Quantum dot model simulation method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention provides a quantum dot model simulation method and device, electronic equipment and a storage medium. According to the scheme, the method comprises the following steps: obtaining device parameters of a to-be-simulated quantum dot model, wherein the device parameters are determined according to model design parameters of the quantum dot model; based on the device parameters and the step function of the charge concentration in the zero-temperature state, determining the potential corresponding to each position in the quantum dot model in the zero-temperature state; and model design parameters are adjusted based on the potential corresponding to each position in the quantum dot model in the zero-temperature state. Through the technical scheme provided by the embodiment of the invention, the difficulty and complexity of charge concentration calculation are reduced, so that the efficiency of determining the potential corresponding to each position in the quantum dot model is improved, and the simulation efficiency of the quantum dot model is improved.

Description

Technical Field

[0001] The present application relates to the field of semiconductor simulation technology, and in particular to a quantum dot model simulation method, device, electronic device and storage medium. Background Art

[0002] Semiconductor Quantum Dots (QDs) devices are nanoscale semiconductor material structures that usually operate at extremely low temperatures (e.g., millikelvin or kelvin levels). Currently, semiconductor simulation software can be used to analyze the rationality of the quantum dot model corresponding to the QD device.

[0003] During the simulation process, the electric potential corresponding to each position in the quantum dot model is an important parameter of the low-temperature simulation model. In the related art, the charge concentration of the low-temperature simulation model, i.e., the electron concentration, hole concentration, and impurity concentration, can be determined by strict Fermi Dirk distribution, and the electric potential corresponding to each position in the quantum dot model can be determined according to the charge concentration.

[0004] Since the above charge concentration is calculated based on a calculation formula including the Fermi Dictator integral, which is a special function with a complex form and only has its series definition, it is relatively complex in numerical calculation, which seriously affects the determination of the corresponding electric potential at each position in the quantum dot model. Summary of the invention

[0005] The purpose of the embodiments of the present application is to provide a quantum dot model simulation method, device, electronic device and storage medium to reduce the difficulty and complexity of charge concentration calculation, thereby improving the efficiency of determining the corresponding potential of each position in the quantum dot model and improving the efficiency of quantum dot model simulation. The specific technical solution is as follows:

[0006] The present application embodiment provides a quantum dot model simulation method, the method comprising:

[0007] Acquiring device parameters of a quantum dot model to be simulated, wherein the device parameters are determined according to model design parameters of the quantum dot model;

[0008] Based on the device parameters and the step function of the charge concentration at zero temperature, determining the potential corresponding to each position in the quantum dot model at zero temperature;

[0009] The model design parameters are adjusted based on the electric potential corresponding to each position in the quantum dot model at zero temperature.

[0010] The present application also provides a quantum dot model simulation device, the device comprising:

[0011] An acquisition module, used to acquire device parameters of a quantum dot model to be simulated, wherein the device parameters are determined according to model design parameters of the quantum dot model;

[0012] A first determination module is used to determine the potential corresponding to each position in the quantum dot model at zero temperature based on the device parameters and the step function of the charge concentration at zero temperature;

[0013] The adjustment module is used to adjust the model design parameters based on the electric potential corresponding to each position in the quantum dot model under the zero-temperature state.

[0014] The embodiment of the present application also provides an electronic device, including a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other via the communication bus;

[0015] Memory, used to store computer programs;

[0016] The processor is used to implement any of the above-mentioned quantum dot model simulation method steps when executing the program stored in the memory.

[0017] An embodiment of the present application also provides a computer-readable storage medium, in which a computer program is stored. When the computer program is executed by a processor, any of the above-mentioned quantum dot model simulation method steps is implemented.

[0018] An embodiment of the present application also provides a computer program product comprising instructions, which, when executed on a computer, enables the computer to execute any of the quantum dot model simulation methods described above.

[0019] Beneficial effects of the embodiments of the present application:

[0020] The technical solution provided in the embodiment of the present application can determine the electric potential at each position in the quantum dot model at zero temperature based on the device parameters of the quantum dot model to be simulated and the step function of the charge concentration at zero temperature, thereby adjusting the model design parameters of the quantum dot model based on the electric potential at each position in the quantum dot model at zero temperature.

[0021] Compared with the method of simulating the quantum dot model based on the charge concentration determined by the Fermi Dirk integral method in the related art, in the embodiment of the present application, according to the Khon-Sham theorem in the density functional theory, that is, the ground state density of a multi-particle system corresponds to the Hamiltonian of the multi-particle system one by one, in the quantum dot model simulation process, the ground state density of the multi-particle system is the charge concentration at zero temperature. At this time, the charge concentration can be expressed in the form of a step function with the Fermi surface position as the boundary. Therefore, when the potential corresponding to each position in the quantum dot model at zero temperature is calculated according to the step function of the charge concentration at zero temperature, the Fermi Dirk integral calculation is no longer required in the potential calculation process, which effectively reduces the complexity and difficulty of the charge concentration calculation, thereby improving the efficiency of determining the corresponding potential of each position in the quantum dot model, while ensuring the accuracy of the quantum dot model simulation, the simulation efficiency of the quantum dot model is improved.

[0022] Of course, implementing any product or method of the present application does not necessarily require achieving all of the advantages described above at the same time. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present application or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying creative work.

[0024] Figure 1 A schematic diagram of a first process flow of a quantum dot model simulation method provided in an embodiment of the present application;

[0025] Figure 2 A second schematic flow chart of the quantum dot model simulation method provided in an embodiment of the present application;

[0026] Figure 3 A schematic diagram of a first flow chart of a method for determining electric potential provided in an embodiment of the present application;

[0027] Figure 4 A second schematic flow chart of the method for determining electric potential provided in an embodiment of the present application;

[0028] Figure 5 A third flow chart of the method for determining electric potential provided in an embodiment of the present application;

[0029] Figure 6 A third flow chart of the quantum dot model simulation method provided in an embodiment of the present application;

[0030] Figure 7-aA first schematic diagram of a three-dimensional quantum dot model provided in an embodiment of the present application;

[0031] Figure 7-b for Figure 7-a A second schematic diagram of the three-dimensional quantum dot model is shown;

[0032] Figure 7-c for Figure 7-a A schematic diagram of the corresponding distribution curve of the bottom energy of the conduction band of the three-dimensional quantum dot model in the X-axis direction;

[0033] Figure 7-d for Figure 7-a A schematic diagram of the corresponding distribution curve of the conduction band bottom energy of the three-dimensional quantum dot model in the Y-axis direction;

[0034] Figure 7-e for Figure 7-a A schematic diagram of the corresponding distribution curve of the bottom energy of the conduction band of the three-dimensional quantum dot model in the Z-axis direction;

[0035] Figure 8 A fourth flow chart of the quantum dot model simulation method provided in an embodiment of the present application;

[0036] Fig. 9 A schematic diagram of a structure of a quantum dot model simulation device provided in an embodiment of the present application;

[0037] Fig.10 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present application to clearly and completely describe the technical solutions in the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Based on the embodiments in the present application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0039] In the related art, the charge concentration under finite temperature conditions is calculated, and then the electric potential corresponding to each position in the quantum dot model is determined according to the calculated charge concentration, and the simulation of the quantum dot model is realized according to the electric potential.

[0040] The above charge concentration can be calculated by the following formula:

[0041]

[0042]

[0043] Where n is the electron concentration, p is the hole concentration, c represents the conduction band, v represents the valence band, and d is the dimension of the quantum dot model, d = 1, 2, 3, m e is the effective mass of the electron, m h is the effective mass of the hole, k B is the Boltzmann constant, T is the temperature, π is the circumference of a circle, is Planck's constant, is the function corresponding to the d-dimensional Fermi-Dirac integral, E F represents the Fermi level, E C is the conduction band bottom energy, E v is the valence band top energy.

[0044] The above d-dimensional Fermi-Dirac integral is a function of x It is expressed as:

[0045]

[0046] in, Γ(1 / 2)=1, is the integration operation from 0 to ∞, ∈ is the dielectric constant.

