energy in electron volts or eV) representing the non-volatile energy in accordance with various embodiments determined from ultraviolet photoelectron spectroscopy (UPS) and ultraviolet-visible (UV-VIS) spectroscopy measurements. Flat-band level alignment of annealed, annealed 1,2-ethanedithiol-nanocrystal (EDT-NC) films and 7-diphenyl-1,10-phenanthroline (Bphen) for hot electron extraction The situation is described.

Figure 28(a) shows a graph of absorbance (arbitrary unit or au) versus wavelength (nanometer or nm) representing the linear absorption spectrum of a Bphen film on glass; (b) normalized negative transmittance change— A graph of ΔT/T versus wavelength (nanometer or nm) for 7-diphenyl-1,10-phenanthroline (Bphen) (300nm pump intensity is 20μJ cm ^-2 ; 400nm pump intensity is 40μJ cm ^{- 2} ), perovskite nanocrystals (NC) (400nm pump intensity of 15 μJ cm ⁻² ) according to various embodiments and 1,2-ethanedithiol nanocrystals/7-diphenyl Negative transient absorption spectrum of 1,10-phenanthroline (EDT-NC/Bphen) (400nm pump intensity 15μJ cm ^-2 ) at 2ps after excitation; (c) time (picosecond or ps) versus wavelength (nano or nm) graph representing 1,2-ethanedithiol-treated nanocrystals/7-diphenyl-1,10-phenanthroline (EDT-NC/Bphen) bis Pseudocolor transient absorption (TA) spectra of the layer film excited by 400nm light with a pump intensity of 15μJ cm ^-2 ; (d) Normalized negative transmittance change——ΔT/T versus time (picosecond or ps) Graph, Bphen excited with 300 nm light, and 1,2-ethanedithiol-treated nanocrystals/7-diphenyl-1,10-phenanthroline (EDT-NC/Bphen) according to various examples Normalized negative transient absorption spectrum of a bilayer film pumped with 400 nm light and probed at 1300 nm.

29 is a graph of normalized transmittance change ΔT/T versus time (picoseconds or ps) for 1,2-ethanedithiol-treated nanocrystal (EDT-NC) films and 1,2-ethanedithiol-treated nanocrystal/7-diphenyl-1,10-phenanthroline (EDT-NC/Bphen) bilayers according to various embodiments at (a) low pump power Normalized band-edge bleaching kinetics for 3.1 eV photoexcitation at density (<N ₀ >～0.1) and (b) high pump power density (<N ₀ >～2.5).

30A is a graph of normalized transmittance change ΔT/T versus energy (electron volts or eV) showing 7-diphenyl-1 with (continuous line) and without (dashed line) annealed according to various embodiments. , 1,2-ethanedithiol-treated (EDT-treated) medium-sized methylamine lead bromide nanocrystal (MAPbBr ₃ NC) films of 10-phenanthroline (Bphen)-extracted layer at low pump power densities <N ₀ > ~ 0.1 normalized transient absorption spectrum.

30B is a graph of carrier temperature (Kelvin or K) versus time (picoseconds or ps) showing extracted hot carrier temperature versus delay time for two samples according to various embodiments.

Figure 30C is a graph of normalized transmittance change ΔT/T versus energy (electron volts or eV) with (continuous line) and without (dashed line) 7-diphenyl-1,10-phenanthroline ( Normalized transient absorption (TA) spectrum of 2×10 ¹⁷ cm ^-3 bulk film (~240nm thick) of methylamine lead bromide (MAPbBr ₃ ) bulk film (~240nm thick) in Bphen) extraction layer at low pump power density.

Figure 30D shows a graph of carrier temperature (Kelvin or K) versus time delay (picoseconds or ps) for two samples according to various embodiments.

31 shows cross-sectional scanning electron microscope (SEM) images of 1,2-ethanedithiol-treated nanocrystals (EDT-NC films) with different thicknesses, according to various embodiments.

Detailed ways

The drawings show, by way of illustration, specific details and embodiments in which the invention may be practiced. The embodiments are described in detail below, by referring to the accompanying drawings, enough to enable those skilled in the art to practice the invention. Other embodiments may be utilized and structural, logical, and electrical changes may be made without departing from the scope of the present invention. The various embodiments are not necessarily mutually exclusive, as some embodiments can be combined with one or more other embodiments to form new embodiments.

Embodiments described in the context of one method or nanocrystal/solar cell/device are similarly valid for other methods or nanocrystals/solar cells/devices. Similarly, embodiments described in the context of a method are similarly valid for nanocrystals/solar cells/devices, and vice versa.

Features described in the context of an embodiment may correspondingly apply to the same or similar features in other embodiments. Even if not explicitly described in these other embodiments, features described in the context of an embodiment may apply to other embodiments accordingly. Furthermore, additions and/or combinations and/or substitutions as described for features in the context of an embodiment may correspondingly apply to identical or similar features in other embodiments.

The term "on" as used with reference to deposited material formed "on" a side or surface may be used herein to indicate that the deposited material may be formed "directly", eg, in direct contact, on the implied side or surface. The term "on" as used with reference to deposited material formed "on" a side or surface may also be used herein to indicate that deposited material may be formed "indirectly" on an implied side or surface, where on the implied side Or one or more additional layers are arranged between the surface and the deposition material. In other words, a first layer "on" a second layer can mean that the first layer is directly on the second layer, or that the first and second layers are separated by one or more intervening layers.

The articles "a", "an" and "the" used with reference to a feature or element in the context of various embodiments include reference to one or more features or elements.

In the context of the various embodiments, the term "about" or "approximately" as applied to a numerical value includes the exact value and a reasonable variance.

As used herein, the term "and/or" includes any and all combinations of one or more of the associated listed items.

Since 2013, organic-inorganic lead halide perovskite semiconductors (such as MAPbX ₃ , MA=CH ₃ NH ₃ , X=I, Br, or Cl) have emerged as the most promising candidates for high-performance and low-cost solar cells. One of the material family. Solution-processed perovskite polycrystalline films have been used as light-absorbing layers in solar cell devices. It is currently documented that the efficiency in the laboratory of perovskite-based solar cells with _MAPbX3 as absorber can be ~20%. Recently, observations of slow hot-carrier cooling and thermal phonon bottleneck effects in MAPbI _thin films suggest that lead halide perovskites may be promising materials for constructing hot-carrier solar cells.

Figure 1 shows a general illustration of a nanocrystal 100 according to various embodiments. Nanocrystal 100 may include a halide perovskite material.

The diameter of the nanocrystals may be selected from the range of 1 nm to 100 nm, eg 4 nm to 14 nm, or 4 nm to 13 nm.

The radius of the nanocrystals may be any value selected from 0.5 nm to 50 nm (eg, from 2 nm to 7 nm).

In the present context, "from X to Y" or "a range of X to Y" means that the range includes the X and Y values in addition to all values between X and Y.

Various embodiments may slow down the hot carrier cooling process through phonon bottleneck effects or inter-band Auger processes (also known as Auger heating). Various embodiments can be used in solar cells that can overcome the SQ limitation by harvesting excess energy from photons above the bandgap, thereby increasing efficiency.

Inorganic semiconductor nanocrystals (NCs) have been previously investigated as candidate materials for slowing down the hot-carrier cooling process. However, hot-carrier harvesting in these inorganic semiconductor nanocrystals is compromised by highly competing relaxation paths (eg, in-band Auger processes, defects) that overwhelm their phonon bottlenecks. For example, the effect of phonon bottlenecks on cadmium selenide (CdSe) quantum dots remains elusive due to Auger processes and structural defects, as reported by Kilina et al. (“Quantum Zeno effect rationalizes phonon bottlenecks in semiconductor quantum dots”, Phys. Review Letters 110, 180404, pp. 1-6, 2013).

The present inventors have surprisingly found that colloidal halide perovskite NCs may transcend these limitations. Compared with their bulk film counterparts, halide perovskite NCs can exhibit ~2 orders of magnitude longer hot-carrier cooling time and ~4 times higher hot-carrier temperature. Surprisingly, at low pump excitations, hot-carrier cooling mediated by the phonon bottleneck may be slower in smaller NCs (compared to conventional NCs, cooling time decreases with size shorten). At high pump power densities, Auger heating may dominate hot-carrier cooling, which is slower in larger NCs (so far not observed in conventional NCs).

The present inventors demonstrated efficient room-temperature hot electron extraction (up to ~83%) within 1 picosecond (ps) via an energy-selective electron extraction layer from a surface-treated perovskite NC thin film. These insights could lead to new approaches for extremely thin absorbers and/or concentrating hot-carrier solar cells.

Halide perovskite materials can be represented by the general formula AMX ₃ , where A can be an organic or inorganic cation (such as an organic radical or organic cation or metal cation or element) with one positive charge, or an organic and/or inorganic Positive ion mixture. M can be a divalent metal cation or an element, and X can be a halogen anion or an element. Examples may include CH ₃ NH ₃ PbI ₃ (MAPbI ₃ ), CH ₃ NH ₃ PbBr ₃ (MAPbBr ₃ ), CH ₃ NH ₃ PbBr ₂ I (MAPbBr ₂ I), CsSnI ₃ , CsPbI ₃ , NH ₂ CH═NH ₂ PbI ₃ (FAPbI ₃ ), FA _1-y Cs _y PbI ₃ or Cs _x (MA _1-y FA _y ) _1-x Pb(I _1-z Br _z ) ₃ (each of x, y or z are numbers between 0 and 1). MA can be formamide (CH ₃ NH ₃ ), and FA can be formamidine (NH ₂ CH=NH ₂ ).

In various embodiments, the divalent positive ion may be Pb ²⁺ or Sn ²⁺ . In other words, M may be lead (Pb) or tin (Sn).

In various embodiments, the halide perovskite material may include one or more halide anions selected from I ⁻ , Cl ⁻ and Br ⁻ . In other words, X ₃ can be I ₃ , Cl ₃ , Br ₃ or combinations thereof (eg, Cl ₂ Br).

In various embodiments, the halide perovskite material can include organic ammonium cations. Organic ammonium cation A can be selected from ammonium cation, hydroxylammonium cation, methylammonium cation (MA ⁺ ), hydrazine cation, azetidine cation, formamidine cation (FA ⁺ ), imidazolium cation , dimethylammonium cation, ethylammonium cation, phenethylammonium cation, guanidinium cation, and combinations thereof. The organoammonium cation may be a cation with the general formula C _n H _2n+1 NH ₃₊ , where 2<n<20. In other words, A may be C _n H _2n+1 NH ₃ . In various embodiments, the halide perovskite material may include metal cations, such as cesium ions (Cs ⁺ ).

Nanocrystal 100 may exhibit a hot carrier cooling lifetime of anywhere from at least 0.5 ps, for example from 0.5 ps to 40 ps. The hot-carrier cooling lifetime can be defined as the time interval from pulse excitation until hot-carrier cooling to 600K.

FIG. 2 shows a general illustration of a hot carrier solar cell 200 according to various embodiments. Solar cell 200 may include nanocrystal layer 202 comprising or comprising one or more nanocrystals (as described herein), each of the one or more nanocrystals comprising a halide perovskite material. The hot carrier solar cell 200 can also include a first electrode 204 in contact with the first side of the nanocrystal layer 202 . The hot carrier solar cell 200 may also include a second electrode 206 in contact with a second side of the nanocrystal, wherein the second side is opposite the first side. Nanocrystal layer 202 may have a thickness of less than 100 nm.

In other words, solar cell 200 may include nanocrystal layer 202 that includes one or more nanocrystals. Layer 202 may be sandwiched between electrodes 204,206.

Nanocrystal layer 202 may also be referred to as an absorber layer or a hot carrier absorber. In various embodiments, the thickness of layer 202 may be less than the hot carrier diffusion length such that hot carriers may be extracted through electrodes 204, 206 prior to cooling.

The hot carrier solar cell 200 may receive incident light (from the sun) and may be configured to generate electrical energy based on solar energy from the incident light.

In various embodiments, the hot carrier solar cell 200 may further include optics to direct solar energy (from the sun) to the nanocrystal layer 202 . In various embodiments, the hot carrier solar cell 200 may be a concentrating hot carrier solar cell. The optics may include one or more optical elements to direct solar energy to nanocrystal layer 202 . The one or more optical elements may be or may include optical lenses and/or mirrors. At higher pump power densities, hot carrier cooling may become slower as the photoexcited charge carrier density increases. At pump power densities above 1 electron-hole pair in nanocrystals (corresponding to an effective bulk carrier density of about 10 ¹⁸ cm ^-3 ), the hot-carrier cooling lifetime may exceed 30 ps (comparable to that in bulk films 1.5ps compared to ), which may be due to the Auger heating effect in the quantum confined system. These features can be advantageously used in concentrating solar cells that operate at higher power densities by focusing light onto a certain point on the photovoltaic cell. As shown later, the hot-carrier lifetime of perovskite NCs may be longer at high pump power densities compared with other materials. These features may be beneficial for the application of concentrating hot-carrier solar cells, which can operate at higher illuminance (on the order of or beyond 1000 suns) by using hot-carrier absorbers.

In various embodiments, the hot carrier solar cell 200 may be a single junction solar cell. In various alternative embodiments, hot carrier solar cell 200 may be a multi-junction solar cell.

