Double quantum dot model simulation method and device, electronic equipment and storage medium

Abstract

Embodiments of the present application provide a double quantum dot model simulation method and device, electronic equipment and storage medium. The scheme is as follows: a double quantum dot model is constructed as a to-be-simulated model; a Hamiltonian including a first energy is generated according to a performance parameter of the to-be-simulated model, wherein the first energy is a tunneling energy between electrons in the to-be-simulated model due to the spin-orbit coupling effect when the left and right quantum dots have opposite spins; based on the Hamiltonian, a target tunneling coefficient between source-drain electrodes and the left and right quantum dots in the to-be-simulated model is calculated; a target function relationship indicating a current in the to-be-simulated model is determined according to the target tunneling coefficient and a preset master equation, and the preset master equation is used to describe the dynamic change of the electron or hole distribution corresponding to the tunneling process in the to-be-simulated model; and the to-be-simulated model is simulated for drain current according to the target function relationship. Through the technical scheme provided by the embodiments of the present application, the drain current simulation of the double quantum dot model can be realized.

Description

Technical Field

[0001] This application relates to the field of semiconductor quantum dot technology, and in particular to a dual quantum dot model simulation method, apparatus, electronic device and storage medium. Background Technology

[0002] In the two-quantum-dot model, electrons (or holes) tunnel from the source electrode through the left quantum dot, right quantum dot, and drain electrode in sequence to form a current. Due to the Pauli exclusion principle, which states that two electrons with the same spin cannot enter the same quantum dot, Pauli spin blocking may occur during the tunneling process. To address this phenomenon, the Pauli spin blocking can be resolved by reversing the spin through spin-orbit coupling, thereby creating a leakage current.

[0003] Currently, the above process cannot be simulated at the quantum dot model simulation level. Summary of the Invention

[0004] The purpose of this application is to provide a method, apparatus, electronic device, and storage medium for simulating a dual quantum dot model, so as to realize the leakage current simulation of a dual quantum dot model. The specific technical solution is as follows:

[0005] This application provides a simulation method for a dual quantum dot model, the method comprising:

[0006] A dual quantum dot model is constructed as the model to be simulated;

[0007] Based on the performance parameters of the model to be simulated, a Hamiltonian including a first energy is generated, wherein the first energy is the tunneling energy between electrons when the left and right quantum dots have opposite spins due to the spin-orbit coupling effect in the model to be simulated.

[0008] Based on the Hamiltonian, the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model is calculated.

[0009] Based on the target tunneling coefficient and the preset master equation, the objective function relationship indicating the current in the simulation model is determined. The preset master equation is used to describe the dynamic changes in the distribution of electrons or holes corresponding to the tunneling process in the simulation model.

[0010] Leakage current simulation is performed on the model to be simulated based on the objective function relationship.

[0011] Optionally, the performance parameters include: the lever arm coefficients corresponding to the left and right quantum dots in the simulation model, the second energy of Zeeman splitting on the quantum dot orbital energy level, the third energy of tunneling between the left and right quantum dots, and the Coulomb interaction coefficient between the left and right quantum dots.

[0012] The step of generating the Hamiltonian including the first energy based on the performance parameters of the model to be simulated includes:

[0013] The lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient are obtained respectively.

[0014] The Hamiltonian, including the first energy, is generated based on the lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient.

[0015] Optionally, the Hamiltonian is represented as:

[0016]

[0017] Among them, H DQD Let be the Hamiltonian of the model to be simulated, α, d, and σ be three quantum numbers representing a quantum state in the two quantum dots, σ ​​be the spin, d be the energy level, L be the left quantum dot, and R be the right quantum dot. 'a' is the lever arm coefficient, V L V is the voltage of the left quantum dot. R Let ΔV be the voltage across the right quantum dot, and ΔV be the voltage change. The voltage V was obtained from the finite element simulation. L and V R The energy levels at time, c and For generating and annihilating operators, t is the third energy, E Z This is the second energy level, where ↑ indicates spin upwards and ↓ indicates spin downwards. t so The first energy is α, β, γ, and δ, which are quantum dots, and σ is the first energy. ′ For spin, is the Coulomb interaction coefficient.

[0018] Optionally, the step of calculating the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model based on the Hamiltonian includes:

[0019] Based on the Hamiltonian, calculate the target eigenstate corresponding to the Hamiltonian of the model to be simulated;

[0020] Based on the target eigenstate and the coupling coefficients between the source / drain electrodes and the left and right quantum dots in the simulation model, the first tunneling coefficient from the source electrode to the left quantum dot, the second tunneling coefficient from the source electrode to the right quantum dot, the third tunneling coefficient from the left quantum dot to the drain electrode, and the fourth tunneling coefficient from the right quantum dot to the drain electrode are calculated respectively.

[0021] Optionally, the first tunneling coefficient Represented as:

[0022]

[0023] Second tunneling coefficient Represented as:

[0024]

[0025] The third tunneling coefficient Represented as:

[0026]

[0027] The fourth tunneling coefficient Represented as:

[0028]

[0029] Where L represents the left quantum dot, R the right quantum dot, N the number of electrons or holes, N+1 represents the number of electrons or holes increased by 1 after tunneling, and N-1 represents the number of electrons and holes decreased by 1 after tunneling, |α D,N > and |β D,N-1 > represents the target eigenstate. To reduce Planck's constant, γ L γ is the coupling coefficient between the source electrode and the left quantum dot. R Let be the coupling coefficient between the drain electrode and the right quantum dot, d be the energy level, <| be the left vector, |> be the right vector, and c and To generate and annihilate operators, σ is the spin, and n F Let Fermi distribution function be used. When there are N+1 electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |β D,N+1 The corresponding intrinsic energy When there are N electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |α D,N The corresponding intrinsic energy, μ L For the chemical potential of the source electrode coupled to the left quantum dot, μ R The chemical potential of the drain electrode coupled to the right quantum dot. When there are N-1 electrons or holes in a quantum dot, the Hamiltonian H DQd Target eigenstate |β D,N-1 The corresponding intrinsic energy.

[0030] Optionally, the step of determining the objective function relationship indicating the current in the simulation model based on the target tunneling coefficient and the preset master equation includes:

[0031] Based on the target tunneling coefficient, the target probability distribution of the simulation model under steady state is calculated using a preset master equation. The steady state indicates that the left and right quantum dots of the simulation model, including electrons or holes, reach dynamic equilibrium during the tunneling process.

[0032] Based on the target probability distribution and the target tunneling coefficient, the target function relationship indicating the current in the simulation model is determined.

[0033] Optionally, the preset master equation is expressed as:

[0034]

[0035] in, This is the derivative operation with respect to P(N), where P(N) is the probability distribution of electrons or holes in the simulation model, N is the number of electrons or holes, N+1 is the number of electrons or holes increased by 1 after tunneling, and N-1 is the number of electrons or holes decreased by 1 after tunneling. N+1,N Fifth tunneling coefficient Γ N-1,N The sixth tunneling coefficient, The first tunneling coefficient, This is the second tunneling coefficient. The third tunneling coefficient, This is the fourth tunneling coefficient.

