Model simulation method and device, electronic equipment and storage medium

Abstract

The embodiment of the invention provides a model simulation method and device, electronic equipment and a storage medium. According to the scheme, on the basis of model parameters of a to-be-simulated model, a wave function corresponding to each electron in the to-be-simulated model is obtained, and the to-be-simulated model is a semiconductor quantum chip model; for a first electron and a second electron in the to-be-simulated model, determining target data associated with the first electron and the second electron according to a wave function corresponding to the first electron and a dielectric constant of a first position where the first electron is located; according to the target data and the wave function corresponding to the first electron, determining a target coefficient of coulomb interaction between the first electron and the second electron; and adjusting model parameters based on the target coefficient. According to the technical scheme provided by the embodiment of the invention, the target coefficient of coulomb interaction between electrons is determined in the simulation process of the semiconductor quantum chip model, so that simulation of the semiconductor quantum chip model is realized based on the target coefficient.

Description

Technical Field

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

[0002] The basic unit of a quantum computer is a qubit. For semiconductor quantum computers, qubits are encoded by the spin state of electrons in semiconductor quantum dots.

[0003] There are multiple quantum bits integrated on the semiconductor quantum chip. The quantum bits are not independent of each other, but are coupled through electronic interactions. In the semiconductor quantum chip, the Coulomb interaction between electrons will cause changes in the energy level structure. Therefore, the Coulomb interaction between electrons is a parameter that needs to be considered in the simulation process of the semiconductor quantum chip model. Summary of the invention

[0004] The purpose of the embodiments of the present application is to provide a model simulation method, device, electronic device and storage medium to determine the target coefficient of the Coulomb interaction between electrons during the simulation of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model based on the target coefficient. The specific technical solution is as follows:

[0005] The present application provides a model simulation method, the method comprising:

[0006] Based on the model parameters of the model to be simulated, a wave function corresponding to each electron in the model to be simulated is obtained, wherein the model to be simulated is a semiconductor quantum chip model;

[0007] For a first electron and a second electron in the to-be-simulated model, according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located, determine target data associated with the first electron and the second electron, wherein the target data is related to a Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the to-be-simulated model is unevenly distributed, and a charge concentration at a second position where the second electron is located;

[0008] Determining a target coefficient of Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron;

[0009] Based on the target coefficients, the model parameters are adjusted.

[0010] Optionally, the step of acquiring a wave function corresponding to each electron in the model to be simulated based on the model parameters of the model to be simulated includes:

[0011] Based on the model parameters of the model to be simulated, solving the first Poisson equation according to the finite element method to obtain the electric potential corresponding to each position on the model to be simulated;

[0012] According to the electric potential corresponding to each position on the model to be simulated, the Schrodinger equation is solved to obtain the wave function corresponding to each electron on the model to be simulated.

[0013] Optionally, the step of determining target data associated with the first electron and the second electron in the to-be-simulated model according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located includes:

[0014] For the first electron and the second electron in the model to be simulated, the second Poisson's equation is solved according to the wave function corresponding to the first electron and the dielectric constant at the position where the first electron is located using the finite element method to obtain target data associated with the first electron and the second electron.

[0015] Optionally, the step of solving the second Poisson's equation according to the wave function corresponding to the first electron and the dielectric constant at the position where the first electron is located by the finite element method to obtain target data associated with the first electron and the second electron in the model to be simulated includes:

[0016] Calculate target data associated with the first electron and the second electron using the following formula;

[0017]

[0018] in, is the gradient operator, r1 is the first position of the first electron, ∈(r1) is the dielectric constant at r1, is target data associated with the first electron and the second electron, is the charge concentration at r1, j is the state after electron scattering, l is the state before electron scattering, is the complex conjugate of the wave function corresponding to the first electron at r1 under j, ψ l (r1) is the wave function corresponding to the first electron at r1 in the l state.

[0019] Optionally, the step of determining a target coefficient of the Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron includes:

[0020] Calculate the target coefficient of the Coulomb interaction between the first electron and the second electron using the following formula;

[0021]

[0022] Among them, V ijkl is the target coefficient of the Coulomb interaction between the first electron and the second electron, i and j are the states after electron scattering, k and l are the states before electron scattering, e is the elementary charge, ∫dr1 is the integral operation on r1, r1 is the first position where the first electron is located, is the charge concentration at r1, is the complex conjugate of the wave function corresponding to the first electron at r1 in state i, ψ k (r1) is the wave function corresponding to the first electron at r1 in the k state.

[0023] The present application also provides a model simulation device, the device comprising:

[0024] An acquisition module, used for acquiring a wave function corresponding to each electron in the model to be simulated based on a model parameter of the model to be simulated, wherein the model to be simulated is a semiconductor quantum chip model;

[0025] A first determination module is used to determine, for a first electron and a second electron in the to-be-simulated model, target data associated with the first electron and the second electron according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located, wherein the target data is related to a Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the to-be-simulated model is unevenly distributed, and a charge concentration at a second position where the second electron is located;

[0026] A second determination module, configured to determine a target coefficient of the Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron;

[0027] An adjustment module is used to adjust the model parameters based on the target coefficient.

