CN115292961A - Method for predicting carrier mobility of semiconductor - Google Patents
Method for predicting carrier mobility of semiconductor Download PDFInfo
- Publication number
- CN115292961A CN115292961A CN202211080234.2A CN202211080234A CN115292961A CN 115292961 A CN115292961 A CN 115292961A CN 202211080234 A CN202211080234 A CN 202211080234A CN 115292961 A CN115292961 A CN 115292961A
- Authority
- CN
- China
- Prior art keywords
- crystal
- carrier mobility
- file
- effective mass
- cell
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Pending
Links
- 239000004065 semiconductor Substances 0.000 title claims abstract description 45
- 238000000034 method Methods 0.000 title claims abstract description 29
- 239000013078 crystal Substances 0.000 claims abstract description 114
- 238000004364 calculation method Methods 0.000 claims abstract description 47
- 238000012937 correction Methods 0.000 claims abstract description 34
- 239000000463 material Substances 0.000 claims description 46
- 239000000969 carrier Substances 0.000 claims description 20
- 239000000592 Artificial Cell Substances 0.000 claims description 10
- 238000000547 structure data Methods 0.000 claims description 10
- 102100021164 Vasodilator-stimulated phosphoprotein Human genes 0.000 claims description 9
- 238000012216 screening Methods 0.000 claims description 7
- 230000005624 perturbation theories Effects 0.000 claims description 4
- 239000003574 free electron Substances 0.000 claims description 3
- 238000005457 optimization Methods 0.000 claims description 3
- 230000003068 static effect Effects 0.000 claims description 3
- 230000010261 cell growth Effects 0.000 claims description 2
- 230000001413 cellular effect Effects 0.000 claims 1
- 230000000694 effects Effects 0.000 abstract description 4
- 238000002474 experimental method Methods 0.000 abstract description 2
- 230000001965 increasing effect Effects 0.000 description 10
- 230000008569 process Effects 0.000 description 5
- 230000008878 coupling Effects 0.000 description 4
- 238000010168 coupling process Methods 0.000 description 4
- 238000005859 coupling reaction Methods 0.000 description 4
- 238000006073 displacement reaction Methods 0.000 description 4
- 230000003287 optical effect Effects 0.000 description 4
- 230000008859 change Effects 0.000 description 3
- 230000005669 field effect Effects 0.000 description 3
- 238000012986 modification Methods 0.000 description 3
- 230000004048 modification Effects 0.000 description 3
- 108010054220 vasodilator-stimulated phosphoprotein Proteins 0.000 description 3
- 230000005535 acoustic phonon Effects 0.000 description 2
- 239000004020 conductor Substances 0.000 description 2
- 239000012212 insulator Substances 0.000 description 2
- 230000008054 signal transmission Effects 0.000 description 2
- 238000004088 simulation Methods 0.000 description 2
- 230000006978 adaptation Effects 0.000 description 1
- 238000004774 atomic orbital Methods 0.000 description 1
- 230000009286 beneficial effect Effects 0.000 description 1
- 238000006243 chemical reaction Methods 0.000 description 1
- 238000004891 communication Methods 0.000 description 1
- 238000010276 construction Methods 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000009826 distribution Methods 0.000 description 1
- 238000005516 engineering process Methods 0.000 description 1
- 230000002708 enhancing effect Effects 0.000 description 1
- 238000000605 extraction Methods 0.000 description 1
- 239000000835 fiber Substances 0.000 description 1
- 229910052736 halogen Inorganic materials 0.000 description 1
- 150000002367 halogens Chemical class 0.000 description 1
- 230000020169 heat generation Effects 0.000 description 1
- 230000010365 information processing Effects 0.000 description 1
- 238000005212 lattice dynamic Methods 0.000 description 1
- 238000004519 manufacturing process Methods 0.000 description 1
- 238000000329 molecular dynamics simulation Methods 0.000 description 1
- 239000002070 nanowire Substances 0.000 description 1
- 239000000382 optic material Substances 0.000 description 1
- 230000005693 optoelectronics Effects 0.000 description 1
- 239000013079 quasicrystal Substances 0.000 description 1
- 238000011160 research Methods 0.000 description 1
- 230000004044 response Effects 0.000 description 1
- 238000004904 shortening Methods 0.000 description 1
- 239000007787 solid Substances 0.000 description 1
- 238000003860 storage Methods 0.000 description 1
- 239000000126 substance Substances 0.000 description 1
- 239000010409 thin film Substances 0.000 description 1
- 230000001131 transforming effect Effects 0.000 description 1
Images
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F30/00—Computer-aided design [CAD]
- G06F30/20—Design optimisation, verification or simulation
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F2119/00—Details relating to the type or aim of the analysis or the optimisation
- G06F2119/02—Reliability analysis or reliability optimisation; Failure analysis, e.g. worst case scenario performance, failure mode and effects analysis [FMEA]
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Computer Hardware Design (AREA)
- Evolutionary Computation (AREA)
- Geometry (AREA)
- General Engineering & Computer Science (AREA)
- General Physics & Mathematics (AREA)
- Testing Or Measuring Of Semiconductors Or The Like (AREA)
Abstract
The invention relates to a method for predicting the carrier mobility of a semiconductor, which comprises the steps of modeling a target crystal and calculating the carrier mobility, carrying out structural distortion on the target crystal by modeling and calculating a correction value, and correcting the calculation result of the carrier mobility by using the correction value. According to the invention, the crystal structure is distorted, the corrected value is calculated, and the target crystal carrier mobility is obtained based on the corrected value, so that the problem that the mobility of the calculated and predicted carrier is higher than the carrier mobility measured in experiments is solved, and the effects that the calculated and predicted result is more accurate and close to the actual situation are achieved.