[0047] When the above x are respectively as well as When , the charge concentration calculation formula includes the d-dimensional Fermi-Dirac integral. At this time, the numerical calculation of the charge concentration is relatively difficult, which will seriously affect the determination of the electric potential at each position in the quantum dot model.

[0048] In order to solve the problems in the related art, the present application embodiment provides a quantum dot model simulation method. Figure 1 As shown, Figure 1 The first flow chart of the quantum dot model simulation method provided in the embodiment of the present application. The method can be applied to an electronic device installed with any semiconductor simulation software. The method includes the following steps.

[0049] Step S101, obtaining device parameters of the quantum dot model to be simulated, wherein the device parameters are determined according to the model design parameters of the quantum dot model.

[0050] Step S102, based on the device parameters and the step function of the charge concentration at the zero temperature state, determine the potential corresponding to each position in the quantum dot model at the zero temperature state.

[0051] Step S103, adjusting the model design parameters based on the electric potential corresponding to each position in the quantum dot model at zero temperature.

[0052] In the embodiment of the present application, the semiconductor simulation software may support software for low temperature simulation model simulation, such as Quantum-Technology Computer-Aided-Design (QTCAD), etc. Here, the semiconductor simulation software is not specifically limited.

[0053] pass Figure 1 The method shown can determine the electric potential at each position in the quantum dot model at zero temperature based on the device parameters of the quantum dot model to be simulated and the step function of the charge concentration at zero temperature, thereby adjusting the model design parameters of the quantum dot model based on the electric potential at each position in the quantum dot model at zero temperature.

[0054] Compared with the method of simulating the quantum dot model based on the charge concentration determined by the Fermi Dirk integral method in the related art, in the embodiment of the present application, according to the Khon-Sham theorem in the density functional theory, that is, the ground state density of a multi-particle system corresponds to the Hamiltonian of the multi-particle system one by one, in the quantum dot model simulation process, the ground state density of the multi-particle system is the charge concentration at zero temperature. At this time, the charge concentration can be expressed in the form of a step function with the Fermi surface position as the boundary. Therefore, when the potential corresponding to each position in the quantum dot model at zero temperature is calculated according to the step function of the charge concentration at zero temperature, the Fermi Dirk integral calculation is no longer required in the potential calculation process, which effectively reduces the complexity and difficulty of the charge concentration calculation, thereby improving the efficiency of determining the corresponding potential of each position in the quantum dot model, while ensuring the accuracy of the quantum dot model simulation, the simulation efficiency of the quantum dot model is improved.

[0055] The embodiments of the present application are described below through specific embodiments. For ease of understanding, the following description is only based on electronic devices as the execution subject, which does not serve any limiting purpose.

[0056] Regarding the above step S101, that is, obtaining the device parameters of the quantum dot model to be simulated, the device parameters are determined according to the model design parameters of the quantum dot model.

[0057] In this step, the user can use semiconductor simulation software on the electronic device to set model design parameters to generate a corresponding quantum dot model as the quantum dot model to be simulated. The electronic device can obtain device parameters corresponding to the quantum dot model.

[0058] In the embodiment of the present application, the quantum dot model may be a one-dimensional model, a two-dimensional model or a three-dimensional model. Here, the dimension of the quantum dot model is not specifically limited.

[0059] The above-mentioned model design parameters may include material design parameters and performance design parameters. Among them, the material design parameters may include the building materials, electrode size, electrode spacing, etc. corresponding to each position in the quantum dot model; the performance design parameters may include the voltage value, current value, etc. corresponding to each position in the quantum dot model.

[0060] The device parameters are determined according to the model design parameters corresponding to the quantum dot model. For example, the device parameters may include the dielectric constant, impurity binding energy, material affinity, material energy gap width, etc. corresponding to each position on the quantum dot model. The determination method of each device parameter can refer to the determination method in the relevant technology, and will not be described in detail here.

[0061] In the embodiments of the present application, the model design parameters and device parameters corresponding to the above quantum dot model are not specifically limited.

[0062] With respect to the above step S102 , based on the device parameters and the step function of the charge concentration at the zero temperature state, the potential corresponding to each position in the quantum dot model at the zero temperature state is determined.

[0063] In this step, the model design parameters corresponding to different positions on the quantum dot model may be different, for example, the materials at different positions may be different. For each position on the quantum dot model, the electronic device can calculate the corresponding electric potential of each position at zero temperature by multiple iterations based on the device parameters corresponding to the position and the step function of the charge concentration at zero temperature. For the method of determining the electric potential, please refer to the description below.

[0064] The above zero-temperature state can be expressed as a state where the ambient temperature is 0. Under the zero-temperature state, according to the Khon-Sham theorem in density functional theory, that is, the ground state density of a multi-particle system corresponds to the Hamiltonian of the multi-particle system, during the simulation, the ground state density of the multi-particle system is the charge concentration under the zero-temperature state. At this time, with the Fermi surface position as the boundary, the charge concentration can be expressed in the form of a step function.

[0065] With respect to the above step S103 , the model design parameters are adjusted based on the electric potential corresponding to each position in the quantum dot model at zero temperature.

[0066] In an optional embodiment, after determining the electric potential corresponding to each position in the quantum dot model under zero temperature conditions, the electronic device can directly adjust the model design parameters corresponding to the quantum dot model by analyzing the determined electric potential.

[0067] In another optional embodiment, after determining the electric potential corresponding to each position in the quantum dot model under zero temperature conditions, the electronic device can calculate other performance parameters of the quantum dot model during the simulation process, such as the number of particles, current, etc., based on the determined electric potential, and thereby adjust the model design parameters corresponding to the quantum dot model based on the calculated other performance parameters.

[0068] The adjustment method of the above model design parameters can be found in the description below and will not be described in detail here.

[0069] In an optional embodiment, according to the above Figure 1 The method shown in the embodiment of the present application also provides a quantum dot model simulation method. Figure 2 As shown, Figure 2 A second flow chart of the quantum dot model simulation method provided in the embodiment of the present application. The method comprises the following steps.

[0070] Step S201, obtaining device parameters of the quantum dot model to be simulated, wherein the device parameters are determined according to the model design parameters of the quantum dot model.

[0071] The above step S201 is the same as the above step S101.

[0072] Step S202, based on the preset charge concentration, using the Poisson equation and the preset charge concentration calculation formula, after a preset number of iterative calculations, obtain the corresponding electric potential of each position in the quantum dot model under the zero temperature state.

[0073] In the embodiment of the present application, the above-mentioned preset charge concentration calculation formula is constructed based on a step function of the charge concentration under the zero-temperature state.

[0074] The charges in the above quantum dot model may include electrons, holes, ionized donor impurities and ionized acceptor impurities. The above preset charge concentration calculation formula may include concentration calculation formulas corresponding to different charges, namely, the first calculation formula, the second calculation formula, the third calculation formula and the fourth calculation formula. Among them, the first calculation formula is a preset electron concentration calculation formula, the second calculation formula is a preset hole concentration calculation formula, the third calculation formula is a preset ionized donor impurity concentration calculation formula, and the fourth calculation formula is a preset ionized acceptor impurity concentration calculation formula.

[0075] The above-mentioned preset number may be a preset maximum number of iterative calculations, and herein, no specific limitation is imposed on the preset number.

[0076] The above step S202 is a refinement of the above step S102.

[0077] Through the above step S202, each time the electronic device performs an iterative calculation, the determined potential will be converged to a certain extent, and the iterative process ends when the number of iterations is equal to the preset number of times, effectively controlling the time of the iterative calculation of the potential, and effectively improving the accuracy and efficiency of the potential calculation. In addition, in each iteration process, the charge concentration is calculated using a preset charge concentration calculation formula, which effectively reduces the difficulty and complexity of the charge concentration calculation, thereby reducing the difficulty and complexity of the iterative calculation of the potential.

[0078] Step S203, adjusting the model design parameters based on the electric potential corresponding to each position in the quantum dot model at zero temperature.

[0079] The above step S203 is the same as the above step S103.

