CN116911236B - Numerical simulation method, device and equipment of semiconductor device and storage medium - Google Patents
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Abstract
The invention discloses a numerical simulation method, a device, equipment and a storage medium of a semiconductor device. The method comprises the following steps: and constructing a current simulation equation set corresponding to the semiconductor device based on current independent variables corresponding to grid points in a semiconductor grid model of the semiconductor device, adding a step of determining the current conductive concentration of each grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to each grid point in the process of each iteration solution, and updating the current independent variables of the grid points based on the judgment result of the current conductive concentration and the preset concentration range until the iteration ending condition is met, and determining the numerical simulation data of the semiconductor device. The embodiment of the invention solves the problem that the traditional iterative solving algorithm only builds an equation set based on a single independent variable, thereby ensuring the accuracy of a numerical simulation result and meeting the convergence speed requirement of the algorithm.
Description
Technical Field
The present invention relates to the field of data simulation technologies, and in particular, to a method, an apparatus, a device, and a storage medium for numerical simulation of a semiconductor device.
Background
With the development of microelectronics technology, the semiconductor technology level and device performance are continuously improved, and TCAD (Technology Computer Aided Design, computer aided design) algorithms play an important role in this process. The TCAD algorithm is a numerical simulation tool based on the physical basis of the semiconductor, and can simulate different process conditions to replace or partially replace expensive and time-consuming process experiments.
At present, two iterative solution algorithms are mainly adopted by the TCAD algorithm, wherein one is the iterative solution independent variableThe second is iterative solutionIndependent variable->And (5) forming an equation set. Wherein (1)>Represents the potential->Represents electron concentration->Represents the hole concentration>，/>，/>，/>Representing an electronic quasi fermi level, +.>Representing the quasi-fermi level of the hole, +.>Indicating electron mobility>Indicating hole mobility, +.>Indicating electron diffusivity, ">Indicating hole diffusivity, +.>Showing constants associated with device materials of the semiconductor device.
Independent variableCorresponding numerical simulation results may be presented +. >Obviously not in line with physical reality, but the argument +.>Can ensure +.>Constant true but iteratively solve for the argument +.>When the equation set is constructed, the algorithm convergence speed is extremely slow, so that an iteration solving method capable of guaranteeing the accuracy of the numerical simulation result and meeting the algorithm convergence speed requirement needs to be found.
Disclosure of Invention
The embodiment of the invention provides a numerical simulation method, a device, equipment and a storage medium of a semiconductor device, which are used for solving the problem that only a single independent variable equation set is constructed in the traditional iterative solving algorithm, not only can the accuracy of a numerical simulation result be ensured, but also the convergence speed requirement of the algorithm can be met.
According to one embodiment of the present invention, there is provided a numerical simulation method of a semiconductor device, the method including:
acquiring current independent variables corresponding to grid points in a semiconductor grid model of a semiconductor device, and constructing a current simulation equation set corresponding to the semiconductor device based on the current independent variables;
performing one-time iterative solving operation on the current simulation equation set to obtain current simulation data corresponding to each grid point respectively; the current simulation data comprise current electron concentration and current hole concentration;
For each grid point, determining the current conductive concentration of the grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to the grid point, and updating the current independent variable of the grid point based on the judgment result of the current conductive concentration and the preset concentration range;
and returning to execute the step of constructing a current simulation equation set corresponding to the semiconductor device based on each current independent variable until the iteration end condition is met, and determining the numerical simulation data of the semiconductor device based on the current simulation data respectively corresponding to each grid point.
According to another embodiment of the present invention, there is provided a numerical simulation apparatus of a semiconductor device, including:
the system comprises a current simulation equation set determining module, a current simulation equation set determining module and a current simulation equation set determining module, wherein the current simulation equation set determining module is used for acquiring current independent variables corresponding to grid points in a semiconductor grid model of a semiconductor device respectively and constructing a current simulation equation set corresponding to the semiconductor device based on the current independent variables;
the current simulation data solving module is used for executing one iteration solving operation on the current simulation equation set to obtain current simulation data corresponding to each grid point respectively; the current simulation data comprise current electron concentration and current hole concentration;
The current independent variable updating module is used for determining the current conductive concentration of each grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to the grid point, and updating the current independent variable of the grid point based on the judging result of the current conductive concentration and the preset concentration range;
and the numerical simulation data determining module is used for returning to execute the step of constructing the current simulation equation set corresponding to the semiconductor device based on each current independent variable until the iteration ending condition is met, and determining the numerical simulation data of the semiconductor device based on the current simulation data corresponding to each grid point respectively.