[0028] Optionally, the acquisition module is specifically used to solve the first Poisson equation according to the finite element method based on the model parameters of the model to be simulated, so as to obtain the electric potential corresponding to each position on the model to be simulated;

[0029] According to the electric potential corresponding to each position on the model to be simulated, the Schrodinger equation is solved to obtain the wave function corresponding to each electron on the model to be simulated.

[0030] Optionally, it is specifically used to solve the second Poisson's equation according to the finite element method for the first electron and the second electron in the model to be simulated, based on the wave function corresponding to the first electron and the dielectric constant at the position of the first electron, to obtain target data associated with the first electron and the second electron.

[0031] 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;

[0032] Memory, used to store computer programs;

[0033] The processor is used to implement any of the above-mentioned model simulation method steps when executing the program stored in the memory.

[0034] An embodiment of the present application further provides a computer-readable storage medium, wherein the computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, any of the above-mentioned model simulation method steps is implemented.

[0035] 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 above-mentioned model simulation methods.

[0036] Beneficial effects of the embodiments of the present application:

[0037] The technical solution provided in the embodiment of the present application can determine the target data associated with the first electron and the second electron according to the wave function corresponding to the first electron and the dielectric constant at the position of the first electron for the semiconductor quantum chip model, that is, the first electron and the second electron in the model to be simulated, thereby determining the target coefficient of the Coulomb interaction between the first electron and the second electron according to the target coefficient and the wave function corresponding to the first electron, and adjusting the model parameters corresponding to the semiconductor quantum chip model according to the target coefficient, so as to adjust the model parameters during the simulation process of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model. That is, the target coefficient of the Coulomb interaction between electrons is determined during the simulation process of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model based on the target coefficient.

[0038] In addition, the above-mentioned target data is determined based on the wave function corresponding to the first electron and the dielectric constant at the first position where the first electron is located, and is no longer determined based on the Coulomb interaction potential between the first electron and the second electron when the dielectric constant is uniformly distributed in the model to be simulated, and the charge concentration at the second position where the second electron is located. This allows the determined target data to be the target data when the dielectric constant is unevenly distributed in the model to be simulated, expanding the applicable scenarios of the determined target data, thereby expanding the applicable scenarios of the target coefficients determined based on the target data, improving the flexibility of semiconductor quantum chip simulation, and expanding the applicability of semiconductor quantum chip simulation.

[0039] 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

[0040] 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.

[0041] Figure 1 A schematic diagram of a first flow chart of a model simulation method provided in an embodiment of the present application;

[0042] Figure 2 A schematic diagram of a Coulomb peak image provided in an embodiment of the present application;

[0043] Figure 3 A second flow chart of the model simulation method provided in the embodiment of the present application;

[0044] Figure 4 A third flow chart of the model simulation method provided in the embodiment of the present application;

[0045] Figure 5 A schematic diagram of the structure of a model simulation device provided in an embodiment of the present application;

[0046] Figure 6 A schematic diagram of the structure of an electronic device provided in an embodiment of the present application. DETAILED DESCRIPTION

[0047] 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.

[0048] In the related art, for a semiconductor quantum chip model to be simulated, when determining the target coefficient of the Coulomb interaction between two electrons in the semiconductor quantum chip model, it is usually assumed that the wave function corresponding to the electron is confined to a smaller area, and the area is constructed with a material with a uniform dielectric constant. The target coefficient of the Coulomb interaction between two electrons, such as a first electron and a second electron, is determined using the following formula.

[0049]

[0050] Among them, Vijkl is the target coefficient of the Coulomb interaction between the first electron and the second electron, i and j are the states after electron scattering, k and l are the states before electron scattering, ∫dr1 is the integral operation on r1, ∫dr2 is the integral operation on r2, r1 is the first position where the first electron is located, is the charge concentration at r1, is the complex conjugate of the wave function corresponding to the first electron at r1 in state i, ψ k (r1) is the wave function corresponding to the first electron at r1 in the k state, r2 is the second position where the second electron is located, π is the circumference of the circle, ∈ is the dielectric constant of the region where r1 and r2 are located, || is the complex modulus operation, e is the elementary charge, e=1.6*10 -19 coulomb, is the charge concentration at r2, is the complex conjugate of the wave function corresponding to the second electron at r2 in the j state, ψ l (r2) is the wave function corresponding to the second electron at r2 in the l state.

[0051] In the above V ijkl In the calculation formula, is the Coulomb interaction potential of two electrons in the simulation model under the condition of uniform dielectric constant. That is, when the corresponding materials at r1 and r2 are the same, the dielectric constants at r1 and r2 are the same. At this time, the interaction potential between the two electrons can be expressed as the Coulomb interaction potential of the two electrons, that is, However, once the dielectric constants at r1 and r2 are different, the Coulomb interaction potential between the first electron and the second electron can no longer be simply expressed as At this time, the above V ijkl The calculation formula will no longer be applicable to scenarios with uneven dielectric constant distribution.

