CN105161586A - LED epitaxial structure having combination barrier multi-quantum well and preparation method - Google Patents

Abstract

An LED epitaxial structure with combined barrier multiple quantum wells and a preparation method thereof, the active layer of the LED epitaxial structure is a combined barrier multiple quantum well structure, which consists of an InGaN potential well layer, an InAlGaN barrier layer, a GaN barrier layer and InAlGaN barrier layers are periodically superimposed. The preparation method comprises the following steps: (1) nitriding a sapphire substrate; (2) sequentially growing a GaN buffer layer, a non-doped GaN layer, an n-type AlGaN layer and an n-type GaN layer on the sapphire substrate; (3) Growth of combined barrier multi-quantum well structure on n-type GaN layer: (A) growth of In _x Ga _1-x N potential well layer; (B) growth of In _a Al _b Ga _1-ab N layer, GaN barrier layer and In _a Al _b Ga _1-ab N layer; the cycle number of step (A) and step (B) is 5-20, step (B) single cycle or multiple cycles; (4) in the combined potential barrier multi-quantum well layer A P-type layer is sequentially grown on it. The invention essentially improves crystal quality and internal quantum efficiency, improves device performance, and increases light extraction efficiency by about 10%.

Description

LED epitaxial structure with combined potential barrier multiple quantum wells and its preparation method

technical field

The invention relates to a high-brightness based LED epitaxial structure with combined potential barrier multi-quantum wells capable of improving light extraction efficiency and a preparation method thereof, belonging to the technical field of LED epitaxial design.

Background technique

In the early 1990s, the third-generation wide-bandgap semiconductor materials represented by nitrides made a historic breakthrough. Researchers successfully prepared blue-green and ultraviolet LEDs on gallium nitride materials, making LED lighting become possible. In 1971, the first gallium nitride LED die came out. In 1994, gallium nitride HEMTs appeared blue light GaN-based diodes with high electron mobility, and gallium nitride semiconductor materials developed very rapidly.

Semiconductor light-emitting diodes have the advantages of small size, ruggedness, strong controllability of light-emitting bands, high luminous efficiency, low heat loss, low light decay, energy saving, and environmental protection. Communication and other fields have a wide range of applications, and gradually become a research hotspot in the field of electronic power. GaN materials have a series of advantages such as wide bandgap, high electron mobility, high thermal conductivity, and high stability, so they have a wide range of applications and huge market prospects in short-wavelength light-emitting devices, photodetection devices, and high-power devices.

Generally, an LED includes an N-type substrate, an N-type epitaxial region formed on the substrate, a quantum well region and a P-type epitaxial region formed on the N-type epitaxial region. Due to the high dissociation pressure of nitrogen during GaN growth at high temperature, it is difficult to obtain large-sized GaN bulk single crystal materials. At present, most GaN epitaxial devices can only be grown on other substrates (such as sapphire substrates) for heteroepitaxial growth. .

The quantum well region is an essential link in the manufacture of GaN-based LED devices. To improve the luminous efficiency of LED epitaxial wafers, the most fundamental way is to enhance the internal quantum efficiency of the epitaxial structure. At present, the internal quantum efficiency of GaN-based LED epitaxial wafers grown by MOCVD in China can only reach about 30%, and there is still a lot of room for development and improvement. The growth of the active layer MQW is particularly important for improving the internal quantum effect.

At present, the industry generally uses GaN/InGaN materials to alternately grow the active layer. After the current is injected, the electrons in the N-type GaN layer will easily pass through the light-emitting layer (active layer quantum well) due to its high mobility, and migrate to the P-type GaN layer above the active layer, and the holes Ineffective radiative recombination is formed, which virtually reduces the internal quantum efficiency, and due to the inherent polarization effect of GaN-based materials, the generated polarization electric field causes bending in the multi-quantum well, resulting in a lower P-type side and a lower N-type One side is raised, so that the sideband of the multi-quantum well changes from a rectangle to a triangle, the baseband energy of the conduction band decreases, and the baseband energy of the valence band increases, narrowing the width of the gap between the two, resulting in a red shift of the emission wavelength , thereby further affecting the luminous efficiency.

Therefore, it is necessary to provide a new method for fabricating the active layer of GaN-based LED epitaxial wafers to further improve the internal quantum efficiency.

