Method and system for analyzing total dose effect of silicon-based MOSFET
Technical Field
The invention belongs to electromagnetic simulation technology of a silicon-based semiconductor device under space irradiation, and particularly relates to a method and a system for analyzing total dose effect of a silicon-based MOSFET.
Background
Silicon is used as a first-generation semiconductor material, and has the advantages of simple preparation process, high equipment integration level, mature technology and wide application field, thereby becoming a key production material of semiconductor devices. Semiconductor devices in electronic equipment are susceptible to degradation or even failure of device performance under the irradiation of high-energy particles in a space radiation environment. Along with the expansion of the application fields of integrated circuits in severe environments such as space, nuclear radiation and the like, analysis of the change of electrical parameters of silicon-based semiconductor devices in the radiation environment is important to improve the reliability of the devices and prolong the service lives of the devices.
The numerical analysis of the electrical characteristics of the Si-based semiconductor device has remarkable advantages, the theoretical analysis of the total dose effect is combined to establish a total dose effect model of the Si-based semiconductor device, and numerical simulation is performed to reveal the rule that the total dose effect influences the device performance, including threshold voltage drift, leakage current increase, transconductance and mobility degradation. Numerical simulation is an effective method with less time consumption and lower cost, can provide preliminary theory and prediction, and has guiding significance for actual experiments.
In order to accurately calculate the electrical characteristics of silicon-based semiconductor devices, different physical models are employed. A numerical model of the accumulation of trapped charges in radiation-induced oxide layers in MOS structures is established in literature 1.Krantz,Richard J.,Lee W.Aukerman,and Thomas C.Zietlow,"Applied field and total dose dependence oftrapped charge buildup in MOS devices."IEEE Transactions on NuclearScience,vol.34,no.2,pp.1196-1201,1987,. The model assumes that both electron and hole traps exist in the oxide layer, which traps can trap electrons and holes during irradiation. By using the model, the final charge distribution in the MOSFET oxide layer under the total dose effect is calculated to be consistent with experimental data. The radiation-induced negative oxide charge distribution in ion-implanted radiation-resistant MOSFETs was successfully analyzed based on a numerical model of the distribution of traps within the oxide layer as in literature 2.Lee D.S.,and Chan C.Y.,"Oxide charge accumulation in metal oxide semiconductor devices during irradiation."Journal ofappliedphysics,vol.69,no.10,pp.7134-7141,1991,. As in literature 3.Rowsey,Nicole L.Quantitative modeling of total ionizing dose reliability effects in device silicon dioxide layers.Diss.University of Florida,2012,, the role of hydrogen-containing defects as reaction centers in the effect of ionization damage is considered, and deep level defects and shallow level defects are introduced. The existing numerical model is mostly an equivalent model, the numerical calculation method is few, and the transient particle and defect distribution in the device cannot be observed.
Disclosure of Invention
The invention aims to provide a method and a system for analyzing total dose effect of a silicon-based MOSFET, which can accurately calculate the degradation condition of the electrical characteristics of the MOSFET, reveal the degradation rule of the device performance and provide important theoretical support for developing new structure and new process research of an anti-radiation reinforced device.
The technical solution for realizing the purpose of the invention is as follows:
A method for analyzing total dose effect of a silicon-based MOSFET utilizes dynamic reaction of moving particles and deep and shallow energy level traps to describe generation processes of positive fixed charges and interface state trap charges of an oxide layer in the silicon-based MOSFET, establishes a MOSFET total dose effect model, adopts a time domain spectral element method value, utilizes a Newton iteration method to solve an equation to solve the MOSFET total dose effect model to obtain instantaneous carrier electron, hole, proton concentration and potential of the silicon-based MOSFET under space irradiation, and further obtains drain current and device threshold voltage at the current moment.