[0052] In order to solve the problems in the related art, the present application embodiment provides a model simulation method. Figure 1 As shown, Figure 1 The first flow chart of the model simulation method provided in the embodiment of the present application. The method can be applied to any electronic device installed with semiconductor simulation software. The method includes the following steps.

[0053] Step S101, based on the model parameters of the model to be simulated, obtaining the wave function corresponding to each electron in the model to be simulated, wherein the model to be simulated is a semiconductor quantum chip model.

[0054] Step S102, for the first electron and the second electron in the model to be simulated, determine target data associated with the first electron and the second electron according to the wave function corresponding to the first electron and the dielectric constant at the first position where the first electron is located, wherein the target data is related to the Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the model to be simulated is unevenly distributed, and the charge concentration at the second position where the second electron is located.

[0055] Step S103, determining a target coefficient of the Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron.

[0056] Step S104: adjusting the model parameters based on the target coefficients.

[0057] 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.

[0058] pass Figure 1 The method shown can determine the target data associated with the first electron and the second electron according to the wave function corresponding to the first electron and the dielectric constant at the location of the first electron for the semiconductor quantum chip model, that is, the first electron and the second electron in the model to be simulated, thereby determining the target coefficient of the Coulomb interaction between the first electron and the second electron according to the target coefficient and the wave function corresponding to the first electron, and adjusting the model parameters corresponding to the semiconductor quantum chip model according to the target coefficient, so as to adjust the model parameters during the simulation of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model. That is, the target coefficient of the Coulomb interaction between electrons is determined during the simulation of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model based on the target coefficient.

[0059] In addition, the above-mentioned target data is determined based on the wave function corresponding to the first electron and the dielectric constant at the first position where the first electron is located, and is no longer determined based on the Coulomb interaction potential between the first electron and the second electron when the dielectric constant is uniformly distributed in the model to be simulated, and the charge concentration at the second position where the second electron is located. This allows the determined target data to be the target data when the dielectric constant in the model to be simulated is unevenly distributed, expands the applicable scenarios of the determined target data, and thus expands the applicable scenarios of the target coefficients determined based on the target data, improves the flexibility of semiconductor quantum chip simulation, and expands the applicability of semiconductor quantum chip simulation.

[0060] 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.

[0061] With respect to the above step S101, that is, based on the model parameters of the model to be simulated, the wave function corresponding to each electron in the model to be simulated is obtained, and the model to be simulated is a semiconductor quantum chip model.

[0062] In the embodiment of the present application, the user can construct a semiconductor quantum chip model in the above semiconductor simulation software as the model to be simulated. After the model to be simulated is constructed, the model parameters of the model to be simulated will also be determined.

[0063] After the electronic device completes the construction of the above-mentioned model to be simulated, for each electron in the model to be simulated, the wave function corresponding to the electron can be determined by solving the Poisson equation (referred to as the first Poisson equation) and the Schrödinger equation according to the model parameters at the current moment. The method for determining the wave function can be found in the following description and will not be described in detail here.

[0064] In an optional embodiment, the wave function corresponding to each electron in the above-mentioned model to be simulated can be expressed as: [ψ1(x, y, z), ψ2(x, y, a), ..., ψ n (x,y,a)]. Where n is the number of quantum states corresponding to the electron, and (x,y,z) is the position coordinates corresponding to the electron.

[0065] In the embodiment of the present application, the above-mentioned model parameters may include material parameters and performance parameters. Among them, the material parameters may include the building material, electrode size, electrode spacing, etc. corresponding to each position. The performance parameters may include the voltage value, current value, energy level, etc. corresponding to each position. Here, the model parameters of the above-mentioned model to be simulated are not specifically limited.

[0066] For the above step S102, that is, for the first electron and the second electron in the model to be simulated, target data associated with the first electron and the second electron are determined according to the wave function corresponding to the first electron and the dielectric constant at the first position where the first electron is located, and the target data is related to the Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the model to be simulated is unevenly distributed, and the charge concentration at the second position where the second electron is located.

[0067] In this step, for the first electron and the second electron in the above-mentioned model to be simulated, the electronic device can obtain the wave function corresponding to the first electron from the wave function obtained in the above-mentioned step S101. The electronic device solves the Poisson equation (referred to as the second Poisson equation) according to the wave function corresponding to the first electron and the dielectric constant at the first position where the first electron is located, and obtains the target data associated with the first electron and the second electron. The method for determining the target data can be found in the description below, which is not described in detail here.

[0068] The dielectric constant at the first position where the first electron is located is determined according to the material at the first position. Here, the dielectric constant at the first position is not specifically limited.

[0069] In the embodiment of the present application, the model to be simulated may include multiple electrons. The first electron and the second electron may be any two electrons among the multiple electrons included in the model to be simulated. For ease of understanding, in the embodiment of the present application, only the first electron and the second electron in the model to be simulated are used as examples for explanation, and do not serve any limiting role.