[0080] Based on the same inventive concept, according to the above Figure 2 The method shown in the figure, the embodiment of the present application also provides a method for determining electric potential. Figure 3 As shown, Figure 3 A first flow chart of a method for determining electric potential provided in an embodiment of the present application. The method comprises the following steps.

[0081] Step S301 : for each position coordinate on the quantum dot model, a preset charge concentration of the position coordinate is obtained as a first charge concentration.

[0082] For each position on the quantum dot model, the preset charge concentration at the position coordinate corresponding to the position may be pre-set for the electron concentration, hole concentration, ionized donor impurity concentration, and ionized acceptor impurity concentration, respectively. The preset charge concentration corresponding to each position coordinate may be set according to user experience, etc.

[0083] In an optional embodiment, the concentration corresponding to each charge in the above-mentioned preset charge concentration may be 0. The following description is only based on the assumption that the preset charge concentration is 0, which does not serve any limiting purpose.

[0084] Step S302: Calculate the potential corresponding to the position coordinates at the first charge concentration according to the Poisson equation as the first potential.

[0085] In an optional embodiment, the above Poisson equation can be expressed as:

[0086]

[0087] in, is the gradient operator, r is the coordinate of any position on the quantum dot model, ∈(r) is the dielectric constant at r, is the electric potential corresponding to point r, for The hole concentration under for The electron concentration under for The ionized donor impurity concentration under for Ionized acceptor impurity concentration, e is the elementary charge, e≈1.6×10 -19 Coulomb (C).

[0088] In the first iteration, that is, the iteration number i=0, for each position coordinate on the quantum dot model, the electronic device can be in the case where the charge concentration is the first charge concentration in the above step S301, that is, in the above Poisson equation When both are 0, solve the above Poisson equation Get the potential corresponding to each position coordinate (recorded as the first potential ).

[0089] The ∈(r) in the above Poisson's equation is determined by the type of material corresponding to r in the quantum dot model. Here, the solution process of the above Poisson's equation is not described in detail.

[0090] Step S303, calculating the charge concentration corresponding to the position coordinates at the first potential according to a preset charge concentration calculation formula as the second charge concentration.

[0091] In an optional embodiment, the first calculation formula in the above preset charge concentration calculation formula can be expressed as:

[0092]

[0093] Where n is the electron concentration, π is the circumference of a circle, is Planck's constant, m c is the effective mass of the electron, E F is the Fermi level, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to r, χ is the affinity of the material at r, Θ() is the step function, and d is the dimension of the quantum dot model.

[0094] In the embodiment of the present application, when the system corresponding to the quantum dot model is in a near-equilibrium state, the Fermi level at each position on the quantum dot model is the same. Therefore, for the convenience of calculation, the above E F =0.

[0095] The second calculation formula in the above preset charge concentration calculation formula can be expressed as:

[0096]

[0097] Where p is the hole concentration, π is the circumference of a circle, is Planck's constant, m h is the effective mass of the hole, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r, E F is the Fermi level, Θ() is the step function, and d is the dimension of the quantum dot model.

[0098] The third calculation formula in the above preset charge concentration calculation formula can be expressed as:

[0099]

[0100] in, is the concentration of ionized donor impurities, N D is the donor impurity concentration, Θ() is the step function, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to r, χ is the affinity of the material at r, is the donor impurity binding energy, E F is the Fermi level.

[0101] The fourth calculation formula in the above preset charge concentration calculation formula can be expressed as:

[0102]

[0103] in, is the concentration of ionized acceptor impurities, N A is the acceptor impurity concentration, Θ() is the step function, is the acceptor impurity binding energy, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r, E F is the Fermi level.

[0104] In the first iterative calculation process, the first potential corresponding to each position coordinate in the quantum dot model is calculated by the above step S302, that is, Then, let the input potential The electronic device can be based on the above E c 、E v and The conversion relationship between Will Substitute into the calculation to get the corresponding E c and E v , so according to the calculated E c and E v , respectively using the above-mentioned first calculation formula, second calculation formula, third calculation formula and fourth calculation formula, calculate the electron concentration, hole concentration, ionized donor impurity concentration and ionized acceptor impurity concentration as the second charge concentration, recorded as

[0105] Step S304: Calculate the potential corresponding to the position coordinates under the second charge concentration according to the Poisson equation as the second potential.

[0106] In this step, the electronic device may refer to the above step S302 and convert the second charge concentration calculated in the above step S303, that is, Substituting into the above Poisson equation, the potential corresponding to each position coordinate position under the second charge concentration is calculated as the second potential, recorded as

[0107] Step S305: calculating a first error of the quantum dot model based on the first potential and the second potential.

[0108] In an optional embodiment, for each position coordinate on the quantum dot model, the electronic device may calculate the difference between the second potential and the first potential corresponding to the position coordinate, and calculate the sum of all the differences as the first error.

[0109] The first error can also be calculated in other ways, such as the electronic device can calculate the weighted sum of the difference between the second potential and the first potential and the preset weight according to the first potential, the second potential and the preset weight corresponding to each position in the quantum dot model as the first error. Here, the calculation method of the first error is not specifically limited.

[0110] Step S306, when the first error is greater than the first error threshold, for each position coordinate on the quantum dot model, based on the preset Newton damping factor, the first preset coefficient, and the first potential and the second potential corresponding to the position coordinate, calculate the third potential corresponding to the position coordinate.

[0111] In this step, after calculating the above-mentioned first error, the electronic device can compare the first error with a preset error threshold (referred to as the first error threshold). When the above-mentioned first error is greater than the above-mentioned first error threshold, the electronic device can determine that the calculated second potential has not converged. At this time, the electronic device can enter the inner loop process, that is, for each position coordinate on the quantum dot model, the electronic device can redetermine the potential corresponding to the position coordinate (referred to as the third potential) based on the preset Newton damping factor according to the first potential and the second potential of the position coordinate calculated in the above-mentioned steps S302 and S304.

[0112] In an optional embodiment, for each position coordinate on the quantum dot model, the electronic device may calculate the third potential corresponding to the position coordinate using the following formula;

[0113]

[0114] in, is the third potential, is the first potential, α is the preset Newton damping factor, j is the first preset coefficient, is the second potential.

[0115] In the embodiment of the present application, the first error threshold can be set according to user needs or user experience. Here, the first error threshold is not specifically limited. In addition, the value range of the preset Newton damping factor is between 0 and 1. Here, the preset Newton damping factor is not specifically limited.

[0116] Step S307 , calculating the charge concentration corresponding to the position coordinates at the third potential according to a preset charge concentration calculation formula as a third charge concentration.

[0117] The calculation method of the third charge concentration may refer to the calculation method of the second charge concentration, which will not be described in detail here.

[0118] Step S308: Calculate the potential corresponding to the position coordinates under the third charge concentration according to the Poisson equation as the fourth potential.

[0119] The calculation of the fourth potential may refer to the calculation method of the first potential, and will not be described in detail here.

[0120] Step S309: calculating a second error of the quantum dot model based on the third potential and the fourth potential.

[0121] The calculation method of the second error may refer to the calculation method of the first error, and will not be described in detail here.

[0122] Step S310: when the second error is less than or equal to the second error threshold, the first potential is updated to the third potential, the second potential is updated to the fourth potential, and the number of iterations is increased by 1.

[0123] In this step, after the second error is calculated by the above step S309, the electronic device can compare the second error with the second error threshold. If the above second error is less than or equal to the second error threshold, the electronic device can determine that the above third potential and the fourth potential meet the inner loop convergence condition. At this time, the electronic device can update the above first potential and the second potential according to the third potential and the fourth potential. That is, the above first potential is updated to the above third potential, and the above second potential is updated to the above fourth potential, and the inner loop process ends. At this time, the electronic device can set the number of iterations to 1, that is, the number of iterations i=0+1=1.

[0124] In an optional embodiment, in order to facilitate the convergence of the inner loop process, the second error threshold may be the product of the first error and the second preset coefficient. The second preset coefficient may be greater than 1. The second preset coefficient may be set according to multiple test results and user experience, for example, the second preset coefficient may be a value such as 1.1. The second preset coefficient is not specifically limited here.