In various embodiments, the first electrode 204 may be or may include a hot electron extraction layer.

In various embodiments, the first electrode 204 may be or may include an n-type layer. The n-type layer or hot electron extraction layer may comprise any one of the following materials: titanium oxide, zinc oxide, phenyl-C61-butyric acid methyl ester (PCBM), 4,7-diphenyl-1,10 -Phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK), 2-(4-biphenyl)-5-phenyl-1,3,4-oxadiazole (PBD), 2 ,2',2"-(1,3,5-phenylpyrrole)-tris(1-phenyl-1-H-benzimidazole) (TPBI), poly(9,9-dioctylfluorene) ( F8) and bathocuprine (BCP).

In various embodiments, the first electrode 204 may be an energy selective contact that allows passage of electrons having an excess energy equal to or above a predetermined value and also reflects electrons having an excess energy below a predetermined value. Returning to nanocrystal layer 202 . In the present context, excess energy may refer to electron energy that exceeds the conduction band minimum of nanocrystal layer 202 . The predetermined value of excess energy may be any value selected from a range from about 0.1 eV to 2 eV.

In various embodiments, the second electrode 206 may be or include a hot hole extraction layer.

In various embodiments, the second electrode 206 may be or may include a p-type layer.

In various embodiments, the second electrode 206 may be an energy-selective contact that allows holes with excess energy equal to or above a predetermined value to pass through, and also passes holes with excess energy below the predetermined value. The holes reflect back to the nanocrystal layer 202. In the present context, excess energy may refer to hole energy that exceeds the valence band maximum of nanocrystal layer 202 . The predetermined value of excess energy may be any value selected from a range from about 0.1 eV to 2 eV. In various embodiments, the second electrode 206 may include a molecular semiconductor material. The p-type layer or the hot hole extraction layer may comprise any one of the following materials: 2,2',7,7'-Tetrakis[N,N-bis(4-methoxyphenyl)amino]- 9,9'-spirobifluorene (spiro-OMeTAD), poly(3-hexylthiophene-2,5-ylidene) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrenesulfonic acid salt (PEDOT:PSS) and poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)diphenylamine (TFB).

In various embodiments, the one or more nanocrystals exhibit a hot carrier cooling lifetime of at least 0.5 ps, eg, greater than 30 ps. The radius of each of the one or more nanocrystals is selected from any value in the range from 0.5nm to 50nm, for example in the range from 2nm to 7nm.

In various embodiments, the halide perovskite material may be an organic-inorganic halide perovskite material such as MAPbI ₃ , MAPbBr ₃ , MAPbBr ₂ I, FAPbI ₃ , FA _1-y Cs _y PbI ₃ , or Cs _x (MA _1-y FA _y ) _1-x Pb(I _1-z Br _z ) ₃ (where each of x, y or z can be any value selected from the range of 0 to 1). Non-limiting specific examples may include CH ₃ NH ₃ PbI ₃ , CH ₃ NH ₃ PbBr ₃ , CH ₃ NH ₃ PbBr ₂ I or NH ₂ CH═NH ₂ PbI ₃ . In various other embodiments, the halide perovskite material can be an inorganic halide perovskite material, such as _CsSnI3 or _CsPbI3 .

Very rapid extraction of hot carriers may be required to limit energy loss, where competition exists between extraction rate and cooling rate, rather than recombination rate. In various embodiments, the one or more nanocrystals can be treated with 1,2-ethanedithiol (EDT).

Here we demonstrate efficient hot-carrier transfer from 1,2-ethanedithiol (EDT)-treated _MAPbBr3 NCs (EDT-NC) to 4,7-diphenyl-1,10-phenanthroline (Bphen) extract. Bphen can be chosen as the hot electron extraction material because this molecular semiconductor has high electron mobility and a higher lowest unoccupied molecular orbital (LUMO) than the conduction band minimum (CBM) of EDT-treated NCs. EDT treatment can be used to replace the long and highly insulating oleic acid ligands present on the surface of the as-prepared NCs with thiolates for more efficient electronic coupling with Bphen within the NC membrane.

FIG. 3 shows a schematic diagram 300 of a method of forming nanocrystals according to various embodiments. The method may include, at 302, using a solution method to form nanocrystals comprising a halide perovskite material.

The diameter of the nanocrystals may be selected from the range of 1 nm to 100 nm, eg 4 nm to 14 nm.

The solution method may include mixing various precursors with a solvent to form a precursor solution. The plurality of precursors may include organic ammonium halides. The solution method may further include adding one or more ligands and/or one or more surfactants to the precursor solution. For example, methylammonium bromide (MABr, where MA represents methylamine) can be mixed with lead bromide ( _PbBr2 ) in a solvent of dimethylformamide (DMF) to form an initial precursor solution. Oleylamine (OAm) and oleic acid (OAc) can be added to the DMF solvent to form the final precursor solution for the formation of methylamine lead bromide perovskite nanocrystals.

The solution method may further include heating an additional solvent. The additional solvent may be heated to a predetermined temperature, for example 60°C. The solution method may additionally include mixing the precursor solution with heated additional solvent with stirring to form nanocrystals. Another solvent may be toluene.

FIG. 4 shows a schematic diagram 400 of a method of forming a hot carrier solar cell according to various embodiments. The method may include, at 402, providing or forming a nanocrystal layer comprising one or more nanocrystals (as described herein), wherein each of the one or more nanocrystals comprises a calcium halide Titanium material. The method may also include, at 404, forming a first electrode such that the first electrode is in contact with the first side of the nanocrystal layer. The method may also include, at 406, forming a second electrode such that the second electrode is in contact with a second side of the nanocrystal layer, wherein the second side is opposite the first side. The nanocrystalline layer may have a thickness of less than 100 nm.

In other words, a method of forming a solar cell as described herein may be provided. A solar cell can include an electrode and a nanocrystal layer comprising one or more nanocrystals as described herein.

For the avoidance of doubt, the method steps shown in Fig. 4 are not necessarily performed sequentially. For example, in various embodiments, the first electrode may be formed prior to forming the nanocrystal layer.

In various embodiments, the method can further include forming an optical device that directs solar energy to the nanocrystal layer. The optical device may include one or more optical elements that direct solar energy to the nanocrystal layer. The one or more optical elements may be or may include optical lenses and/or mirrors.

In various embodiments, the first electrode 204 may be or may include a hot electron extraction layer.

In various embodiments, the first electrode 204 may be or may include an n-type layer. The n-type layer or hot electron extraction layer may comprise any one of the following materials: titanium oxide, zinc oxide, phenyl-C61-butyric acid methyl ester (PCBM), 4,7-diphenyl-1,10 -Phenanthroline (Bphen), poly(9-vinylcarbazole) (PVK), 2-(4-biphenyl)-5-phenyl-1,3,4-oxadiazole (PBD), 2 ,2',2"-(1,3,5-phenylpyrrole)-tris(1-phenyl-1-H-benzimidazole) (TPBI), poly(9,9-dioctylfluorene) ( F8) and bathocuprine (BCP).

In various embodiments, the first electrode 204 may be an energy selective contact that allows passage of electrons having an excess energy equal to or above a predetermined value and also reflects electrons having an excess energy below a predetermined value. Returning to nanocrystal layer 202 . In the present context, excess energy may refer to electron energy that exceeds the conduction band minimum of nanocrystal layer 202 . The predetermined value of excess energy may be any value selected from a range from about 0.1 eV to 2 eV.

In various embodiments, the second electrode 206 may be or include a hot hole extraction layer.

In various embodiments, the second electrode 206 may be or may include a p-type layer.

In various embodiments, the second electrode 206 may be an energy-selective contact that allows holes with excess energy equal to or above a predetermined value to pass through, and also passes holes with excess energy below the predetermined value. The holes are reflected back to the nanocrystal layer 202 . In the present context, excess energy may refer to hole energy that exceeds the valence band maximum of nanocrystal layer 202 . The predetermined value of excess energy may be any value selected from a range from about 0.1 eV to 2 eV. In various embodiments, the second electrode 206 may include a molecular semiconductor material. The p-type layer or the hot hole extraction layer may comprise any one of the following materials: 2,2',7,7'-Tetrakis[N,N-bis(4-methoxyphenyl)amino]- 9,9'-spirobifluorene (spiro-OMeTAD), poly(3-hexylthiophene-2,5-ylidene) (P3HT), poly(3,4-ethylenedioxythiophene) polystyrenesulfonic acid salt (PEDOT:PSS) and poly(9,9-dioctyl-fluorene-co-N-(4-butylphenyl)diphenylamine (TFB).

In various embodiments, the one or more nanocrystals exhibit a hot carrier cooling lifetime of at least 0.5 ps, eg, greater than 30 ps. The radius of each of the one or more nanocrystals is selected from any value in the range from 0.5nm to 50nm, such as any value in the range from 2nm to 7nm.

In various embodiments, the halide perovskite material may be an organic-inorganic halide perovskite material such as MAPbI ₃ , MAPbBr ₃ , MAPbBr ₂ I, FAPbI ₃ , FA _1-y Cs _y PbI ₃ , or Cs _x (MA _1-y FA _y ) _1-x Pb(I _1-z Br _z ) ₃ (where each of x, y or z can be any value selected from the range of 0 to 1). Non-limiting specific examples may include CH ₃ NH ₃ PbI ₃ , CH ₃ NH ₃ PbBr ₃ , CH ₃ NH ₃ PbBr ₂ I or NH ₂ CH═NH ₂ PbI ₃ . In various other embodiments, the halide perovskite material can be an inorganic halide perovskite material, such as _CsSnI3 or _CsPbI3 .

Various embodiments may provide solution-processed colloidal MAPbBr ₃ (methylamine lead bromide) perovskite nanocrystals (NCs), a very promising absorber material for hot-carrier solar cells. Hot-carrier cooling may be significantly slower than bulk perovskite films. Under comparable photoexcitation conditions, the hot-carrier cooling time in _MAPbBr3 NCs can be increased to 30 ps (or higher), which is about 2 orders of magnitude slower than its bulk film counterpart. Furthermore, the hot-carrier temperature of _MAPbBr3 NCs is 4 times larger than that of their bulk film counterparts under comparable photoexcitation conditions.

Controlling hot-carrier cooling dynamics can be challenging but is critical to improving the performance of many semiconductor photonic and electronic devices. In NCs, the hot carrier cooling time/rate can depend on volume and carrier density. Therefore, these findings can be exploited to control hot-carrier cooling by tuning the NC size and carrier injection density.

Hot carrier cooling in NCs according to various embodiments can be tuned by varying the dimensions of the NCs. The hot-carrier cooling rate may be lower in smaller-sized NCs due to the confinement-induced phonon bottleneck effect. In addition to MAPbBr ₃ perovskite NCs, there are perovskite NCs substituted by other organic components and/or metal elements, such as MAPbI ₃ , MAPbBr _x I _1-x (x is the ratio of Br/(Br+I), in The synthesis process is determined by the content of Br and I in the precursor), CsSnI ₃ , CsPbI ₃ , FAPbI ₃ . NCs can allow the selection of a wide variety of hot-carrier absorbers with different bandgaps. Furthermore, hot electrons from NC films can be efficiently injected (up to ~83%) into the electron extraction layer within ~1 ps after surface chemical treatment. These insights can provide new approaches for hot-carrier and light-harvesting perovskite NC photovoltaic devices.

Various embodiments may relate to the preparation of low-temperature solution-processed organic-inorganic perovskite nanocrystals, the observation of slow hot-carrier cooling, and/or the use of these nanocrystals in hot-carrier solar cells and concentrator thermal Potential applications of flowon solar cells. In contrast to conventional hot-carrier solar cell systems, concentrated hot-carrier solar cells can focus sunlight by a factor of 300 to 1000 on a small cell area using focusing lenses or curved mirrors. Thus, the concentrating cells can be operated at much higher light-generating current densities than conventional hot-carrier solar cells. Higher injection density can lead to higher hot-carrier temperature and longer hot-carrier lifetime, which can further improve the efficiency of hot-carrier solar cells.

Nanocrystals can be prepared using low temperature solution processing methods in the atmosphere. In contrast, traditional silicon-based solar cells are typically produced at high temperatures using high-vacuum growth techniques, requiring large infrastructure investments.

Thermodynamic calculations show that the conversion efficiency of single-junction solar cells can reach about 66% under 1-sun irradiation if the excess energy of thermal photogenerated carriers is utilized before cooling to the lattice temperature. The key to efficiently extracting hot-carrier energy is to delay hot-carrier cooling. It is widely believed that the conservation of energy and momentum and the impossibility of multiphonon processes will lead to phonon bottlenecks that slow down hot-carrier cooling in semiconductor nanoscale systems. However, further research revealed that the cooling rate becomes faster as the size of the nanoscale inorganic semiconductor decreases.

Hot-carrier cooling can be critical in many photonic and electronic devices. For integration with existing silicon-based technologies, solution-processable materials offer greater versatility than conventional materials. It can be applied to a wider range of device designs and substrates by simple spin, dip or drop coating.

Compared to traditional silicon thin films produced using expensive gas-phase methods, solution-processed organic-inorganic perovskite nanocrystals could provide a simple and inexpensive material alternative for potential photovoltaic applications. Low-temperature processing could also enable the integration of these materials into flexible substrates. Perovskite NCs can have slower hot-carrier cooling than current perovskite films used as absorbers in solar cells that allow efficient hot-carrier extraction. These features may be beneficial for the realization of hot-carrier solar cells. Furthermore, as first observed in perovskite NCs, the hot-carrier cooling time/rate can also be tuned by modifying the NC size.