For improving the internal quantum effect, there are some patent documents at home and abroad. Chinese patent document CN104157746A discloses "LED Epitaxial Growth Method and Epitaxial Layer of New Quantum Well Barrier Layer", which inserts and grows an AlGaN thin layer in the traditional GaN barrier layer of the active layer. However, the higher potential barrier of this method not only limits the injection of electrons, but also limits the injection of holes.

"An InGaN/AlGaN-GaN-based multiple quantum well structure and its preparation method" disclosed by CN104201262A uses InGaN with fixed In composition as the well layer, uses different AlGaN-GaN as barrier layers, and includes AlGaN with fixed Al composition The barrier layer, the AlGaN barrier layer and the GaN barrier layer whose Al composition decreases continuously along the growth direction relieve the stress at the interface between the barrier and the well and relieve the bending of the energy band, but the effect is not obvious.

Contents of the invention

The present invention aims at the problems of low quantum efficiency and large stress in existing multi-quantum wells, and provides an LED epitaxial structure with combined potential barrier multi-quantum wells, which can effectively reduce the stress between well-barrier interfaces and ease the bending of energy bands , improve the efficiency of hole and electron injection into the active region and the efficiency of radiative recombination. At the same time, a preparation method of the structure is provided.

The LED epitaxial structure with combined potential barrier multiple quantum wells of the present invention adopts the following technical solutions:

The LED epitaxial structure is sequentially provided with a substrate layer, a GaN buffer layer, a non-doped GaN layer, an n-type AlGaN layer, an n-type GaN layer, an active layer, a P-type AlGaN layer, a P-type GaN layer and a P-type GaN layer from bottom to top. Type InGaN ohmic contact layer, the active layer is a combined barrier multi-quantum well structure, the combined barrier multi-quantum well structure is composed of InGaN potential well layer, InAlGaN barrier layer, GaN barrier layer and InAlGaN barrier layer. constitute.

The substrate is sapphire.

The thickness of the GaN buffer layer is 20-40nm.

The thickness of the non-doped GaN layer is 2-3 μm.

The thickness of the n-type AlGaN layer is 30-60nm.

The thickness of the n-type GaN layer is 2-3 μm.

The thickness of the P-type AlGaN layer is 50-100 nm.

The thickness of the P-type layer is 150-300nm.

The thickness of the P-type InGaN ohmic contact layer is 2-10 nm.

The thickness of the InGaN potential well layer in the combined barrier multi-quantum well structure is 2-4nm, the thickness of the InAlGaN barrier layer is 10-20nm, the thickness of the GaN barrier layer is 10-20nm, and the thickness of the InAlGaN barrier layer is 10-20nm .

The overlapping period of the potential well layer and the potential barrier layer in the combined potential barrier multi-quantum well structure is 5-20.

The three potential barrier layers in the combined barrier multi-quantum well structure are single-cycle or multi-cycle, and the multi-cycle period is 3-5. Single cycle means that there is only one InAlGaN barrier layer, GaN barrier layer and InAlGaN barrier layer in each combined barrier multi-quantum well cycle; multi-cycle means that the InAlGaN barrier layer in each combined barrier multi-quantum well cycle layer, GaN barrier layer and InAlGaN barrier layer have 3-5 periods.

The method for preparing the above-mentioned LED epitaxial structure with combined potential barrier multiple quantum wells comprises the following steps:

(1) Put the sapphire substrate into the reaction chamber of metal-organic chemical vapor deposition (MOCVD) equipment, heat it to 1000-1350°C in a hydrogen atmosphere, and treat it at a pressure of 200mbar for 5-10 minutes; increase the pressure to 600mbar, and the temperature is 650°C, pass through ammonia gas, nitriding treatment for 2-3 minutes;

(2) growing GaN buffer layer on the sapphire substrate of nitriding treatment;

(3) growing a non-doped GaN layer on the GaN buffer layer;

The growth temperature is 1100° C., the growth pressure is 600 mbar, the growth thickness is 2-3 μm, and the growth rate is 2-2.5 μm/h.

(4) growing an n-type AlGaN layer on the non-doped GaN layer;

The silicon doping concentration is 5E18-1E19atom/cm ³ , the Al doping concentration is 5E19-1E20atom/cm ³ , the thickness is 30-60nm, the growth temperature is about 1000°C, and the pressure is 133mbar.

