CN111400861A - Simulation calculation method of two-dimensional ferroelectric tunnel junction - Google Patents
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- 238000004364 calculation method Methods 0.000 title claims abstract description 20
- 238000004088 simulation Methods 0.000 title claims abstract description 16
- 230000010287 polarization Effects 0.000 claims abstract description 62
- 238000005421 electrostatic potential Methods 0.000 claims abstract description 27
- 230000004888 barrier function Effects 0.000 claims abstract description 21
- 230000005641 tunneling Effects 0.000 claims abstract description 19
- 239000013078 crystal Substances 0.000 claims abstract description 18
- 230000002441 reversible effect Effects 0.000 claims abstract description 16
- 230000000694 effects Effects 0.000 claims abstract description 15
- 238000000034 method Methods 0.000 claims abstract description 13
- -1 tin sulfide-tin selenide Chemical compound 0.000 claims abstract description 12
- AFNRRBXCCXDRPS-UHFFFAOYSA-N tin(ii) sulfide Chemical compound [Sn]=S AFNRRBXCCXDRPS-UHFFFAOYSA-N 0.000 claims abstract description 6
- MFIWAIVSOUGHLI-UHFFFAOYSA-N selenium;tin Chemical compound [Sn]=[Se] MFIWAIVSOUGHLI-UHFFFAOYSA-N 0.000 claims abstract description 5
- 238000003775 Density Functional Theory Methods 0.000 claims abstract description 4
- 238000004613 tight binding model Methods 0.000 claims abstract description 4
- 238000005457 optimization Methods 0.000 claims description 7
- 230000000737 periodic effect Effects 0.000 claims description 5
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- 241000764238 Isis Species 0.000 claims 1
- 239000000463 material Substances 0.000 abstract description 9
- 238000013461 design Methods 0.000 abstract description 4
- 125000004429 atom Chemical group 0.000 description 8
- 238000010586 diagram Methods 0.000 description 4
- 239000010409 thin film Substances 0.000 description 3
- 230000008859 change Effects 0.000 description 2
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- 230000005621 ferroelectricity Effects 0.000 description 2
- 238000011160 research Methods 0.000 description 2
- 230000005476 size effect Effects 0.000 description 2
- ATJFFYVFTNAWJD-UHFFFAOYSA-N Tin Chemical group [Sn] ATJFFYVFTNAWJD-UHFFFAOYSA-N 0.000 description 1
- 230000009471 action Effects 0.000 description 1
- 238000013500 data storage Methods 0.000 description 1
- 230000007547 defect Effects 0.000 description 1
- 238000011161 development Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 125000003748 selenium group Chemical group *[Se]* 0.000 description 1
- 239000004065 semiconductor Substances 0.000 description 1
- 230000002269 spontaneous effect Effects 0.000 description 1
- 238000006467 substitution reaction Methods 0.000 description 1
- 150000004763 sulfides Chemical class 0.000 description 1
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Abstract
The invention provides a simulation calculation method of a two-dimensional ferroelectric tunnel junction, which comprises the steps of firstly constructing a paraelectric crystal structure of tin sulfide and tin selenide in ATK software to enable the paraelectric crystal structure to be converted into a ferroelectric state; respectively constructing forward polarized and reverse polarized tin sulfide-tin selenide heterojunctions; carrying out p-type doping on the left electrode, and carrying out n-type doping on the right electrode; after modeling of the device is completed, setting truncation energy and real space grid density; setting a convergence standard and a boundary condition of energy; solving the shielding length and the electrostatic potential of the left electrode and the right electrode, and comparing the barrier heights of the two polarization states; and solving the conductivity in two polarization states by combining a density functional theory with an unbalanced Green function method, and calculating the tunneling electroresistance effect of the two polarization states. The method has the advantages of reliability, high calculation efficiency and wide applicability, and can quickly measure the tunneling electroresistance effect of the two-dimensional ferroelectric tunnel junction device so as to guide the optimal design of the ferroelectric tunnel junction based on the two-dimensional material and the heterojunction thereof.
Description
Technical Field
The invention belongs to the field of design of two-dimensional material nano-electronic effect and nano-functional devices, and particularly relates to a simulation method of a two-dimensional ferroelectric tunnel junction.