[0036] Optionally, the objective function relationship is expressed as:

[0037]

[0038] Where I is the current and e is the elementary charge. To reduce Planck's constant, N is the number of electrons or holes, and P(N) is the probability distribution of electrons or holes in steady state. The fifth tunneling coefficient of the left quantum dot. is the sixth tunneling coefficient of the left quantum dot.

[0039] Optionally, the step of performing leakage current simulation on the model to be simulated based on the objective function relationship includes:

[0040] When the first energy is zero, based on the objective function relationship, the current in the simulation model under different voltage conditions is obtained, where the voltage condition is the voltage applied to the left and right quantum dots;

[0041] Based on the current in the model to be simulated under each voltage condition, generate a current fitting image of the model to be simulated;

[0042] Based on the voltage applied to the left and right quantum dots in the current fitting image, the magnetic field of the simulation model is changed, and leakage current fitting images of the simulation model under different magnetic field conditions are obtained.

[0043] This application embodiment also provides a dual quantum dot model simulation device, the device comprising:

[0044] The building module is used to construct a dual quantum dot model as the model to be simulated.

[0045] The generation module is used to generate a Hamiltonian including a first energy based on the performance parameters of the model to be simulated, wherein the first energy is the tunneling energy between electrons when the left and right quantum dots have opposite spins due to the spin-orbit coupling effect in the model to be simulated.

[0046] The calculation module is used to calculate the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model based on the Hamiltonian.

[0047] The determination module is used to determine the target function relationship indicating the current in the simulation model based on the target tunneling coefficient and the preset master equation. The preset master equation is used to describe the dynamic changes in the distribution of electrons or holes corresponding to the tunneling process in the simulation model.

[0048] The simulation module is used to perform leakage current simulation on the model to be simulated based on the objective function relationship.

[0049] This 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 through the communication bus;

[0050] Memory, used to store computer programs;

[0051] When the processor executes the program stored in the memory, it implements any of the steps of the dual quantum dot model simulation method described above.

[0052] This application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above-described dual quantum dot model simulation methods.

[0053] This application also provides a computer program product containing instructions that, when run on a computer, cause the computer to execute any of the above-described dual quantum dot model simulation methods.

[0054] Beneficial effects of the embodiments in this application:

[0055] The technical solution provided in this application, after constructing a dual quantum dot model, i.e. the model to be simulated, can generate a Hamiltonian including a first energy based on the performance parameters of the model to be simulated, and calculate the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the model to be simulated based on the Hamiltonian. Then, based on the target tunneling coefficient and the preset master equation, the target function relationship indicating the current in the model to be simulated is determined, and the leakage current simulation is performed on the model to be simulated based on the target function relationship.

[0056] Since the objective function relationship is determined based on the target tunneling coefficient and the preset master equation, and the target tunneling coefficient is determined based on the Hamiltonian including the first energy, the objective function relationship must include the first energy. When performing model simulation based on the objective function relationship, the existence of the first energy can accurately characterize the spin reversal that occurs between the left and right quantum dots of the model under the influence of spin-orbit coupling. This effectively eliminates the Pauli spin blocking phenomenon during tunneling. Therefore, this objective function relationship can be used to simulate the leakage current generated during tunneling; that is, leakage current simulation of the model under simulation can be performed based on this objective function relationship, thus realizing leakage current simulation of the dual quantum dot model.

[0057] Of course, implementing any product or method of this application does not necessarily require achieving all of the advantages described above at the same time. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of this application or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a schematic diagram of the first flowchart of the dual quantum dot model simulation method provided in the embodiments of this application;

[0060] Figure 2 This is a schematic diagram of the first structure of the simulation model provided in the embodiments of this application;

[0061] Figure 3 This is a second flowchart illustrating the simulation method for the dual quantum dot model provided in the embodiments of this application;

[0062] Figure 4 This is a schematic diagram of a second structure of the simulation model provided in the embodiments of this application;

[0063] Figure 5 A schematic diagram of the third process for simulating a dual quantum dot model provided in an embodiment of this application;

[0064] Figure 6 This is a schematic diagram of the fourth process of the dual quantum dot model simulation method provided in the embodiments of this application;

[0065] Figure 7 A fifth flowchart illustrating the simulation method for the dual quantum dot model provided in this application embodiment;

[0066] Figure 8 This is a first schematic diagram of a current fitting image provided in an embodiment of this application;

[0067] Figure 9 This is a second schematic diagram of a current fitting image provided in an embodiment of this application;

[0068] Figure 10 This is a first schematic diagram of a leakage current fitting image provided in an embodiment of this application;

[0069] Figure 11 This is a second schematic diagram of a leakage current fitting image provided in an embodiment of this application;

[0070] Figure 12 A schematic diagram of a dual quantum dot model simulation device provided in an embodiment of this application;

[0071] Figure 13 This is a schematic diagram of the structure of an electronic device provided in an embodiment of this application. Detailed Implementation

[0072] The technical solutions of the embodiments of this application will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of this application, and not all embodiments. Based on the embodiments of this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0073] To address the problems in related technologies, embodiments of this application provide a simulation method for a dual quantum dot model. For example... Figure 1 As shown, Figure 1 This is a schematic diagram of a first flowchart illustrating a dual-quantum dot model simulation method provided in this application. This method can be applied to any electronic device equipped with semiconductor simulation software. Figure 1 The method shown includes the following steps.

[0074] Step S101: Construct a dual quantum dot model as the model to be simulated.

[0075] Step S102: Based on the performance parameters of the model to be simulated, generate a Hamiltonian including a first energy, wherein the first energy is the tunneling energy between electrons in the model to be simulated when the left and right quantum dots have opposite spins due to the spin-orbit coupling effect.

[0076] Step S103: Based on the Hamiltonian, calculate the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model.

[0077] Step S104: Based on the target tunneling coefficient and the preset master equation, determine the objective function relationship indicating the current in the simulation model. The preset master equation is used to describe the dynamic changes in the distribution of electrons or holes corresponding to the tunneling process in the simulation model.

[0078] Step S105: Perform leakage current simulation on the model to be simulated based on the objective function relationship.

[0079] In this embodiment, the semiconductor simulation software described above can support software for finite element simulation of semiconductor devices, such as Quantum-Technology Computer-Aided Design (QTCAD). No specific limitations are imposed on the semiconductor simulation software described above.

[0080] pass Figure 1 The method shown, after constructing the dual quantum dot model, i.e. the model to be simulated, can generate a Hamiltonian including the first energy based on the performance parameters of the model to be simulated, and calculate the target tunneling coefficient between the source and drain electrodes and the left and right quantum dots in the model to be simulated based on the Hamiltonian. Then, based on the target tunneling coefficient and the preset master equation, the target function relationship indicating the current in the model to be simulated is determined, and the leakage current simulation is performed on the model to be simulated based on the target function relationship.