According to another embodiment of the present invention, there is provided an electronic apparatus including:
at least one processor; and
a memory communicatively coupled to the at least one processor; wherein,
the memory stores a computer program executable by the at least one processor to enable the at least one processor to perform the numerical simulation method of the semiconductor device according to any one of the embodiments of the present invention.
According to another embodiment of the present invention, there is provided a computer readable storage medium storing computer instructions for causing a processor to execute a numerical simulation method of a semiconductor device according to any one of the embodiments of the present invention.
According to the technical scheme, the current simulation equation set corresponding to the semiconductor device is constructed based on the current independent variables corresponding to each grid point in the semiconductor grid model of the semiconductor device, in the process of each iteration solving, the current conductive concentration of each grid point is determined based on the grid doping concentration corresponding to the grid point, the current electron concentration and the current hole concentration in the current simulation data, and the current independent variables of the grid points are updated based on the judging result of the current conductive concentration and the preset concentration range until the iteration ending condition is met, the numerical simulation data of the semiconductor device is determined, the problem that the equation set is constructed based on only a single independent variable in the traditional iteration solving algorithm is solved, the accuracy of the numerical simulation result of the semiconductor device is guaranteed, and the algorithm convergence speed requirement of the numerical simulation process of the semiconductor device is met.
It should be understood that the description in this section is not intended to identify key or critical features of the embodiments of the invention or to delineate the scope of the invention. Other features of the present invention will become apparent from the description that follows.
Drawings
In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings required for the description of the embodiments will be briefly described below, and it is apparent that the drawings in the following description are only some embodiments of the present invention, and other drawings may be obtained according to these drawings without inventive effort for a person skilled in the art.
Fig. 1 is a flowchart of a numerical simulation method of a semiconductor device according to an embodiment of the present invention;
fig. 2 is a flowchart of a specific example of a numerical simulation method of a semiconductor device according to an embodiment of the present invention;
FIG. 3 is a flow chart of another method for simulating the numerical value of a semiconductor device according to an embodiment of the present invention;
fig. 4 is a schematic structural diagram of a numerical simulation apparatus for a semiconductor device according to an embodiment of the present invention;
fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present invention.
Detailed Description
In order that those skilled in the art will better understand the present invention, a technical solution in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in which it is apparent that the described embodiments are only some embodiments of the present invention, not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the present invention without making any inventive effort, shall fall within the scope of the present invention.
It should be noted that the terms "first," "second," "target," "reference," "current," "preset," and the like in the description and claims of the present invention and in the above figures are used for distinguishing between similar objects and not necessarily for describing a particular sequential or chronological order. It is to be understood that the data so used may be interchanged where appropriate such that the embodiments of the invention described herein may be implemented in sequences other than those illustrated or otherwise described herein. Furthermore, the terms "comprises," "comprising," and "having," and any variations thereof, are intended to cover a non-exclusive inclusion, such that a process, method, system, article, or apparatus that comprises a list of steps or elements is not necessarily limited to those steps or elements expressly listed but may include other steps or elements not expressly listed or inherent to such process, method, article, or apparatus.
Fig. 1 is a flowchart of a numerical simulation method of a semiconductor device according to an embodiment of the present invention, where the method may be performed by a numerical simulation apparatus of a semiconductor device, and the numerical simulation apparatus of a semiconductor device may be implemented in hardware and/or software, and the numerical simulation apparatus of a semiconductor device may be configured in a terminal device. As shown in fig. 1, the method includes:
s110, current independent variables corresponding to grid points in a semiconductor grid model of the semiconductor device are obtained, and a current simulation equation set corresponding to the semiconductor device is constructed based on the current independent variables.
Specifically, in this embodiment, the term "current" before the parameter data such as "independent variable", "simulation equation set", "electron concentration", "hole concentration", and "conductive concentration" corresponds to the current iteration solving operation, and the parameter data may be the same or may be changed in different iteration solving operations.
Wherein, in particular, the semiconductor mesh model may be used to characterize a three-dimensional mesh model of the semiconductor device. Illustratively, a geometric model of the semiconductor device is constructed based on geometric parameter data of the semiconductor device, and the geometric model is subjected to grid division to obtain a semiconductor grid model of the semiconductor device. Wherein the geometric parameter data comprises but is not limited to geometric parameters such as the length, the width, the height, the volume and the like of the semiconductor device, and the adopted grid division algorithm comprises but is not limited to a finite volume method, a Delaunay triangle algorithm and the like.