Further, the method specifically comprises the steps of:
Firstly, establishing a MOSFET structure model, and splitting the model by adopting a curved hexahedron to obtain structural grid information of the model, wherein the structural grid information comprises the unit numbers of the hexahedron and the physical coordinates of nodes;
Establishing and normalizing a MOSFET total dose effect model comprising an electron current continuity equation, a hole current continuity equation, a proton continuity equation and a Poisson equation based on grid information, introducing radiation into the current continuity equation to generate a composite term and a Shokrill-Reed-Hall composite term, introducing particles related to deep and shallow energy level defects into the Poisson equation, fully considering the influence of silicon-silicon dioxide interface state trap charges on carrier distribution, and designing a boundary condition of a solving area of the MOSFET total dose effect model equation set;
performing time difference on the MOSFET total dose effect model by using backward Euler, performing Galerkin test and expansion on the whole model solving area by using a GLL test basis function and an expansion basis function, and imposing electric field boundary conditions and importing initial values;
And step four, solving the step three by utilizing a Newton iteration method to obtain a MOSFET total dose effect model, solving the electron, hole, proton concentration and potential of different nodes after meeting convergence conditions and stability conditions in the iteration process, and calculating the current at different electrodes according to a current density equation.
Further, the MOSFET total dose effect model is:
wherein n represents electron concentration, p represents hole concentration, H + represents proton concentration, For potential, mu n、μp andRepresenting electron, hole and proton mobilities, (G-R) SRH is Shokrill-Reed-Hall resulting in a complex, G radiation represents irradiation resulting in a complex,AndThe resultant composite term ,Voγ +、Voδ +、VoγH+、VoδH+、VoγH2 +, which is caused by the kinetic reaction of three different particles, electron, hole and proton, with the occurrence of deep and shallow level defects, and V oδH2 +, which is the concentration of charged particles generated by the reaction.
Further, the irradiation produces a complex term G radiation of:
Gradiation=g0D·Y(E) (5)
where D represents the radiation dose rate, g 0 represents the rate of generation of electron-hole pairs, and Y (E) is the ratio of the number of holes not involved in the initial recombination to the number of holes generated by ionizing radiation.
Further, the shore-reed-hall generating complex (G-R) SRH is:
where τ n and τ p are the lifetimes of electrons and holes, respectively.
Further, the designing the boundary condition of the solving area of the MOSFET total dose effect model equation set includes:
In poisson's equation, the fixed boundary conditions are designed as The floating boundary condition isThe Si-SiO 2 interface is:
In the formula, For the boundary potential, r is the outer normal component at the boundary,Is a silicon dioxide dielectric constant which is set,For silicon dielectric constant, Q ss is a strong value.
The fixed boundary conditions designed in the electron current continuity equation and the hole current continuity equation are that an N area is n=N, p=1/N, a P area is n= -1/N, p= -N, and a default floating boundary condition is designed as follows: Wherein N represents a doping concentration, N region represents a doping region having a doping concentration higher than a threshold value, and P region represents a doping region having a doping concentration lower than the threshold value.
Further, the MOSFET total dose effect model performs time difference by using backward Euler, and performs Galerkin test on the whole model solving area by using a GLL test basis function and an unfolding basis function, and the method comprises the following steps of:
The coupling form is as follows:
Wherein, n m,pm, Representing the concentration of electrons, holes and protons at the current time, n m-1,pm-1,Representing the concentration of electrons, holes and protons at the previous time,Is the potential at the current moment.
The final matrix form is obtained by appropriate derivation:
Further, the current density equation is:
Wherein the method comprises the steps of The potential is represented by a value representing the potential,For displacement current, J n、Jp is electron concentration and hole concentration, respectively.
The system comprises a model structure gridding unit, a MOSFET total dose effect model construction unit and a model solving unit, wherein the model structure gridding unit adopts a curved hexahedron to divide a MOSFET structure model to obtain structural grid information of the model, the structural grid information comprises hexahedron unit numbers and node physical coordinates, the MOSFET total dose effect model construction unit utilizes dynamic reaction of moving particles and deep and shallow energy level traps to describe the generation process of positive fixed charges and interface state trap charges of an oxide layer in the silicon-based MOSFET to establish the MOSFET total dose effect model, the model solving unit adopts a time domain spectral element method numerical value to solve an equation by utilizing a Newton iteration method to obtain instantaneous carrier electrons, holes, proton concentrations and electric potentials of the silicon-based MOSFET under space irradiation, and further drain current and device threshold voltage at the current moment are obtained.