[0081] Since the objective function relationship is determined based on the target tunneling coefficient and the preset master equation, and the target tunneling coefficient is determined based on the Hamiltonian including the first energy, the objective function relationship must include the first energy. When performing model simulation based on the objective function relationship, the existence of the first energy can accurately characterize the spin reversal that occurs between the left and right quantum dots of the model under the influence of spin-orbit coupling. This effectively eliminates the Pauli spin blocking phenomenon during tunneling. Therefore, this objective function relationship can be used to simulate the leakage current generated during tunneling; that is, leakage current simulation of the model under simulation can be performed based on this objective function relationship, thus realizing leakage current simulation of the dual quantum dot model.

[0082] The embodiments of this application will be described below through specific examples.

[0083] For step S101 above, namely, constructing a dual quantum dot model as the model to be simulated.

[0084] In this step, the user can use the semiconductor simulation software in the aforementioned electronic device to construct a dual quantum dot model (denoted as the model to be simulated). For example, the user can set the model parameters corresponding to the model to be simulated through the electronic device, and the semiconductor simulation software in the electronic device will generate the model to be simulated based on the model parameters. These model parameters include, but are not limited to, the materials and dimensions of different electrodes.

[0085] In an optional embodiment, the simulation model described above can be as follows: Figure 2 As shown, Figure 2 This is a schematic diagram of the first structure of the simulation model provided in an embodiment of this application. Figure 2 The simulation model shown includes: two confining electrodes (i.e., confining electrode 1 and confining electrode 2), two lead electrodes (i.e., lead electrode 1 and lead electrode 2), two pump electrodes (i.e., pump electrode 1 and pump electrode 2), and three barrier electrodes (i.e. barrier electrode 1 to barrier electrode 3).

[0086] In this embodiment of the application, the simulation model may include two quantum dots, namely a left quantum dot and a right quantum dot. For example... Figure 2 As shown, the left quantum dot can be located at Figure 2 Below the pump electrode 1 shown, the right quantum dot can be located... Figure 2 Below the pump electrode 2 shown. Additionally, the simulation model may also include source and drain electrodes, i.e., source and drain electrodes (…). Figure 2 (Not shown in the image).

[0087] The simulation model described above contains multiple electrons or holes. Under the influence of an external magnetic field, electrons or holes can tunnel between the source and drain electrodes through the left and right quantum dots. For ease of understanding, the following explanation only uses the example of electrons tunneling sequentially through the source electrode, left quantum dot, right quantum dot, and drain electrode, and does not serve as a limitation.

[0088] Regarding step S102 above, that is, based on the performance parameters of the model to be simulated, a Hamiltonian including a first energy is generated, wherein the first energy is the tunneling energy between electrons when the left and right quantum dots have opposite spins due to the spin-orbit coupling effect in the model to be simulated.

[0089] In this step, the electronic device can acquire the performance parameters of the model to be simulated, and then generate the Hamiltonian corresponding to the model based on these performance parameters. This Hamiltonian includes the tunneling energy (denoted as the first energy) between electrons when the left and right quantum dots have opposite spins due to the spin-orbit effect.

[0090] In an optional embodiment, the above performance parameters may include: the lever arm coefficients corresponding to the left and right quantum dots in the simulation model, the second energy of Zeeman splitting on the quantum dot orbital energy level, the third energy of tunneling between the left and right quantum dots, and the Coulomb interaction coefficient between the left and right quantum dots.

[0091] In one alternative embodiment, such as Figure 3 As shown, Figure 3 This is a schematic diagram of a second flowchart illustrating the dual-quantum dot model simulation method provided in an embodiment of this application. Figure 3 The method shown above, step S102, can be further refined into the following steps, namely step S1021-step S1022.

[0092] Step S1021: Obtain the lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient, respectively.

[0093] In the embodiments of this application, the above-mentioned lever coefficient (also known as the energy conversion coefficient) usually reflects the influence of the gate voltage on the quantum dot energy level, and can be specifically expressed as the degree of response of the quantum dot energy level to the change of the quantum dot gate voltage.

[0094] In an optional embodiment, when obtaining the lever arm coefficients corresponding to the left and right quantum dots, the electronic device can obtain the correspondence between the voltage change and the corresponding quantum dot energy level by changing the voltage applied to the pump electrode, and then determine the lever arm coefficient corresponding to the quantum dot based on the correspondence.

[0095] To facilitate understanding, we will use the lever arm coefficient of the left quantum dot as an example. Electronic devices can change the force applied to... Figure 2 The voltage on pump electrode 1 is shown. The energy levels corresponding to the left quantum dot under different voltage changes are obtained, and a corresponding fitting curve is generated. The slope of this fitting curve is the lever arm coefficient corresponding to the left quantum dot. The method for determining the lever arm coefficient corresponding to the right quantum dot can be the same as that for the left quantum dot, and will not be specifically explained here.

[0096] The aforementioned second energy is the Zeeman splitting energy at the quantum dot orbital energy level. This second energy can be calculated based on the interaction between the electron's magnetic moment and an external magnetic field. The specific calculation process can be found in relevant technical documentation and will not be described in detail here.

[0097] The aforementioned third energy is used to describe the probability of an electron tunneling from one quantum dot to another, that is, the tunneling energy of an electron tunneling between left and right quantum dots.

[0098] In one optional embodiment, the electronic device can apply different voltages to the barrier electrode and adjust the voltages applied to the two pump electrodes. When the overall ground state wave function of the coupled left and right quantum dots is symmetrically distributed or the overall excited state wave function is antisymmetrically distributed, half of the energy difference between the left and right quantum dots is the third energy corresponding to the voltage of the barrier electrode at that moment. The electronic device can generate a target relationship indicating the third energy corresponding to the barrier electrode under different voltages, so that when obtaining the above-mentioned third energy, the third energy corresponding to the current moment can be determined by combining the voltage applied to the barrier electrode at the current moment with the target relationship.

[0099] The barrier electrode corresponding to the voltage in the above target relationship can be one of the above. Figure 2 Barrier electrode 2 is located between pump electrode 1 and pump electrode 2.

[0100] The Coulomb interaction coefficient described above can be used to describe the interaction between electrons in a quantum dot generated by an electromagnetic field. This Coulomb interaction coefficient can be obtained through finite element simulation based on the wave functions of the left and right quantum dots. The specific process for obtaining the Coulomb interaction coefficient will not be explained here.

[0101] Step S1022: Based on the lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient, generate the Hamiltonian including the first energy.