Description
Technical Field
The invention belongs to the field of semiconductors, and particularly relates to a method for predicting the mobility of semiconductor carriers and a method for screening semiconductor materials.
Background
The semiconductor refers to a material having electrical conductivity between a conductor and an insulator at normal temperature. Semiconductor refers to a material with controllable conductivity ranging from an insulator to a conductor. The photoelectric material refers to a material used for manufacturing various photoelectric devices, such as various active and passive photoelectric sensors, optical information processing and storage devices, optical communication and the like; infrared materials, laser materials, fiber optic materials, nonlinear optical materials, and the like. The mobility of carriers in semiconductors and optoelectronic materials directly affects the performance of electronic devices, and devices with high carrier mobility are generally desired. Based on the first principle, the carrier mobility of the semiconductor and the photoelectric material can be calculated, the property of the photoelectric material can be predicted, and then the material is screened according to the required property and the photoelectric device is designed.
The carrier mobility generally refers to the speed of movement of electrons and holes in the semiconductor, and is an important physical quantity for measuring the performance of the semiconductor device. Mobility affects two properties of the semiconductor: one is that together with the carrier concentration, the magnitude of the conductivity (inverse of the resistivity) of the semiconductor material is determined. The higher the mobility, the lower the resistivity, and the lower the power consumption and the higher the current carrying capacity when passing the same current. Secondly, the working frequency of the device is influenced. The most significant limitation of the frequency response characteristic of a bipolar transistor is the time for minority carriers to transit the base region. The larger the mobility is, the shorter the required transit time is, and the cut-off frequency of the transistor is in direct proportion to the carrier mobility of the base region material, so that the carrier mobility is improved, the power consumption can be reduced, the current carrying capacity of the device is improved, and meanwhile, the switching conversion speed of the transistor is improved.
At present, the mobility of the carriers of semiconductors and photoelectric materials can be measured through experiments, and the mobility of the carriers can be calculated and predicted through a boltzmann transport theory, a deformation potential theory and the like. However, the mobility of carriers predicted by these theoretical calculations is higher than that measured experimentally, so researchers are dedicated to finding a carrier mobility prediction method, which results are more accurate and fit the actual situation. It is expected that more conforming materials can be found and more precise electronic devices can be designed through more accurate performance prediction.
Disclosure of Invention
In view of the above, the present invention provides a method for predicting the mobility of semiconductor carriers and a method for screening semiconductor materials. These solutions solve the problems that carrier mobility prediction is often not practical, not accurate enough, and that the material screened by prediction is not as expected.
To achieve the above object, according to an embodiment of the present invention, there is provided a method of predicting a mobility of a semiconductor carrier by modeling a target crystal and calculating a mobility of the carrier, wherein the modeling includes subjecting the target crystal to structural distortion and calculating a correction value, and correcting the result of the calculation of the mobility of the carrier by using the correction value.
Optionally, the method comprises the following steps:
acquiring a target crystal structure data file; calculating a carrier mobility influence parameter of the target crystal according to the target crystal structure data file; performing structural distortion on the target crystal, and calculating a correction value; and obtaining the target crystal carrier mobility according to the carrier mobility influence parameters and the corrected values.
Optionally, the structure distortion is performed on the target crystal, and the calculation of the correction value includes:
constructing a primitive cell crystal file of a target crystal, and performing structure distortion on the primitive cell crystal file to obtain a distorted primitive cell crystal file;
respectively calculating the band gaps of the primitive cell crystal file and the distorted primitive cell crystal file to respectively obtain a primitive cell band gap and a super-cell band gap;
and calculating the effective mass correction value according to the primitive cell band gap and the super cell band gap.