[0070] In an optional embodiment, the relationship between the above target data and the Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the model to be simulated is unevenly distributed, and the charge concentration at the second position where the second electron is located can be expressed as:

[0071]

[0072] Wherein, V(r1) is the above target data, ∫dr2 is the integral operation on r2, G(r1, r2) is the Green's function about r1 and r1, r1 is the position of the first electron, r2 is the second position of the second electron, is the charge concentration at r2, is the complex conjugate of the wave function corresponding to the second electron at r2 in the j state, ψ l (r2) is the wave function corresponding to the second electron at r2 in the l state.

[0073] In the embodiment of the present application, when the dielectric constants at r1 and r2 are different, that is, when the dielectric constant distribution is uneven, the Coulomb interaction potential between the first electron and the second electron is no longer expressed as At this time, the Coulomb interaction potential between the first electron and the second electron can be expressed by the Green's function about r1 and r2, that is, G(r1, r2), which satisfies the following formula:

[0074]

[0075] Among them, δ(r1-r2) is the Dirac delta function, and only when r1-r2=0, δ(r1-r2) is not zero.

[0076] Therefore, when the dielectric constant is unevenly distributed, the above V(r1) can be expressed as:

[0077]

[0078] Compared with the calculation formula of V(r1) when the dielectric constant is uniformly distributed, the calculation formula of V(r1) when the dielectric constant is unevenly distributed takes into account the situation that different positions in the model to be simulated correspond to different construction materials, that is, the situation that the dielectric constants corresponding to the first position where the first electron is located and the second position where the second electron is located on the model to be simulated are different. Therefore, the target data determined by the electronic device based on the wave function corresponding to the first electron, the dielectric constant at the first position where the first electron is located, and the wave function of the first electron are no longer determined based on the Coulomb interaction potential when the dielectric constant is uniformly distributed in the model to be simulated, which makes the determined target data applicable to the scenario where the dielectric constant is unevenly distributed in the model to be simulated, expands the applicable scenarios of the determined target data, and thus expands the applicable scenarios of the target coefficients determined based on the target data, improves the flexibility of semiconductor quantum chip simulation, and expands the applicability of semiconductor quantum chip simulation.

[0079] With respect to the above step S103, that is, based on the target data and the wave function corresponding to the first electron, a target coefficient of the Coulomb interaction between the first electron and the second electron is determined.

[0080] In an optional embodiment, in the above step S103, according to the target data and the wave function corresponding to the first electron, the target coefficient of the Coulomb interaction between the first electron and the second electron is determined, which can be specifically expressed as:

[0081] The electronic device calculates a target coefficient of the Coulomb interaction between the first electron and the second electron using the following formula;

[0082]

[0083] Among them, V ijkl is the target coefficient of the Coulomb interaction between the first electron and the second electron, i and j are the states after electron scattering, k and l are the states before electron scattering, e is the elementary charge, ∫dr1 is the integral operation on r1, r1 is the first position where the first electron is located, is the charge concentration at r1, is the complex conjugate of the wave function corresponding to the first electron at r1 in state i, ψ k(r1) is the wave function corresponding to the first electron at r1 in the k state.

[0084] In the embodiment of the present application, after the target data V(r1) is determined in step S102, and ψ k (r1) can be determined based on the wave function corresponding to the first electron, through the above V ijkl The calculation formula can be used to calculate V ijkl .

[0085] For the above V ijkl The calculation formula and ψ k (r1), the electronic device can arbitrarily select the wave functions corresponding to two quantum states from the wave function corresponding to the first electron, and use the wave function corresponding to one of the quantum states as ψ k (r1), and the complex conjugate of the wave function corresponding to the other quantum state is taken as Here, the above and ψ k (r1) is not particularly limited.

[0086] With respect to the above step S104, the model parameters are adjusted based on the target coefficients.

[0087] In this step, after determining the target coefficient of the Coulomb interaction between the first electron and the second electron, the electronic device can adjust the material thickness, electrode spacing and other parameters in the above model parameters according to the target coefficient.

[0088] In an optional embodiment, the above target coefficient may be expressed as the distance between adjacent peaks in the Coulomb peak image corresponding to the model to be simulated.

[0089] Specifically, based on the above target coefficients, the Hamiltonian corresponding to the quantum dots in the above simulation model can be expressed as:

[0090]

[0091] Among them, H is the Hamiltonian, E m is the energy level of the mth electron, is the electron annihilation operator, c is the electron production operator, i and j are the states after electron scattering, k and l are the states before electron scattering, V ijkl is the target coefficient of the Coulomb interaction between the first electron and the second electron.

[0092] The above V ijkl Generally, it is not zero when i=k, j=l. For the single quantum dot to be simulated model, V ijkl Approximately a constant, namely the charging energy EC At this point, the above Hamiltonian can be simplified to:

[0093]

[0094] Among them, H(N) is the Hamiltonian when the total number of quanta is N, E i is the energy level of the ith quantum state, n i is the number of electrons in the ith quantum state, E C is the charging energy, N is the total number of electrons in the model to be simulated, N = ∑ i n i .

[0095] Based on the total number of electrons N, the energy (i.e. chemical potential) required to add one electron can be expressed as:

[0096] μ(N)=H(N+1)-H(N)=E C N+E i+1

[0097] Where μ(N) is the chemical potential corresponding to adding one electron when the total number of electrons is N, H(N+1) is the Hamiltonian when the total number of electrons is N+1, H(N) is the Hamiltonian when the total number of electrons is N, and E C is the charging energy, N is the total number of electrons, E i+1 is the energy level corresponding to the i+1th quantum state.