[0125] In the embodiment of the present application, after the electronic device updates the first potential to the third potential and updates the second potential to the fourth potential, the internal cycle process ends.

[0126] Step S311, when the number of iterations is less than a preset number, the first potential is updated to the second potential, and based on the updated first potential, the step of returning to the preset charge concentration calculation formula to calculate the charge concentration corresponding to the position coordinates under the first potential as the second charge concentration is performed.

[0127] In this step, the electronic device can obtain the number of iterations at the current moment, that is, the number of iterations after the addition of 1 in the above step S310. If the number of iterations at the current moment is less than the preset number, the electronic device can determine that the number of iterative calculations at the current moment has not reached the preset number of times. The electronic device can determine that it is necessary to continue the iterative calculation. At this time, the electronic device can update the above first potential to the above second potential, that is, the updated first potential is the above fourth potential, and return to execute the above step S303, and calculate the charge concentration corresponding to the position coordinates under the first potential according to the preset charge concentration calculation formula as the second charge concentration step.

[0128] Step S312, when the number of iterations is equal to the preset number, the second potential at the current moment is determined as the potential corresponding to the position coordinate in the zero-temperature state.

[0129] In this step, if the number of iterations at the current moment is equal to the above-mentioned preset number, the electronic device can determine that the number of iterative calculations at the current moment has reached the preset number of times, and at this time, the electronic device can determine that no more iterative calculations are required. For each position coordinate on the quantum dot model, the electronic device can determine the second potential at the current moment as the potential corresponding to the position coordinate in the zero-temperature state.

[0130] In the embodiment of the present application, since the number of iterations increases by 1 each time the electronic device performs an iterative calculation, and once the number of iterations is equal to the preset number, the iterative calculation process will end, therefore, the situation where the number of iterations is greater than the preset number will not occur.

[0131] The above steps S311 and S312 are steps respectively executed by the electronic device when the comparison result of the above iteration number is different from the preset number. Here, the execution of the above steps S311 and S312 is not specifically limited.

[0132] In the above Figure 3 In the illustrated embodiment, the electronic device can determine that the second potential at the current moment has not converged when the first error is greater than the first error threshold, and at this time, the electronic device enters the inner loop process. During the inner loop process, the electronic device appropriately increases the first potential based on the preset Newton damping factor, the first potential and the second potential to obtain the third potential, and then calculates the fourth potential based on the third potential, and ends the inner loop process when the third potential and the fourth potential meet the inner loop convergence condition, which effectively speeds up the convergence efficiency of the potential and improves the accuracy of the determined potential.

[0133] In addition, by effectively limiting the above preset number, the number of iterative calculations in the iterative calculation process can be limited, avoiding the phenomenon that the potential cannot converge and iterative calculations are carried out continuously, effectively controlling the time required for iterative calculations, and improving the efficiency of potential determination.

[0134] In an optional embodiment, according to the above Figure 3 The method shown in the figure, the embodiment of the present application also provides a method for determining electric potential. Figure 4 As shown, Figure 4 A second flow chart of the potential determination method provided in the embodiment of the present application. Figure 4 The following step is added to the method shown, namely step S313.

[0135] Step S313, when the first error is less than or equal to the first error threshold, the second potential at the current moment is determined as the potential corresponding to the position coordinate in the zero-temperature state.

[0136] In this step, after comparing the first error with the first error threshold, if the first error is less than or equal to the first error threshold, the electronic device can determine that the potential has converged. At this time, for each position coordinate on the quantum dot model, the electronic device can determine the second potential at the current moment as the potential corresponding to the position coordinate under the zero temperature state.

[0137] In an embodiment of the present application, when the above-mentioned first error is less than or equal to the above-mentioned first error threshold, the electronic device can end the iterative calculation process while determining the second potential at the current moment as the potential corresponding to each position coordinate in the zero-temperature state. At this time, the number of times the electronic device performs the calculation can be once or multiple times. That is, if the above-mentioned preset charge concentration is set reasonably, the electronic device can obtain the potential corresponding to each position coordinate in the quantum dot model in the zero-temperature state by performing only one iterative calculation.

[0138] Through the above-mentioned step S313, the electronic device ends the iterative calculation process when the first error is less than or equal to the first error threshold based on the comparison result between the first error and the above-mentioned first error threshold. While ensuring the accuracy of the determined electric potential, the iterative calculation process is effectively ended, the efficiency of electric potential determination is improved, and the waste of computing resources is avoided.

[0139] exist Figure 4 In the illustrated embodiment, the above step S306 and step S313 are steps respectively executed by the electronic device when the comparison result between the first error and the first error threshold is different. Here, the execution of the above step S306 and step S313 is not specifically limited.

[0140] In the above Figure 3 and Figure 4 In the method shown, since the electronic device may or may not perform the above inner loop process, the determined electric potential at each position in the quantum dot model at zero temperature may be the second electric potential in the above step S304, or the fourth electric potential determined in the above step S308. Here, the electric potential determined in the last iterative calculation process is not specifically limited.

[0141] In an optional embodiment, according to the above Figure 4 The method shown in the figure, the embodiment of the present application also provides a method for determining electric potential. Figure 5 As shown, Figure 5 A third flow chart of the potential determination method provided in the embodiment of the present application. Figure 5 The following steps are added to the method shown, namely step S314.

[0142] Step S314, when the second error is greater than the second error threshold, update the first preset coefficient, and based on the updated first preset coefficient, return to execute the step of calculating the third potential corresponding to each position coordinate on the quantum dot model based on the preset Newton damping factor, the first preset coefficient, and the first potential and the second potential corresponding to the position coordinate.

[0143] In this step, when the second error is greater than the second error threshold, the electronic device can determine that the preset Newton damping factor is large. At this time, the electronic device can update the first preset coefficient, such as adding 1 to the value of the first preset coefficient. The electronic device can return to execute the above step S306 according to the updated first preset coefficient, that is, return to execute the step of calculating the third potential corresponding to each position coordinate on the quantum dot model based on the preset Newton damping factor, the first preset coefficient, and the first and second potentials corresponding to the position coordinate, to achieve iterative calculation in the inner loop process.

[0144] In an optional embodiment, the initial value of the first preset coefficient may be 0. The value range of the first preset coefficient is between 0 and 5.

[0145] In the embodiment of the present application, the above step S310 and step S314 are steps respectively executed by the electronic device when the comparison result between the second error and the second error threshold is different. Here, the execution of the above step S310 and step S314 is not specifically limited.

[0146] Through the above step S314, in the iterative calculation process of the above inner loop, according to the calculation formula of the third potential, as the first preset coefficient is updated, that is, after the first preset coefficient is increased by 1, 2 j has increased, accordingly, It is reduced, thereby realizing the disguised adjustment of the above-mentioned preset Newton damping factor, so that the third potential calculated in the inner loop process gradually approaches the first potential, realizing the dynamic adjustment of the third potential, facilitating the determined potential to converge quickly, and effectively improving the efficiency of potential determination while ensuring the accuracy of the final determined potential.

[0147] In the above Figure 3 , Figure 4 , Figure 5 In the illustrated embodiment, only one iterative calculation process is used as an example for description. When multiple iterations are performed, the above iterative calculation process can be referred to, and no specific description is given here.

[0148] In an optional embodiment, according to the above Figure 1 The method shown in the embodiment of the present application also provides a quantum dot model simulation method. Figure 6 As shown, Figure 6 The third flow chart of the quantum dot model simulation method provided in the embodiment of the present application is as follows. Figure 6 In the method shown, the above step S103 can be refined into the following steps, namely step S1031-step S1032.

[0149] Step S1031 , generating a potential distribution curve of the quantum dot model according to the potential corresponding to each position in the quantum dot model under a zero-temperature state.

[0150] In this step, the electronic device can generate a potential distribution curve of the quantum dot model according to the potentials at different positions in various directions in the quantum dot model at zero temperature.

[0151] For ease of understanding, combined Figure 7-a and Figure 7-b The three-dimensional quantum dot model shown is used as an example for explanation. Figure 7-a The first schematic diagram of the three-dimensional quantum dot model provided in the embodiment of the present application is: Figure 7-b for Figure 7-a A second schematic diagram of the three-dimensional quantum dot model is shown.