Background
Ferroelectric materials have spontaneous charge polarization and can change orientation under the action of an applied electric field, and Ferroelectric Tunnel Junctions (FTJ) based on ferroelectric materials are one of the hot spots of the current research. The ferroelectric tunnel junction is a heterostructure in which a ferroelectric thin film is used as a barrier layer, and electrodes are sandwiched between both surfaces of the barrier layer. The most obvious characteristic of a ferroelectric tunnel junction is the tunneling electroresistance effect (TER), i.e. the direction of polarization in the ferroelectric thin film layer can be changed by an applied electric field, thereby causing a change in resistance in the tunnel junction. Therefore, two resistance states, high and low, exist in the ferroelectric tunnel junction, and can be used to represent two logic states of "1" and "0", so that data storage can be realized. Therefore, the ferroelectric tunnel junction has wide application prospect in the field of nonvolatile information storage devices.
With the increasing demand for miniaturization of devices, when the thickness of the conventional ferroelectric thin film is reduced to a nanometer level, the problems of reduced ferroelectricity, unstable room temperature, poor repeatability and the like exist, and the commercial requirements are difficult to meet. Two-dimensional materials possessing ferroelectricity are becoming a focus of research due to the size effect in conventional ferroelectric materials. In these studies, group IV-VI sulfides have excellent ferroelectric properties and are considered to be the most promising class of two-dimensional ferroelectric materials. How to design and regulate a ferroelectric tunnel junction based on a two-dimensional ferroelectric material and study the in-plane ferroelectric polarization and quantum tunneling effect of the ferroelectric tunnel junction has important significance for breaking through the size effect and the development of information storage equipment of the next generation.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a simulation calculation method of a two-dimensional ferroelectric tunnel junction.
The present invention achieves the above object by the following technical means.
A simulation calculation method of a two-dimensional ferroelectric tunnel junction is characterized by comprising the following steps:
(1) constructing a paraelectric crystal structure of tin sulfide and tin selenide in ATK software, adjusting the atom position to convert the paraelectric crystal structure into a ferroelectric state from the paraelectric state, and optimizing the lattice constant of the paraelectric crystal structure;
(2) respectively constructing and optimizing a forward polarization tin sulfide-tin selenide heterojunction and a reverse polarization tin sulfide-tin selenide heterojunction;
(3) selecting a proper period as a source electrode and a drain electrode through a Device module to form a left electrode-ferroelectric heterojunction-right electrode type Device structure;
(4) carrying out p-type doping on the left electrode, and carrying out n-type doping on the right electrode;
(5) setting truncation energy and real space grid density;
(6) setting a convergence standard and a boundary condition of energy;
(7) solving the shielding length and the electrostatic potential of the left electrode and the right electrode, and comparing the barrier heights of the two polarization states;
(8) and solving the conductivity in two polarization states by combining a density functional theory with an unbalanced Green function method, and calculating the tunneling electroresistance effect of the two polarization states.
Further, the structure of the crystal is optimized by adopting an exchange correlation functional of GGA + PBE in the step (1), the displacement directions of the same kind of atoms are the same, the displacement directions of different kinds of atoms are opposite, the structure optimization does not limit the X, Z direction of crystal lattices, and the convergence standard of force is not more than
Further, in the step (2), the heterojunction is constructed along the Z direction, the structure is optimized without limiting the X, Z direction of the crystal lattice, and the convergence standard of the force is not more than
During optimization, atoms with proper periods are selected on the left side and the right side respectively, Rigid constraint is applied to the positions of the atoms, and the relative positions are kept unchanged.
Further, the length of the electrode selected in the step (3) is not less than twice the electrode period, so that the calculation convergence is ensured. In the Y direction not less than
The thickness of the vacuum layer(s) avoids interaction caused by periodic repetition in the Y direction.
Further, the doping of the electrode in the step (4) is heavy doping, and the number of holes per cubic centimeter of p-type doping is not less than 1.24 × 1020N-type doping with electron number not less than 1.24 × 10/cubic centimeter20And (4) respectively.
Further, the truncation energy in the step (5) can be set to be 75-150 Hartee, so that the calculation accuracy and efficiency are guaranteed, and the real space grid density in the X, Y, Z direction is set to be m × 1 × k, wherein m is not less than 7, and k is not less than 50.
Further, the convergence criterion of the energy in the step (6) is not more than 10-5eV, the X direction is set as the periodic boundary condition, the Y direction is set as the Neumann boundary condition, and the Z direction is set as the Dirichet boundary condition.
Further, in the step (7), the shielding length and the electrostatic potential of the left and right electrodes are solved, and the barrier heights of the two polarization states are compared, which can be calculated through the following steps:
step (7.1) calculating the shielding length of the left electrode and the right electrode according to a Thomas-Fermi model;
Thomas-Fermi model:
where is the dielectric constant, ρ is the density of states at the fermi level, and is the shielding length of the electrode.