[0102] In an optional embodiment, the Hamiltonian described above can be expressed as:

[0103]

[0104] Among them, H DQD Let be the Hamiltonian of the model to be simulated, α, d, and σ be three quantum numbers representing a quantum state in the two quantum dots, σ ​​be the spin, d be the energy level, L be the left quantum dot, and R be the right quantum dot. 'a' is the lever arm coefficient, V L V is the voltage of the left quantum dot. R Let ΔV be the voltage across the right quantum dot, and ΔV be the voltage change. The voltage V was obtained from the finite element simulation. L and V R The energy levels at time, c and For generating and annihilating operators, t is the third energy, E Z This is the second energy level, where ↑ indicates spin upwards and ↓ indicates spin downwards. t so The first energy is α, β, γ, and δ, which are quantum dots, and σ is the first energy. ′ For spin, is the Coulomb interaction coefficient.

[0105] In this embodiment, the lever arm coefficient 'a' in the Hamiltonian can be a matrix form of the lever arm coefficients corresponding to the left and right quantum dots, respectively. Furthermore, the first energy 't' in the Hamiltonian... so It is an unknown quantity.

[0106] For step S103 above, that is, based on the Hamiltonian, the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model is calculated.

[0107] In an optional embodiment, the simulation model described above can also be as follows: Figure 4 As shown, Figure 4 This is a second structural schematic diagram of the simulation model provided in the embodiments of this application. Under the action of an external magnetic field, electrons in the simulation model start from the source electrode, tunnel to the left quantum dot, then tunnel to the right quantum dot, and finally tunnel to the drain electrode, forming a current.

[0108] During the tunneling process described above, different tunneling coefficients exist between the source and drain electrodes and their respective neighboring and non-neighboring quantum dots. Specifically, there is a first tunneling coefficient from the source electrode to the left quantum dot, a second tunneling coefficient from the source electrode to the right quantum dot, a third tunneling coefficient from the left quantum dot to the drain electrode, and a fourth tunneling coefficient from the right quantum dot to the drain electrode. Electronic devices can calculate these first, second, third, and fourth tunneling coefficients based on the aforementioned Hamiltonian.

[0109] In one alternative embodiment, such as Figure 5 As shown, Figure 5 This is a schematic diagram of a third process for simulating a dual-quantum dot model provided in an embodiment of this application. Figure 5 The above step S103 in the method shown can be further refined into the following steps, namely step S1031-step S1032.

[0110] Step S1031: Calculate the target eigenstate corresponding to the Hamiltonian of the model to be simulated based on the Hamiltonian.

[0111] In the embodiments of this application, the aforementioned Hamiltonian is used to describe the Hamiltonian of the model to be simulated. The eigenstates of the model to be simulated are obtained by diagonalizing the aforementioned Hamiltonian in the particle number subspace.

[0112] In an optional embodiment, when the above target eigenstate is |α D,N When |α > , the electronic device can use the following formula to determine |α D,N >, that is:

[0113]

[0114] Among them, H DQD Let |α| be the Hamiltonian of the model to be simulated. D,N >For HDQD The target eigenstate in a subspace with N particles. For |α D,N >The corresponding eigenvalues ​​(i.e., energies).

[0115] Electronic devices can directly transmit the above information about H DQD The eigenstate equation is transformed into a matrix equation over a subspace with N particles, and its eigenstates |α are obtained by diagonalizing the solution. D,N >and intrinsic energy .

[0116] In this embodiment of the application, the target eigenstate may include |α D,N >、|β D,N-1 >and |β D,N+1 >。|β D,N-1 > and |β D,N+1 The determination method for > can be referred to the above |α D,N The method for determining > will not be explained in detail here.

[0117] Step S1032: Based on the target eigenstate and the coupling coefficients between the source / drain electrodes and the left and right quantum dots in the simulation model, calculate the first tunneling coefficient from the source electrode to the left quantum dot, the second tunneling coefficient from the source electrode to the right quantum dot, the third tunneling coefficient from the left quantum dot to the drain electrode, and the fourth tunneling coefficient from the right quantum dot to the drain electrode.

[0118] In the embodiments of this application, the asymmetric coupling between the source / drain electrodes and the left and right quantum dots in the above simulation model can be expressed as the difference in the coupling coefficients between the source / drain electrodes and the left and right quantum dots.

[0119] For ease of understanding, in conjunction with the above Figure 4 Let's take an example to illustrate. In the above... Figure 4 In the middle, the coupling coefficient between the source electrode and the left quantum dot is γ. L The coupling coefficient between the source electrode and the right quantum dot is 0, and the coupling coefficient between the right quantum dot and the drain electrode is γ. R The coupling coefficient between the left quantum dot and the drain electrode is 0.

[0120] The coupling coefficient γ between the source electrode and the left quantum dot mentioned above L and the coupling coefficient γ between the quantum dot and the drain electrode R Settings can be adjusted based on user experience values, etc., and no specific limitations are specified here.

[0121] In an optional embodiment, the electronic device can calculate the first tunneling coefficient, the second tunneling coefficient, the third tunneling coefficient, and the fourth tunneling coefficient respectively using the following formula, based on the aforementioned eigenstates and the coupling coefficients between the source / drain electrodes and the left and right quantum dots.

[0122] The aforementioned first tunneling coefficient It can be represented as:

[0123]

[0124] The aforementioned second tunneling coefficient It can be represented as:

[0125]

[0126] The aforementioned third tunneling coefficient It can be represented as:

[0127]

[0128] The aforementioned fourth tunneling coefficient It can be represented as:

[0129]

[0130] Where L represents the left quantum dot, R the right quantum dot, N the number of electrons or holes, N+1 represents the number of electrons or holes increased by 1 after tunneling, and N-1 represents the number of electrons and holes decreased by 1 after tunneling, |α D,N > and |β D,N-1 >For the target eigenstate, To reduce Planck's constant, γ L γ is the coupling coefficient between the source electrode and the left quantum dot. R Let be the coupling coefficient between the drain electrode and the right quantum dot, d be the energy level, <| be the left vector, |> be the right vector, and c and To generate operators and annihilation operators, v is spin, n F Let Fermi distribution function be used. When there are N+1 electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |β D,N+1 The corresponding intrinsic energy, E αN When there are N electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |α D,N The corresponding intrinsic energy, μ L For the chemical potential of the source electrode coupled to the left quantum dot, μ R The chemical potential of the drain electrode coupled to the right quantum dot. When there are N-1 electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |β D,N-1 The corresponding intrinsic energy.

[0131] The first tunneling coefficient, the second tunneling coefficient, the third tunneling coefficient, and the fourth tunneling coefficient mentioned above are the target tunneling coefficients.

[0132] Regarding step S104 above, that is, determining the objective function relationship of the current in the simulation model based on the target tunneling coefficient and the preset master equation, the preset master equation is used to describe the dynamic changes of the electron or hole distribution corresponding to the tunneling process in the simulation model.