A computer storage medium storing an executable program executable by a processor to implement the method of silicon-based MOSFET total dose effect analysis.
Compared with the prior art, the invention has the remarkable advantages that:
(1) The numerical model of the method can freely adjust and control different parameters, and saves a great deal of resource cost and time;
(2) The existing total dose effect numerical model is mostly an equivalent model, the internal particles of the device and the defects induced by irradiation are directly equivalent to positive and negative charges, the dynamic reaction of the related moving particles and the deep and shallow energy level traps is utilized to describe the generation process of the positive fixed charges and the interface state trap charges of the oxide layer to be more fit with the actual situation, and the calculation result is more accurate;
(3) The time domain spectral element method used in the invention adopts a curved hexahedron subdivision, has flexible modeling and convenient subdivision, uses a specific orthogonal polynomial as a basis function, and reduces calculation errors exponentially along with the increase of polynomial orders.
Drawings
Fig. 1 is a structural dimension diagram of a silicon-based MOSFET.
Fig. 2 is a two-dimensional cross-sectional view of a silicon-based MOSFET.
Fig. 3 is a logarithmic electron concentration distribution diagram at 0.01ns time when the drain bias voltage is 0.5V.
Fig. 4 is a logarithmic electron concentration distribution plot at 0.31ns time with a drain bias of 0.5V.
Fig. 5 is a logarithmic electron concentration distribution diagram at 0.1ns time when the drain bias voltage is 0.5V.
Fig. 6 is a graph of MOSFET transfer characteristics at different irradiation doses.
Fig. 7 is a graph of MOSFET transfer characteristics at different interface trap charge concentrations.
Detailed Description
The invention provides a method for analyzing total dose effect of a silicon-based MOSFET, which utilizes dynamic reaction of moving particles and deep and shallow energy level traps to describe the generation process of positive fixed charges and interface state trap charges of an oxide layer in the silicon-based MOSFET, establishes a physical model of the total dose effect of the silicon-based MOSFET, adopts a time domain spectral element method to numerically solve the instantaneous carrier concentration and potential distribution of the silicon-based MOSFET under space irradiation, and obtains drain current and device threshold voltage at the current moment. The method has important practical significance for the irradiation resistance reinforcement research of the silicon-based MOSFET device. The specific steps of the present invention will be described in further detail below with reference to the drawings, taking the MOSFET shown in fig. 1 as an example.
Referring to the schematic structure of the silicon-based MOSFET shown in FIG. 1, the geometric dimensions of the model are as follows, the length of the substrate Si in the MOSFET is 1.2 μm, the width is 10 μm, the height is 1 μm, the length of the oxide layer SiO 2 is 0.6 μm, the width is 10 μm, and the height is 50nm. The method for analyzing the total dose effect value of the MOSFET shown in fig. 1 according to the present invention comprises the following specific operation steps:
Firstly, modeling according to a geometric model of the silicon-based MOSFET shown in fig. 1 by using Ansys software, and meshing the model by adopting a curved hexahedron to obtain node coordinate information and cell information of the structure.
Secondly, based on the action mechanism of the total dose effect on the silicon-based semiconductor device, proton and related motion particles are introduced into the original semiconductor drift diffusion equation set to establish a total dose effect numerical model of the silicon-based semiconductor device, and the normalized total dose effect numerical model equation set of the silicon-based MOSFET can be expressed as:
wherein n represents electron concentration, p represents hole concentration, H + represents proton concentration, For potential, mu n、μp andRepresenting electron, hole and proton mobilities, (G-R) SRH is Shokrill-Reed-Hall (SRH) generating a complex, G radiation is irradiation generating a complex,AndThe resultant composite term ,Voγ +、Voδ +、VoγH+、VoδH+、VoγH2 +, which is caused by the kinetic reaction of three different particles, electron, hole and proton, with the occurrence of deep and shallow level defects, and V oδH2 +, which is the concentration of charged particles generated by the reaction.