Various embodiments can be widely used in photovoltaic applications as absorber materials, such as NC-sensitized nanocrystalline _TiO2 solar cells, concentrator solar cells, NC conductive polymer hybrid solar cells, pin-structured solar cells, and/or concentrator solar cells .

FIG. 5 shows a schematic diagram 500 of Auger process hot carrier cooling in semiconductor nanocrystals. In (a), hot-carrier cooling is made possible by in-band Auger-type energy transfer. Hot electrons (dots) can be cooled to densely spaced hole states (e.g., CdSe NCs) by Auger-type energy transfer, and then hot holes (circles) can be rapidly relaxed by single phonon cascade emission (arrows); (b ) shows the phonon bottleneck effect causing slow hot-carrier cooling in the symmetric conduction and valence bands with discrete energy levels, while (c) shows the thermal Carrier re-excitation, also known as Auger-heating.

Alternative fast relaxation pathways (e.g., in-band Auger-type energy transfer in Figure 5 (a in Figure 5), atomic fluctuations, and surface effects) suppress this perceived acoustic Sub-bottlenecks are very efficient.

The reduced dimensionality also creates a competing effect at higher carrier densities: interband Auger recombination. The latter Auger re-excitation process (also known as Auger heating, as shown in (c) in Fig. 5) will decelerate the hot-carrier cooling process. Thus, hot-carrier cooling in nanoscale inorganic semiconductors is involved in a complex interplay of different mechanisms. To date, slow hot-carrier cooling has been extremely challenging, even with strongly quantum-confined inorganic semiconductor nanocrystals. Despite advances in theory and materials synthesis, practical hot-carrier colloidal nanocrystal (NC) photovoltaics remain elusive. Although slow in-band hot electron cooling is found at the lowest excitation level (1P _e −1S _e ) in strongly confined PbSe quantum dots, the confined hot electrons must interact with holes with a particularly well-designed epitaxially grown multi-outer layer dissociated in order to reduce the aforementioned competing relaxation pathways. However, multiple outer layers complicate subsequent charge extraction. Therefore, it may be necessary to design NCs that can simultaneously meet the two criteria of slow hot-carrier cooling and efficient charge extraction.

Organic-inorganic lead halide perovskite semiconductors ₍ eg _MAPbX3 , where MA= _CH3NH3 , X=I, Br or Cl) have recently become the main contenders in low-cost high-performance solar cells. Recent observations of the thermophonon bottleneck effect in _MAPbI thin films at high carrier densities suggest that lead halide perovskites are also promising candidates for the development of hot-carrier solar cells. Analogous to semiconductor nanoscience, an interesting question is whether the hot-carrier cooling rate in halide perovskites can be further tuned through confinement effects. Here, the hot-carrier cooling in colloidal _MAPbBr3 NCs (Fig. 6) and their bulk film counterparts (Fig. 7) of different sizes (average radius ~2.5–5.6 nm) are compared using room temperature transient absorption (TA) spectroscopy. Kinetics and Mechanisms.

Figure 6 shows the structure of methylamine lead bromide perovskite (MAPbBr ₃ ) nanocrystals (NCs) with relatively (a) small size, (c) medium size and (e) large size, according to various embodiments. Typical transmission electron microscope (TEM) image with corresponding size histograms (b,d,f) on the right. The size distribution can be modeled with a Gaussian distribution. Figure 7 shows scanning electron microscope (SEM) images of (a) top view and (b) side view of a methylamine lead bromide ( _MAPbBr3 ) bulk film.

Figure 8 shows (a) a graph of photoluminescence (PL) intensity (arbitrary units or au) versus wavelength (nanometers or nm) representing methylamine lead bromide dispersed in toluene according to various embodiments Photoluminescence (PL) spectra of perovskite (MAPbBr ₃ ) nanocrystals (NCs) and their bulk film counterparts; (b) plot of absorbance (arbitrary units or au) versus wavelength (nanometers or nm), indicating dispersion Ultraviolet-visible (UV-vis) absorption spectra of methylamine lead bromide perovskite (MAPbBr ₃ ) nanocrystals (NCs) and bulk film counterparts according to various examples in toluene; (c) 1s Graph of exciton energy E _1s (electron volts or eV) versus nanocrystal mean radius a (nanometers or nm) representing the 1s excitons of methylamine lead bromide perovskite (MAPbBr ₃ ) according to various embodiments and (d) plots of X-ray diffraction (XRD) intensity (arbitrary units or au) versus angle 2θ (in degrees) for three different sizes of formazan according to various embodiments XRD patterns of amine lead bromide perovskite (MAPbBr ₃ ) nanocrystals (NC).

The exciton Bohr radius a _B of _MAPbBr3 is reported to be ∼2 nm. Given that the radius of the NCs (from ~2.5 to 5.6 nm, see the size distribution histogram in Fig. 6) is larger than _aB , the NCs are weakly confinement. Therefore, the slight blue shift in the emission of NCs (from 525 to 517 nm, Fig. 8(a)) as the size of NCs decreases may be due to the weak confinement effect. In the weak confinement, the relationship of the first exciton resonance of the NC to the radius a of the NC can be written as:

E_b是激子结合能。使用上面的等式(1)和有效质量的报告值

可以合理地拟合NC的吸收边(参见图8(c)中的线)以产生带隙为E_g0～2.38eV，结合能为E_b～50meV，接近MAPbBr₃NC的报告值。这些拟合结果进一步验证了根据各种实施例的钙钛矿NC中的弱限制。where E _g0 is the bandgap energy without quantum confinement, while the second term represents the confinement energy, μ is the electron-hole reduction mass,

E _b is the exciton binding energy. Using equation (1) above and the reported value of the effective mass

The absorption edge of the NC (see line in Fig. 8(c)) can be reasonably fitted to yield a bandgap of _Eg0 ~2.38eV and a binding energy of _Eb ~50meV, close to the reported values for _MAPbBr3NC . These fitting results further validate the weak confinement in perovskite NCs according to various embodiments.

The results show that weakly confinement MAPbBr ₃ NCs (Fig. 8) are very promising hot-carrier absorber materials due to their higher hot-carrier temperature and longer cooling time (compared to compared to typical perovskite bulk films under the same conditions). This may be attributed to their intrinsic phonon bottleneck and Auger heating effect at low and high carrier densities, respectively. Importantly, hot carriers can be efficiently extracted from _MAPbBr3 NC thin films at room temperature by using molecular semiconductors as energy-selective contacts.

Figure 9A shows a false-color transient absorption (TA) map of medium-sized methylamine lead bromide perovskite nanocrystals ( _MAPbBr3NC ) (radius ~4-5 nm) in solution according to various embodiments ( Upper panel, time (picosecond or ps) vs. energy (electron volts or eV) plot) and normalized transient absorption (TA) spectrum (lower panel, normalized transmittance change ΔT/T vs. energy (electron volts or eV) volts or eV), where at low pump power densities (left graph), the average electron-hole pairs generated per nanocrystal initially are <N ₀ >～0.1 (average current-carrying per nanocrystal volume sub-density n _0avg ～2.6×10 ¹⁷ cm ^-3 ), at high pump power density (right figure) <N ₀ >～2.5 (n _0avg ～6.5×10 ¹⁸ cm ^-3 ). Figure 9B shows a false-color representation of the bulk film of MAPbBr ₃ (upper panel, time (picosecond or ps) and normalized transient absorption (TA) spectrum (lower panel, normalized transmittance change ΔT/T vs. Energy (electron volts or eV)). At low pump power density (left), the initial carrier density is n ₀ ~ 2.1×10 ¹⁷ cm ³ , and at high pump power density ( Right picture) n ₀ ~ 1.5×10 ¹⁹ cm ³ .

Figures 9A-B show false-color TA plots and TA spectral comparisons of medium-sized _MAPbBr3 NCs (radius ~4.5nm) and _MAPbBr3 bulk films at low and high pump power densities, respectively. For both types of samples, the plots/spectra show prominent photobleaching (PB) peaks with high energy band tails near the band gap due to state filling effects. Similar results were also observed in small and large NCs.

Figure 10 shows a graph of time (picoseconds or ps) versus energy (electron volts or eV) representing (a) small and (b) large size methylammonium bromide in solution according to various embodiments Pbbr perovskite nanocrystal (MAPbBr ₃ NC) pseudocolor transient absorption (TA) spectra (time in picoseconds or ps versus energy in electron volts or eV). After 3.1eV photoexcitation, the initial average electron-hole pairs per nanocrystal are <N ₀ >～0.1 at low pump power density (left figure), and <N at high pump power density (right figure) ₀ > ~ 2.5.

For bulk film samples, the high-energy band tail of the PB peak originates from the initial nonequilibrium carrier through elastic scattering characterized by the carrier temperature _Tc (including electron-hole scattering at low pump power density and at Carrier-carrier scattering at high pump energy densities) quickly distributes into the Fermi-Dirac distribution. T _c can thus be extracted by fitting the high-energy band tail of the TA spectrum to the simple Maxwell-Boltzmann function exp(E _f -E/κ _B T _c ), where κ _B is the Boltzmann constant, _Ef is the quasi-Fermi energy.

For NC, in the case of thermal energy k _B T >> energy level spacing ΔE, discrete energy levels can be approximately regarded as continuous. Compared with conventional semiconducting NCs with strong confinement, perovskite NCs may be in a weakly confinement state with more closely spaced energy levels. Therefore, in the microscopic image of a single point, we expect efficient electron-hole scattering (due to the enhanced Coulomb interaction) and carrier-carrier scattering at high pump power densities can make the fast athermal energy distribution evolve into a Fermi-Dirac-like distribution within 150 fs. In macroscopic maps, TA spectra can be collected from collections of NCs whose size distribution can lead to inhomogeneous broadening (i.e., overlapping TA spectra from individual NCs). All these properties correctly lead to continuous TA spectra of NC ensembles similar to those of bulk materials. Therefore, the high-energy band tail of the TA spectrum of NC can also be described by the Maxwell-Boltzmann distribution. A representative fit of the high-energy band tail and unnormalized TA spectra is shown in Fig. 11. Figure 11 shows (a) a plot of normalized transmittance change ΔT/T versus energy (electron volts or eV) for meso-sized methylamine lead bromide calcium titanium in toluene according to various embodiments Normalized TA spectra of ore nanocrystals (MAPbBr ₃ NC) at different short delay times, the average electron-hole pairs <N ₀ >~0.1 generated per nanocrystal (after 3.1eV photoexcitation); and (b ) Unnormalized transient absorption (TA) spectrum of (a). The solid black line in (a) fits the high-energy band tail using the Maxwell-Boltzmann distribution function.

It is evident from the false-color TA curves and spectra that for NCs the high-energy band tail of the PB peak (starting from a kink in the spectrum starting from the exponentially decaying region, see Fig. 11) persists much longer than the bulk film, It shows that the carrier temperature is higher and the hot carrier cooling is slower.

The analysis and interpretation of the TA spectra of halide perovskites are well documented in the literature. The TA spectra of _MAPbBr3 perovskites (both bulk and nanocrystalline) are similar to previous studies. The positive TA peak (~2.3eV, as shown in Figure 11) is caused by ground state bleaching (GSB) due to the state filling of carriers at the band edge. On the high-energy side of the GSB peak, the first slope (i.e., the slope closer to the GSB peak) is determined by ground-state transitions that affect its width and shape; while the second, gentler slope of the high-energy band tail (e.g., from ~2.5eV start) is generated by hot carrier distribution. The negative part of this high energy side (photoinduced absorption) is caused by the photoinduced change of the imaginary part of the refractive index. Whereas the negative part at the low energy side of the GSB is attributed to the bandgap renormalization.

The hot-carrier temperature T _c was extracted by fitting the high-energy band tail of the TA spectrum using a Maxwell-Boltzmann function. When the difference between the energy of the carriers and the Fermi level is large compared to κ _B T (ie, EE _f > κ _B T), the Fermi-Dirac distribution function can be described by an exponential approximation, that is, Maxwell-Bo Altzmann distribution:

Approximating the Fermi-Dirac distribution of hot-carrier energies >> _Ef with the Maxwell-Boltzmann distribution is an efficient and generally accepted practice for extracting the hot-carrier temperature _Tc . For intrinsic (untreated) perovskite NCs and bulk films, the Fermi level can be located between the valence and conduction band edges (~0.4eV below the conduction band minimum of ultraviolet photoelectron spectroscopy (UPS) data (see below)). Therefore, hot carriers generated may be far away from the Fermi energy (above ~1 eV). Although the Fermi level may shift slightly towards the band edge (~0.1eV) under intense photoexcitation, the energy difference can still be very large (i.e. EE _f >>κ _BT (~25meV at room temperature). Therefore, one can The high-energy band tail of the TA spectrum was fitted using a Maxwell-Boltzmann distribution to extract _Tc .