[0133] In an optional embodiment, the electronic device stores a preset master equation, which can be expressed as:

[0134]

[0135] in, This is the derivative operation with respect to P(N), where P(N) is the probability distribution of electrons or holes in the simulation model, N is the number of electrons or holes, N+1 is the number of electrons or holes increased by 1 after tunneling, and N-1 is the number of electrons or holes decreased by 1 after tunneling. N+1,N Fifth tunneling coefficient, Γ N-1,N The sixth tunneling coefficient, The first tunneling coefficient, This is the second tunneling coefficient. The third tunneling coefficient, This is the fourth tunneling coefficient.

[0136] In this embodiment, the aforementioned target tunneling coefficients, namely the first, second, third, and fourth tunneling coefficients, can be used to represent the tunneling rates of electrons or holes in the left and right quantum dots during the tunneling process. Therefore, the fifth tunneling rate can represent the rate of increase of electrons or holes in the left and right quantum dots, and the sixth tunneling rate can represent the rate of decrease of electrons or holes in the left and right quantum dots. Furthermore, P(N), P(N+1), and P(N-1) in the aforementioned pre-defined master equation represent the probability distributions of electrons or holes during the tunneling process. Therefore, the aforementioned pre-defined master equation is used to describe the probability distributions of electrons or holes corresponding to the tunneling process in the simulation model.

[0137] In one alternative embodiment, such as Figure 6 As shown, Figure 6 This is a schematic diagram of the fourth process for simulating a dual-quantum dot model provided in an embodiment of this application. Figure 6 The above step S104 in the method shown can be further refined into the following steps, namely step S1041-step S1042.

[0138] Step S1041: Based on the target tunneling coefficient, calculate the target probability distribution of the model to be simulated in steady state using the preset master equation. Steady state indicates that the left and right quantum dots of the model to be simulated, including electrons or holes, reach dynamic equilibrium during the tunneling process.

[0139] In this embodiment, since the aforementioned preset master equation is used to describe the dynamic changes in the probability distribution of electrons or holes corresponding to the tunneling process in the simulation model, when the derivative of P(N) in the aforementioned preset master equation is zero, that is... At this point, the electrons or holes included in the left and right quantum dots in the above simulation model reach a dynamic equilibrium, that is, the number of electrons or holes tunneling into the left and right quantum dots is the same as the number of electrons or holes tunneling out. At this time, the simulation model reaches a steady state.

[0140] The electronic device can, based on the aforementioned target tunneling coefficients (i.e., the first tunneling coefficient, the second tunneling coefficient, the third tunneling coefficient, and the fourth tunneling coefficient), in the aforementioned preset master equation. In the case of P(N), calculate P(N) to obtain the probability distribution of the model to be simulated in steady state (denoted as the target probability distribution).

[0141] Step S1042: Determine the objective function relationship indicating the current in the simulation model based on the target probability distribution and the target tunneling coefficient.

[0142] In an optional embodiment, the above objective function relationship can be expressed as:

[0143]

[0144] Where I is the current and e is the elementary charge. To reduce Planck's constant, N is the number of electrons or holes, and P(N) is the probability distribution of electrons or holes in steady state, i.e., the target probability distribution mentioned above. The fifth tunneling coefficient of the left quantum dot. is the sixth tunneling coefficient of the left quantum dot.

[0145] In this embodiment of the application, the aforementioned fifth tunneling coefficient It can represent the rate of increase of electrons or holes in a left quantum dot, the sixth tunneling coefficient. This can represent the rate of decrease of electrons or holes in the left quantum dot; therefore, the difference between the fifth and sixth tunneling coefficients, i.e. This can represent the net flux of electrons or holes in the left quantum dot. Using this net flux and the target probability distribution at steady state, the current generated by electron or hole tunneling in the simulation model can be accurately determined, improving the accuracy of current calculations in the simulation model.

[0146] For step S105 above, leakage current simulation is performed on the simulation model based on the objective function relationship.

[0147] In one alternative embodiment, such as Figure 7 As shown, Figure 7This is a fifth flowchart illustrating the simulation method for the dual quantum dot model provided in this application. Figure 7 The above step S105 in the method shown can be further refined into the following steps, namely step S1051-step S1053.

[0148] Step S1051: When the first energy is zero, based on the objective function relationship, obtain the current in the simulation model under different voltage conditions. The voltage conditions are the voltages applied to the left and right quantum dots.

[0149] In this embodiment of the application, since the Hamiltonian includes the unknown quantity, the first energy t so Therefore, the target eigenstate |α is calculated based on the Hamiltonian mentioned above. D,N > and |β D,N-1 >Includes the first energy t sO Correspondingly, the target probability distribution and target tunneling coefficient determined based on the target eigenstates also include the first energy t. so Therefore, the objective function relationship described above also includes the first energy t. so .

[0150] When electronic devices perform model simulations based on the aforementioned objective function relationship, the first energy t in the aforementioned objective function relationship can be obtained. so When the voltage is zero, a positive bias voltage is applied between the source and drain electrodes to obtain the current corresponding to the left and right quantum dots under different voltage conditions.

[0151] Step S1052: Generate a current fitting image of the model to be simulated based on the current in the model under each voltage condition.

[0152] like Figure 8 and Figure 9 As shown, Figure 8 This is a first schematic diagram of a current fitting image provided in an embodiment of this application. Figure 9 This is a second schematic diagram of a current fitting image provided in an embodiment of this application. Figure 8 and Figure 9 In the current fitting image shown, the horizontal axis represents voltage 1 corresponding to the left quantum dot, and the vertical axis represents voltage 2 corresponding to the right quantum dot. The color corresponding to each coordinate point in the coordinate system is the current under the corresponding voltage 1 and voltage 2.

[0153] For ease of understanding, the above... Figure 4The following example illustrates the situation where a right quantum dot in the simulation model contains a spin-up (or spin-down) electron. If a positive bias is applied between the source and drain electrodes of the electronic device, a spin-down (or spin-up) electron tunnels into the left quantum dot. Due to the Pauli exclusion principle, this electron cannot occupy the ground state orbital of the right quantum dot; that is, the electron cannot tunnel to the right quantum dot. Simultaneously, because the electron's energy is less than the source electrode energy, it also cannot transition back to the source electrode. This is a Pauli spin blocking phenomenon. As described above... Figure 8 As shown, Figure 8 It includes only one tunneling line, namely the excited-state tunneling line 801, which is caused by the Pauli spin blocking phenomenon. Figure 8 The current fitting image shown lacks a ground-state tunneling line.

[0154] For ease of comparison, the above Figure 9 This is a current fitting image generated when a negative bias voltage is applied between the source and drain electrodes under the same conditions. Figure 9 In the current fitting image shown, the presence of reversed spin effectively relieves the Pauli spin blocking phenomenon, specifically as follows: Figure 9 The current fitting image shown contains two tunneling lines: the excited-state tunneling line 901 and the ground-state tunneling line 902. A comparison reveals that... Figure 8 The current fitting image shown clearly lacks features such as... Figure 9 The ground-state tunneling line is shown.

[0155] Through steps S1051-S1052, the electronic device can simulate the Pauli spin blocking phenomenon in the simulation model based on the objective function relationship, thereby improving the accuracy of the simulation of the model corresponding to the simulation model.