[0098] The interval between two adjacent chemical potentials can be expressed as:

[0099] μ(N)-μ(N-1)=E C +(E i+1 -E i )

[0100] Wherein, μ(N) is the chemical potential corresponding to adding one electron when the total number of electrons is N, μ(N-1) is the chemical potential corresponding to adding one electron when the total number of electrons is N-1, μ(N)-μ(N-1) is the chemical potential interval between two adjacent chemical potentials, E C is the charging energy, E i+1 is the energy level corresponding to the i+1th quantum state, E i is the energy level corresponding to the i-th quantum state.

[0101] Since the energy level interval between adjacent quantum states is generally relatively small, that is, the above E i+1 -E i is relatively small, so the interval between adjacent chemical potentials can be approximated as:

[0102] μ(N)-μ(N-1)=E C

[0103] Wherein, μ(N) is the chemical potential corresponding to the increase of one electron when the total number of electrons is N, μ(N-1) is the chemical potential corresponding to the increase of one electron when the total number of electrons is N-1, μ(N)-μ(N-1) is the interval between two adjacent chemical potentials, E C For charging energy.

[0104] Therefore, the interval between two adjacent chemical potentials can be approximated as the above charging energy, which is proportional to the distance between adjacent peaks on the Coulomb peak image. ijkl It is approximately equal to the above charging energy. Therefore, the above target coefficient can be expressed as the spacing between adjacent peaks in the Coulomb peak image corresponding to the model to be simulated.

[0105] When the above target coefficient is expressed as the distance between adjacent peaks in the Coulomb peak image corresponding to the model to be simulated, combined with Figure 2 The adjustment of the above model parameters is described as an example. Figure 2 A schematic diagram of a Coulomb peak image provided in an embodiment of the present application.

[0106] In the above Figure 2 In the Coulomb peak image shown, the horizontal direction is the voltage value corresponding to the electrode above the electron, and the vertical direction is the current value between the source and the drain. Figure 2 The curve 201 in FIG. 2 is a curve generated according to the corresponding relationship between the voltage value and the current value. The distance 202 is the distance between the adjacent chemical potentials.

[0107] In an optional embodiment, the above Figure 2 When the interval between adjacent chemical potentials in is less than the preset value, that is, the above V ijkl is less than the preset value, then the electronic device can increase V by adjusting the above model parameters ijkl , thereby increasing the spacing between adjacent chemical potentials. For example, an electronic device can achieve V by increasing the material thickness at the first position, thereby increasing the dielectric constant at the first position. ijkl increase.

[0108] In another optional embodiment, in the above Figure 2 When the interval between adjacent chemical potentials in is greater than a preset number, that is, the above V ijkl is greater than the preset value, then the electronic device can reduce V by adjusting the above model parameters ijkl , thereby reducing the interval between adjacent chemical potentials. For example, an electronic device can reduce the dielectric constant at the first position by reducing the thickness of the material at the first position to achieve V ijkl of reduction.

[0109] In the embodiment of the present application, when the electronic device adjusts the model parameters according to the target coefficients, one or more of the model parameters may be adjusted. Here, the adjustment process of the model parameters corresponding to the model to be simulated is not specifically limited.

[0110] In an optional embodiment, according to the above Figure 1 The method shown in the embodiment of the present application also provides a model simulation method. Figure 3 As shown, Figure 3 A second flow chart of the model simulation method provided in the embodiment of the present application. Figure 3 In the method shown, the above step S101 can be refined into the following steps, namely step S1011-step S1012.

[0111] Step S1011, based on the model parameters of the model to be simulated, solving the first Poisson equation according to the finite element method to obtain the electric potential corresponding to each position on the model to be simulated.

[0112] In an optional embodiment, the first Poisson equation can be expressed as:

[0113]

[0114] in, is the gradient operator, r is any position on the model to be simulated, ∈(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 The concentration of ionized acceptor impurities, e is the elementary charge.

[0115] The electronic device can perform a preset number of iterative calculations according to the first Poisson equation using a finite element method based on the model parameters of the model to be simulated, to obtain the electric potential corresponding to each position on the model to be simulated.

[0116] For example, the electronic device can be in the first Poisson equation above All are preset values. For example, if the value is 0, the calculated Thus based on this Re-determine the new Then, based on the newly determined Re-determine the new Electronic devices are determined twice Calculate the error to determine the next Is it convergent and in If it does not converge, proceed in the same way Iterate until the determination Convergence, or the number of iterative calculations reaches a preset number, obtains the electric potential corresponding to each position on the model to be simulated.

[0117] The iterative calculation process of the above electric potential can refer to the iterative calculation process in the related art, and will not be described in detail here.

[0118] Step S1012, solving the Schrödinger equation according to the electric potential corresponding to each position on the model to be simulated to obtain the wave function corresponding to each electron on the model to be simulated.