Figure 12 shows a graph of carrier temperature (Kelvin or K) versus time (picoseconds or ps), representing meso-sized nanocrystals (NC) and Time evolution of the hot-carrier temperature _Tc of the bulk film: hot-carrier density n ₀ for initial photoexcitation (bulk film) and electron-hole pairs <N ₀ > averagely generated per NC, where <N ₀ >=Jσ, where J is the pump power density, and σ is the absorption cross section.

Figure 13 shows (a) a graph of photoluminescence (PL) intensity (arbitrary units or au) versus time (nanoseconds or ns) for mesoscale methylamine lead bromide perovskites according to various embodiments Pump power density dependence of time-resolved photoluminescence (PL) of ore nanocrystals (MAPbBr ₃ NC) under 3.1eV light excitation; (b) transient photoluminescence (PL) intensity (arbitrary unit or au) on pump Graph of intensity (microjoules/cm2 or μJ cm ⁻² ) representing normalized PL intensity versus pump power density at measurement time Δt=4 ns for three different sizes of MAPbBr ₃ NCs according to various embodiments and (c) a plot of the probability of occupancy (percentage or %) versus the number of electron-hole (eh) pairs per NC according to various embodiments.

给出，其中<N₀>＝Jσ是最初生成的每个NC的e-h对的平均数量(J是泵浦功率密度，σ是NC的吸收截面)。当光激发后的延迟时间比多载流子复合(例如，俄歇复合)长得多时，NC可能主要与单个激子发射复合，因此后期PL强度可能与光激发的NC的占据概率成比例，为/>

图13(b)显示当完成多载流子复合时，泵浦功率密度相关的TRPL的时间分辨光致发光(PL)的泵浦功率密度依赖在时间t＝4ns时归一化，并且PL强度代表仅具有一个电子-空穴对的发射NC。通过将数据拟合为/>

方程(实线)，可以获得NC的σ。对于从小到大的NC，拟合的σ分别为8.5±0.5×10^-15,3.2±0.2×10^-14和6.8±0.3×10^-14cm²。Based on the Poisson distribution of the initial photon occupancy in the NC, the probability that the NC contains an i pair of eh pairs is given by

where <N ₀ >=Jσ is the average number of eh pairs per NC initially generated (J is the pump power density, σ is the absorption cross-section of the NC). When the delay time after photoexcitation is much longer than multi-carrier recombination (e.g., Auger recombination), NCs may mainly recombine with single exciton emission, so the late PL intensity may be proportional to the occupancy probability of photoexcited NCs, for />

Figure 13(b) shows that the pump power density dependence of the time-resolved photoluminescence (PL) of TRPL with respect to the pump power density is normalized at time t = 4 ns when multi-carrier recombination is complete, and the PL intensity represents an emitting NC with only one electron-hole pair. By fitting the data to />

Equation (solid line), the σ of NC can be obtained. For small to large NCs, the fitted σ were 8.5±0.5×10 ⁻¹⁵ , 3.2±0.2×10 ⁻¹⁴ and 6.8±0.3×10 ⁻¹⁴ cm ² , respectively.

For comparison with bulk films, the average carrier density per NC volume in the NC can also be determined, defined as n _0avg =N ₀ /V _NC , where V _NC is the NC volume. For NCs, the maximum _Tc for <N ₀ >˜0.1 at the onset of excitation can be about 1700 K, which is about 4 times higher than for bulk film samples with comparable carrier densities. The smaller _Tc in the latter can be attributed to the ultrafast cooling of hot carriers, which occurs on a much shorter timescale than the temporal resolution of the TA measurements.

It should be noted that the complex interplay of hot-carrier cooling times results from several factors: (i) the pump energy (i.e., the excess energy of the carriers - in general, higher excess energy leads to longer hot-carrier lifetimes) ; (ii) initial hot-carrier density (i.e., generally higher carrier density results in longer hot-carrier lifetime); and/or (iii) energy loss rate at a specific hot-carrier temperature (i.e., generally The lower the hot carrier temperature, the smaller the energy loss rate). Therefore, due care must be taken to make a fair comparison of values reported in the literature. More discussion on hot-carrier lifetime comparisons between different materials can be found in the "Hot-carrier lifetime" section below.

Furthermore, in order to compare the hot-carrier cooling lifetimes of different materials reported in the literature more clearly and easily, the hot-carrier cooling lifetime described in this paper can be defined as the time from pulse excitation to hot-carrier cooling to 600K interval. This temperature is used as a benchmark, as previous theoretical calculations have shown that for _Tc >600K, significant hot-carrier conversion efficiencies (ie >40%) are still possible over a wide range of absorber bandgaps.

Taking these factors into account, hot-carrier cooling lifetimes from <0.1 ps to 0.8 ps at n ₀ ~2.1-15×10 ¹⁸ cm ⁻³ were obtained for the control MAPbBr ₃ bulk film. These lifetimes are identical to those of _MAPbI3 films excited at similar n ₀ and excess energy of 0.7 eV; but shorter than that of highly excited hot carriers at twice the excess energy (~1.44 eV). Notably, MAPbBr ₃ NCs can exhibit 1–2 orders of magnitude longer hot-carrier cooling lifetimes than the perovskite bulk film control samples at similar n _{0 avg} (as shown in Fig. 14). Table 1400 shown in FIG. 14 compares methylamine lead bromide perovskite nanocrystals (MAPbBr ₃ NC) according to various embodiments, methylamine lead bromide perovskite bulk films, and reported in the literature. properties of other materials. As mentioned earlier, the hot-carrier cooling lifetime can be defined as the time interval from pulse excitation to hot-carrier cooling to 600K. 600K can be used as a benchmark, as previous theoretical calculations have shown that, for _Tc >600K, significant hot-carrier conversion efficiencies (i.e., >40%) are still possible over a wide range of absorber bandgaps. TA refers to "transient absorption" and TRPL refers to "time-resolved photoluminescence".

15 shows the carrier temperature ( _Kelvin or K) Graphs versus time delay (picoseconds or ps), where (a) at low pump power densities (equivalent to <N ₀ > ~ 0.1 in NC, n ₀ ~ 2.1×10 ¹⁷ cm in bulk membranes ³ ), (b) under high pump power density (equivalent to <N ₀ >~2.5 in NC, n ₀ ~1.5×10 ¹⁹ cm ³ in bulk membrane). The lifetime of large-scale NCs can be about 40 times longer than that of bulk film samples excited with almost an order of magnitude higher carrier density of 1.5 × ¹⁰ cm ⁻³ . For example, for large-sized NCs with <N ₀ >˜2.5 (or n _0avg ˜3.5×10 ¹⁸ cm ⁻³ ), the hot-carrier cooling lifetime can be as long as ˜32 ps ( FIG. 15 ). In fact, the hot-carrier cooling lifetime of _MAPbBr3 NCs may be much longer than that of other semiconductor bulk and nanomaterials. Referring to Figure 14, for GaAs thin films, the reported cooling lifetime is ~2ps, the carrier density is ~6.0× ^{1018cm -3} , and the excess energy is 1.7eV; for CdSe nanorods, the reported cooling lifetime is ~0.8ps, The carrier density is ~5.5×10 ¹⁸ cm ⁻³ and the excess energy is 1.1 eV. MAPbBr ₃ NCs can have a longer lifetime comparable to 18 ps, excited at a much lower excess energy ~0.7 eV at a comparable carrier density of 6.5×10 ¹⁸ cm ⁻³ .

To discern the slower hot-carrier cooling mechanism in MAPbBr ₃ NCs, the relaxation kinetics under low pump excitations were observed. For <N ₀ >˜0.1, up to 10% of NCs were excited with one eh pair based on a Poisson distribution ( FIG. 13 ). As can be seen from the absence of fast decay of band-edge carriers in NCs (Fig. 16), multi-particle recombination is negligible at such low carrier densities.

Figure 16 shows a graph of normalized transmittance change ΔT/T versus time (picoseconds or ps) for methylamine lead bromide in solution (a) bulk film, (b) according to various Small-sized nanocrystals (NCs) of the embodiments, (c) medium-sized nanocrystals (NCs) according to various embodiments, and (d) large-sized nanocrystals (NCs) according to various embodiments, respectively, at high pump power Density and low pump power density, normalized photobleaching kinetics at band-edge detection; and (e) meso-sized nanocrystals (NC) in solution according to various embodiments and Transient absorption (TA) kinetics comparison of spin-coated nanocrystal (NC) films of Pump power density dependence of probed bleaching kinetics. The (f) inset in Figure 16 shows the Auger recombination component extracted after subtracting single-exciton decay at longer times. The photoexcitation energy is about 3.1 eV.

Therefore, the hot-carrier relaxation mechanism under low pump excitation can represent an intrinsic property of the material and can be immune to extrinsic effects such as multi-particle Auger recombination.

At low pump power densities, _Tc can decay faster with increasing NC size (Fig. 15). Figure 17 shows (a) a plot of energy loss rate (electron volts per picosecond eV ps ^-1 ) versus carrier temperature (Kelvin or K) for methylamine lead calcium bromide according to various embodiments Titanium nanocrystal (MAPbBr ₃ NC) (where <N ₀ >～0.1) and methylamine lead bromide perovskite (MAPbBr ₃ ) bulk film (where n ₀ ～2.1×10 ¹⁷ cm ^-3 ) supported Graph of carrier temperature _Tc versus energy loss rate of hot carriers; (b) graph of normalized transmittance change ΔT/T versus time (picoseconds or ps), representing colloidal Normalized bleaching kinetics of band-edge probing of methylamine lead bromide perovskite nanocrystals (MAPbBr ₃ NC) and bulk films at low carrier densities; and (c) rise time (femtosecond or fs )/confinement energy (electron volts or eV), representing methylamine lead bromide perovskite nanocrystals (MAPbBr ₃ NC) (black solid squares), bulk films (light colored solid squares) (particle sizes given by The size dependence of the rise time of band-edge bleaching in cadmium selenide nanocrystals (CdSe NCs) (closed circles), and the quantum confinement energy in _MAPbBr3 NCs (open squares) and CdSe NCs (open circles) rely. Error bars represent standard errors. The photoexcitation energy of Fig. 17(a)-(c) is 3.1 eV. 18 shows a graph of Raman intensity (arbitrary units or au) versus wavenumber (per centimeter or cm ⁻¹ ) for methylamine lead bromide perovskite nanocrystals (MAPbBr _{3 )} prepared according to various embodiments. NC) Room temperature Raman spectra of drop-coating on glass substrates. The peaks originate from LO phonons. From the Raman measurements shown in Fig. 18, it can be seen that the available phonon models for hot-carrier cooling in _MAPbBr3 NCs are located at about 150 cm ⁻¹ (specified as the stretching of the Pb–Br bond) and 300 cm ⁻¹ ( Possibly from the torsional mode of the 150cm ^-1 second order and/or MA positive ions.

The solid line in Fig. 17(a) represents the numerical fit of the LO-phonon model. Arrows indicate the maximum _Tc achieved by bulk membranes. The inset in Fig. 17(a) shows representative TEM images of small-size (S), medium-size (M) and large-size (L) perovskite NCs. The solid line in Figure 17(b) is a single exponential fit. The inset in Fig. 17(b) shows a schematic diagram of the phonon bottleneck-induced slow thermal carrier cooling in symmetric conduction and valence bands with discrete energy levels.

For all three NCs, the energy loss rate J _r (−1.5κ _B dT _c /dt) per carrier can be slowly decreased in the range of 0.6–0.3 eVps ⁻¹ until T _c reaches ~700K (Fig. 17 (a)), below which _Jr drops by several orders of magnitude until _Tc approaches the lattice temperature. This cooling trend is similar to that of bulk film samples as well as other bulk inorganic semiconductors and nanostructures. Here, the initial rapid cooling (i.e., higher cooling rate) can be attributed to carrier coupling to longitudinal optical (LO)-phonons, which establish thermal equilibrium between the LO phonon population and hot carriers. Comparing different NCs, the initial _Jr of small-sized NCs is ~2 times smaller than that of large-sized NCs (indicating weaker carrier-phonon interactions in the former). The slower cooling of hot carriers near the band edge (ie ~300-500 K in Fig. 17(a)) is then determined by the thermal equilibrium between longitudinal optical phonons (LO phonons) and acoustic phonons.

By fitting the energy loss rate using the LO-phonon interaction model (see LO-phonon model below), the fitted τ _LO (characteristic LO-phonon decay time) increases with decreasing NC dimensionality ( See Fig. 17(a)), which can provide direct evidence that quantum confinement reduces optical phonon relaxation. This is characteristic of the phonon bottleneck effect, thus delaying hot carrier cooling. Although NCs are weakly confinement with confinement energies around ~15–60 meV, several early theoretical papers have shown that even in such weak confinement conditions where energy levels are separated by only a few meV, phonon interactions mediated Carrier relaxation can also still be severely hindered. This is because of the constraints imposed by the conservation of energy and momentum and the weak energy dispersion of longitudinal optical (LO) phonons, which together cause the phonon bottleneck. Furthermore, the acoustic phonon temperature (Ta) of all three NC samples corresponds to ∼310 K, which is close to the lattice temperature at room temperature, strongly suggesting that the slowdown of hot-carrier cooling may be less likely caused by the acoustic phonon bottleneck. cause.