(5) growing an n-type GaN layer on the n-type AlGaN layer;

The silicon doping concentration is 8E19-1.3E19atom/cm ³ , the thickness is 2-3μm, the growth temperature is 1080°C, and the growth pressure is 600mbar.

(6) Growing combined barrier multi-quantum well structures (InGaN potential well layer, InAlGaN barrier layer, GaN barrier layer and InAlGaN barrier layer) on the n-type GaN layer, the specific process is as follows:

(A) In the reaction chamber where the atmosphere is nitrogen, at a growth temperature of 730-760°C and a pressure of 200-400mbar, a mixture of triethylgallium and trimethylindium in a molar ratio of 1:2 or through Add a mixture of trimethylgallium and trimethylindium at a molar ratio of 1:2 to continuously grow an In _x Ga _1-x N potential well layer with a thickness of 2-4nm, where 0<x<1, and the In doping concentration is 2E20-4E20atom/ ^cm3 ;

(B) After stopping the growth of the In _x Ga _1-x N potential well layer, the temperature is raised to 880-920°C to grow the In _a Al _b Ga _1-ab N layer, where 0<a<0.3, 0<b<0.7 , growth thickness 10-20nm, Al doping concentration 5E19-1E20atom/cm ³ , In doping concentration 2E19-4E19atom/cm ³ , silicon doping concentration 1E17-1E18atom/cm ³ ; continuous growth of GaN barrier layer, growth thickness 10-20nm, silicon doping concentration is 1E17-1E18atom/cm ³ ; then continuously grow In _a Al _b Ga _1-ab N layer, where 0<a<0.3, 0<b<0.7, growth thickness 10-20nm, Al Doping concentration 5E19-1E20atom/cm ³ , In doping concentration 2E19-4E19atom/cm ³ , silicon doping concentration 1E17-1E18atom/cm ³ ;

The number of cycles of the above step (A) and step (B) is 5-20, step (B) single cycle or multiple cycles of 3-5 cycles;

(7) A P-type AlGaN layer, a P-type GaN layer and a P-type InGaN ohmic contact layer are sequentially grown on the composite barrier multi-quantum well layer.

The growth temperature of the P-type AlGaN layer is 830°C, the growth thickness is 50-100nm, the Mg doping concentration is 5E19atom/cm ³ , the Al doping concentration is 8E19atom/cm ³ , and the growth pressure is 200mbar; the growth temperature of the P-type GaN layer is 1000°C , the growth thickness is 150-300nm, the Mg doping concentration is 1E20atom/cm ³ , and the growth pressure is 200mbar; the growth temperature of the P-type PInGaN contact layer is 750°C, the pressure is 300-400mbar, the growth thickness is 2-10nm, and the Mg doping concentration is 2E20atom/cm ³ , In doping concentration is 1E20atom/cm ³ .

The invention enables the LED epitaxial structure to have a combined potential barrier multi-quantum well structure. Because of its special energy band combined potential barrier, it can significantly block and diffuse the injection of N-type electrons, enhance the ability of quantum wells to confine electrons, and improve the efficiency of hole and electron injection. Active area efficiency and radiative recombination efficiency, adjusting polarization charges to eliminate built-in polarization electric field, effectively reducing stress between well barrier interfaces, relieving energy band bending, essentially improving crystal quality and internal quantum efficiency, and improving device performance , Improve the light extraction efficiency by about 10%.

Description of drawings

Fig. 1 is a schematic diagram of the LED epitaxial structure with composite potential barrier multiple quantum wells according to the present invention.

Fig. 2 is a diagram of the energy band structure of the composite barrier multi-quantum well structure in the present invention.

In Fig. 1, 1, substrate, 2, buffer layer, 3, non-doped GaN layer, 4, n-type AlGaN layer, 5, n-type GaN layer, 6, active layer, 7, p-type AlGaN layer, 8 . P-type GaN layer, 9. P-type InGaN contact layer, 10. InGaN potential well layer, 11. InAlGaN barrier layer, 12. GaN barrier layer, 13. InAlGaN barrier layer.