Optionally, constructing a cell crystal file of the target crystal, and performing structure distortion on the cell crystal file to obtain a distorted cell crystal file, including: constructing a primitive cell crystal file of a target crystal; carrying out cell expansion treatment on the protocell crystal file; applying greater than zero and less than or equal to all atomsTo distort the lattice, resulting in a distorted cell crystal file.
Optionally, calculating an effective mass correction value according to the primitive cell band gap and the super cell band gap, including:
calculating the effective mass of the zone edge of the primitive cell and the effective mass of the zone edge of the super cell respectively corresponding to the band gap of the primitive cell and the band gap of the super cell according to the effective mass k.p perturbation theory; and obtaining an effective mass correction value according to the effective mass of the primitive cell band edge and the effective mass of the supercell band edge.
Optionally, calculating, according to the primitive cell band gap and the super cell band gap, the valid masses of the primitive cell band edge and the super cell band edge corresponding respectively by an effective mass k.p perturbation theory, where the band edge valid mass calculation formula is:
wherein,is a band edge state | n0>0 represents the momentum of the position of the band edge, m 0 Is the mass of free electrons, E n0 -E l0 Is the band gap, | l0>Is the other eigenstate at 0.
Optionally, the structure distortion is performed on the target crystal, and the calculation of the correction value includes:
performing structure distortion on the primitive cell crystal of the target crystal to obtain a distorted primitive cell crystal; relaxation, self-consistent calculation and state density calculation of a distorted cell crystal structure; comparing the primitive cell crystal with the distorted primitive cell crystal, and calculating a correction value;
wherein, the structure relaxation of the distorted protocell crystal is carried out by VASP software, PBE (Perdex-Burke-Ernzehf) exchange correlation functional is adopted for the relaxation, and the convergence standards of energy and force are respectively 1 × 10 -6 eV andthe cutoff energy was set at 600eV; taking the relaxed CONTCAR as POSCAR for static calculation and density of state calculation; and the k-point density in the KPOINTS file is made to be the same as that of the protocell crystal.
Optionally, calculating a carrier mobility influence parameter of the crystal according to the crystal structure data file, including: performing structural optimization on the crystal structure data file; calculating the effective mass, elastic constant and deformation potential of the crystal.
Optionally, obtaining the target crystal carrier mobility according to the carrier mobility influencing parameter and the corrected value, includes:
substituting the effective mass, the elastic constant and the deformation potential into the following formula, and multiplying the formula by a corrected value to obtain the target crystal carrier mobility mu;
where e is the electron charge, k B Is the Boltzmann constant, T is the temperature,is a reduced planck constant; m is * Is the effective mass of the distortion correction, D 1 Is deformation potential, C ii Is the elastic constant.
Alternatively, the effective mass of the crystal is calculated by the formula:
whereinIs a reduced Planck constant, m * Is the effective mass of electrons or holes, k is the wavevector, the value of the E (k) energy band is obtained by calculating a crystal structure data file, and a PBE (Perdex-Burke-Ernzehf) exchange correlation functional is adopted; and set the convergence criteria of energy and force to 1 x 10, respectively -6 eV andthe cutoff energy was set at 600eV.
In order to achieve the above object, according to an embodiment of the present invention, the present invention further provides a method for screening a semiconductor material, which performs prediction by the method for predicting semiconductor carrier mobility as described above, and performs screening according to the semiconductor carrier mobility.
The invention has the beneficial effects that:
the inventor finds that the existing calculation mode leads to a predicted value higher than an actual value because the crystal is distorted in reality, and the local distortion of the crystal breaks the spatial symmetry of the original crystal, which leads to the increase of the band gap. The existing calculation mode does not consider the point, so that the inventor calculates a correction value by twisting the crystal structure, and simulates the situation closer to reality; and obtaining the target crystal carrier mobility according to the carrier mobility influence parameters and the corrected values. Because carrier mobility variation is taken into account by correcting the lattice distortion, the result of calculation prediction is more accurate and closer to the actual situation.
Drawings
FIG. 1: csPbCl 3 E of perovskite material vbm -E 1s A graph of variation with stress;
FIG. 2: csPbCl 3 E of perovskite material cbm -E 1s A graph of variation with stress;
FIG. 3: csPbCl 3 2x2x2 twisted supercell and protocell calculated state density contrast diagram;
FIG. 4: csPbCl 3 Crystal carrier mobility prediction flow chart.
Detailed Description
The examples are given for the purpose of better illustration of the invention, but the invention is not limited to the examples. Therefore, those skilled in the art should make insubstantial modifications and adaptations to the embodiments of the present invention in light of the above teachings and remain within the scope of the invention.