The band-edge bleached stacking method was also used to elucidate the hot-carrier cooling properties. In addition to the approach of fitting the high-energy band tail of the PB peak to elucidate the hot-carrier cooling properties, another approach is to probe the in-band relaxation of photoexcited carriers above the band edge. This can be achieved by monitoring the band-edge bleach buildup, since the recombination (~ns) of band-edge carriers is much slower than its in-band relaxation process (from a few to tens of ps). The latter approach is often used to study hot-carrier dynamics in strongly confined quantum colloidal semiconductor NCs, since overlapping PB bands from discrete energy levels make resolving their hot-carrier distribution extremely challenging. The latter approach can be used for a fair comparison of hot-carrier cooling of perovskite NCs with that of conventional inorganic semiconducting NCs, such as CdSe NCs.

Figure 17(b) shows the normalized TA spectra of perovskite samples detected at their band-edge PB peaks after photoexcitation with similar excess energy at low carrier densities. Each stacking process is fitted with a single exponential growth function to yield a rise time (τ _rise ). Band-edge bleaching rise occurs on sub-picosecond timescales, becoming slower with decreasing NC size, consistent with the smaller _Jr and slower hot-carrier temperature of smaller perovskite NCs Attenuation (Figure 15) is consistent. Surprisingly, perovskite NCs exhibit the exact opposite trend to that of CdSe NCs (spanning the strong to weak quantum confinement region—Fig. 17(c) and Fig. 19).

Figure 19 shows (a) a plot of normalized transmittance change ΔT/T versus time (picoseconds or ps) for colloidal CdSe NCs with different diameters (indicated in the legend) at low pump power densities Normalized bleaching kinetics for lower band edge detection; and (b) a plot of time (picoseconds or ps) versus energy (electron volts or eV) showing initial generation of <N ₀ >∼0.1 at low pump power densities (left), <N ₀ >~2.5 at high pump power density (right). The photoexcitation energy is 3.1 eV. The solid line in Figure 19(a) is a monoexponential growth fit curve. The inset in Fig. 19(a) schematically shows the hot-carrier cooling process by Auger-type energy transfer.

In addition, the rise time of perovskite NCs can also be longer. With the reduction of CdSe NCs, hot-carrier cooling is faster, which is consistent with previous reports, which is attributed to the Auger-type energy transfer from hot electrons to dense hole states. The results clearly demonstrate that this Auger transfer mechanism present in conventional inorganic semiconducting NCs can be naturally suppressed in perovskite NCs. Regarding the schematic energy level diagram of CdSe NCs (Fig. 5), one possible reason could be the symmetric energy dispersion and small effective mass of electrons and holes of perovskite NCs shown in the inset of Fig. 17(b). Other factors such as surface reconstruction, surface defects, atomic fluctuations, etc. may also cause hot-carrier cooling to become faster as the size of inorganic semiconductors decreases (for example, in the quantum-confined IV-VI semiconductor PbSe, with the same and small electron and hole effective mass). Therefore, the low defect density of perovskite NCs (consistent with the high PL quantum yield (∼80%) of _MAPbBr3 NCs) may also be another reason for this unique behavior (i.e., the inherent phonon bottleneck effect). These new insights into the slow hot-carrier cooling of perovskite colloidal NCs (under low pump excitation) may challenge the conventional wisdom of traditional semiconducting NCs.

These perovskite NCs also exhibit unique hot-carrier cooling properties under high pump excitation. 20 shows (a) a plot of energy loss rate (electron volts per picosecond or eV ps ⁻¹ ) versus carrier temperature (Kelvin or K) for methylamine lead bromide according to various embodiments. The relationship between energy loss rate and carrier temperature T _c of perovskite nanocrystal MAPbBr ₃ NC (<N ₀ >～2.5) and MAPbBr ₃ bulk film (n ₀ ～1.5×10 ¹⁹ cm ^-3 ); (b ) lifetime (picosecond or ps) versus nanocrystal volume (cubic nanometer or nm ³ ), illustrating perovskite nanocrystal (NC) volume versus Auger recombination lifetime and hot carrier cooling according to various embodiments Dependence of time, and (c) a plot of normalized hot carrier concentration _nhot versus time (picoseconds or ps), showing the normalized heat load at different pump power densities according to various embodiments Flow decay. The solid line in Fig. 20(a) represents the LO-phonon model at low carrier density. The dashed line in Fig. 20(b) shows the square root of nanocrystal (NC) volume versus lifetime, while the inset illustrates the hot-carrier re-excitation of band-edge carrier Auger recombination (also known as Auger heating ), and the error bars represent standard errors. The solid line in Figure 20(c) is a double exponential decay fit. The photoexcitation energy of Fig. 20(a)-(c) is 3.1 eV. The bulk film thickness is about 240nm.

Figure 20(a) shows the energy loss rate versus carrier temperature between three different sizes of NCs (<N ₀ >~2.5) and bulk film samples (n ₀ ~1.5×10 ¹⁹ cm ^-3 ) comparative trend. For both NC and bulk films, the initial hot-carrier cooling controlled by carrier-LO-phonon interactions may be almost independent of carrier density. This conclusion can be drawn from (i) the initial fast decay _Tc at different carrier densities is almost the same (Fig. 12), and (ii) the initial energy loss rate at high The carrier density is similar to that at high carrier density (Fig. 17(a) and Fig. 20(a)). For bulk films, the extension of hot-carrier lifetime below 600 K (Fig. 12) and the slight deviation of _Jr from the LO phonon model (line in Fig. 20(a)) may be due to the “thermal phonon bottleneck effect” (commonly observed in bulk inorganic semiconductors and recently reported for _MAPbI thin films). This can be attributed to the reduced LO phonon attenuation caused by partial heating of the acoustic model. This assumption can be supported by the higher acoustic phonon temperature _T of 350 K at high pump power density.

Figure 21 is a graph of energy loss rate (electron volts per picosecond or eV ps ^-1 ) versus carrier temperature (Kelvin or K) showing a bulk film of methylamine lead bromide (MAPbBr ₃ ) at low current-carrying Carrier density and hot carrier energy loss rate at high carrier density as a function of carrier temperature _Tc . The solid line represents the fit of the numerical fit equation (3) (shown in the "LO-phonon model" section below). The fitted LO phonon lifetime τ _LO and acoustic temperature T _a at low and high carrier densities are 150±20, 280±20fs, and 305±10 and 350±10K, respectively.

However, for NCs, as shown in Fig. 20(a), although the J _r (<N ₀ > ~ 2.5) of NCs initially follow the LO-phonon model at high carrier temperatures, they are not consistent with the LO-phonon model There is a big difference as the hot carrier population cools below 1500K. For the temperature range <1000K, _Jr decreases sharply by several orders of magnitude when the carrier density increases from <N ₀ >∼0.1 (Fig. 17(a)) to <N ₀ >∼2.5 (Fig. 20(a)) . For example, J _r at 700K is about 0.3 eV ps ^-1 at <N ₀ >∼0.1, and ~0.008 eV ps ⁻¹ at <N ₀ >∼2.5. In addition, when <N ₀ >～2.5 and carrier temperature <1200K, J _r decreases with the increase of NC size. All these features point to the existence of another slow hot-carrier cooling mechanism, which only dominates at high carrier densities, which we consider to be the Auger heating mechanism because it is well known that due to the carrier-carrier Sub-interactions increase and Auger recombination is strongly enhanced in confined semiconductor NCs. Therefore, the relaxed hot carriers (at the band edge) have some possibility to be re-excited to higher energy states by the Auger recombination of the band-edge carriers (inset of Fig. 20(b)).

Figure 20(c) shows that the calculated concentration of hot carriers (n _hot (t)) of NCs of different sizes relaxes in a biexponential manner, with fast decay within 1 ps and slower decay within tens of ps— - similar to the hot carrier temperature (Fig. 12 and Fig. 15). The fast decay can be attributed to carrier-LO-phonon interactions. Furthermore, the fitted slow decay lifetime n _hot (t) perfectly matches the Auger lifetime τ _Aug of 1/3 (i.e. τ _hot ∼τ _Aug /3 - Fig. 20(b)), see also "Auger heating model "part). For example, the slower decay lifetime of small-sized NCs is fitted at ~12 ps, very close to 1/3 of τ _Aug 's 38 ps. The good agreement between the experimental data and a simple model including the Auger effect can strongly confirm the dominant contribution of Auger heating in the further delayed hot-carrier cooling at high carrier densities. Given τ _Aug ∼√(V _NC ) and slow hot-carrier lifetime τ _hot ∼τ _Aug /3, the Auger-induced hot-carrier cooling lifetime can sublinearly depend on the NC volume (Fig. 20(b)) . Although Auger heating results in a slowdown of the hot-carrier cooling rate, which is beneficial to hot-carrier extraction, it should also be noted that the Auger effect may conversely reduce the carrier density. Therefore, in the application of concentrating hot-carrier solar cells, it may be necessary to balance the hot-carrier lifetime and carrier loss at high pump power densities.

In addition to slow hot-carrier cooling, the feasibility of efficient hot-carrier extraction may be another challenging issue for hot-carrier solar cells. Very rapid extraction of hot carriers may be required to limit energy loss, where competition exists between extraction rate and cooling rate, rather than recombination rate. Taking into account that the estimated hot-carrier diffusion length for _MAPbBr3 thin films is ~16-90 nm (depending on hot-carrier lifetime and diffusion coefficient) (see "Estimation of hot-carrier diffusion length" below), the hot-carrier sub is technically feasible. Here, we demonstrate efficient thermionic extraction from 1,2-ethanedithiol (EDT)-treated _MAPbBr3 NCs (EDT-NCs) to 4,7-diphenyl-1,10-phenanthroline (Bphen).

Figure 22 shows a graph of photoelectron intensity (counts per second or cts/s) versus energy (electron volts or eV) representing (a) 1,2-ethanedithiol on an indium tin oxide (ITO) substrate (EDT) treated and (b) post-annealed EDT treated methylamine lead bromide (MAPbBr ₃ ) nanocrystalline (NC) films according to various embodiments, and (c) 7-diphenyl-1 , Ultraviolet photoelectron spectroscopy (UPS) of 10-phenanthroline (Bphen) film. The valence band maximum (VBM) can be determined by linear extrapolation of the valence band front to the background intensity, which are 1.9±0.1, 2.3±0.1 and 2.9±0.1 eV in Fig. 22(a)-(c), respectively.

Bphen could be chosen as the hot electron extraction material because this molecular semiconductor has high electron mobility and has a higher lowest unoccupied molecular orbital (LUMO) than the conduction band minimum (CBM) of our EDT-treated NCs (see Fig. 22 , UPS measurement), only implying that hot carriers with sufficient excess energy at the band edge can be injected into Bphen (see Figure 23A).

23A is a flat-band energy diagram (vertical axis electron volts or eV) to illustrate thermal electron transfer from perovskite nanocrystals to 7-diphenyl-1,10-phenanthroline (Bphen) according to various embodiments Extraction and competition of thermionic cooling pathways. The conduction band minimum (CBM) (or LUMO level) and valence band minimum (VBM) (or highest occupied molecular orbital (HOMO) level) of NC (or Bphen) can be determined from UPS and UV-Vis measurements. Figure 23B shows an atomic force microscope (AFM) image of a 1,2-ethanedithiol (EDT)-treated nanocrystalline (NC) film according to various embodiments. 23C is a scanning electron scan of a 1,2-ethanedithiol (EDT)-treated nanocrystal (NC)/7-diphenyl-1,10-phenanthroline (Bphen) bilayer film according to various embodiments Microscope (SEM) images. Scale bar is 100 nm.

FIG. 23D is a graph of normalized transmittance change ΔT/T versus energy (electron volts or eV) with (continuous line)/without (dashed line) 7-diphenyl-1,10 according to various embodiments. -Normalization of about 35 nm thick 1,2-ethanedithiol (EDT)-treated nanocrystalline (NC) films of phenanthroline (Bphen) after 3.1 eV photoexcitation (<N ₀ >about 0.1) Transient Absorption (TA) Spectroscopy. The inset of Figure 23D shows the unnormalized transient absorption (TA) spectrum at 0.8 ps. 23E is 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film and 1,2-ethanedithiol (EDT)-treated nanocrystal (NC) film/7 according to various embodiments - Plot of hot carrier temperature (Kelvin or K) versus delay time (picoseconds or ps) for biphenyl-1,10-phenanthroline (Bphen) bilayer films at different pump power densities. The dashed arrows indicate the decrease in the initial hot-carrier temperature after adding the Bphen layer, indicating efficient hot-electron extraction.

23F is a graph of extraction efficiency η _hot (percentage or %) versus hot electron excess energy (electron volts or eV), showing the efficiency of about 35 nm thick 1,2-ethanedithiol (EDT) treatment according to various embodiments. Pump energy dependence of hot electron extraction efficiency in nanocrystalline (NC)/7-diphenyl-1,10-phenanthroline (Bphen) bilayers. The inset of FIG. 23F shows the unnormalized TA spectra at 0.8 ps after 2.5 eV photoexcitation (<N ₀ >about 0.1 ) of an approximately 35 nm thick EDT-NC film with/without Bphen. Figure 23G is a graph of extraction efficiency η _hot (percentage or %) versus thickness (nanometers or nm) representing 1,2-ethanedithiol (EDT)-treated nanocrystals (NC)/7 according to various embodiments -Diphenyl-1,10-phenanthroline (Bphen) bilayer film and bulk film/7-diphenyl-1,10-phenanthroline (Bphen) bilayer film excited by 3.1eV pump energy Perovskite film thickness dependence of hot electron extraction efficiency. The inset shows the unnormalized TA spectrum at 0.8 ps after 3.1 eV photoexcitation (<N ₀ >about 0.1 ) of a ~140 nm thick EDT-NC film with/without Bphen. The error bars on the x-axis represent the uncertainty in the excess energy measured in Figure 23F and the sample thickness measured in Figure 23G, and the error bars on the y-axis represent the uncertainty in the extraction efficiency measured.