[0152] Figure 7-a and Figure 7-b The three-dimensional quantum dot model shown can be a double quantum dot model of a metal-oxide-semiconductor field-effect transistor (MOSFET or MOS). The materials used in different regions of the three-dimensional quantum dot model are different, such as Figure 7-b As shown, the material at region 704 may be silicon dioxide, and the material at region 705 may be silicon. In the three-dimensional quantum dot model, multiple electrodes may be included, such as Figure 7-a Electrode 701, electrode 702 and electrode 703 are shown.

[0153] Electronic devices determine the above quantum dot model, that is, Figure 7-a and Figure 7-b After calculating the potential at each position in the three-dimensional quantum dot model at zero temperature, a potential distribution curve is generated according to the potential corresponding to each position of the three-dimensional quantum dot model in the directions corresponding to the X-axis, Y-axis and Z-axis in the spatial rectangular coordinate system.

[0154] Step S1032: adjusting the model design parameters based on the potential well width and the potential barrier height in the potential distribution curve.

[0155] In this step, the electronic device can adjust the model design parameters such as the electrode spacing and electrode size corresponding to the above quantum dot model according to the potential well width and barrier height in the above potential distribution curve.

[0156] In the related art, in order to bind electrons in the quantum dot model to form quantum dots, the potential distribution curve corresponding to the quantum dot model needs to meet the requirements of a deeper potential well and a higher potential barrier. Therefore, when adjusting the above model design parameters, the electronic device can adjust the model design parameters such as electrode size and electrode spacing in the quantum dot model according to the potential well width and barrier height in the above potential distribution curve. Here, there is no specific limitation on the adjustment of the above model design parameters by the electronic device according to the potential distribution curve.

[0157] Through the above steps S1031-S1032, the electronic device can directly adjust the model design parameters such as energy level spacing, electrode size, electrode spacing, etc. corresponding to the above quantum dot model according to the potential well width and barrier height in the potential distribution curve corresponding to the quantum dot model, thereby adjusting the model design parameters corresponding to the quantum dot model, realizing the simulation of the quantum dot model, and providing theoretical support for the design of real quantum dot devices.

[0158] In an optional embodiment, in addition to adjusting the model design parameters of the quantum dot model according to the above potential, the electronic device can also adjust the model design parameters of the quantum dot model based on the above potential and other data. For example, for each position in the quantum dot model, the electronic device can determine the conduction band bottom energy E of the position at zero temperature based on the potential corresponding to the position at zero temperature. c or valence band top energy E v , thereby adjusting the model design parameters of the quantum dot model according to the distribution curve corresponding to the bottom energy of the conduction band or the top energy of the valence band.

[0159] For ease of understanding, we will only take the distribution curve corresponding to the bottom energy of the conduction band as an example. Figure 7-c to Figure 7-e As shown. Among them, Figure 7-c for Figure 7-a A schematic diagram of the corresponding distribution curve of the conduction band bottom energy of the three-dimensional quantum dot model in the X-axis direction. Figure 7-d for Figure 7-a A schematic diagram of the corresponding distribution curve of the conduction band bottom energy of the three-dimensional quantum dot model in the Y-axis direction. Figure 7-e for Figure 7-a The three-dimensional quantum dot model shown is a schematic diagram of the corresponding distribution curve of the conduction band bottom energy in the Z-axis direction.

[0160] In the above Figure 7-c to Figure 7-e In the horizontal direction, the distance from the coordinates of different positions on the quantum dot model to the origin of the spatial rectangular coordinate system is given by Figure 7-bThe lower left vertex of the three-dimensional quantum dot model is shown. The vertical direction is the conduction band bottom energy corresponding to different position coordinates on the quantum dot model, and curves 706, 709 and 710 are the distribution curves of the conduction band bottom energy produced by the electronic device according to different position coordinates on the quantum dot model.

[0161] For ease of understanding, only Figure 7-c Take the adjustment of the design parameters of the above model as an example to illustrate.

[0162] exist Figure 7-c In the above three-dimensional quantum dot model, since it is a double quantum dot model, Figure 7-c There are two potential wells and two potential barriers.

[0163] Electronic devices can be based on Figure 7-c Determine the barrier height and potential well width corresponding to the three-dimensional quantum dot model. Figure 7-c As shown, the potential well width is the width 707 and the width 708 in Figure 7. When adjusting the model design parameters, the electronic device can adjust the size, spacing, etc. of the corresponding electrodes in the quantum dot model according to the width 707 and the width 708.

[0164] For example, when adjusting the spacing between electrodes according to the width 707, if you want to increase the potential well width 707, the electronic device can increase the distance between the electrodes corresponding to the two end points of the width 707 in the quantum dot model; if you want to reduce the potential well width 707, the electronic device can shorten the distance between the electrodes corresponding to the two end points of the width 707 in the quantum dot model.

[0165] The adjustment method of the model design parameters corresponding to the quantum dot model can be determined according to the user's design requirements, the size of the potential barrier height and the potential well width in the distribution curve, etc. Here, the adjustment method of the model design parameters of the quantum dot model is not specifically limited.

[0166] In an optional embodiment, according to the above Figure 1 The method shown in the embodiment of the present application also provides a quantum dot model simulation method. Figure 8 As shown, Figure 8 The fourth flow chart of the quantum dot model simulation method provided in the embodiment of the present application is as follows. Figure 8 In the method shown, the above step S103 can be refined into the following steps, namely step S1033 to step S1035.

[0167] Step S1033, according to the electric potential corresponding to each position in the quantum dot module under the zero-temperature state, the Schrödinger equation is solved to obtain a plurality of eigenquantum states and the eigenenergy corresponding to each eigenquantum state.

[0168] In an optional embodiment, the electronic device may use the following formula to calculate multiple eigenquantum states and the eigenenergy corresponding to each eigenquantum state.

[0169]

[0170]

[0171] in, is Planck's constant, m c is the effective mass of the electron, is the gradient operator, Ψ(r) is the eigenvalue state at r, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity energy of the material at point r, E is the intrinsic energy, m h is the effective mass of the hole, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r.

[0172] Step S1034, for each eigenvalue quantum state, according to the eigenvalue energy corresponding to the eigenvalue quantum state, calculate the average number of particles corresponding to the eigenvalue quantum state at a preset temperature.

[0173] In this step, the electronic device can calculate the expected value of any mechanical quantity O at a preset temperature according to the corresponding electric potential of each position in the quantum dot model at zero temperature according to the standard thermodynamic statistical method, so that when any mechanical quantity O is a particle number operator n i , according to the Fermi distribution function, the average number of particles corresponding to each intrinsic quantum state at a preset temperature is determined.

[0174] In an optional embodiment, the electronic device can use the following formula to calculate the expected value of any mechanical quantity O at a finite temperature.

[0175]

[0176]

[0177] Where O is an arbitrary mechanical quantity, <o>is the expected value of O, Z is the partition function, Tr[ ] is the trace operation, e is a natural constant, e≈2.718, E i is the eigenenergy corresponding to the ith quantum state, E F is the Fermi level, n i is the number of particles in the ith quantum state, k B is the Boltzmann constant and T is the temperature.

[0178] In an optional embodiment, for each intrinsic quantum state, the electronic device may use the following formula (ie, the above-mentioned Fermi distribution function) to calculate the average number of particles corresponding to the intrinsic quantum state at a preset temperature.

[0179]

[0180] in, <n i > is the average number of particles corresponding to the ith intrinsic quantum state at the preset temperature T, e is a natural constant, E i is the eigenenergy corresponding to the i-th eigenquantum state, E F is the Fermi level, k B is the Boltzmann constant.

[0181] In the embodiment of the present application, the above-mentioned preset temperature can be set according to the ambient temperature of the actual application scenario of the quantum dot device corresponding to the quantum dot model. Here, the above-mentioned preset temperature is not specifically limited.

[0182] Step S1035 , adjusting the model design parameters according to the average number of particles corresponding to each intrinsic quantum state at a preset temperature.