Step (7.2) calculating the electrostatic potential in the left and right electrodes according to the electrostatic potential formula;
electrostatic potential formula:
wherein i-1 denotes a left electrode, i-2 denotes a right electrode, and PsFor the polarization, is the shielding length of the electrode,0is the dielectric constant of the vacuum layer,1is the dielectric constant of the left electrode and,2is the dielectric constant of the right electrode and,FEis the dielectric constant of the heterojunction and,
is the electrostatic potential within the electrode, d is the distance of polarization; the positive polarization left electrode takes a plus sign, and the right electrode takes a minus sign; the left electrode of the reverse polarization takes a minus sign, and the right electrode takes a plus sign;
step (7.3) calculating the average effective barrier height in the electron tunneling process, and comparing the heights;
wherein
Which represents the electrostatic potential of the heterojunction,
which represents the electrostatic potential of the left electrode,
which represents the electrostatic potential of the right electrode,
represents the average effective barrier height for forward polarization,
indicating the average effective barrier height for reverse polarization.
Further, in the step (8), the conductivity in two polarization states is solved, and the tunneling electroresistance effect is calculated, which can be calculated through the following steps:
respectively calculating the conductivities G in two polarization states according to an L andrauer-B ü ttiker formula (8.1);
l andauer-B ü ttiker formula:
wherein G is0Is the quantum conductance, T (E)F,k||) Is the transmission coefficient at the Fermi level, EFIs the Fermi level, k||Is the bloch wave vector.
Step (8.2) calculating the tunneling electroresistance effect TER according to the definition;
wherein G is+Denotes the conductivity in the forward polarization, G_Indicating the conductivity in the reverse polarization.
The invention relates to a simulation calculation method of a two-dimensional ferroelectric tunnel junction, which adopts ATK software to establish a two-dimensional ferroelectric tunnel junction device model of a left electrode-ferroelectric heterojunction-electrode, simulates the electron tunneling process of the two-dimensional ferroelectric tunnel junction in two polarization states by combining a density functional theory and an unbalanced Green function method, solves the electric conductivity in the two polarization states and analyzes the tunneling electric resistance effect. The method has the advantages of reliability, high calculation efficiency and wide applicability, and can quickly measure the tunneling electroresistance effect of the two-dimensional ferroelectric tunnel junction device so as to guide the optimal design of the ferroelectric tunnel junction based on the two-dimensional material and the heterojunction thereof.
Drawings
FIG. 1 is a schematic structural view of a paraelectric state and a ferroelectric state of tin sulfide;
FIG. 2 is a schematic structural diagram of a tin sulfide-tin selenide ferroelectric tunnel junction;
FIG. 3 is an electrostatic potential energy distribution for two polarization states;
fig. 4 is a schematic diagram of the average effective barrier for two polarization states.
Detailed Description
The invention will be further described with reference to the following figures and specific examples, but the scope of the invention is not limited thereto.
Taking a tin sulfide-tin selenide ferroelectric heterojunction as an example, the simulation calculation method of the two-dimensional ferroelectric tunnel junction disclosed by the invention is explained in detail and comprises the following steps:
(1) constructing a paraelectric crystal structure of tin sulfide and tin selenide in ATK software, adjusting the atom position to convert the paraelectric crystal structure into a ferroelectric state from the paraelectric state, and optimizing the lattice constant of the paraelectric crystal structure;
the paraelectric lattice constants of tin sulfide and tin selenide are respectively
And
moving sulfur atoms or selenium atoms to the left, moving tin atoms to the right, optimizing the structure by adopting a GGA + PBE exchange correlation functional, wherein the X, Z direction is not fixed in the optimization process, and the force convergence standard is set as
The optimized lattice constants are respectively
And
the structural schematic of the paraelectric and ferroelectric states is shown in figure 1.
(2) Respectively constructing and optimizing a forward polarization tin sulfide-tin selenide heterojunction and a reverse polarization tin sulfide-tin selenide heterojunction;
the structure is optimized without limiting X, Z direction of crystal lattice, and the force convergence criterion is
During optimization, atoms with proper periods are selected on the left side and the right side respectively, Rigid constraint is applied to the positions of the atoms, and the relative positions are kept unchanged.
(3) Selecting a proper period as a source electrode and a drain electrode through a Device module to form a left electrode-ferroelectric heterojunction-right electrode type Device structure;
specifically, the schematic structural diagram of the tin sulfide-tin selenide ferroelectric tunnel junction in two polarization states is shown in fig. 2, and the tin sulfide-tin selenide ferroelectric tunnel junction is composed of a left electrode, a middle region and a right electrode, wherein the width of the left electrode is
The width of the right electrode is
In the Y direction is left
The thickness of the vacuum layer.