Figure 24(a) shows a graph of transmittance (arbitrary units or au) versus wavenumber (per centimeter or cm ^-1 ) for methylamine lead bromide nanocrystals (MAPbBr ₃ NCs), 1,2-ethanedithiol (EDT)-treated nanocrystals (EDT-NC) and 70°C annealed 1,2-ethanedithiol nanocrystals (Ann-EDT-NC) attenuated total reflection- Fourier transform infrared (ATR-FTIR) spectra; and plots of light emission intensity (arbitrary units or au) versus binding energy (electron volts or eV) representing (b) unannealed and (c) according to various embodiments Sulfur (S)2p X-ray photoelectron spectroscopy (XPS) of 1,2-ethanedithiol (EDT)-treated nanocrystal (EDT-NC) films annealed at 70 °C. S 2p can be deconvoluted on the NC surface into unbound thiols and bound thiolates (see Discussion section on FTIR and XPS analysis of ligand exchange).

Bphen has a narrow electronic bandwidth, which could bring it close to the energy-selective contacts needed in hot-carrier solar cells. EDT treatment can be used to replace the long and highly insulating oleic acid ligands present on the surface of as-prepared NCs with thiolates (see ATR-FTIR and XPS measurements in Figure 24 and the section on FTIR and XPS analysis of ligands ) to more effectively electronically couple with Bphen within the NC membrane (as shown in the TEM image in Figure 25, the NCs are packed more tightly after treatment). Figure 25 shows (a) atomic force microscopy (AFM) images of untreated medium-sized methylamine lead bromide nanocrystal (MAPbBr ₃ NC) films according to various embodiments, and (b) Representative transmission electron microscope (TEM) image of 1,2-ethanedithiol-treated methylamine lead bromide nanocrystals (EDT-treated MAPbBr ₃ NC). Figure 26 shows (a) medium-sized methylamine lead bromide nanocrystal (MAPbBr ₃ NC) film according to various embodiments, (b) 1,2-ethanedithiol-treated Nanocrystalline (EDT-treated NC) films, and (c) 1,2-ethanedithiol-treated nanocrystalline films/7-diphenyl-1,10-phenanthroline (EDT-treated False-color transients of NC film/Bphen) bilayer film at low pump power density (left picture, <N ₀ >～0.1) and high pump power density (right picture, <N ₀ >～2.5) Absorption (TA) Spectrum. After 3.1eV photoexcitation, the high-energy band tail of EDT-NC/Bphen may be reduced.

Thermionic extraction by spin-coated EDT-NC thin films of Bphen (see AFM and SEM images in Fig. 23B–C) can be verified by the apparent reduction of high-energy band-tail transient occurrence in the TA spectra of EDT-NC/Bphen bilayer films (See Figure 23D, the false-color TA spectrum in Figure 26 and the section on "Effect of Trions in Photonic NCs and NC Films on Hot Carriers").

For ~35 nm thick EDT-NC film, the initial _Tc cools from ~1300K to 450K at low pump intensity after adding the Bphen layer, and cools from ~1800 to 800K at high pump intensity within ~200fs after photoexcitation (FIG. 23E), indicating that carriers with higher energy and temperature can be injected into Bphen. From the conduction band minima and LUMO shift between EDT-NC and Bphen, hot carriers with excess energy ≥0.2±0.1 eV can be extracted (Fig. 27). Figure 27 shows an energy graph (y-axis: energy in electron volts or eV) representing the non-volatile energy in accordance with various embodiments determined from ultraviolet photoelectron spectroscopy (UPS) and ultraviolet-visible (UV-VIS) spectroscopy measurements. Flat-band level alignment of annealed, annealed 1,2-ethanedithiol-nanocrystal (EDT-NC) films and 7-diphenyl-1,10-phenanthroline (Bphen) for hot electron extraction The situation is explained. The excess energy (E _hot-excess ) of the extracted hot electrons can be determined from the band shift between the conduction band minima of NC and the LUMO of Bphen.

Considering the increased diffusion coefficient of hot carriers (see the section on hot-carrier diffusion length estimation) and the ultrafast hot-carrier hopping between NCs (within tens of fs), hot electrons may pass through the NC interior Electron diffusion and hopping at the NC interface inject Bphen. The driving force for hot electron transfer can be the energy difference between the hot carrier energy and the LUMO energy relative to the Fermi energy, as shown in Figure 23A. A large density of states is typical for organic molecules. Therefore, the efficient hot-carrier transfer can be attributed to the large density of acceptor states in the LUMO level of Bphen and the strong electronic coupling between Bphen and NC. Additional control experiments prove that Bphen may be the only way to extract hot carriers from NCs in EDT-NC/Bphen, and there are transferred charge carriers in Bphen. See "Control experiments to verify hot carrier transfer" and section "PIA signal for transfer of charge carriers in Bphen".

Figure 28(a) shows a graph of absorbance (arbitrary unit or au) versus wavelength (nanometer or nm) representing the linear absorption spectrum of a Bphen film on glass; (b) normalized negative transmittance change— A graph of ΔT/T versus wavelength (nanometer or nm) for 7-diphenyl-1,10-phenanthroline (Bphen) (300nm pump intensity is 20μJ cm ^-2 ; 400nm pump intensity is 40μJ cm ^{- 2} ), perovskite nanocrystals (NC) (400nm pump intensity of 15 μJ cm ⁻² ) according to various embodiments and 1,2-ethanedithiol nanocrystals/7-diphenyl Negative transient absorption spectrum of 1,10-phenanthroline (EDT-NC/Bphen) (400nm pump intensity 15μJ cm ^-2 ) at 2ps after excitation; (c) time (picosecond or ps) versus wavelength (nano or nm) graph representing 1,2-ethanedithiol-treated nanocrystals/7-diphenyl-1,10-phenanthroline (EDT-NC/Bphen) bis Pseudocolor transient absorption (TA) spectra of the layer film excited by 400nm light with a pump intensity of 15μJ cm ^-2 ; (d) Normalized negative transmittance change——ΔT/T versus time (picosecond or ps) Graph, Bphen excited with 300 nm light, and 1,2-ethanedithiol-treated nanocrystals/7-diphenyl-1,10-phenanthroline (EDT-NC/Bphen) according to various examples Normalized negative transient absorption spectrum of a bilayer film pumped with 400 nm light and probed at 1300 nm. The solid line is the fitted curve of the double exponential decay function.

Notably, we also observed similar near-infrared (NIR) photoinduced absorption (PIA) signals for EDT-NC/Bphen bilayers (in which only NCs are selectively excited) and Bphen (excited above the bandgap) (see Fig. 28 and section "PIA signal of transferred charge carriers in Bphen"), which may be caused by photogenerated radical anions in Bphen. Therefore, the photoinduced absorption (PIA) signal in the EDT-NC/Bphen bilayer film can be attributed to the hot carrier population transferred from NC to Bphen (Fig. 28(b)). Nevertheless, another alternative explanation could be the excited singlet absorption caused by the thermal state energy transfer from NC to Bphen.

Hot electron extraction efficiency (η _hot ) can be estimated based on the percent reduction in band-edge photobleaching intensity at ~0.8 ps after addition of Bphen (because when hot electrons relax to the band-edge, the reduced band-edge bleaching intensity can be attributed to in the extraction of hot carriers). For ~35 nm thick EDT-NC/Bphen bilayer films, the calculated η _hot is ~72% and ~58% at <N ₀ > ~0.1 and 2.5 pump intensities, respectively. The reduced multi-hot electron injection efficiency at higher pump power densities may be due to increased back electron transfer from Bphen to NC, with an estimated back electron transfer time of ~80 ps (Fig. ).

29 is a graph of normalized transmittance change ΔT/T versus time (picoseconds or ps) for 1,2-ethanedithiol-treated nanocrystal (EDT-NC) films and 1,2-ethanedithiol-treated nanocrystal/7-diphenyl-1,10-phenanthroline (EDT-NC/Bphen) bilayers according to various embodiments at (a) low pump power Normalized band-edge bleaching kinetics for 3.1 eV photoexcitation at density (<N ₀ >～0.1) and (b) high pump power density (<N ₀ >～2.5). 30A is a graph of normalized transmittance change ΔT/T versus energy (electron volts or eV) showing 7-diphenyl-1 with (continuous line) and without (dashed line) annealed according to various embodiments. , 1,2-ethanedithiol-treated (EDT-treated) medium-sized methylamine lead bromide nanocrystal (MAPbBr ₃ NC) films of 10-phenanthroline (Bphen)-extracted layer at low pump power densities <N ₀ > ~ 0.1 normalized transient absorption spectrum. The inset of Figure 30A shows the unnormalized TA spectrum at 0.8 ps, with η _hot determined to be -83%. 30B is a graph of carrier temperature (Kelvin or K) versus time (picoseconds or ps) showing extracted hot carrier temperature versus delay time for two samples according to various embodiments. Figure 30C is a graph of normalized transmittance change ΔT/T versus energy (electron volts or eV) with (continuous line) and without (dashed line) 7-diphenyl-1,10-phenanthroline ( Normalized transient absorption (TA) spectrum of 2×10 ¹⁷ cm ^-3 bulk film (~240nm thick) of methylamine lead bromide (MAPbBr ₃ ) bulk film (~240nm thick) in Bphen) extraction layer at low pump power density. The inset of Figure 30C shows the unnormalized TA spectrum at 0.8 ps, with η _hot determined to be -16%. Figure 30D shows a graph of carrier temperature (Kelvin or K) versus time delay (picoseconds or ps) for two samples according to various embodiments. The photoexcitation energy is 3.1 eV.

Considering the voids in the NC film (Fig. 23B AFM image), some Bphen molecules can penetrate the upper layer of the NC film, which can further improve the heat loading by increasing the NC/Bphen interface in the thinner NC film/Bphen bilayer Fluor extraction efficiency. Furthermore, moderate post-heating (e.g., 5 min at 70 °C) of EDT-NC can not only further enhance the electronic coupling (see XPS spectra in Fig _. ~83% (FIG. 30A), and can also increase the Fermi level of NCs relative to the valence band minimum (VBM) (FIG. 27) (probably due to sulfur doping during annealing). This enables extraction of hot carriers with excess energy above the band edge (up to 0.5 ± 0.1 eV) with _Tc cooling from ~1300 to 400K (Fig. 30B).

Further evidence for hot electron injection into Bphen can be revealed by pump energy-dependent η _hot . As shown in Figure 23F, as the hot carrier excess energy decreases from ~0.7eV to 0.1eV (excitation from 3.1eV to 2.5eV using pump energy above the band edge), _ηhot decreases from ~72% to 15% . These results can verify that only hot carriers with sufficient excess energy can be injected into Bphen (consistent with the energy level diagram in Fig. 4a). They also demonstrate high selectivity for hot electron extraction using Bphen and a narrow LUMO. Importantly, when the thickness of the NC film was increased from ~35nm to ~140nm (Fig. 31), η _hot dropped sharply from ~72% to 20% after 3.1 eV photoexcitation (Fig. 23G). The reduced hot electron extraction may be caused by the limited hot electron diffusion/hopping range within the NC film. 31 shows cross-sectional scanning electron microscope (SEM) images of 1,2-ethanedithiol-treated nanocrystals (EDT-NC films) with different thicknesses, according to various embodiments. The scale bar in Figure 31(a)-(d) is 100 nm.

In contrast, bulk film/Bphen with a thickness of ∼240 nm has an _ηhot of ∼16% and _Tc only changes from ∼450 to 380K under similar photoexcitation conditions due to the initial rapid hot-carrier cooling (FIG. 30C-D). Even when the bulk film thickness is reduced to ~40 nm, η _hot is still much smaller than that of EDT-NC film.

In summary, under similar photoexcitation conditions, colloidal _MAPbBr3 NCs can exhibit about 2 orders of magnitude slower hot-carrier cooling time and about 4 times higher hot-carrier temperature compared with bulk perovskite films. At low pump power densities, hot-carrier cooling in NCs may be mediated by a phonon bottleneck effect, which is unexpectedly slower in smaller NCs (compared to conventional NCs). This finding is contrary to the conventional understanding in traditional colloidal semiconductor nanocrystals, that is, as the dimensionality decreases, the in-band Auger effect is more significant, thereby breaking through the phonon bottleneck. At high pump power densities, Auger heating dominates the hot-carrier cooling rate, which may be slower in larger NCs (previously not observed in conventional NCs). Importantly, the enhanced slow hot-carrier cooling in these colloidal perovskite nanocrystals enables efficient hot-carrier extraction. The results show that hot electrons with excess energy up to ∼0.6 eV can be efficiently injected (up to ∼83%) from the surface-treated _MAPbBr3 NCs film into the electron extraction layer with an injection time of ∼0.2 ps.