[0183] In this step, the electronic device can determine the average number of particles corresponding to each of the above-mentioned intrinsic quantum states at a preset temperature, and then determine some performance parameters corresponding to the quantum dot model based on the average number of particles, such as current, voltage, etc., so as to adjust the model design parameters of the quantum dot model according to the determined performance parameters.

[0184] For example, when the number of particles mentioned above is relatively small, the electronic device can increase the voltage on the electrode directly above the corresponding position in the quantum dot model, thereby increasing the potential well depth corresponding thereto, so that it can accommodate more particles, thereby increasing the number of particles therein in disguised form.

[0185] In an embodiment of the present application, considering the low temperature environment in which the quantum dot device is actually applied, through the above steps S1033 to S1035, the electronic device can introduce temperature parameters, that is, the above preset temperature, during the simulation process, thereby effectively improving the matching degree between the adjusted model design parameters and the actual application scenario of the quantum dot device.

[0186] In addition, compared with the method of calculating the electric potential through Fermi Dictator integral under finite temperature conditions in the related art, the above-mentioned preset temperature can match the actual application scenario of the quantum dot device, effectively improving the accuracy of the adjusted model design parameters, and the matching degree between the adjusted model design parameters and the actual application scenario of the quantum dot device, thereby improving the accuracy of the simulation results and laying the foundation for the effective construction of quantum dot devices.

[0187] In the above embodiment, only one adjustment of the model design parameters by the electronic device is used as an example for explanation. In actual application, after the model design parameters of the above quantum dot model are adjusted, the electronic device can use the same method to adjust the model design parameters of the quantum dot model for multiple times until the preset conditions are met, such as the number of adjustments reaches a certain number threshold, or a certain functional parameter corresponding to the quantum dot model is an ideal value. Here, the number of adjustments to the model design parameters during the quantum dot model simulation process is not specifically limited.

[0188] Based on the same inventive concept, according to the quantum dot model simulation method provided in the above embodiment of the present application, the embodiment of the present application also provides a quantum dot model simulation device. Fig. 9 As shown, Fig. 9 A schematic diagram of the structure of a quantum dot model simulation device provided in an embodiment of the present application. The device includes the following modules.

[0189] An acquisition module 901 is used to acquire device parameters of a quantum dot model to be simulated, where the device parameters are determined according to model design parameters of the quantum dot model;

[0190] A first determination module 902 is used to determine the potential corresponding to each position in the quantum dot model at zero temperature based on device parameters and a step function of charge concentration at zero temperature;

[0191] The adjustment module 903 is used to adjust the model design parameters based on the electric potential corresponding to each position in the quantum dot model under the zero temperature state.

[0192] Optionally, the first determination module 902 may be specifically configured to obtain the electric potential corresponding to each position in the quantum dot model at zero temperature by using the Poisson equation and a preset charge concentration calculation formula based on a preset charge concentration and performing a preset number of iterative calculations;

[0193] Among them, the preset charge concentration calculation formula is constructed based on the step function of the charge concentration under the zero temperature state.

[0194] Optionally, the first determining module 902 may include:

[0195] An acquisition submodule, for acquiring, for each position coordinate on the quantum dot model, a preset charge concentration of the position coordinate as a first charge concentration;

[0196] A first calculation submodule, used for calculating the potential corresponding to the position coordinates at the first charge concentration according to the Poisson equation as the first potential;

[0197] A second calculation submodule, used to calculate the charge concentration corresponding to the position coordinates at the first potential according to a preset charge concentration calculation formula as a second charge concentration;

[0198] A third calculation submodule is used to calculate the potential corresponding to the position coordinates under the second charge concentration according to the Poisson equation as the second potential;

[0199] A fourth calculation submodule, configured to calculate a first error of the quantum dot model based on the first potential and the second potential;

[0200] a fifth calculation submodule, configured to calculate, for each position coordinate on the quantum dot model, a third electric potential corresponding to the position coordinate when the first error is greater than a first error threshold, based on a preset Newton damping factor, a first preset coefficient, and the first electric potential and the second electric potential corresponding to the position coordinate;

[0201] a sixth calculation submodule, configured to calculate, according to the preset charge concentration calculation formula, a charge concentration corresponding to the position coordinates at the third potential as a third charge concentration;

[0202] a seventh calculation submodule, configured to calculate, according to the Poisson equation, the electric potential corresponding to the position coordinates under the third charge concentration as a fourth electric potential;

[0203] an eighth calculation submodule, configured to calculate a second error of the quantum dot model based on the third potential and the fourth potential;

[0204] an updating submodule, configured to update the first potential to the third potential, update the second potential to the fourth potential, and increase the number of iterations by 1 when the second error is less than or equal to a second error threshold;

[0205] a calling submodule, configured to update the first potential to the second potential when the number of iterations is less than the preset number, and based on the updated first potential, call the second calculation submodule to return to the step of calculating the charge concentration corresponding to the position coordinates under the first potential according to the preset charge concentration calculation formula as the second charge concentration;

[0206] The determination submodule is used to determine the second electric potential at the current moment as the electric potential corresponding to the position coordinate in the zero-temperature state when the number of iterations is equal to the preset number.

[0207] Optionally, the above quantum dot model simulation may further include:

[0208] The second determination module is used to determine the second electric potential at the current moment as the electric potential corresponding to the position coordinate in a zero-temperature state when the first error is less than or equal to the first error threshold.

[0209] Optionally, the quantum dot model simulation device may further include:

[0210] The calling module is used to update the first preset coefficient when the second error is greater than the second error threshold, and based on the updated first preset coefficient, return to call the first calculation module to execute the step of calculating the third potential corresponding to each position coordinate on the quantum dot model based on the preset Newton damping factor, the first preset coefficient, and the first potential and the second potential corresponding to the position coordinate.

[0211] Alternatively, the above Poisson equation can be expressed as:

[0212]

[0213] in, is the gradient operator, r is the coordinate of any position on the quantum dot model, ∈(r) is the dielectric constant at r, is the electric potential corresponding to point r, for The hole concentration under for The electron concentration under for The ionized donor impurity concentration under for Ionized acceptor impurity concentration, e is the elementary charge, e≈1.6×10 -19 coulomb;

[0214] The above-mentioned preset charge concentration calculation formula may include a first calculation formula, a second calculation formula, a third calculation formula and a fourth calculation formula;

[0215] The first calculation formula can be expressed as:

[0216]

[0217] Where n is the electron concentration, π is the circumference of a circle, is Planck's constant, m c is the effective mass of the electron, E F is the Fermi level, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to r, χ is the affinity of the material at r, Θ() is the step function, and d is the dimension of the quantum dot model;

[0218] The second calculation formula can be expressed as:

[0219]

[0220] Where p is the hole concentration, π is the circumference of a circle, is Planck's constant, m h is the effective mass of the hole, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r, E F is the Fermi level, Θ() is the step function, and d is the dimension of the quantum dot model;

[0221] The third calculation formula can be expressed as:

[0222]

[0223] in, is the concentration of ionized donor impurities, N D is the donor impurity concentration, Θ() is the step function, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to r, χ is the affinity of the material at r, is the donor impurity binding energy, E F is the Fermi level;

[0224] The fourth calculation formula can be expressed as:

[0225]

[0226] in, is the concentration of ionized acceptor impurities, N A is the acceptor impurity concentration, Θ() is the step function, is the acceptor impurity binding energy, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r, E F is the Fermi level.

[0227] Optionally, the first calculation module may be specifically used to calculate the third potential corresponding to each position coordinate on the quantum dot model using the following formula:

[0228]

[0229] in, is the third potential, is the first potential, α is the preset Newton damping factor, j is the first preset coefficient, is the second potential.

[0230] Optionally, the adjustment module 903 may include:

[0231] A generation submodule, used to generate a potential distribution curve of the quantum dot model according to the potential corresponding to each position in the quantum dot model under a zero-temperature state;

[0232] The first adjustment submodule is used to adjust the model design parameters based on the potential well width and the potential barrier height in the potential distribution curve.