Hereinafter, the present application will be described in detail with reference to the accompanying drawings so that those skilled in the art can easily practice the present invention. The invention may, however, be embodied in many different forms and should not be construed as being limited to the exemplary embodiments set forth herein.
Objects and advantages of exemplary embodiments of the present invention will be understood and made apparent by reference to the following description, but not limited to the following description. In the description of the exemplary embodiments, detailed explanations of the prior art will be omitted when it is considered that they may unnecessarily obscure the point of the present invention.
Example one
Description of the basic principle:
in the present example, the mobility of the carriers is mainly calculated by taking a deformation potential theory as an example, the deformation potential theory is based on scattering of electrons and acoustic phonons, it is considered that lattice vibration can change the potential of crystals, the change of the potential can cause the carriers to scatter in different states, and the mobility μ of the carriers can be finally calculated by simplifying the following formula:
where e is the electron charge, k B Is the Boltzmann constant, T is the temperature,is the reduced planck constant. From the above equation, it can be seen that calculating the mobility of the carriers requires calculating the effective mass m of the material separately, in addition to some constants * Strain potential D 1 And elastic constant C ii Three physical quantities. By the first principle, the above three physical quantities and the carrier mobility can be calculated from the crystal structure and the energy band structure of the semiconductor.
Where we can calculate the effective mass m usually by the band structure of the crystal * . The band structure refers to the fact that when atoms form molecules and even form a three-dimensional structure, atomic orbitals interact to generate orbitals with isolated energy levels, and the band structure of a three-dimensional material and the extraction of k points along a high symmetry line direction in a brillouin zone are discussed in detail in (Computational Materials Science 128 (2017) 140-184).
When the band structure of a crystal is known, the effective mass of electrons and holes can be calculated using the following formula:
whereinIs a reduced Planck constant, m * Is the effective mass of an electron or hole, E (k) is the calculated band, and k is the wavevector.
In practice, however, the crystal is distorted, and the local distortion of the crystal breaks the spatial symmetry of the original crystal, so that the band structure is changed, and particularly, the band gap is increased (the band gap means that two adjacent energy bands can be connected, overlapped or separated, and when the energy bands are separated, the band gap is generated), and the band edge effective mass is increased due to the increase of the band gap. Therefore, the inventor calculates the correction value of the effective mass by simulating the distortion of the crystal, and then calculates the corrected effective mass m * Strain potential D 1 And elastic constant C ii Three physical quantities, the mobility mu of the current carrier is calculated by the formula; alternatively, the correction value for the carrier mobility as a whole may be directly calculated from the correction value for the effective mass, and then the carrier mobility may be corrected.
The related calculation can be performed by various methods such as a human, a processor, a computer and the like, and can also be performed by using various software and programs for assisting the calculation. For example, VASP is known as ViennaAb-initio Simulation Package, which is currently one of the most popular software in material Simulation and computational material science research. It can handle atoms, molecules, clusters, nanowires (or tubes), thin films, crystals, quasicrystals and amorphous materials, as well as surface systems and solids, calculate structural parameters and configurations of materials, calculate equations of state and mechanical properties (bulk elastic modulus and elastic constant) of materials, calculate electronic structure (energy levels, charge density distribution, energy bands, electronic density of states) of materials, calculate optical properties, magnetic properties, lattice dynamics and molecular dynamics simulations of materials.
Specifically, as shown in FIG. 4, the perovskite photoelectric material CsPbCl of No. 221 space group (Pm-3 m) is used herein 3 For example, the calculation process of the carrier mobility prediction, especially the correction of the acoustic phonon scattering, is described in detail.
Step S1: csPbCl acquisition using Materials Project crystal database 3 And transforming the crystal structure file into a vasop file by means of VESTA software.
Step S2: and setting VASP structure calculation parameter files including a calculation function setting file (INCAR), a crystal system coordinate file (POSCAR), a pseudopotential file (POTCAR) and a reciprocal lattice vector space description file (KPOINTS).
And step S3: based on the parameters set in step S2, the obtained CsPbCl is subjected to VASP software 3 And performing structure optimization, self-consistent calculation and energy band structure calculation on the crystal structure, wherein a Perdev-Burke-Ernzerhof (PBE) exchange correlation functional with higher efficiency is adopted in the calculation process, and spin-orbit coupling (SOC) is not considered. And we set the convergence criteria for energy and force to be 1 x 10, respectively -6 eV andthe cutoff energy was set at 600eV.