The hot-carrier properties in perovskite NCs may provide new opportunities for extremely thin absorbers (ETAs) and concentrating hot-carrier solar cells. For the former, ETA-solar cells may conceptually approach dye-sensitized heterojunctions. Molecular dyes can be replaced by extremely thin (~tens of nanometers) semiconductor absorber layers. By nanostructuring electrodes (e.g., using highly porous _TiO2 scaffolds, ZnO nanowire arrays, etc.), the effective area covered by thin absorbers can be increased by several orders of magnitude due to surface enlargement and multiple scattering. Most importantly, the ETA layer may be very beneficial for hot-carrier extraction due to the shorter transport path length of hot-carriers. For the latter, the illumination power in concentrator solar cells can be increased up to 1000suns, much larger than the 1-sun intensity in typical cells, as is the slower hot-carrier cooling in perovskite NCs induced by Auger heating. Can be used.

Synthesis of Perovskite Nanocrystals of Different Sizes

Zhang et al. reported the synthesis of methylamine lead bromide (MAPbBr ₃ ) nanocrystals (NCs) via a ligand-assisted reprecipitation (LARP) method (see "Bright Luminescent and Color-Tunable Colloidal CH ₃ NH ₃ PBX ₃ (X=Br, I, Cl) Quantum Dots: A Potential Alternative for Display Technology", ACS Nano 9, 4533-4542, 2015). First in a glass vial, mix 0.16 mmol methylammonium bromide (MABr), 0.2 mmol lead bromide (PbBr ₂ ) in 5 mL dimethylformamide (DMF) solution, then 50 μL oleylamine (OAm) and 0.5 mL of oleic acid (OAc) was mixed in DMF solution to form the final precursor solution. Another round-bottomed flask containing 5 mL of toluene was preheated to 60 °C in an oil bath, and then 250 μL of the prepared precursor solution was quickly injected into the hot toluene solution under vigorous stirring conditions, and the solution immediately turned green, confirming that MAPbBr ₃ NC Formation. The reaction was continued for 5 minutes and stopped by cooling in a water bath. Transfer the reaction solution to a centrifuge tube and centrifuge at the desired speed for spherical MAPbBr ₃ NCs of different sizes. The _MAPbBr3NC precipitate was redissolved in toluene solution for further study. For small, medium and large sized NCs, centrifugation speeds of 12000 rpm, 8000 rpm and 4000 rpm were used to separate the precipitates, respectively. The mean diameters were -4.9, 8.9 and 11.6 nm for small, medium and large size NCs, respectively (Fig. 6).

MAPbBr3 _Bulk Membrane Preparation

A DMF solution containing 0.6 M MAPbBr ₃ was spin-coated on a quartz substrate (5000 rpm, 12 seconds). During spin coating, add a few drops of toluene to the film 3 s after the start of the spin. The films were then dried at room temperature for 30 min and annealed at 70 °C for 5 min. All film deposition and annealing were done in a _N2- filled glove box. The bulk film has a grain size greater than ~1 μm and a thickness of approximately 240 nm (Fig. 7).

Preparation of MAPbBr ₃ NC and EDT-treated MAPbBr ₃ NC membrane

MAPbBr ₃ NC films and 1,2-ethanedithiol (EDT)-treated NCs were grown by a layer-by-layer spin-coating process. All spin-coating steps were set at 1000 rpm and the spin time was fixed at 30 s. To prepare NC films, NCs in toluene (10 mg ml ⁻¹ ) were spin-coated on glass substrates in two layers. For EDT-treated NC films, the growth of each layer of EDT-treated NC films involved three steps: (1) spin-coating NC solution on top of the substrate; (2) covering the NC film with 0.2 M EDT in 2-propanol solution, and waiting for Spin coating after 30 seconds; (3) add anhydrous toluene dropwise on the membrane, and then spin coating to clean the remaining long-chain ligands. Repeat the above process 2-10 times to obtain NC films with different thicknesses. For the annealed samples, the annealing was performed at 70 °C for 5 min. All treatments were performed in a _N2 -filled glove box.

Bphen film preparation

4,7-Diphenyl-1,10-phenanthroline (rubphenanthroline or Bphen) was deposited by a thermal evaporation method at a pressure of 10 ⁻⁶ Torr. Bphen was deposited on spin-coated, non-annealed or annealed perovskite NC films at a rate of 0.1–0.2 nm s ⁻¹ .

CdSe nanocrystals

CdSe nanocrystals dispersed in toluene were purchased from Sigma-Aldrich Company.

TA measurement

Transient absorption (TA) measurements were performed in the fs-ns time range using a Helios spectrometer (Ultrafast Systems). The pump pulses were generated by an optical parametric amplifier (Coherent OPerA Solo ^TM or Light ConversionTOPAS-C ^TM ), which was pumped by a 1-kHz regenerative amplifier (i.e., Coherent Libra ^TM (50fs, 1KHz, 800nm) or Coherent Legend ^TM (150fs, 1KHz ,800nm)), or by doubling the output of an 800nm basic regenerative amplifier with a BBO crystal to obtain a 400nm pulse. Both systems use a mode-locked Ti:Sapphire oscillator (Coherent Vitesse ^™ , 80MHz). A white-light continuous probe beam (in the 400nm–1500nm range) is generated by focusing a small portion (~10 μJ) of the fundamental 800nm laser pulse from the regenerative amplifier into a 2mm sapphire crystal (visible range) or a 1cm sapphire crystal (near infrared range). The probe beam is collected using a CMOS sensor for the UV-VIS region and an InGaAs diode array sensor for the NIR region. During the measurements, the samples were kept in a N2 _- filled chamber at room temperature. For hot carrier extraction measurements, the pump beam excites the sample from the Bphen side for the sample structure of Bphen/perovskite/glass substrate.

PL and Time-Resolved PL Measurements

Steady-state PL spectra were collected in conventional backscattering geometry and detected by a charge-coupled device array (Princeton Instruments, Pixis ^™ ) coupled to a monochromator (Acton, SpectraPro ^™ ). The temporal evolution of PL is resolved by the Optronis Optoscope ^TM ultrafast scanning camera system. The excitation source was the same regenerative amplifier (Coherent Libra ^™ ) and optical parametric amplifier (Coherent OPerA Solo ^™ ) as above. All the above measurements were performed at room temperature.

TEM, AFM and SEM measurements

The shape and size of NCs were determined by transmission electron microscopy (TEM, JEOL JEM-2010). The surface morphology of the perovskite NC films was recorded by atomic force microscopy (AFM, Asylum Research MFP-3D), with the silicon cantilever operating in the tapping force mode. The morphology and thickness of the samples were characterized by scanning electron microscopy (SEM, JEOL JSM-7600F).

UPS and XPS measurements

Ultraviolet photoelectron spectroscopy (UPS) was used to study the interface level alignment of valence band occupied states. Spectral collection was performed using the same instrumentation as in XPS. The excitation light source is He-I (h=21.2eV), and the lamp power is 50W. Photoelectrons were collected at the surface normal using CAE mode with a pass energy of 2.00 eV and a sample bias of −10 V. The composition of the samples was analyzed by X-ray photoelectron spectroscopy (XPS). Samples were transferred from the glove box to an ultra-high vacuum (UHV) analysis chamber via an airtight sample transfer container. The pressure of the UHV chamber was maintained at 1 x 10 ^-9 Torr. A 200W Al Kα (hν=1486.6eV) photon source was used to excite the sample while spectrum collection was performed by a hemispherical electron energy analyzer (Omicron EA-125). The measurements are performed at room temperature and the photoelectrons are collected along the surface normal direction.

XRD, UV-VIS, AR-FTIR and Raman measurements

The crystal structure was analyzed by powder X-ray diffraction (XRD, Bruker D8 Advance). Absorption spectra were recorded using a UV-VIS spectrometer (SHIMADZU UV-3600 UV-VIS-NIR spectrophotometer) with an integrating sphere (ISR-3100). FTIR spectra of all samples were measured by a Frontier FT-IR/NIR spectrometer (PerkinElmer, Waltham, MA, USA) equipped with a universal attenuated total reflectance (ATR) sampling accessory (PerkinElmer, Waltham, MA, USA). Raman spectra were recorded using a WITec Raman microscope (WITec GmbH, Ulm, Germany) with a 633 nm HeNe laser as excitation source.

hot carrier lifetime

It should be noted that the complex interplay of hot carrier cooling times results from several factors:

(i) pumping energy (i.e. excess energy of the carriers - in general, higher excess energy results in longer hot-carrier lifetime);

(ii) initial hot carrier density (i.e. generally higher carrier density results in longer hot carrier lifetime); and

(iii) Energy loss rate at a specific hot-carrier temperature (as shown in Figure 17a, where the energy loss rate varies by several orders of magnitude for hot-carrier temperatures from 1600 to 300K)—generally, lower thermal The carrier temperature produces a smaller energy loss rate. (It should be noted that the lifetimes listed are the time interval from pulse excitation to hot-carrier cooling to 600K.)

Without specifying the above parameters/conditions, it is difficult to generalize and a very unfair comparison of hot carrier lifetimes between different materials. Furthermore, the measured hot-carrier lifetime may be limited by the temporal resolution of the experimental technique used, resulting in artificially longer lifetimes that are limited by the system's temporal response rather than its intrinsic hot-carrier lifetime. For example, measuring hot-carrier lifetimes by time-resolved photoluminescence (TRPL) techniques using ultrafast scanning cameras or time-correlated single-photon counting (TCSPC) systems may be limited by the system resolution of these devices (i.e., for most ultra- ~10 ps for fast scan cameras, ~1 ps for Hamamatsu systems, typically ~50 ps for TCSPC systems). On the other hand, TA or fluorescent up-conversion PL technology has a higher system time response of <150 fs, which can identify a more realistic hot-carrier lifetime of the material. Therefore, due care must be taken to make a fair comparison of values reported in the literature.

To ensure a fair comparison of hot-carrier temperature and cooling kinetics, a summary of materials was done taking into account the above parameters (i.e., carrier density, carrier temperature, pumping energy, and technology), shown in Fig. out. In addition, it should be noted that the hot-carrier cooling lifetime in Fig. 14 is defined as the time interval from pulse excitation to hot-carrier cooling reaching 600 K ((iii) above). This temperature is taken as a benchmark, since previous theoretical calculations have shown that for _Tc >600K, significant hot-carrier conversion efficiencies (ie >40%) are still possible over a wide range of absorber bandgaps. As the hot carrier distribution approaches the thermal equilibrium of the lattice (300K), the energy loss rate may become much slower (see Fig. 17(a)). Although these pseudo "hot carriers" generate long lifetimes, they actually contribute little to the operation of hot-carrier solar cells. Therefore, this article does not make a comparison.

LO Phonon Model

The rate of energy loss per carrier _Jr is determined in terms of _Tc extracted from −1.5kb _dTc /dt _. J _r can fit the following models:

是声子能量(～42meV)，N_LO(T)是温度T下的LO-声子占据数。图2a的拟合产生了与MAPbBr₃NC(～310K)和体块膜(～305K)相当的T_a。对于小、中和大NC，τ_LO分别为～340fs、220fs和180fs，相比之下，体块膜的快速τ_LO约为150fs。where _τLO is the characteristic LO phonon decay time, _Ta is the acoustic phonon temperature,

is the phonon energy (~42meV), and N _LO (T) is the LO-phonon occupancy at temperature T. The fit of Fig. 2a yielded a T _a comparable to that of _MAPbBr3 NCs (~310K) and bulk membranes (~305K). For small, medium, and large NCs, the τ _LO was ~340 fs, 220 fs, and 180 fs, respectively, compared to the fast τ _LO of ~150 fs for bulk membranes.

Auger heating model

The Auger decay lifetime of MAPbBr ₃ NCs is extracted from the pump power density dependence of the band-edge photobleaching kinetics (Fig. 16(f)), which exhibits a sublinear dependence on the NC volume (V _NC ) as τ _Aug ∼ √(V _NC ) (Fig. 20(a)). This behavior is consistent with recent observations of biexciton Auger recombination in weakly confinement _CsPbBr3 NCs, but contrasts with the linear dependence of τ _Auger on NC size in strongly confinement systems. Therefore, the sublinear dependence can be attributed to the weaker confinement in our perovskite NCs.

Given that Auger recombination is a three-particle process, the Auger heating rate in NCs is proportional to ^∼n3 , where n is the band-edge effective carrier density. Therefore, the evolution of the hot carrier population can be described by the following equation:

where the first term represents the relaxation of hot carriers independent of Auger heating, and the second term corresponds to the Auger heating contribution; C refers to the Auger recombination coefficient of band edge carriers. During the lifetime of hot carriers, single exciton recombination can be ignored because of its long lifetime (a few nanoseconds). The band-edge carriers recombine by the principal Auger process given by n(t)∼e ^−t/τAug , as a first approximation. Direct integration of this equation yields the following time evolution:

where n _hot0 is the initial population of generated hot carriers, and D is equal to c/(A-3/τ _Aug ). Thus, equation (4) predicts that the hot carrier population decays exponentially, with one of its lifetimes corresponding to τ _Aug /3.

Considering the Fermi-Dirac distribution of hot carriers, the effective hot carrier density can be calculated using the following relationship:

Figure 20(c) shows a plot of the normalized calculated hot carrier density versus decay time at different pump power densities.