Detailed ways

As shown in Figure 1, the present invention has a high-brightness base LED epitaxial structure with combined potential barriers and multiple quantum wells, which are sequentially provided with a substrate layer 1, a GaN buffer layer 2, an undoped GaN layer 3, and an n-type AlGaN layer. 4. An n-type GaN layer 5 , a multi-quantum well active light-emitting layer 6 , a P-type AlGaN layer 7 , a P-type GaN layer 8 and a P-type InGaN ohmic contact layer 9 . The substrate is sapphire. The thickness of the GaN buffer layer is 20-40nm. The thickness of the non-doped GaN layer is 2-3 μm. The thickness of the n-type AlGaN layer is 30-60 nm. The thickness of the n-type GaN layer is 2-3 μm. The thickness of the P-type AlGaN layer is 50-100 nm. The thickness of the P-type layer is 150-300nm. The thickness of the P-type ohmic contact layer is 2-10 nm. The multi-quantum well active light-emitting layer 6 is a combined barrier. The multi-quantum well layer is composed of periodic superposition of InGaN potential well layer 10, InAlGaN barrier layer 11, GaN barrier layer 12 and InAlGaN barrier layer 13, and the number of periods is 5. -20 pcs, barrier layer single cycle or multi cycle. The thickness of the InGaN potential well layer is 2-4nm, the thickness of the InAlGaN barrier layer is 10-20nm, the thickness of the GaN barrier layer is 10-20nm, and the thickness of the InAlGaN barrier layer is 10-20nm.

The high-brightness LED epitaxial wafer of the present invention is grown on a sapphire substrate by metal-organic chemical vapor deposition (MOCVD) equipment, using high-purity H ₂ or high-purity N ₂ or high-purity H ₂ and N ₂ mixed gas as carrier gas, high-purity _NH3 as N source, metal-organic source trimethylgallium or triethylgallium as gallium source, trimethylindium as indium source, N-type dopant using silane, trimethylgallium The base aluminum is used as the aluminum source, the P-type dopant is magnesium dicene, and the reaction chamber pressure is between 100mabar-900mbar, specifically including the following steps:

(1) Put the sapphire substrate 1 into the reaction chamber of the metal organic chemical vapor deposition furnace (MOCVD) equipment, heat to 1000-1350° C. under a hydrogen atmosphere, press 200 mbar, and treat with hydrogen for 5-10 minutes;

(2) The reaction chamber is boosted to 600mbar, the growth temperature is 650°C, ammonia gas is introduced, and the sapphire substrate 1 is nitrided for 2-3 minutes, and then Sanjiajiga is injected into the sapphire substrate 1 to grow GaN buffer Layer 2, thickness 20-40nm;

(3) A non-doped GaN layer 3 is grown on the GaN buffer layer 2 at a growth temperature of 1100° C., a growth pressure of 600 mbar, a growth thickness of 2-3 μm, and a growth rate of 2-2.5 μm/h.

(4) An n-type AlGaN layer 4 is grown on the non-doped GaN layer 3, the silicon doping concentration is 5E18-1E19atom/cm ³ , the Al doping concentration is 5E19-1E20atom/cm ³ , the thickness is 30-60nm, and the growth temperature is about It is 1000°C and the pressure is 133mbar.

(5) An n-type GaN layer 5 is grown on the n-type AlGaN layer 4 with a silicon doping concentration of 8E19-1.3E19atom/cm ³ , a thickness of 2-3μm, a growth temperature of about 1080°C, and a growth pressure of 600mbar.

(6) grow the multi-quantum well light-emitting layer 6 on the n-type GaN layer 5, the growth pressure is 200-400mbar, and the steps are as follows:

(A) A mixture of triethylgallium and trimethylindium (the two are mixed in a molar ratio of 1:2) or trimethylgallium and trimethylindium (both are mixed in a molar ratio of 1:2) Mixture) to grow In _x Ga _1-x N potential well layer 11, wherein 0<x<1, the In doping concentration is 2E20-4E20atom/cm ³ , the growth temperature is 730-760°C, and the growth thickness is 2-4nm ;

(B) After stopping the growth of the In _x Ga _1-x N potential well layer 11, the temperature is raised to 880-920° C. to grow the In _a Al _b Ga _1-ab N potential well layer 12, where 0<a<0.3, 0 <b<0.7, growth thickness 10-20nm, In concentration 1E18-5E18atom/cm ³ , Al doping concentration 5E19-1E20atom/cm ³ , silicon doping concentration 1E17-1E18atom/cm ³ ;