The No. 221 space group CsPbCl is calculated 3 The effective mass of electrons and holes can be calculated using the following equation:
whereinIs a reduced Planck constant, m * Is the effective mass of an electron or hole, E (k) is the calculated band, and k is the wavevector. We investigated along CsPbCl 3 [100]Mobility in the crystal orientation direction, csPbCl 3 Both the valence and conduction band bases of (1) are at the highly symmetric R (0.5 ) points of the Brillouin zone, and therefore it is desirable to select BrillouinThe mobility was calculated from the high symmetry line R-M (0.5, 0) of the Brillouin region.
And step S4: csPbCl with optimized structure by adopting VASP software 3 The crystals were subjected to elastic constant calculation. The PBE exchange correlation functional is adopted in the calculation process, and Spin Orbit Coupling (SOC) is not considered. And we set the convergence criteria for energy and force to be 1 x 10, respectively -6 eV andthe cutoff energy was set at 600eV.
Calculation of CsPbCl 3 When the elastic constant of the crystal is determined, the CsPbCl of No. 221 space group needs to be noticed 3 Belonging to the cubic phase, it has three independent elastic constants, namely: c 11 ,C 12 And C 44 They can be calculated by setting IBRION =6 in INCAR and along [100 []The mobility in the crystal orientation direction is: c ii =C 11 。
Step S5: csPbCl with optimized structure by adopting VASP software 3 And (4) performing deformation potential calculation on the crystal. The PBE exchange correlation functional is adopted in the calculation process, and Spin Orbit Coupling (SOC) is not considered. And we set the convergence criteria for energy and force to be 1 x 10, respectively -6 eV andthe cutoff energy was set at 600eV.
Calculation of CsPbCl 3 When the deformation potential of the crystal is changed, it is necessary to apply Δ a to the lattice constant along the x direction 0 /a 0 Strains of-0.01, -0.005,0,0.005 and 0.01, and then the energy E at the conduction band bottom (CBM) and valence band top (VBM) is plotted cbm And E vbm The graph of the change with stress is shown in FIG. 1, and the corresponding deformation potential is obtained by the fitted slope, wherein a 0 To be unstrained CsPbCl 3 The lattice constant of the crystal. In discussing CBM and VBM energy shifts under stress, we choose the 1s level E1s of the halogen as the reference energy, and then discuss E cbm -E 1s And E vbm -E 1s See fig. 1 and 2 below as a function of stress. Wherein FIG. 1 isCsPbCl 3 E of perovskite material cbm -E 1s FIG. 2 is a graph of CsPbCl as a function of strain 3 E of perovskite material vbm -E 1s Graph of variation with strain. Through fitting, the deformation potentials of the bottom of the guide belt and the top of the valence belt are respectively as follows: d 1c =7.37eV and D 1v =5.44eV。
Step S6: construction of 2x2x2CsPbCl by VASPKIT software 3 The cells are superbasic and their structure is distorted. When constructing, we first expand the 2x2x2CsPbCl 3 The super cell has 40 atoms, and then one is applied to each atomThe micro-displacement of (2) achieves the effect of twisting the lattice to destroy the symmetry of the original No. 221 space group. The minute displacement is random displacement (direction is not uniform) and is not more thanThe displacement of (A) is to ensure that the crystal is distorted without destroying the chemical bonds of the crystal, thereby maintaining the crystal structure and simulating the distortion of the crystal.
Step S7: csPbCl for constructed twisted 2x2x2 3 And performing structural relaxation, self-consistent calculation and state density calculation on the super-primitive cells, wherein spin-orbit coupling is not considered in the calculation process. Firstly, distorted 2x2x2CsPbCl is subjected to VASP software 3 Performing structural relaxation on the super protocell, adopting a PBE exchange correlation functional with higher calculation efficiency during relaxation, and respectively setting the convergence standards of energy and force to be 1 multiplied by 10 -6 eV andthe cutoff energy was set at 600eV. Taking the relaxed CONTCAR as POSCAR for static calculation and density of states calculation, when performing density of states calculation by VASP, the density of k points in the KPOINTS file should be kept the same as the density calculated by primitive cells for comparison with the result of primitive cell calculation.
Step S8: comparison of 2x2x2CsPbCl with distortion 3 Calculated bandgap of the superlattice and use of CsPbCl 3 The band gap calculated by the primitive cell is obtained to obtain the distorted CsPbCl 3 The effective mass of the material is increased, and the CsPbCl after distortion is considered is further obtained by the calculation formula of the carrier mobility mu 3 Modification of the perovskite material mobility.