Estimation of Hot Carrier Diffusion Length

The hot-carrier diffusion length in _MAPbBr3 can be estimated as follows. First, the carrier diffusion coefficient depends on the defect density of the prepared material. At room temperature (~300K), the electron diffusion coefficient D can be ~1 cm ² s ^-1 for polycrystalline perovskite thin films and 5-8 cm ² s ^-1 for bulk films MAPbBr ₃ . Secondly, D can also depend on the carrier temperature (T _c ), the relationship D=μκ _B T _c /e. For NC film, with 800K as the average hot carrier temperature, the lower D value is 1cm ² s ^-1 , and the hot carrier lifetime is 1ps at low pump power density, the hot carrier diffusion length can be passed by L=√(D _hot τ _hot )≈16nm obtained. The high pump power density at a hot-carrier lifetime of ~32 ps yields a diffusion length L≈90 nm. Considering the excitation of the perovskite/Bphen sample on the Bphen side, and the initial exponential carrier distribution in the semiconductor after fs laser pulse excitation, a higher concentration of hot carriers in the perovskite closest to the Bphen can be more easily Ground injection of Bphen. For NC membranes, considering that some Bphen molecules can permeate into the upper layer of NC membranes, and hot carriers undergo rapid hopping, ∼70% of the hot carriers extracted by ∼35 nm thick NC membranes at low pump power densities Transfer efficiency may be reasonable. For the bulk film, with 400K as the average hot carrier temperature, the higher D value is 5cm ² s ^-1 , and the hot carrier lifetime is 0.15ps at low pump power density, the hot carrier diffusion length Can be ≈10 nm. Therefore, a transfer efficiency of ~15% for bulk membranes is also reasonable.

FTIR and XPS analysis of ligand exchange

FTIR spectra of EDT-treated MAPbBr ₃ NPs showed efficient removal of native oleic acid and oleylamine ligands ( FIG. 24 ). The removal of these ligands is clearly observed from the reduction of _CH2 stretching at 2921 and 2841 cm ⁻¹ . The complete removal of the C=O stretch at ¹⁷¹⁰ cm, together with the rocking vibration of NH at 800 ^cm and the disappearance of the COH bond at 1384 ^cm further supports the EDT ligand exchange of oleic acid and oleylamine ligands .

XPS analysis of sulfur in non-annealed and post-annealed EDT-treated _MAPbBr3 NCs revealed two sets of S 2p doublets, with 2p ^3/2 peaks located at binding energies of ~162.5 eV and ~164.2 eV (post-annealed ~162.7 eV and ˜164.3 eV), bound thiolate and unbound thiol from EDT, respectively, were generated on the NC surface ( FIG. 24 ). The bound-to-unbound thiol group ratio was ~1.04 in NCs without post-annealing and increased to ~1.47 in NCs post-annealed at 70 °C. Therefore, the post-annealing treatment further increases the electronic coupling between EDT-NC and Bphen.

Influence of Trions in Optoelectronic NC and NC Films on Hot Carriers

Figure 16(e) shows a comparison of band-edge photobleaching kinetics of meso-sized nanocrystals (NCs) in solution and spin-coated films. From the exponential fit (solid curve), the lifetime varies from ∼4.5 to ∼3 ns at low pump power densities, and the acceleration may be due to the presence of photocharged NCs. At high pump power densities, in addition to Auger recombination, fast decay lifetimes ~290 ps may occur in spin-coated NC films, which can be attributed to Trions (photoexcitons). However, they only cause broadening of the lower energy side of the GSB (see bleached band tail on the lower energy side of the NC film in Fig. 26 compared to NC in solution in the false-color TA spectrum in Fig. 10) . The reduced energy of Trions may be due to exciton-exciton interactions. Trions in the NC film may not affect the dynamics of hot carriers located on the higher energy side of the GSB.

Control experiments to verify hot carrier transfer

The _MAPbBr3 NC films exhibit similar hot-carrier cooling kinetics with/without EDT treatment. Without EDT treatment, NCs exhibited similar hot-carrier cooling kinetics to those with/without Bphen extraction layer. Furthermore, we found that in NC films subjected to exactly the same treatment in a thermal evaporator, except that no Bphen layer was actually deposited, there was no noticeable change in the hot carrier properties.

PIA signal of transferred charge carriers in Bphen

For the pristine Bphen film, when excited above the bandgap of 300 nm light (refer to the absorption spectrum in Fig. 28(a)), there is a very broad photoinduced absorption in the NIR range (PIA, Fig. 28(b)), typical Organic semiconductors (eg P3HT, PCBM). Its intensity gradually increases with the probe wavelength. The PIA band can temporarily mainly point to the absorption of photogenerated radical anions in Bphen. Control experiments with excitation of Bphen at 400 nm (below the bandgap) (at low and high pump power densities) produced inactive (PIA) features (Fig. 28(b)), indicating the absence of photogenerated freedom in Bphen Base negative ions.

For EDT-NC/Bphen samples (NC film thickness ~50 nm), NCs were selectively excited with 400 nm light. At low pump power densities, there may be no measurable TA signal. This may be due to the fact that the TA signal (indirectly generated radical anions) is below the detection limit set by TA (10 ⁻⁴ ΔT/T). At higher pump power densities (ie ~15 μJ cm ⁻² , corresponding to <N> ~2.5), weak PIA bands similar to pristine Bphen could be observed ( FIG. 28( b ) and (c )). However, any further increase in pump power may lead to degradation of the perovskite.

Control experiments also showed that there is no EDT-NC/Bphen sample from excitation at 500 nm (i.e., the photoexcited carriers in NCs have negligible excess energy) and excitation at high pump power density at 400 nm (Fig. 28(b)). TA signal of individual NC membranes. Therefore, these experiments suggest that the PIA observed in EDT-NC/Bphen hybrids may only be caused by hot-carrier injection from NCs into Bphen.

Furthermore, the relaxation of PIA can have a fast decay lifetime (~70 ps for pristine Bphen, ~25 ps for NC/Bphen) and a slow decay lifetime (~1 ns for pristine Bphen, ~0.5 ns for NC/Bphen) (Fig. 28( d)). The fast decay may be due to the carrier trapping into the defects of pristine Bphen and the inversion of extra electrons to the NC of NC/Bphen. The slow decay may be due to the recombination of radical anions/excitons in Bphen with holes in NCs in NC/Bphen hybrids. Finally, considering that the energy difference between hot electrons and hot holes in NCs (~3.1eV in most extreme cases) is small compared to the Bphen bandgap (3.5eV), the energy from hot carrier recombination It is highly unlikely that transport would generate carriers in Bphen.

Estimating the back electron transfer time

The reverse transfer of injected electrons from Bphen to NCs can cause an increase in the relaxation time of electrons in NCs in the TA signal. The inverse electron transfer rate (1/τ _bk ) can be determined by the band edge bleaching relaxation rate of the NC between the EDT-NC film (1/τ _NC ) and the EDT-NC/Bphen bilayer film (1/τ _NC/Bp ). Estimated by the amount of change, that is, 1/τ _bk =1/τ _NC -1/τ _NC/Bp ).

At low pump power densities (<N ₀ >∼0.1), the invariance of the relaxation kinetics of EDT-NC membranes and EDT-NC/Bphen bilayers (Fig. The electron transport rate and the long transport time beyond the time window of our measurement, which may be due to the rapid trapping and localization hinder the drift of carriers back to the NC film. Therefore, long _τbk is favorable for hot electron injection. At high pump power densities (<N ₀ >˜2.5), τ _NC /Bp was significantly prolonged ( FIG. 29 ). Using the above relation, the estimated anti-electron time τ _bk is -80 ps. The reduced back-electron transfer time (ie, increased back-electron transfer rate) is consistent with reduced hot electron injection efficiency from 72% for <N ₀ >∼0.1 to 58% for <N ₀ >∼2.5.

While the present invention has been particularly shown and described with reference to particular embodiments, it will be understood by those skilled in the art that various changes in form and details may be made without departing from the spirit and scope of the invention. The scope of the invention is thus indicated by the appended claims and all changes which come within the meaning and range of equivalency of the claims are therefore embraced.

Claims (22)

1. A hot carrier solar cell comprising:

a nanocrystal layer comprising one or more nanocrystals, each of the one or more nanocrystals comprising a halide perovskite material;

a first electrode in contact with a first side of the nanocrystal layer; and

a second electrode in contact with a second side of the nanocrystal layer, the second side opposite the first side;

wherein the thickness of the nanocrystal layer is less than 100nm.

2. The hot carrier solar cell according to claim 1, further comprising: an optical device comprising one or more optical elements that direct solar energy to the nanocrystal layer.

3. The hot carrier solar cell according to claim 2, wherein the one or more optical elements are optical lenses.

4. The hot carrier solar cell according to claim 1, wherein the first electrode is a hot electron extraction layer comprising any one selected from the following materials: titanium oxide, zinc oxide, phenyl-C61-butanoic acid methyl ester, 4, 7-diphenyl-1, 10-phenanthroline, poly (9-vinylcarbazole), 2- (4-biphenyl) -5-phenyl-1, 3, 4-oxadiazole, 2'' - (1, 3, 5-phenylclaw) -tris (1-phenyl-1-H-benzimidazole), poly (9, 9-dioctylfluorene) and bathocuproine.

5. The hot carrier solar cell according to claim 1, wherein the second electrode is a hot hole extraction layer comprising any one selected from the following materials: 2,2', 7' -tetrakis [ N, N-bis (4-methoxyphenyl) amino ] -9,9' -spirobifluorene, poly (3-hexylthiophene-2, 5-ylidene), poly (3, 4-ethylenedioxythiophene) polystyrene sulfonate and poly (9, 9-dioctyl-fluorene-co-N- (4-butylphenyl) diphenylamine.

6. The hot carrier solar cell according to claim 1, wherein the first electrode is an energy selective contact point that allows electrons having an excess energy equal to or higher than a predetermined value to pass through and reflects electrons having an excess energy lower than a predetermined value back to the nanocrystal layer.

7. The hot carrier solar cell according to claim 1, wherein the second electrode is an energy selective contact point that allows holes having an excess energy equal to or higher than a predetermined value to pass through and reflects holes having an excess energy lower than a predetermined value back to the nanocrystal layer.

8. The hot carrier solar cell according to claim 1, wherein the one or more nanocrystals exhibit a hot carrier cooling lifetime of greater than 30 ps.

9. The hot carrier solar cell according to claim 1, wherein the radius of each of the one or more nanocrystals is any value selected from 2nm to 7 nm.

10. The hot carrier solar cell according to any one of claims 1 to 9, wherein the halide perovskite material is an organic-inorganic halide perovskite material.

11. The hot carrier solar cell according to any one of claims 1 to 9, wherein the halide perovskite material is an inorganic halide perovskite material.

12. A method of forming a hot carrier solar cell, comprising:

providing a nanocrystal layer comprising one or more nanocrystals, each of the one or more nanocrystals comprising a halide perovskite material;

forming a first electrode such that the first electrode is in contact with a first side of the nanocrystal layer; and

forming a second electrode layer such that the second electrode is in contact with a second side of the nanocrystal layer, wherein the second side is opposite the first side;

wherein the thickness of the nanocrystal layer is less than 100nm.

13. The method of claim 12, further comprising: an optical device is formed that includes one or more optical elements that direct solar energy to the nanocrystal layer.

14. The method of claim 13, wherein the one or more optical elements are optical lenses.

15. A method according to claim 12, wherein the first electrode is a hot electron extraction layer comprising any one selected from the group consisting of: titanium oxide, zinc oxide, phenyl-C61-butanoic acid methyl ester, 4, 7-diphenyl-1, 10-phenanthroline, poly (9-vinylcarbazole), 2- (4-biphenyl) -5-phenyl-1, 3, 4-oxadiazole, 2'' - (1, 3, 5-phenylclaw) -tris (1-phenyl-1-H-benzimidazole), poly (9, 9-dioctylfluorene) and bathocuproine.

16. The method of claim 12, wherein the second electrode is a hot hole extraction layer comprising any one selected from the group consisting of: 2,2', 7' -tetrakis [ N, N-bis (4-methoxyphenyl) amino ] -9,9' -spirobifluorene, poly (3-hexylthiophene-2, 5-ylidene), poly (3, 4-ethylenedioxythiophene) polystyrene sulfonate and poly (9, 9-dioctyl-fluorene-co-N- (4-butylphenyl) diphenylamine.

17. The method of claim 12, wherein the second electrode is an energy selective contact that allows holes having excess energy equal to or above a predetermined value to pass through and reflects holes having excess energy below a predetermined value back to the nanocrystal layer.

18. The method of claim 12, wherein the first electrode is an energy selective contact point that allows electrons having excess energy equal to or above a predetermined value to pass through and reflects electrons having excess energy below a predetermined value back to the nanocrystal layer.

19. The method of claim 12, wherein the one or more nanocrystals exhibit a hot carrier cooling lifetime of greater than 30 ps.

20. The method of claim 12, wherein the radius of each of the one or more nanocrystals is any value selected from 2nm to 7 nm.

21. A method according to any one of claims 12 to 20, wherein the halide perovskite material is an organic-inorganic halide perovskite material.

22. A method according to any one of claims 12 to 20, wherein the halide perovskite material is an inorganic halide perovskite material.

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