(4) Carrying out p-type doping on the left electrode, and carrying out n-type doping on the right electrode;
the p-type doping of the left electrode has a hole number per cubic centimeter of 2.48 × 1020The number of n-type doped electrons per cubic centimeter of the right electrode is 2.48 × 1020And (4) respectively.
(5) Setting truncation energy and real space grid density;
the truncation energy was set to 100Hartee, ensuring computational accuracy and efficiency the real space grid density in the X, Y, Z direction was set to 11 × 1 × 101.
(6) Setting a convergence standard and a boundary condition of energy;
the convergence criterion of the energy is 10-5eV, the X direction is set as the periodic boundary condition, the Y direction is set as the Neumann boundary condition, and the Z direction is set as the Dirichlet boundary condition.
(7) Solving the shielding length and the electrostatic potential of the left electrode and the right electrode, and comparing the barrier heights of the two polarization states;
first, the shield length of the left and right electrodes was calculated according to the Thomas-Fermi model.
Thomas-Fermi model:
knowing the density of states ρ of the left electrode at the fermi level1Greater than the density of states ρ of the right electrode at the fermi level2So that the shield length of the left electrode is smaller than that of the right electrode according to the formula, i.e.1＜2。
Then, the magnitude of the electrostatic potential in the left and right electrodes is calculated according to the electrostatic potential shielding formula.
Electrostatic potential formula:
i-1 denotes a left electrode, and i-2 denotes a right electrode; psFor the polarization, is the shielding length of the electrode,0is the dielectric constant of the vacuum layer,1is the dielectric constant of the left electrode and,2is the dielectric constant of the right electrode and,FEis the dielectric constant of the heterojunction and,
is the electrostatic potential within the electrode, d is the distance of polarization; in forward polarization: the left electrode is in a plus sign, and the right electrode is in a minus sign; the left electrode of the reverse polarization is marked with a sign of < - > and the right electrode is marked with a sign of + ".
Due to the fact that1＜2From the formula
Specifically, the schematic diagram of the electrostatic potential distribution in the forward polarization state and the reverse polarization state is shown in fig. 3, and it can be seen that the magnitude relationship of the electrostatic potential at the semiconductor electrode/ferroelectric barrier is as follows:
finally, the intrinsic barrier of the tin sulfide-tin selenide ferroelectric heterojunction is taken into account
The average effective barriers during electron tunneling in the forward and reverse polarization states are compared.
Specifically, the average effective barrier heights in the forward and reverse polarization states are shown in FIG. 4, and it can be seen that there is an average in the forward polarization stateThe effective barrier height is less than the average effective barrier height in the reverse polarization state, i.e.
Electron tunneling occurs more easily in the forward polarization state.
(8) And solving the conductivity in the two polarization states, and calculating the tunneling electroresistance effect of the two polarization states.
First, the conductivities in the two polarization states were calculated according to the L andrauer-B ü ttiker formula.
Conductivity formula:
wherein G is0Is the quantum conductance, T (E)F,k||) Is the transmission coefficient at the Fermi level, EFIs the Fermi level, k||Is the bloch wave vector.
Calculated to obtain, G+＝9.157×10-10S,G-＝6.971×10-11S。
Then, the tunneling electroresistance effect TER is calculated by definition.
The present invention is not limited to the above-described embodiments, and any obvious improvements, substitutions or modifications can be made by those skilled in the art without departing from the spirit of the present invention.
Claims (9)
1. A simulation calculation method of a two-dimensional ferroelectric tunnel junction is characterized by comprising the following steps:
(1) constructing a paraelectric crystal structure of tin sulfide and tin selenide in ATK software, adjusting the atom position to convert the paraelectric crystal structure into a ferroelectric state from the paraelectric state, and optimizing the lattice constant of the paraelectric crystal structure;
(2) respectively constructing and optimizing a forward polarization tin sulfide-tin selenide heterojunction and a reverse polarization tin sulfide-tin selenide heterojunction;
(3) selecting a proper period as a source electrode and a drain electrode through a Device module to form a left electrode-ferroelectric heterojunction-right electrode type Device structure;
(4) carrying out p-type doping on the left electrode, and carrying out n-type doping on the right electrode;
(5) setting truncation energy and real space grid density;
(6) setting a convergence standard and a boundary condition of energy;
(7) solving the shielding length and the electrostatic potential of the left electrode and the right electrode, and comparing the barrier heights of the two polarization states;
(8) and solving the conductivity in two polarization states by combining a density functional theory with an unbalanced Green function method, and calculating the tunneling electroresistance effect of the two polarization states.