[0119] In an optional embodiment, the electronic device can use the following formula to calculate the wave function corresponding to each electron in the model to be simulated.

[0120]

[0121] in, is Planck's constant, m c is the effective mass of the electron, is the gradient operator, Ψ(r) is the wave function corresponding to 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 r, and E is the intrinsic energy.

[0122] Through the above steps S1011 to S1012, the electronic device can determine the wave function corresponding to each electron in the model to be simulated by solving the above first Poisson equation and Schrödinger equation, thereby ensuring the accuracy of the determined wave function.

[0123] In addition, in the above-mentioned electric potential calculation process, the integration problem is solved according to the finite element method, which avoids the problem of reduced accuracy caused by sampling of each position coordinate in the integration process, effectively improves the accuracy of the calculated electric potential, and thus improves the accuracy of the wave function calculated based on the electric potential.

[0124] In an optional embodiment, according to the above Figure 1 The method shown in the embodiment of the present application also provides a model simulation method. Figure 4 As shown, Figure 4 The third flow chart of the model simulation method provided in the embodiment of the present application is as follows. Figure 4 In the method shown, the above step S102 can be refined into the following steps, namely step S1021.

[0125] Step S1021, for the first electron and the second electron in the model to be simulated, according to the wave function corresponding to the first electron and the dielectric constant at the position of the first electron, solve the second Poisson's equation according to the finite element method to obtain target data associated with the first electron and the second electron.

[0126] In an optional embodiment, in the above step S1021, for the first electron and the second electron in the model to be simulated, according to the wave function corresponding to the first electron and the dielectric constant at the position where the first electron is located, the second Poisson equation is solved according to the finite element method to obtain the target data associated with the first electron and the second electron, which can be expressed as:

[0127] The electronic device may calculate target data associated with the first electron and the second electron using the following formula, i.e., the second Poisson equation described above;

[0128]

[0129] in, is a gradient operator, r1 is a first position where the first electron is located, ∈(r1) is a dielectric constant at r1, V(r1) is target data associated with the first electron and the second electron, is the charge concentration at r1, j is the state after electron scattering, l is the state before electron scattering, is the complex conjugate of the wave function corresponding to the first electron at r1 under j, ψ l (r1) is the wave function corresponding to the first electron at r1 in the l state.

[0130] In the embodiment of the present application, the second Poisson equation is based on the V(r1) calculation formula when the dielectric constant is unevenly distributed, that is, At the same time, the calculation formula is transformed on both sides of the equal sign. Operation, get:

[0131]

[0132] At this point, the second Poisson equation can be obtained, that is, According to the second Poisson's equation, the electronic device can determine the above target data, namely V(r1), according to the dielectric constant and wave function corresponding to the first electron at r1.

[0133] In an embodiment of the present application, the correlation between the wave function corresponding to the first electron, the dielectric constant at the first position where the first electron is located, and the target data is obtained by transforming the calculation formula corresponding to the target data when the dielectric constant is unevenly distributed.

[0134] The process of solving the second Poisson's equation according to the finite element method can refer to the process of solving the first Poisson's equation according to the finite element method, and will not be described in detail here.

[0135] Through the above-mentioned step S1021, the electronic device can accurately determine the target data associated with the first electron and the second electron, and in the calculation process, it is no longer determined based on the Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the model to be simulated is uniformly distributed, and the charge concentration of the second electron at the second position. This allows the determined target data to be the target data when the dielectric constant in the model to be simulated is unevenly distributed, expands the applicable scenarios of the determined target data, and thus expands the applicable scenarios of the target coefficients determined based on the target data, improves the flexibility of semiconductor quantum chip simulation, and expands the applicability of semiconductor quantum chip simulation.

[0136] In addition, in the above-mentioned target data calculation process, the integration problem is solved according to the finite element method, which avoids the problem of reduced accuracy caused by sampling of each position coordinate in the integration process, effectively improves the accuracy of the calculated target data, and thus improves the accuracy of the target coefficient determined based on the target data.

[0137] Based on the same inventive concept, according to the model simulation method provided in the above embodiment of the present application, the embodiment of the present application also provides a model simulation device. Figure 5 As shown, Figure 5 A schematic diagram of the structure of a model simulation device provided in an embodiment of the present application. The device includes the following modules.

[0138] An acquisition module 501 is used to acquire a wave function corresponding to each electron in the model to be simulated based on a model parameter of the model to be simulated, wherein the model to be simulated is a semiconductor quantum chip model;

[0139] A first determination module 502 is used to determine, for a first electron and a second electron in the to-be-simulated model, target data associated with the first electron and the second electron according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located, wherein the target data is related to a Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the to-be-simulated model is unevenly distributed, and a charge concentration at a second position where the second electron is located;

[0140] A second determination module 503 is used to determine a target coefficient of the Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron;

[0141] The adjustment module 504 is used to adjust the model parameters based on the target coefficients.

[0142] Optionally, the acquisition module 501 may be specifically used to solve the first Poisson equation according to the finite element method based on the model parameters of the model to be simulated, so as to obtain the electric potential corresponding to each position on the model to be simulated;

[0143] According to the electric potential corresponding to each position on the model to be simulated, the Schrodinger equation is solved to obtain the wave function corresponding to each electron on the model to be simulated.