[0156] Step S1053: Based on the voltage applied to the left and right quantum dots in the current fitting image, change the magnetic field of the model to be simulated, and obtain the leakage current fitting image of the model to be simulated under different magnetic field conditions.

[0157] In this embodiment, when only the third energy t is present, the tunneling process between the left and right quantum dots does not allow for spin change, which leads to the aforementioned Pauli spin blocking phenomenon. The introduction of spin-orbit coupling reverses the spin, therefore, leakage current will occur in the original Pauli spin blocking region when spin-orbit coupling is involved. As described above... Figure 8 The Pauli spin blocking region, i.e. Figure 8 The region indicated by the red arrow in the middle is affected by the introduction of spin-orbit coupling effects (such as at the first energy t). so When the value is not zero, a ground-state tunneling line will exist. The leakage current mentioned above is the current generated when the Pauli spin blocking phenomenon is removed in the simulation model.

[0158] In an optional embodiment, the electronic device fixes the voltage of the left and right quantum dots at the center point of the current fitting image, such as fixing it at the aforementioned position. Figure 8 The image center point is shown. By adjusting the magnetic field of the model under simulation, a leakage current fitting image indicating the change of leakage current with the magnetic field can be obtained. Specifically, it can be done as follows: Figure 10 As shown, Figure 10 This is a first schematic diagram of a leakage current fitting image provided in an embodiment of this application. Figure 10 In the leakage current fitting image shown, the horizontal axis represents the magnetic field, and the vertical axis represents the leakage current.

[0159] In the aforementioned semiconductor simulation software, the magnetic field of the model to be simulated can be introduced in the form of parameters. Therefore, a change in the magnetic field of the model to be simulated can be represented as a change in the relevant parameters.

[0160] In another optional embodiment, by changing the magnetic field of the model to be simulated, the electronic device can fit the current to the image described above, and can move along the aforementioned path. Figure 8 The voltage applied to the quantum dots in the direction of the red arrows shown in the image yields a leakage current fitting image that varies with detuning and magnetic field, as shown in the image. Figure 11 As shown, Figure 11 This is a second schematic diagram of a leakage current fitting image provided in an embodiment of this application. Figure 11 In the leakage current fitting image shown, the horizontal axis represents the magnetic field, and the vertical axis represents the detuning between the left and right quantum dots, i.e., the difference between voltage 2 and voltage 1 mentioned above. The color of each coordinate point in the coordinate system represents the leakage current.

[0161] In step S1053 above, after simulating the Pauli spin blocking phenomenon based on the above objective function relationship, the electronic device can simulate the leakage current of the model to be simulated based on the current fitting image obtained from the simulation.

[0162] In an optional embodiment, according to the above... Figure 10 and Figure 11 The leakage current fitting image shown indicates that electronic devices can determine the first energy t in the above objective function relationship by fitting the leakage current. so This updates the objective function relationship described above, allowing the electronic device to perform more simulations on the model to be simulated, such as quantum bit simulations, based on the updated objective function relationship.

[0163] Based on the same inventive concept, and according to the dual quantum dot model simulation method provided in the above embodiments of this application, this application also provides a dual quantum dot model simulation device. For example... Figure 12 As shown, Figure 12This is a schematic diagram of a dual quantum dot model simulation device provided in an embodiment of this application. The device includes the following modules.

[0164] Module 1201 is used to build a dual quantum dot model as the model to be simulated.

[0165] The generation module 1202 is used to generate a Hamiltonian including a first energy based on the performance parameters of the model to be simulated, wherein the first energy is the tunneling energy between electrons when the left and right quantum dots have opposite spins due to the spin-orbit coupling effect in the model to be simulated.

[0166] Calculation module 1203 is used to calculate the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model based on the Hamiltonian.

[0167] The determination module 1204 is used to determine the objective function relationship of the current in the simulation model based on the target tunneling coefficient and the preset master equation. The preset master equation is used to describe the dynamic changes of the electron or hole distribution corresponding to the tunneling process in the simulation model.

[0168] Simulation module 1205 is used to perform leakage current simulation on the model to be simulated based on the objective function relationship.

[0169] Optionally, the above performance parameters may include: the lever arm coefficients corresponding to the left and right quantum dots in the simulation model, the second energy of Zeeman splitting on the quantum dot orbital energy level, the third energy of tunneling between the left and right quantum dots, and the Coulomb interaction coefficient between the left and right quantum dots.

[0170] The aforementioned generation module 1202 can be used to obtain the lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient respectively; and to generate a Hamiltonian including the first energy based on the lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient.

[0171] Optionally, the above Hamiltonian can be expressed as:

[0172]

[0173] Among them, H DQD Let be the Hamiltonian of the model to be simulated, α, d, and σ be three quantum numbers representing a quantum state in the two quantum dots, σ ​​be the spin, d be the energy level, L be the left quantum dot, and R be the right quantum dot. 'a' is the lever arm coefficient, V L V is the voltage of the left quantum dot. R Let ΔV be the voltage across the right quantum dot, and ΔV be the voltage change. The voltage V was obtained from the finite element simulation. L and V R The energy levels at time, c and For generating and annihilating operators, t is the third energy, E z This is the second energy level, where ↑ indicates spin upwards and ↓ indicates spin downwards. t so The first energy is α, β, γ, and δ, which are quantum dots, and σ is the first energy. ′ For spin, is the Coulomb interaction coefficient.

[0174] Optionally, the above-mentioned calculation module 1203 can be used to calculate the target eigenstate corresponding to the Hamiltonian of the model to be simulated based on the Hamiltonian.

[0175] Based on the target eigenstate and the coupling coefficients between the source / drain electrodes and the left and right quantum dots in the simulation model, the first tunneling coefficient from the source electrode to the left quantum dot, the second tunneling coefficient from the source electrode to the right quantum dot, the third tunneling coefficient from the left quantum dot to the drain electrode, and the fourth tunneling coefficient from the right quantum dot to the drain electrode are calculated respectively.

[0176] Optionally, the aforementioned first tunneling coefficient It can be represented as:

[0177]

[0178] The aforementioned second tunneling coefficient It can be represented as:

[0179]

[0180] The aforementioned third tunneling coefficient It can be represented as:

[0181]

[0182] The aforementioned fourth tunneling coefficient It can be represented as:

[0183]

[0184] Where L represents the left quantum dot, R the right quantum dot, N the number of electrons or holes, N+1 represents the number of electrons or holes increased by 1 after tunneling, and N-1 represents the number of electrons and holes decreased by 1 after tunneling, |α D,N > and |β D,N-1 >For the target eigenstate, To reduce Planck's constant, γ L γ is the coupling coefficient between the source electrode and the left quantum dot. R Let be the coupling coefficient between the drain electrode and the right quantum dot, d be the energy level, <| be the left vector, |> be the right vector, and c and To generate and annihilate operators, σ is the spin, and n F Let Fermi distribution function be used. When there are N+1 electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |β D,N+1 The corresponding intrinsic energy, E αN When there are N electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |α D,N The corresponding intrinsic energy, μ L For the chemical potential of the source electrode coupled to the left quantum dot, μ R The chemical potential of the drain electrode coupled to the right quantum dot. When there are N-1 electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |β D,N-1 The corresponding intrinsic energy.