2. The simulation calculation method of a two-dimensional ferroelectric tunnel junction according to claim 1, characterized in that: in the step (1), the structure of the crystal is optimized by adopting a GGA + PBE exchange correlation functional, the displacement directions of the same kind of atoms are the same, the displacement directions of different kinds of atoms are opposite, the structure optimization does not limit the X, Z direction of crystal lattices, and the force convergence standard is not more than
3. The simulation calculation method of a two-dimensional ferroelectric tunnel junction according to claim 1, characterized in that: in the step (2), the heterojunction is constructed along the Z direction, the structure optimization does not limit the X, Z direction of the crystal lattice, and the force convergence standard is not more than
During optimization, atoms with proper periods are selected on the left side and the right side respectively, Rigid constraint is applied to the positions of the atoms, and the relative positions are kept unchanged.
4. The method of claim 1 for simulation computation of a two-dimensional ferroelectric tunnel junction, which isIs characterized in that: the length of the electrode selected in the step (3) is not less than twice of the electrode period, so that the calculation convergence is ensured; in the Y direction not less than
The thickness of the vacuum layer(s) avoids interaction caused by periodic repetition in the Y direction.
5. The simulation calculation method of two-dimensional ferroelectric tunnel junction according to claim 1, wherein the doping of the electrode in step (4) is heavily doped, and the number of p-type doped holes per cubic centimeter is not less than 1.24 × 1020N-type doping with electron number not less than 1.24 × 10/cubic centimeter20And (4) respectively.
6. The simulation calculation method of the two-dimensional ferroelectric tunnel junction according to claim 1, wherein the truncation energy in the step (5) is set to 75-150 Harte to ensure the calculation accuracy and efficiency, and the real space grid density in the X, Y, Z direction is set to m × 1 × k, wherein m is not less than 7, and k is not less than 50.
7. The simulation calculation method of a two-dimensional ferroelectric tunnel junction according to claim 1, characterized in that: the convergence standard of the energy in the step (6) is not more than 10-5eV, the X direction is set as the periodic boundary condition, the Y direction is set as the Neumann boundary condition, and the Z direction is set as the Dirichet boundary condition.
8. The simulation calculation method of a two-dimensional ferroelectric tunnel junction according to claim 1, characterized in that: in the step (7), the shielding length and the electrostatic potential of the left and right electrodes are solved, and the barrier heights of the two polarization states are compared, which can be calculated through the following steps:
(7.1) calculating the shielding lengths of the left electrode and the right electrode according to a Thomas-Fermi model;
where is the dielectric constant, ρ is the density of states at the fermi level, and is the shielding length of the electrode.
(7.2) calculating the electrostatic potential in the left electrode and the right electrode according to an electrostatic potential formula;
electrostatic potential formula:
i is 1 or 2
Wherein i-1 denotes a left electrode, i-2 denotes a right electrode, and PsFor the polarization, is the shielding length of the electrode,0is the dielectric constant of the vacuum layer,1is the dielectric constant of the left electrode and,2is the dielectric constant of the right electrode and,FEis the dielectric constant of the heterojunction and,
is the electrostatic potential within the electrode, d is the distance of polarization; in forward polarization: the left electrode is in a plus sign, and the right electrode is in a minus sign; the left electrode of the reverse polarization takes a minus sign, and the right electrode takes a plus sign;
(7.3) calculating the average effective barrier height in the forward polarization and reverse polarization electron tunneling processes respectively, and comparing the heights;
wherein
Which represents the electrostatic potential of the heterojunction,
which represents the electrostatic potential of the left electrode,
which represents the electrostatic potential of the right electrode,
represents the average effective barrier height for forward polarization,
indicating the average effective barrier height for reverse polarization.
9. The method of computing a two-dimensional ferroelectric tunnel junction of claim 1, wherein: in the step (8), the conductivity in two polarization states is solved, and the tunneling electroresistance effect is calculated, which can be obtained by the following steps:
(8.1) calculating the conductivities G in the two polarization states respectively according to the L andrauer-B ü ttiker formula;
l andauer-B ü ttiker formula:
wherein G is0Is the quantum conductance, T (E)F,k||) Is the transmission coefficient at the Fermi level, EFIs the Fermi level, k||Is the bloch wave vector;
(8.2) calculating the tunneling electroresistance effect TER according to the definition;
wherein G is+Denotes the conductivity in the forward polarization, G_Indicating the conductivity in the reverse polarization.
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