[0144] Optionally, the above-mentioned first determination module 502 can be specifically used to solve the second Poisson's equation according to the finite element method for the first electron and the second electron in the model to be simulated, based on the wave function corresponding to the first electron and the dielectric constant at the position where the first electron is located, to obtain target data associated with the first electron and the second electron.

[0145] Optionally, the first determination module 502 may be specifically configured to calculate target data associated with the first electron and the second electron using the following formula:

[0146]

[0147] in, is the gradient operator, r1 is the first position of the first electron, ∈(r1) is the dielectric constant at r1, is target data associated with the first electron and the second electron, is the charge concentration at r1, j is the state after electron scattering, l is the state before electron scattering, is the complex conjugate of the wave function corresponding to the first electron at r1 under j, ψ l (r1) is the wave function corresponding to the first electron at r1 in the l state.

[0148] Optionally, the second determination module 503 may be specifically configured to calculate a target coefficient of the Coulomb interaction between the first electron and the second electron using the following formula:

[0149]

[0150] Among them, V ijkl is the target coefficient of the Coulomb interaction between the first electron and the second electron, i and j are the states after electron scattering, k and l are the states before electron scattering, e is the elementary charge, ∫d r1 is the integral operation on r1, r1 is the first position where the first electron is located, is the charge concentration at r1, is the complex conjugate of the wave function corresponding to the first electron at r1 in state i, ψ k(r1) is the wave function corresponding to the first electron at r1 in the k state.

[0151] Through the device provided in the embodiment of the present application, for the semiconductor quantum chip model, that is, the first electron and the second electron in the model to be simulated, according to the wave function corresponding to the first electron and the dielectric constant at the position of the first electron, the target data associated with the first electron and the second electron can be determined, thereby determining the target coefficient of the Coulomb interaction between the first electron and the second electron according to the target coefficient and the wave function corresponding to the first electron, and adjusting the model parameters corresponding to the semiconductor quantum chip model according to the target coefficient, realizing the adjustment of the model parameters during the simulation process of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model. That is, the target coefficient of the Coulomb interaction between electrons is determined during the simulation process of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model based on the target coefficient.

[0152] In addition, the above-mentioned target data is determined based on the wave function corresponding to the first electron and the dielectric constant at the first position where the first electron is located, and is no longer determined based on the Coulomb interaction potential between the first electron and the second electron when the dielectric constant is uniformly distributed in the model to be simulated, and the charge concentration at the second position where the second electron is located. This allows the determined target data to be the target data when the dielectric constant in the model to be simulated is unevenly distributed, expands the applicable scenarios of the determined target data, and thus expands the applicable scenarios of the target coefficients determined based on the target data, improves the flexibility of semiconductor quantum chip simulation, and expands the applicability of semiconductor quantum chip simulation.

[0153] Based on the same inventive concept, according to the 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 Figure 6 As shown, it includes a processor 601, a communication interface 602, a memory 603 and a communication bus 604, wherein the processor 601, the communication interface 602, and the memory 603 communicate with each other through the communication bus 604.

[0154] Memory 603, used for storing computer programs;

[0155] The processor 601 is used to execute the program stored in the memory 603 to implement the following steps:

[0156] Based on the model parameters of the model to be simulated, a wave function corresponding to each electron in the model to be simulated is obtained, wherein the model to be simulated is a semiconductor quantum chip model;

[0157] For a first electron and a second electron in the to-be-simulated model, according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located, determine target data associated with the first electron and the second electron, wherein the target data is related to a Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the to-be-simulated model is unevenly distributed, and a charge concentration at a second position where the second electron is located;

[0158] Determining a target coefficient of Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron;

[0159] Based on the target coefficients, the model parameters are adjusted.

[0160] Through the electronic device provided by the embodiment of the present application, for the semiconductor quantum chip model, that is, the first electron and the second electron in the model to be simulated, according to the wave function corresponding to the first electron and the dielectric constant at the position of the first electron, the target data associated with the first electron and the second electron can be determined, thereby determining the target coefficient of the Coulomb interaction between the first electron and the second electron according to the target coefficient and the wave function corresponding to the first electron, and adjusting the model parameters corresponding to the semiconductor quantum chip model according to the target coefficient, realizing the adjustment of the model parameters during the simulation process of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model. That is, the target coefficient of the Coulomb interaction between electrons is determined during the simulation process of the semiconductor quantum chip model, thereby realizing the simulation of the semiconductor quantum chip model based on the target coefficient.

[0161] In addition, the above-mentioned target data is determined based on the wave function corresponding to the first electron and the dielectric constant at the first position where the first electron is located, and is no longer determined based on the Coulomb interaction potential between the first electron and the second electron when the dielectric constant is uniformly distributed in the model to be simulated, and the charge concentration at the second position where the second electron is located. This allows the determined target data to be the target data when the dielectric constant is unevenly distributed in the model to be simulated, expanding the applicable scenarios of the determined target data, thereby expanding the applicable scenarios of the target coefficients determined based on the target data, improving the flexibility of semiconductor quantum chip simulation, and expanding the applicability of semiconductor quantum chip simulation.