[0185] Optionally, the aforementioned determining module 1204 can be specifically used to calculate the target probability distribution of the model to be simulated in steady state based on the target tunneling coefficient using a preset master equation. The steady state indicates that the left and right quantum dots of the model to be simulated, including electrons or holes, reach dynamic equilibrium during the tunneling process.

[0186] Based on the target probability distribution and the target tunneling coefficient, the target function relationship indicating the current in the simulation model is determined.

[0187] Optionally, the above-mentioned pre-defined master equation can be expressed as:

[0188]

[0189] in, This is the derivative operation with respect to P(N), where P(N) is the probability distribution of electrons or holes in the simulation model, N is the number of electrons or holes, N+1 is the number of electrons or holes increased by 1 after tunneling, and N-1 is the number of electrons or holes decreased by 1 after tunneling. N+1,N Fifth tunneling coefficient, Γ N-1,N The sixth tunneling coefficient, The first tunneling coefficient, This is the second tunneling coefficient. The third tunneling coefficient, This is the fourth tunneling coefficient.

[0190] Optionally, the above objective function relationship can be expressed as:

[0191]

[0192] Where I is the current and e is the elementary charge. To reduce Planck's constant, N is the number of electrons or holes, and P(N) is the probability distribution of electrons or holes in steady state. The fifth tunneling coefficient of the left quantum dot. is the sixth tunneling coefficient of the left quantum dot.

[0193] Optionally, the simulation module 1205 mentioned above can be used to obtain the current in the model to be simulated under different voltage conditions based on the objective function relationship when the first energy is zero. The voltage condition is the voltage applied to the left and right quantum dots.

[0194] Based on the current in the model to be simulated under each voltage condition, a current fitting image of the model to be simulated is generated.

[0195] Based on the voltage applied to the left and right quantum dots in the current fitting image, the magnetic field of the model to be simulated is changed, and the leakage current fitting images of the model to be simulated under different magnetic field conditions are obtained.

[0196] The apparatus provided in this application provides that, after constructing a dual quantum dot model, i.e., the model to be simulated, a Hamiltonian including a first energy can be generated based on the performance parameters of the model to be simulated. Based on the Hamiltonian, the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the model to be simulated can be calculated. Then, based on the target tunneling coefficient and the preset master equation, the target function relationship indicating the current in the model to be simulated can be determined, and the leakage current simulation of the model to be simulated can be performed based on the target function relationship.

[0197] Since the objective function relationship is determined based on the target tunneling coefficient and the preset master equation, and the target tunneling coefficient is determined based on the Hamiltonian including the first energy, the objective function relationship must include the first energy. When performing model simulation based on the objective function relationship, the existence of the first energy can accurately characterize the spin reversal that occurs between the left and right quantum dots of the model under the influence of spin-orbit coupling. This effectively eliminates the Pauli spin blocking phenomenon during tunneling. Therefore, this objective function relationship can be used to simulate the leakage current generated during tunneling; that is, leakage current simulation of the model under simulation can be performed based on this objective function relationship, thus realizing leakage current simulation of the dual quantum dot model.

[0198] Based on the same inventive concept, and according to the dual quantum dot model simulation method provided in the above embodiments of this application, this application also provides an electronic device, such as... Figure 13 As shown, it includes a processor 1301, a communication interface 1302, a memory 1303, and a communication bus 1304. The processor 1301, the communication interface 1302, and the memory 1303 communicate with each other through the communication bus 1304.

[0199] Memory 1303 is used to store computer programs;

[0200] The processor 1301 is used to execute the program stored in the memory 1303 to implement the method steps of simulating the dual quantum dot model as described above.

[0201] The communication bus mentioned in the above electronic devices can be a Peripheral Component Interconnect (PCI) bus or an Extended Industry Standard Architecture (EISA) bus, etc. This communication bus can be divided into address bus, data bus, control bus, etc. For ease of illustration, only one thick line is used to represent it in the diagram, but this does not mean that there is only one bus or one type of bus.

[0202] The communication interface is used for communication between the aforementioned electronic devices and other devices.

[0203] The memory may include random access memory (RAM) or non-volatile memory (NVM), such as at least one disk storage device. Optionally, the memory may also be at least one storage device located remotely from the aforementioned processor.

[0204] The processors mentioned above can be general-purpose processors, including central processing units (CPUs), network processors (NPs), etc.; they can also be digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, or discrete hardware components.

[0205] Based on the same inventive concept, and according to the dual quantum dot model simulation method provided in the above embodiments of this application, this application also provides a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of any of the above dual quantum dot model simulation methods.

[0206] Based on the same inventive concept, and according to the dual quantum dot model simulation method provided in the above embodiments of this application, this application also provides a computer program product containing instructions, which, when run on a computer, causes the computer to execute any of the dual quantum dot model simulation methods in the above embodiments.

[0207] In the above embodiments, implementation can be achieved entirely or partially through software, hardware, firmware, or any combination thereof. When implemented using software, it can be implemented entirely or partially 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, all or part of the processes or functions described in the embodiments of this application are generated. The computer can be a general-purpose computer, a special-purpose computer, a computer network, or other programmable device. The computer instructions can be stored in a computer-readable storage medium or transmitted from one computer-readable storage medium to another. For example, the computer instructions can be transmitted from one website, computer, server, or data center to another website, computer, server, or data center via wired (e.g., coaxial cable, fiber optic, digital subscriber line (DSL)) or wireless (e.g., infrared, wireless, microwave, etc.) means. The computer-readable storage medium can be any available medium that a computer can access or a data storage device such as a server or data center that integrates one or more available media. The available medium can be a magnetic medium (e.g., floppy disk, hard disk, magnetic tape), an optical medium (e.g., DVD), or a semiconductor medium (e.g., solid state disk (SSD)).

[0208] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such a process, method, article, or apparatus. Without further limitations, an element defined by the phrase "comprising one..." does not exclude the presence of other identical elements in the process, method, article, or apparatus that includes said element.

[0209] The various embodiments in this specification are described in a related manner. Similar or identical parts between embodiments can be referred to mutually. Each embodiment focuses on describing the differences from other embodiments. In particular, embodiments such as apparatuses, electronic devices, computer-readable storage media, and computer program products are basically similar to the method embodiments, and therefore the descriptions are relatively simple; relevant parts can be referred to the descriptions of the method embodiments.

[0210] The above description is merely a preferred embodiment of this application and is not intended to limit the scope of protection of this application. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of this application are included within the scope of protection of this application.