[0233] Optionally, the adjustment module 903 may include:

[0234] A solving submodule, used to solve the Schrödinger equation according to the electric potential corresponding to each position in the quantum dot module at zero temperature to obtain multiple eigenquantum states and the eigenenergy corresponding to each eigenquantum state;

[0235] A ninth calculation submodule, for calculating, for each intrinsic quantum state, an average number of particles corresponding to the intrinsic quantum state at a preset temperature according to the intrinsic energy corresponding to the intrinsic quantum state;

[0236] The second adjustment submodule is used to adjust the model design parameters according to the average number of particles corresponding to each intrinsic quantum state at a preset temperature.

[0237] Optionally, the above-mentioned solution submodule can be specifically used to calculate multiple eigenquantum states and the eigenenergy corresponding to each eigenquantum state using the following formula;

[0238]

[0239]

[0240] in, is Planck's constant, m c is the effective mass of the electron, is the gradient operator, Ψ(r) is the eigenvalue state at r, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity energy of the material at point r, E is the intrinsic energy, m h is the effective mass of the hole, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r;

[0241] The ninth calculation submodule may be specifically used to calculate, for each intrinsic quantum state, the average number of particles corresponding to the intrinsic quantum state at a preset temperature using the following formula;

[0242]

[0243] in, <n i > is the average number of particles corresponding to the ith intrinsic quantum state at the preset temperature T, e is a natural constant, E i is the eigenenergy corresponding to the i-th eigenquantum state, E F is the Fermi level, k B is the Boltzmann constant.

[0244] Through the device provided in the embodiment of the present application, the electric potential at each position in the quantum dot model at zero temperature can be determined according to the device parameters of the quantum dot model to be simulated and the step function of the charge concentration at zero temperature, thereby adjusting the model design parameters of the quantum dot model according to the electric potential at each position in the quantum dot model at zero temperature.

[0245] Compared with the method of simulating the quantum dot model based on the charge concentration determined by the Fermi Dirk integral method in the related art, in the embodiment of the present application, according to the Khon-Sham theorem in the density functional theory, that is, the ground state density of a multi-particle system corresponds to the Hamiltonian of the multi-particle system one by one, in the quantum dot model simulation process, the ground state density of the multi-particle system is the charge concentration at zero temperature. At this time, the charge concentration can be expressed in the form of a step function with the Fermi surface position as the boundary. Therefore, when the potential corresponding to each position in the quantum dot model at zero temperature is calculated according to the step function of the charge concentration at zero temperature, the Fermi Dirk integral calculation is no longer required in the potential calculation process, which effectively reduces the complexity and difficulty of the charge concentration calculation, thereby improving the efficiency of determining the corresponding potential of each position in the quantum dot model, while ensuring the accuracy of the quantum dot model simulation, the simulation efficiency of the quantum dot model is improved.

[0246] Based on the same inventive concept, according to the quantum dot model simulation method provided in the above embodiment of the present application, the embodiment of the present application also provides an electronic device, such as Fig.10 As shown, it includes a processor 1001, a communication interface 1002, a memory 1003 and a communication bus 1004, wherein the processor 1001, the communication interface 1002, and the memory 1003 communicate with each other through the communication bus 1004.

[0247] Memory 1003, used for storing computer programs;

[0248] The processor 1001 is used to implement the following steps when executing the program stored in the memory 1003:

[0249] Obtaining device parameters of the quantum dot model to be simulated, where the device parameters are determined according to model design parameters of the quantum dot model;

[0250] Based on the device parameters and the step function of the charge concentration at zero temperature, determine the potential corresponding to each position in the quantum dot model at zero temperature;

[0251] Based on the corresponding electric potential of each position in the quantum dot model at zero temperature, the model design parameters are adjusted.

[0252] The electronic device provided by the embodiment of the present application can determine the electric potential at each position in the quantum dot model at zero temperature based on the device parameters of the quantum dot model to be simulated and the step function of the charge concentration at zero temperature, thereby adjusting the model design parameters of the quantum dot model based on the electric potential at each position in the quantum dot model at zero temperature.

[0253] Compared with the method of simulating the quantum dot model based on the charge concentration determined by the Fermi Dirk integral method in the related art, in the embodiment of the present application, according to the Khon-Sham theorem in the density functional theory, that is, the ground state density of a multi-particle system corresponds to the Hamiltonian of the multi-particle system one by one, in the quantum dot model simulation process, the ground state density of the multi-particle system is the charge concentration at zero temperature. At this time, the charge concentration can be expressed in the form of a step function with the Fermi surface position as the boundary. Therefore, when the potential corresponding to each position in the quantum dot model at zero temperature is calculated according to the step function of the charge concentration at zero temperature, the Fermi Dirk integral calculation is no longer required in the potential calculation process, which effectively reduces the complexity and difficulty of the charge concentration calculation, thereby improving the efficiency of determining the corresponding potential of each position in the quantum dot model, while ensuring the accuracy of the quantum dot model simulation, the simulation efficiency of the quantum dot model is improved.

[0254] The communication bus mentioned in the above electronic device can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. The communication bus can be divided into an address bus, a data bus, a control bus, etc. For ease of representation, only one thick line is used in the figure, but it does not mean that there is only one bus or one type of bus.

[0255] The communication interface is used for communication between the above electronic device and other devices.

[0256] The memory may include a random access memory (RAM) or a non-volatile memory (NVM), such as at least one disk memory. Optionally, the memory may also be at least one storage device located away from the aforementioned processor.

[0257] The above-mentioned processor can be a general-purpose processor, including a central processing unit (CPU), a network processor (NP), etc.; it can also be a digital signal processor (DSP), an application specific integrated circuit (ASIC), a field programmable gate array (FPGA) or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components.

[0258] Based on the same inventive concept, according to the quantum dot model simulation method provided in the above-mentioned embodiments of the present application, the embodiments of the present application also provide a computer-readable storage medium, which stores a computer program. When the computer program is executed by a processor, the steps of any of the above-mentioned quantum dot module simulation methods are implemented.

[0259] Based on the same inventive concept, according to the quantum dot model simulation method provided in the above-mentioned embodiments of the present application, the embodiments of the present application also provide a computer program product containing instructions, which, when run on a computer, enables the computer to execute any quantum dot model simulation method in the above-mentioned embodiments.

[0260] In the above embodiments, it can be implemented in whole or in part by software, hardware, firmware or any combination thereof. When implemented using software, it can be implemented in whole or in part in the form of a computer program product. The computer program product includes one or more computer instructions. When the computer program instructions are loaded and executed on a computer, the process or function described in the embodiment of the present application is generated in whole or in part. The computer may be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions may be stored in a computer-readable storage medium, or transmitted from one computer-readable storage medium to another computer-readable storage medium, for example, the computer instructions may be transmitted from a website site, computer, server or data center by wired (e.g., coaxial cable, optical fiber, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) mode to another website site, computer, server or data center. The computer-readable storage medium may be any available medium that a computer can access or a data storage device such as a server or data center that includes one or more available media integrated. The available medium may be a magnetic medium, (e.g., a floppy disk, a hard disk, a tape), an optical medium (e.g., a DVD), or a semiconductor medium (e.g., a solid-state drive Solid State Disk (SSD)), etc.

[0261] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "comprise", "include" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device. In the absence of further restrictions, an element defined by the sentence "comprises a ..." does not exclude the presence of other identical elements in the process, method, article or device including the element.

[0262] Each embodiment in this specification is described in a related manner, and the same or similar parts between the embodiments can be referred to each other, and each embodiment focuses on the differences from other embodiments. In particular, for embodiments such as devices, electronic devices, computer-readable storage media, and computer program products, since they are basically similar to method embodiments, the description is relatively simple, and the relevant parts can be referred to the partial description of the method embodiments.

[0263] The above description is only a preferred embodiment of the present application and is not intended to limit the protection scope of the present application. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present application are included in the protection scope of the present application.< / o>

Claims

1. A quantum dot model simulation method, characterized in that: The method comprises: Acquiring device parameters of a quantum dot model to be simulated, wherein the device parameters are determined according to model design parameters of the quantum dot model; Based on the device parameters and the step function of the charge concentration at zero temperature, determining the potential corresponding to each position in the quantum dot model at zero temperature; The model design parameters are adjusted based on the electric potential corresponding to each position in the quantum dot model at zero temperature.