Specifically, the distorted band gap size is obtained through the state density calculated by the supercell and is compared with the band gap size calculated by the primitive cell to obtain the CsPbCl after the crystal lattice distortion 3 As a result of the bandgap enhancement. According to the effective mass k.p perturbation theory, the effective mass of the band edge of the semiconductor material can be expressed as:
whereinIs a semiconductor band edge state | n0>0 represents the momentum of the position of the band edge, m 0 Is the mass of free electrons, E n0 -E l0 Is the semiconductor bandgap, | l0>Is the other eigenstate at 0. From the above expression, it can be seen that the semiconductor band gap E n0 -E l0 Will result in effective band edge qualityIs added, this is therefore also the basis for our correction of effective mass. Our calculations show that CsPbCl is present after warping 3 Bandgap ratio CsPbCl of supercell 3 The band gap of the primitive cell is larger, as shown in fig. 3 below, fig. 3 (the left arrow in the figure indicates the super cell, and the right arrow indicates the primitive cell): csPbCl 3 The calculated density of states (DOS) for the material was compared to that for the 2x2x2 twisted supercell and the protocell, respectively. It can be seen from the figure that the bandgap calculated for the twisted supercell is larger than for the primary cell, increasing from approximately 2.19eV to 2.55eV. Therefore, the band gap after correction is increased by about 1.164 times, and correspondingly the effective mass is increased by 1.164 times (the value is the effective mass correction value), and the band gap after correction is increased by 1.164 timesThe mobility is reduced to 1/1.1645/2=0.684 (this value is the overall correction coefficient), that is, the effective mass can be calculated and then the corrected effective mass is substituted into the carrier mobility calculation formula, or the mobility can be calculated first and then multiplied by the overall correction coefficient.
It should be noted that the steps marked by S1-S8, etc. do not represent the execution sequence of the present invention, and can be executed simultaneously or adjusted sequentially on the premise of not affecting the effect of the present invention; in addition, the above-mentioned embodiments can be replaced by alternative embodiments without creative efforts, and the embodiments can be combined or combined with each other to form the steps under the condition that the steps can achieve the purpose of the invention, and also fall into the protection scope of the right of the invention.
Example two
The present embodiment takes the calculation of the conductivity as an example, and illustrates that various performance parameters of the semiconductor can be further calculated and predicted through the predicted carrier mobility.
That is, after the carrier mobility is obtained through the above steps, various performance parameters of the semiconductor can be calculated through a formula.
For example, the calculation for hole conductivity is:
wherein, mu p Is the hole carrier mobility; p is the hole concentration and e is the electron charge.
For n-type semiconductors:
wherein, mu n Is the carrier mobility; n is the electron concentration and e is the electron charge. When two carriers are simultaneously conducted in a semiconductor, the conductivity is the sum of the two carriers.
EXAMPLE III
In this embodiment, for example, the screening of semiconductor Materials is performed, according to a parameter range required by an electronic device for the semiconductor Materials, for example, the minimum carrier mobility requirement of a certain function is met, and then according to crystal structure model data provided by crystal data such as Materials Project, attributes such as carrier mobility, conductivity, work efficiency, and the like are obtained through the above prediction, so as to screen out Materials that may be suitable for use, and finally, an electronic component is manufactured.
For example, for a bipolar transistor, high carrier mobility can shorten the time for a carrier to transit the base region, resulting in a characteristic frequency (f) T ) The frequency, speed, noise and other performances of the device can be improved well. Therefore, for bipolar transistors, it is desirable to screen semiconductor materials with higher carrier mobility.
For a field effect transistor, enhancing the mobility μ of carriers in a channel has the same effect as shortening the channel length L, and the driving capability of the device can be improved, thereby improving the operating speed of the device. Therefore, for field effect transistors, there is a need to screen semiconductor materials with higher carrier mobility.
Delay time tau of signal transmission in integrated circuit for increasing speed of large scale integrated circuit d Logic voltage swing V of AND signal m And carrier mobility mu in inverse proportion. In order to ensure that the integrated circuit can stably work without being influenced by heat generation, the logic voltage swing should be properly reduced; at the same time, however, in order to ensure a higher operating speed of the integrated circuit, the mobility of the carriers is only increased to shorten the delay time of the signal transmission. Therefore, ultra-high speed field effect logic integrated circuits must have high carrier mobility to be realized.
For CMOS, which is a basic device of ULSI, it is more important to enhance the mobility of carriers, especially to increase the mobility of holes. Since the mobility of holes in Si is about 2.5 times smaller than that of electrons, S is caused i Two major problems arise in CMOS technology: first, in designing CMOSIn order to ensure the consistency of current passing through the PMOSFET and the NMOSFET, the width of a grid electrode of the PMOSFET must be increased by 2.5 times, which inevitably leads to the increase of the area of a chip; second one S i The maximum operating frequency and speed of CMOS devices and their circuits will be limited by the PMOSFET performance, and therefore, in developing radio frequency CMOS integrated circuits and very large scale CMOS integrated circuits, the semiconductor properties that need to be screened are higher hole mobility.