Claims

1. A simulation method for a dual quantum dot model, characterized in that, The method includes: A dual quantum dot model is constructed as the model to be simulated; Based on the performance parameters of the model to be simulated, a Hamiltonian including a first energy is generated, wherein the first energy is the tunneling energy between electrons when the left and right quantum dots have opposite spins due to the spin-orbit coupling effect in the model to be simulated. Based on the Hamiltonian, the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model is calculated. Based on the target tunneling coefficient and the preset master equation, the objective function relationship indicating the current in the simulation model is determined. The preset master equation is used to describe the dynamic changes in the distribution of electrons or holes corresponding to the tunneling process in the simulation model. Leakage current simulation is performed on the model to be simulated based on the objective function relationship.

2. The method according to claim 1, characterized in that, The performance parameters include: the lever arm coefficients corresponding to the left and right quantum dots in the simulation model, the second energy of Zeeman splitting on the quantum dot orbital energy level, the third energy of tunneling between the left and right quantum dots, and the Coulomb interaction coefficient between the left and right quantum dots. The step of generating the Hamiltonian including the first energy based on the performance parameters of the model to be simulated includes: The lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient are obtained respectively. The Hamiltonian, including the first energy, is generated based on the lever arm coefficient, the second energy, the third energy, and the Coulomb interaction coefficient.

3. The method according to claim 1 or 2, characterized in that, The Hamiltonian is expressed as: Among them, H DQD Let be the Hamiltonian of the model to be simulated, α, d, and σ be three quantum numbers representing a quantum state in the two quantum dots, σ ​​be the spin, d be the energy level, L be the left quantum dot, and R be the right quantum dot. 'a' is the lever arm coefficient, V L V is the voltage of the left quantum dot. R Let ΔV be the voltage across the right quantum dot, and ΔV be the voltage change. The voltage V was obtained from the finite element simulation. L and V R The energy levels at time, c and For generating and annihilating operators, t is the third energy, E z For the second energy, ↑ indicates spin upward, ↓ indicates spin downward, t so The first energy is α, β, γ, and δ, which are quantum dots, and σ is the first energy. ′ For spin, is the Coulomb interaction coefficient.

4. The method according to claim 1, characterized in that, The step of calculating the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model based on the Hamiltonian includes: Based on the Hamiltonian, calculate the target eigenstate corresponding to the Hamiltonian of the model to be simulated; Based on the target eigenstate and the coupling coefficients between the source / drain electrodes and the left and right quantum dots in the simulation model, the first tunneling coefficient from the source electrode to the left quantum dot, the second tunneling coefficient from the source electrode to the right quantum dot, the third tunneling coefficient from the left quantum dot to the drain electrode, and the fourth tunneling coefficient from the right quantum dot to the drain electrode are calculated respectively.

5. The method according to claim 4, characterized in that, First tunneling coefficient Represented as: Second tunneling coefficient Represented as: The third tunneling coefficient Represented as: The fourth tunneling coefficient Represented as: Where L represents the left quantum dot, R the right quantum dot, N the number of electrons or holes, N+1 represents the number of electrons or holes increased by 1 after tunneling, and N-1 represents the number of electrons and holes decreased by 1 after tunneling, |α D,N > and |β D,N-1 > represents the target eigenstate, h is the reduced Planck constant, and γ is the eigenstate. L γ is the coupling coefficient between the source electrode and the left quantum dot. R Let be the coupling coefficient between the drain electrode and the right quantum dot, d be the energy level, <| be the left vector, |> be the right vector, and c and To generate and annihilate operators, σ is the spin, and n F Let Fermi distribution function be used. When there are N+1 electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |β D,N+1 The corresponding intrinsic energy When there are N electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |α D,N The corresponding intrinsic energy, μ L For the chemical potential of the source electrode coupled to the left quantum dot, μ R The chemical potential of the drain electrode coupled to the right quantum dot. When there are N-1 electrons or holes in a quantum dot, the Hamiltonian H DQD Target eigenstate |β D,N-1 The corresponding intrinsic energy.

6. The method according to claim 1, characterized in that, The step of determining the objective function relationship indicating the current in the simulation model based on the target tunneling coefficient and the preset master equation includes: Based on the target tunneling coefficient, the target probability distribution of the simulation model under steady state is calculated using a preset master equation. The steady state indicates that the left and right quantum dots of the simulation model, including electrons or holes, reach dynamic equilibrium during the tunneling process. Based on the target probability distribution and the target tunneling coefficient, the target function relationship indicating the current in the simulation model is determined.

7. The method according to claim 6, characterized in that, The preset master equation is expressed as: in, This is the derivative operation with respect to P(N), where P(N) is the probability distribution of electrons or holes in the simulation model, N is the number of electrons or holes, N+1 is the number of electrons or holes increased by 1 after tunneling, and N-1 is the number of electrons or holes decreased by 1 after tunneling. N+1,N Fifth tunneling coefficient, Γ N-1,N The sixth tunneling coefficient, The first tunneling coefficient, This is the second tunneling coefficient. The third tunneling coefficient, This is the fourth tunneling coefficient.

8. The method according to claim 6, characterized in that, The objective function relationship is expressed as follows: Where I is the current and e is the elementary charge. To reduce Planck's constant, N is the number of electrons or holes, and P(N) is the probability distribution of electrons or holes in steady state. The fifth tunneling coefficient of the left quantum dot. is the sixth tunneling coefficient of the left quantum dot.

9. The method according to claim 1, characterized in that, The step of performing leakage current simulation on the model to be simulated based on the objective function relationship includes: When the first energy is zero, based on the objective function relationship, the current in the simulation model under different voltage conditions is obtained, where the voltage condition is the voltage applied to the left and right quantum dots; Based on the current in the model to be simulated under each voltage condition, generate a current fitting image of the model to be simulated; Based on the voltage applied to the left and right quantum dots in the current fitting image, the magnetic field of the simulation model is changed, and leakage current fitting images of the simulation model under different magnetic field conditions are obtained.

10. A dual quantum dot model simulation device, characterized in that, The device includes: The building module is used to construct a dual quantum dot model as the model to be simulated. The generation module is used to generate a Hamiltonian including a first energy based on the performance parameters of the model to be simulated, wherein the first energy is the tunneling energy between electrons when the left and right quantum dots have opposite spins due to the spin-orbit coupling effect in the model to be simulated. The calculation module is used to calculate the target tunneling coefficient between the source / drain electrodes and the left and right quantum dots in the simulation model based on the Hamiltonian. The determination module is used to determine the objective function relationship indicating the current in the simulation model based on the target tunneling coefficient and the preset master equation. The preset master equation is used to describe the dynamic changes in the distribution of electrons or holes corresponding to the tunneling process in the simulation model. The simulation module is used to perform leakage current simulation on the model to be simulated based on the objective function relationship.

11. 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, when executing a program stored in memory, implements the steps of the method described in any one of claims 1-9.

12. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method described in any one of claims 1-9.

Images