The Shokrill-Reed-Hall (SRH) yield complex term (G-R) SRH can be expressed as:
where τ n and τ p are the lifetimes of electrons and holes, respectively.
The irradiation-generated composite term G radiation can be expressed as:
Gradiation=g0D·Y(E) (20)
where D represents the radiation dose rate, g 0 represents the rate of generation of electron-hole pairs, and Y (E) is the ratio of the number of holes not involved in the initial recombination to the number of holes generated by ionizing radiation.
The mechanism of action of the total dose effect of the Si-based MOS tube is described based on 20 reactions involving 16 different species, each reaction formula and its corresponding forward and reverse reaction rates are shown in table 3.3.1:
TABLE 3.3.1 reaction Rate Table
The reaction produced under irradiation is generally reversible, and the following two reversible equations are used to describe the corresponding equations:
Under non-equilibrium conditions each reaction has a corresponding production term and complex term. Taking a as an example, the generation and compound terms are as follows:
Wherein k f、kr is a forward reaction rate and a reverse reaction rate, respectively, A, B, C, L, M and N represent different substances, and [ A ] represents the concentration of substance A. The resulting composite term (G-R) Particles for the kinetic reaction of different particles with defects can be obtained by the above table and related reactions.
Third, boundary conditions are set for the entire solving area of the MOSFET, as shown in fig. 2:
in poisson's equation, the boundary gh+ec+ab+df is set as a fixed boundary condition:
The boundary ac+bd+eg+fh is set as a floating boundary condition:
CD is Si-SiO 2 interface:
In the formula, For the boundary potential, r is the outer normal component at the boundary,Is a silicon dioxide dielectric constant which is set,For silicon dielectric constant, Q ss is a strong value.
In the current continuity equation, ec+df+gh is a fixed boundary condition:
boundary EG+FH+CD is set by default as a floating boundary condition:
and (3) carrying out time difference on the normalized continuity equations (15), (16) and (17) by using a backward Euler method to obtain:
(30) In the formulas (31) and (32), n m,pm, Representing the concentration of electrons, holes and protons at the current time, n m-1,pm -1,Representing the concentration of electrons, holes and protons at the previous time,Is the potential at the current moment. Galerkin testing and development of formulas (30), (31), (32) and (18), respectively, yields:
solving an equation by using a coupling method:
The final matrix form is obtained by appropriate derivation:
Fourthly, solving an equation by utilizing a Newton iteration method, and solving an unknown quantity n t,m+1、pt,m+1 to be solved at the current moment after meeting a convergence condition and a stability condition in the iteration process, Is a value of (2). From this, the total current density inside the MOSFET can be calculated as:
Wherein the method comprises the steps of Is the displacement current.
According to the method provided by the invention, the silicon-based MOSFET shown in the figure 1 is simulated, the simulation diagrams are shown in figures 3-7, and the fact that the threshold voltage of the device negatively shifts and the leakage current increases along with the increase of irradiation dose can be seen. According to the invention, oxygen vacancy defects generated by the reaction of deep and shallow energy level defects and four particles are introduced to represent the effect of positive fixed charges and silicon-silicon dioxide interface trap charges in an oxide layer on the internal carrier distribution of the device, a total dose effect simulation model is established, the electrical characteristic change of the device is obtained by adopting a time domain spectral element method to carry out numerical solution, the calculation of the degradation condition of the electrical characteristic of the MOSFET caused by the total dose effect is completed, the influence rule of the total dose effect on the performance of the device is revealed, and a certain theoretical support is provided for the anti-irradiation reinforcement work of the silicon-based semiconductor device.
Embodiments of the present invention provide a non-volatile computer readable storage medium storing computer executable instructions for execution by a processor to perform steps in a silicon-based MOSFET total dose effect analysis method embodying various exemplary embodiments of the present invention.
It will be apparent to those skilled in the art that various modifications and variations can be made to the embodiments of the present invention without departing from the spirit or scope of the embodiments of the invention. Thus, if such modifications and variations of the embodiments of the present invention fall within the scope of the claims and the equivalents thereof, the present invention is also intended to include such modifications and variations.