(C) keep the temperature constant, grow GaN barrier layer 13, the growth thickness is 10-20nm, and the silicon doping concentration is 1E17-1E18atom/cm ³ ;

(D) keep the temperature constant, grow In _a Al _b Ga _1-ab N barrier layer 14, wherein 0<a<0.3, 0<b<0.7, growth thickness 10-20nm, growth thickness 10-20nm, In concentration 1E18-5E18atom/cm ³ , Al doping concentration 5E19-1E20atom/cm ³ , silicon doping concentration 1E17-1E18atom/cm ³ ;

Steps (A), (B), (C) and (D) can be directly cyclically grown for 5-20 cycles, or steps (B), (C) and (D) can be internally cyclically grown for 3-5 cycles , and then grow cyclically together with step (A).

(7) Grow a P-type AlGaN layer 7 on the multi-quantum well light-emitting layer 6, the growth temperature is 830°C, the growth thickness is 50-100nm, the Mg doping concentration is 5E19atom/cm ³ , the Al doping concentration is 8E19atom/cm ³ , and the growth pressure is 200mbar.

(8) A P-type GaN layer 8 is grown on the P-type AlGaN layer 7 at a growth temperature of 1000° C., a growth thickness of 150-300 nm, a Mg doping concentration of 1E20 atom/cm ³ , and a growth pressure of 200 mbar.

(9) Grow the P-type PInGaN contact layer 9 on the P-type GaN layer 8, the reaction chamber temperature is 750°C, the pressure is 300-400mbar, the growth thickness is 2-10nm, the Mg doping concentration is 2E20atom/cm ³ , and the In doping The concentration is 1E20atom/cm ³ .

Fig. 2 has provided the energy band structure of combined potential barrier multi-quantum well structure in the present invention, because its special energy band combined potential barrier can significantly block and diffuse the injection of N-type electrons, enhance the ability of quantum wells to restrain electrons, improve the space Hole and electron injection in the active region efficiency and radiation recombination efficiency, adjust the polarization charge to eliminate the built-in polarization electric field, effectively reduce the stress between the well-barrier interface, relieve the bending of the energy band, and essentially improve the crystal quality and internal quantum efficiency and improve device performance.

Claims (10)

1. one kind has the LED epitaxial structure of combination potential barrier Multiple Quantum Well, be disposed with substrate layer, GaN resilient coating, undoped GaN layer, N-shaped AlGaN layer, n-type GaN layer, active layer, P type AlGaN layer, P type GaN layer and P type InGaN ohmic contact layer from bottom to top, it is characterized in that, active layer is combination potential barrier multi-quantum pit structure, and this combination potential barrier multi-quantum pit structure is periodically superposed by InGaN potential well layer, InAlGaN barrier layer, GaN barrier layer and InAlGaN barrier layer to form.

2. the LED epitaxial structure with combination potential barrier Multiple Quantum Well according to claim 1, it is characterized in that, the thickness of described GaN resilient coating is 20-40nm; The thickness of described undoped GaN layer is 2-3 μm; The thickness 30-60nm of described N-shaped AlGaN layer; The thickness 2-3 μm of described n-type GaN layer; The thickness of described P type AlGaN layer is 50-100nm; The thickness of described P-type layer is 150-300nm; The thickness of described P type InGaN ohmic contact layer is 2-10nm.

3. the LED epitaxial structure with combination potential barrier Multiple Quantum Well according to claim 1, it is characterized in that, in described combination potential barrier multi-quantum pit structure, the thickness of InGaN potential well layer is 2-4nm, InAlGaN barrier layer thickness is 10-20nm, GaN barrier layer thickness is 10-20nm, InAlGaN barrier layer thickness is 10-20nm.

4. the LED epitaxial structure with combination potential barrier Multiple Quantum Well according to claim 1, is characterized in that, in described combination potential barrier multi-quantum pit structure, the superposition cycle of potential well layer and barrier layer is 5-20.

5. the LED epitaxial structure with combination potential barrier Multiple Quantum Well according to claim 1, it is characterized in that, three barrier layers in described combination potential barrier multi-quantum pit structure are single cycle or multi cycle, and the multi cycle cycle is 3-5.