The above does not list all possible applications.
Finally, although the present invention has been described in detail with reference to the preferred embodiments, it should be understood by those skilled in the art that various changes and modifications may be made therein without departing from the spirit and scope of the invention as defined by the appended claims.
Claims (10)
1. A method for predicting the carrier mobility of a semiconductor is characterized in that the modeling comprises the steps of carrying out structural distortion on a target crystal and calculating a correction value, and correcting the calculation result of the carrier mobility by using the correction value.
2. The method of predicting semiconductor carrier mobility of claim 1, comprising the steps of:
acquiring a target crystal structure data file;
calculating a carrier mobility influence parameter of the target crystal according to the target crystal structure data file;
performing structural distortion on the target crystal, and calculating a correction value;
and obtaining the target crystal carrier mobility according to the carrier mobility influence parameters and the corrected values.
3. The method of predicting mobility of semiconductor carriers of claim 2, wherein the step of applying a structural distortion to the target crystal and calculating the correction value comprises:
constructing a primitive cell crystal file of a target crystal, and performing structure distortion on the primitive cell crystal file to obtain a distorted primitive cell crystal file;
respectively calculating the band gaps of the primitive cell crystal file and the distorted primitive cell crystal file to respectively obtain a primitive cell band gap and a super-cell band gap;
and calculating the effective mass correction value according to the primitive cell band gap and the super cell band gap.
4. The method of claim 3, wherein constructing a cell crystal file of a target crystal and subjecting the cell crystal file to structure distortion to obtain a distorted cell crystal file comprises:
constructing a primitive cell crystal file of a target crystal;
carrying out cell expansion treatment on the protocell crystal file;
5. A method of predicting semiconductor carrier mobility according to claim 3 wherein calculating the effective mass correction based on the cellular bandgap and the super-cellular bandgap comprises:
calculating the effective mass of the zone edge of the primitive cell and the effective mass of the zone edge of the super cell respectively corresponding to the band gap of the primitive cell and the band gap of the super cell according to the effective mass k.p perturbation theory;
the band edge effective mass calculation formula is as follows
Wherein,is a band edge state | n0>0 represents the momentum of the position of the band edge, m 0 Is the mass of free electrons, E n0 -E l0 Is the band gap, | l0>Is the other eigenstate at 0;
and obtaining an effective mass correction value according to the effective mass of the primitive cell band edge and the effective mass of the supercell band edge.
6. A method of predicting semiconductor carrier mobility according to any one of claims 2 to 5 wherein the target crystal is subjected to structural distortion and the calculation of the correction value comprises:
performing structural distortion on the primitive cell crystal of the target crystal to obtain a distorted primitive cell crystal;
relaxation, self-consistent calculation and state density calculation of a twisted protocell crystal structure;
comparing the primitive cell crystal with the distorted primitive cell crystal, and calculating a correction value;
wherein, the structure relaxation of the distorted protocell crystal is carried out by VASP software, PBE (Perdex-Burke-Ernzehf) exchange correlation functional is adopted for the relaxation, and the convergence standards of energy and force are respectively 1 × 10 -6 eV andthe cutoff energy was set at 600eV; taking the relaxed CONTCAR as POSCAR for static calculation and density of state calculation; and the k-point density in the KPOINTS file is made to be the same as that of the protocell crystal.
7. The method of predicting the mobility of semiconductor carriers of claim 2 wherein calculating carrier mobility influencing parameters of the crystal based on the crystal structure data file comprises:
performing structural optimization on the crystal structure data file;
calculating the effective mass, elastic constant and deformation potential of the crystal.
8. The method of claim 7, wherein obtaining the target crystal carrier mobility from the carrier mobility influencing parameter and the correction value comprises:
substituting the effective mass, the elastic constant and the deformation potential into the following formula, and multiplying the formula by a corrected value to obtain the target crystal carrier mobility mu;
9. The method of predicting semiconductor carrier mobility of claim 8 wherein the effective mass of the crystal is calculated by the formula:
whereinIs a reduced Planck constant, m * Is the effective mass of electrons or holes, k is the wave vector, the value of the E (k) energy band is obtained by calculating a crystal structure data file, and a PBE (Perdex-Burke-Ernzetrhof) exchange correlation functional is adopted; and set the convergence criteria of energy and force to 1 x 10, respectively -6 eV andthe cutoff energy was set at 600eV.