2. The method according to claim 1, characterized in that The step of determining the potential corresponding to each position in the quantum dot model at zero temperature based on the device parameters and the step function of the charge concentration at zero temperature comprises: Based on the preset charge concentration, using the Poisson equation and the preset charge concentration calculation formula, after a preset number of iterative calculations, the electric potential corresponding to each position in the quantum dot model under the zero temperature state is obtained; Wherein, the preset charge concentration calculation formula is constructed based on a step function of the charge concentration under zero temperature state.

3. The method according to claim 2, characterized in that The step of obtaining the electric potential corresponding to each position in the quantum dot model at zero temperature by using the Poisson equation and the preset charge concentration calculation formula based on the preset charge concentration and performing a preset number of iterative calculations comprises: For each position coordinate on the quantum dot model, obtaining a preset charge concentration of the position coordinate as a first charge concentration; According to the Poisson equation, calculating the potential corresponding to the position coordinates under the first charge concentration as the first potential; Calculate the charge concentration corresponding to the position coordinates at the first potential according to a preset charge concentration calculation formula as the second charge concentration; According to the Poisson equation, calculating the potential corresponding to the position coordinates at the second charge concentration as the second potential; Calculating a first error of the quantum dot model based on the first potential and the second potential; When the first error is greater than a first error threshold, for each position coordinate on the quantum dot model, based on a preset Newton damping factor, a first preset coefficient, and a first potential and a second potential corresponding to the position coordinate, calculating a third potential corresponding to the position coordinate; According to the preset charge concentration calculation formula, the charge concentration corresponding to the position coordinates at the third potential is calculated as the third charge concentration; According to the Poisson equation, calculating the potential corresponding to the position coordinates under the third charge concentration as the fourth potential; Calculating a second error of the quantum dot model based on the third potential and the fourth potential; When the second error is less than or equal to a second error threshold, updating the first potential to the third potential, updating the second potential to the fourth potential, and increasing the number of iterations by 1; When the number of iterations is less than the preset number, updating the first potential to the second potential, and returning to the step of calculating the charge concentration corresponding to the position coordinates under the first potential as the second charge concentration based on the updated first potential according to the preset charge concentration calculation formula; When the number of iterations is equal to the preset number, the second potential at the current moment is determined as the potential corresponding to the position coordinate in the zero-temperature state.

4. The method according to claim 3, characterized in that The method further comprises: When the first error is less than or equal to the first error threshold, the second electric potential at the current moment is determined as the electric potential corresponding to the position coordinate in a zero-temperature state.

5. The method according to claim 3, characterized in that: The method further comprises: When the second error is greater than the second error threshold, the first preset coefficient is updated, and based on the updated first preset coefficient, the step of returning to execute, for each position coordinate on the quantum dot model, the step of calculating the third potential corresponding to the position coordinate based on the preset Newton damping factor, the first preset coefficient, and the first and second potentials corresponding to the position coordinate.

6. The method according to any one of claims 2 to 5, characterized in that: The Poisson equation is expressed as: in, is the gradient operator, r is the coordinate of any position on the quantum dot model, ∈(r) is the dielectric constant at r, is the electric potential corresponding to point r, for The hole concentration under for The electron concentration under for The ionized donor impurity concentration under for Ionized acceptor impurity concentration, e is the elementary charge, e≈1.6×10 -19 coulomb; The preset charge concentration calculation formula includes a first calculation formula, a second calculation formula, a third calculation formula and a fourth calculation formula; The first calculation formula is expressed as: Where n is the electron concentration, π is the circumference of a circle, is Planck's constant, m c is the effective mass of the electron, E F is the Fermi level, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to r, χ is the affinity of the material at r, Θ() is a step function, and d is the dimension of the quantum dot model; The second calculation formula is expressed as: Where p is the hole concentration, π is the circumference of a circle, is Planck's constant, m h is the effective mass of the hole, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r, E F is the Fermi level, Θ() is a step function, and d is the dimension of the quantum dot model; The third calculation formula is expressed as: in, is the concentration of ionized donor impurities, N D is the donor impurity concentration, Θ() is the step function, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to r, χ is the affinity of the material at r, is the donor impurity binding energy, E F is the Fermi level; The fourth calculation formula is expressed as: in, is the concentration of ionized acceptor impurities, N A is the acceptor impurity concentration, Θ() is the step function, is the acceptor impurity binding energy, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r, E F is the Fermi level.

7. The method according to claim 4, characterized in that The step of calculating, for each position coordinate on the quantum dot model, a third potential corresponding to the position coordinate based on a preset Newton damping factor, a first preset coefficient, and a first potential and a second potential corresponding to the position coordinate, comprises: For each position coordinate on the quantum dot model, the third potential corresponding to the position coordinate is calculated using the following formula; in, is the third potential, is the first potential, α is the preset Newton damping factor, j is the first preset coefficient, is the second potential.

8. The method according to claim 1, characterized in that The step of adjusting the model design parameters based on the electric potential corresponding to each position in the quantum dot model at zero temperature includes: Generating a potential distribution curve of the quantum dot model according to the potential corresponding to each position in the quantum dot model under a zero-temperature state; The model design parameters are adjusted based on the potential well width and the potential barrier height in the potential distribution curve.

9. The method according to claim 1, characterized in that: The step of adjusting the model design parameters based on the electric potential corresponding to each position in the quantum dot model at zero temperature includes: Solving the Schrödinger equation according to the electric potential corresponding to each position in the quantum dot module at zero temperature to obtain a plurality of eigenquantum states and an eigenenergy corresponding to each eigenquantum state; For each eigenquantum state, according to the eigenenergy corresponding to the eigenquantum state, the average number of particles corresponding to the eigenquantum state at a preset temperature is calculated; The model design parameters are adjusted according to the average number of particles corresponding to each intrinsic quantum state at a preset temperature.

10. The method according to claim 9, characterized in that The step of solving the Schrödinger equation according to the electric potential corresponding to each position in the quantum dot module at zero temperature to obtain a plurality of eigenquantum states and the eigenenergy corresponding to each eigenquantum state comprises: Using the following formula, multiple eigenquantum states and the eigenenergy corresponding to each eigenquantum state are calculated; in, is Planck's constant, m c is the effective mass of the electron, is the gradient operator, Ψ(r) is the eigenvalue state at r, E c is the conduction band bottom energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity energy of the material at point r, E is the intrinsic energy, m h is the effective mass of the hole, E v is the valence band top energy, e is the elementary charge, is the potential corresponding to point r, χ is the affinity of the material at r, E g is the energy gap width of the material at r; The step of calculating, for each eigenquantum state, the average number of particles corresponding to the eigenquantum state at a preset temperature according to the eigenenergy corresponding to the eigenquantum state, comprises: For each intrinsic quantum state, the average number of particles corresponding to the intrinsic quantum state at a preset temperature is calculated using the following formula; in, <n i > is the average number of particles corresponding to the ith intrinsic quantum state at the preset temperature T, e is a natural constant, E i is the eigenenergy corresponding to the i-th eigenquantum state, E F is the Fermi level, k B is the Boltzmann constant.

11. A quantum dot model simulation device, characterized in that: The device comprises: An acquisition module, used to acquire device parameters of a quantum dot model to be simulated, wherein the device parameters are determined according to model design parameters of the quantum dot model; A first determination module is used to determine the potential corresponding to each position in the quantum dot model at zero temperature based on the device parameters and the step function of the charge concentration at zero temperature; The adjustment module is used to adjust the model design parameters based on the electric potential corresponding to each position in the quantum dot model under the zero-temperature state.

12. An electronic device, characterized in that: It includes a processor, a communication interface, a memory and a communication bus, wherein the processor, the communication interface and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, for implementing the method steps described in any one of claims 1 to 10 when executing a program stored in a memory.

13. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the method steps described in any one of claims 1 to 10 are implemented.

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