6. there is described in claim 1 preparation method for the LED epitaxial structure of combination potential barrier Multiple Quantum Well, it is characterized in that, comprise the following steps:

(1) Sapphire Substrate is put into the reative cell of metal-organic chemical vapor deposition equipment (MOCVD) equipment, be heated to 1000-1350 DEG C in a hydrogen atmosphere, pressure 200mbar, process 5-10 minute; Boost to 600mbar, temperature is 650 DEG C, passes into ammonia, nitrogen treatment 2-3 minute;

(2) at the Grown on Sapphire Substrates GaN resilient coating of nitrogen treatment;

(3) on GaN resilient coating, undoped GaN layer is grown;

(4) growing n-type AlGaN layer in undoped GaN layer;

(5) growing n-type GaN layer in N-shaped AlGaN layer;

(6) growth combination potential barrier multi-quantum pit structure (InGaN potential well layer, InAlGaN barrier layer, GaN barrier layer and InAlGaN barrier layer) in n-type GaN layer, detailed process is as described below:

(A) in the reative cell that atmosphere is nitrogen, growth temperature be 730-760 DEG C, under pressure is the environment of 200-400mbar, pass into triethyl-gallium and trimethyl indium by the mixture of 1:2 mol ratio or pass into trimethyl gallium and the trimethyl indium mixture by 1:2 mol ratio, continued propagation thickness is the In of 2-4nm _xga _1-xn potential well layer, wherein 0 < x < 1, In doping content is 2E20-4E20atom/cm ³;

(B) stop growing In _xga _1-xafter N potential well layer, temperature is increased to 880-920 DEG C, growth In _aal _bga _1-a-bn layer, wherein 0 < a < 0.3,0 < b < 0.7, growth thickness 10-20nm, Al doping content 5E19-1E20atom/cm ³, In doping content 2E19-4E19atom/cm ³, doping concentration is 1E17-1E18atom/cm ³; Continuous growing GaN barrier layer, growth thickness 10-20nm, doping concentration is 1E17-1E18atom/cm ³; Grow In continuously again _aal _bga _1-a-bn layer, wherein 0 < a < 0.3,0 < b < 0.7, growth thickness 10-20nm, Al doping content 5E19-1E20atom/cm ³, In doping content 2E19-4E19atom/cm ³, doping concentration is 1E17-1E18atom/cm ³;

The circulating cycle issue of above-mentioned steps (A) and step (B) is 5-20, the multi cycle of step (B) single cycle or cycle 3-5;

(7) growing P-type AlGaN layer, P type GaN layer and P type InGaN ohmic contact layer successively on combination potential barrier multiple quantum well layer.

7. there is the preparation method of the LED epitaxial structure of combination potential barrier Multiple Quantum Well according to claim 6, it is characterized in that, in described step (3), the growth temperature of undoped GaN layer is 1100 DEG C, growth pressure 600mbar, growth thickness is 2-3 μm, growth rate 2-2.5 μm/h.

8. have the preparation method of the LED epitaxial structure of combination potential barrier Multiple Quantum Well according to claim 6, it is characterized in that, in described step (4), the doping concentration of N-shaped AlGaN layer is 5E18-1E19atom/cm ³, Al doping content 5E19-1E20atom/cm ³, thickness is 30-60nm, and growth temperature is 1000 DEG C, pressure 133mbar.

9. have the preparation method of the LED epitaxial structure of combination potential barrier Multiple Quantum Well according to claim 6, it is characterized in that, in described step (5), the doping concentration of n-type GaN layer is 8E19-1.3E19atom/cm ³, thickness is 2-3 μm, and growth temperature is about 1080 DEG C, growth pressure 600mbar.

10. there is the preparation method of the LED epitaxial structure of combination potential barrier Multiple Quantum Well according to claim 6, it is characterized in that, in described step (7), the growth temperature of P type AlGaN layer is 830 DEG C, growth thickness 50-100nm, Mg doping content 5E19atom/cm ³, Al doping content 8E19atom/cm ³, growth pressure is 200mbar; The growth temperature of P type GaN layer is 1000 DEG C, growth thickness 150-300nm, Mg doping content 1E20atom/cm ³, growth pressure is 200mbar; The growth temperature of P type PInGaN contact layer is 750 DEG C, pressure 300-400mbar, and growth thickness is 2-10nm, Mg doping content is 2E20atom/cm ³, In doping content is 1E20atom/cm ³.