[0162] 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.

[0163] The communication interface is used for communication between the above electronic device and other devices.

[0164] 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.

[0165] 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.

[0166] Based on the same inventive concept, according to the 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, and when the computer program is executed by a processor, it implements the steps of any of the above-mentioned model simulation methods.

[0167] Based on the same inventive concept, according to the 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 running on a computer, enables the computer to execute any model simulation method in the above-mentioned embodiments.

[0168] 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.

[0169] 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 "include", "comprise" 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, the elements defined by the sentence "comprise a ..." do not exclude the existence of other identical elements in the process, method, article or device including the elements.

[0170] 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.

[0171] 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.

Claims

1. A model simulation method, characterized in that: The method comprises: Based on the model parameters of the model to be simulated, a wave function corresponding to each electron in the model to be simulated is obtained, wherein the model to be simulated is a semiconductor quantum chip model; For a first electron and a second electron in the to-be-simulated model, according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located, determine target data associated with the first electron and the second electron, wherein the target data is related to a Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the to-be-simulated model is unevenly distributed, and a charge concentration at a second position where the second electron is located; Determining a target coefficient of Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron; Based on the target coefficients, the model parameters are adjusted.

2. The method according to claim 1, characterized in that The step of obtaining the wave function corresponding to each electron in the model to be simulated based on the model parameters of the model to be simulated comprises: Based on the model parameters of the model to be simulated, solving the first Poisson equation according to the finite element method to obtain the electric potential corresponding to each position on the model to be simulated; According to the electric potential corresponding to each position on the model to be simulated, the Schrodinger equation is solved to obtain the wave function corresponding to each electron on the model to be simulated.

3. The method according to claim 1, characterized in that The step of determining target data associated with the first electron and the second electron in the to-be-simulated model according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located comprises: For the first electron and the second electron in the model to be simulated, the second Poisson's equation is solved according to the wave function corresponding to the first electron and the dielectric constant at the position where the first electron is located using the finite element method to obtain target data associated with the first electron and the second electron.

4. The method according to claim 3, characterized in that: The step of solving the second Poisson's equation according to the wave function corresponding to the first electron and the dielectric constant at the position where the first electron is located by the finite element method to obtain target data associated with the first electron and the second electron in the to-be-simulated model comprises: Calculate target data associated with the first electron and the second electron using the following formula; in, is a gradient operator, r1 is a first position where the first electron is located, ∈(r1) is a dielectric constant at r1, V(r1) is target data associated with the first electron and the second electron, is the charge concentration at r1, j is the state after electron scattering, l is the state before electron scattering, is the complex conjugate of the wave function corresponding to the first electron at r1 under j, ψ l (r1) is the wave function corresponding to the first electron at r1 in the l state.

5. The method according to claim 1, characterized in that The step of determining a target coefficient of the Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron comprises: Calculate the target coefficient of the Coulomb interaction between the first electron and the second electron using the following formula; Among them, V ijkl is the target coefficient of the Coulomb interaction between the first electron and the second electron, i and j are the states after electron scattering, k and l are the states before electron scattering, e is the elementary charge, ∫dr1 is the integral operation on r1, r1 is the first position where the first electron is located, is the charge concentration at r1, is the complex conjugate of the wave function corresponding to the first electron at r1 in state i, ψ k (r1) is the wave function corresponding to the first electron at r1 in the k state.

6. A model simulation device, characterized in that: The device comprises: An acquisition module, used for acquiring a wave function corresponding to each electron in the model to be simulated based on a model parameter of the model to be simulated, wherein the model to be simulated is a semiconductor quantum chip model; A first determination module is used to determine, for a first electron and a second electron in the to-be-simulated model, target data associated with the first electron and the second electron according to a wave function corresponding to the first electron and a dielectric constant at a first position where the first electron is located, wherein the target data is related to a Coulomb interaction potential between the first electron and the second electron when the dielectric constant in the to-be-simulated model is unevenly distributed, and a charge concentration at a second position where the second electron is located; A second determination module, configured to determine a target coefficient of the Coulomb interaction between the first electron and the second electron according to the target data and a wave function corresponding to the first electron; An adjustment module is used to adjust the model parameters based on the target coefficient.

7. The device according to claim 6, characterized in that The acquisition module is specifically used to solve the first Poisson equation according to the finite element method based on the model parameters of the model to be simulated, so as to obtain the electric potential corresponding to each position on the model to be simulated; According to the electric potential corresponding to each position on the model to be simulated, the Schrodinger equation is solved to obtain the wave function corresponding to each electron on the model to be simulated.

8. The device according to claim 6, characterized in that The first determination module is specifically used to solve the second Poisson's equation according to the finite element method for the first electron and the second electron in the model to be simulated, based on the wave function corresponding to the first electron and the dielectric constant at the position where the first electron is located, to obtain target data associated with the first electron and the second electron.

9. 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 5 when executing a program stored in a memory.

10. 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 5 are implemented.

Images