10. A method of screening semiconductor material, characterized in that prediction is performed by the method of predicting the mobility of semiconductor carriers according to any one of claims 1 to 9, and screening is performed based on the mobility of semiconductor carriers.
Priority Applications (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211080234.2A CN115292961A (en) | 2022-09-05 | 2022-09-05 | Method for predicting carrier mobility of semiconductor |
Applications Claiming Priority (1)
Application Number | Priority Date | Filing Date | Title |
---|---|---|---|
CN202211080234.2A CN115292961A (en) | 2022-09-05 | 2022-09-05 | Method for predicting carrier mobility of semiconductor |
Publications (1)
Publication Number | Publication Date |
---|---|
CN115292961A true CN115292961A (en) | 2022-11-04 |
Family
ID=83834605
Family Applications (1)
Application Number | Title | Priority Date | Filing Date |
---|---|---|---|
CN202211080234.2A Pending CN115292961A (en) | 2022-09-05 | 2022-09-05 | Method for predicting carrier mobility of semiconductor |
Country Status (1)
Country | Link |
---|---|
CN (1) | CN115292961A (en) |
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN118039044A (en) * | 2024-04-11 | 2024-05-14 | 西南交通大学 | Method, apparatus and medium for determining transparency and conductivity of transparent conductive material |
-
2022
- 2022-09-05 CN CN202211080234.2A patent/CN115292961A/en active Pending
Cited By (1)
Publication number | Priority date | Publication date | Assignee | Title |
---|---|---|---|---|
CN118039044A (en) * | 2024-04-11 | 2024-05-14 | 西南交通大学 | Method, apparatus and medium for determining transparency and conductivity of transparent conductive material |
Similar Documents
Publication | Publication Date | Title |
---|---|---|
Dhar et al. | Electron mobility model for strained-Si devices | |
Shi et al. | Theoretical prediction of intrinsic electron mobility of monolayer InSe: first-principles calculation | |
CN110083964A (en) | Multiscale Simulation Method based on quaternary compounds heterojunction structure | |
CN115292961A (en) | Method for predicting carrier mobility of semiconductor | |
Yang et al. | Intrinsic carrier mobility of monolayer GeS and GeSe: First-principles calculation | |
Watling et al. | The impact of interface roughness scattering and degeneracy in relaxed and strained Si n-channel MOSFETs | |
Chaudhuri et al. | Accurate leakage estimation for FinFET standard cells using the response surface methodology | |
Hafsi et al. | TCAD Simulations of graphene field-effect transistors based on the quantum capacitance effect | |
Kallepelli et al. | A novel circular double-gate SOI MOSFET with raised source/drain | |
Dadkhah et al. | Improved quasiparticle self-consistent electronic band structure and excitons in β-LiGaO 2 | |
Sun et al. | Investigation of process variation in vertically stacked gate-all-around nanowire transistor and SRAM circuit | |
Dinh et al. | Improving the high-frequency performance of SiGe HBTs by a global additional uniaxial stress | |
Chatzikyriakou et al. | A systematic method for simulating total ionizing dose effects using the finite elements method | |
Chaudhary et al. | Physical insights of interface traps and self-heating effect on electrical response of DMG FinFETs in overlap and underlap configurations: analog/RF perspective | |
Tsuboi et al. | Development of electrical conductivity estimation method based on tight-binding quantum chemical molecular dynamics simulation | |
She et al. | Transport and thermoelectric properties of strongly anharmonic full-heusler compounds csk2m (m= as, bi) | |
Inaba et al. | Temperature Dependent Variations of Low-Frequency Noise Sources in Cryogenic Short-Channel Bulk MOSFETs | |
Mehrara et al. | I–V characteristics of two-dimensional nanodot-array single electron transistors | |
Meguellati et al. | RADFET dosimeter design for environment monitoring applications | |
Kumari et al. | Impact of process induced strain on the sensitivity of charge plasma doped TMD TFET biosensor | |
Lakhdara et al. | Mathematical approach and optimisation of nanometric base thickness for a SiGeC HBT dedicated to radiofrequency applications | |
Rubel | One-dimensional electron gas in strained lateral heterostructures of single layer materials | |
Fu et al. | Effect of charge trapping on electrical characteristics of silicon junctionless nanowire transistor | |
Raleva et al. | Monte carlo device simulations | |
Persson | Impurity induced band-gap narrowing in p-type CuIn1− xGax (S, Se) 2 |
Legal Events
Date | Code | Title | Description |
---|---|---|---|
PB01 | Publication | ||
PB01 | Publication | ||
SE01 | Entry into force of request for substantive examination | ||
SE01 | Entry into force of request for substantive examination |