Specifically, the area volumes of the grid device areas to which the grid points respectively belong in the semiconductor grid model may be the same or different, and the area shapes of the grid device areas may be the same or different. The mesh division algorithm and the specific division standard are not limited, and can be specifically set in a self-defined manner according to actual requirements.
In an alternative embodiment, the first iterative solution operation is performed prior to being based on the argumentsAnd independent variable->Corresponding preset proportion, and determining current independent variables corresponding to the grid points respectively. For example, when the preset ratio is 100:0, the current independent variables corresponding to the grid points in the semiconductor grid model are independent variablesWhen the preset ratio is 0:100, the current independent variables corresponding to each grid point in the semiconductor grid model are independent variables +.>When the preset ratio is 40:60, the current independent variables corresponding to 40% grid points in the semiconductor grid model are independent variables +.>The current independent variables respectively corresponding to 60% of grid points are independent variablesThe grid points corresponding to the independent variables can be selected randomly or sequentially. The preset proportion and the screening mode of each grid point are not limited, and the screening mode can be specifically set in a self-defined mode according to actual requirements.
In an alternative embodiment, the argumentAnd independent variable->The corresponding preset ratio is 100:0. The advantage of this arrangement is that,since the accuracy requirement on the current simulation data obtained by the first iterative solving operation is not high, the method is based on independent variable +.>The speed of iterative solution of the constructed simulation equation set is compared to the speed based on the independent variable +.>The iterative solution of the constructed simulation equation set is fast, so that the algorithm convergence speed of the numerical simulation process of the semiconductor device can be further improved to a certain extent.
Wherein, specifically, for each grid point, based on the independent variableThe constructed simulation equation set (1) is as follows:
(1)
the 1 st equation in the simulation equation set (1) is an electrostatic poisson equation, the 2 nd equation is an electron concentration change equation, the 3 rd equation is a hole concentration change equation, and the 4 th to 5 th equations are collectively called as migration diffusion equations of current. Wherein,representing the permittivity of the semiconductor device, +.>Representing Nabla operator->Representing the potential of grid points>Representing the unit charge amount,/-, and>electron concentration representing grid points +.>Hole concentration of grid points, +.>Grid doping concentration representing grid points, +.>Time of presentation- >Represents the carrier generation amount, < >>Represents the carrier recombination amount, < >>Representing electron current density, ">Representing hole current density, ">Indicating electron mobility>Indicating hole mobility, +.>Indicating electron diffusivity, ">Indicating the hole diffusivity. Wherein electrons and holes are collectively referred to as carriers.
Wherein, in particular, the argumentAnd independent variable->The following parameter conversion relations exist:
for each grid point, the parameter conversion relation is adopted to the independent variableParameter substitution is carried out on the constructed simulation equation set (1) to obtain a parameter-based independent variable +.>And constructing a simulation equation set.
Specifically, the current simulation equation set corresponding to the semiconductor device includes a simulation equation set corresponding to each grid point in the semiconductor grid model.
S120, performing one iteration solving operation on the current simulation equation set to obtain current simulation data corresponding to each grid point respectively.
The iterative solution algorithm may be, for example, a newton iterative algorithm, which is not limited herein, and specifically may be set in a user-defined manner according to actual requirements.
In this embodiment, the current simulation data includes the current electron concentration and the current hole concentration. In an alternative embodiment, the current simulation data also contains the current potential.
S130, judging whether the iteration ending condition is met, if not, executing S140, and if so, executing S150.
In an alternative embodiment, the iteration end condition is that the current iteration number reaches a preset number threshold, or the iteration end condition is that the current iteration time reaches a preset end time, or the iteration end condition is that the current simulation residual is smaller than a preset residual threshold.
In one embodiment, the iteration end condition is that the current simulation residual is less than a preset residual threshold. Since carrier time is when the semiconductor device reaches steady stateThe partial derivative of (2) is 0, i.e. the above is based on an independent variableIn the constructed simulation equation set (1)，And (3) deforming the simulation equation set (1) to obtain a simulation equation set (2):
(2)
the simulation equation set (2) is deformed again to obtain a first residual errorSecond residual->And a third residual errorFirst residual->Second residual->And third residual->The following residual equation set (3) is satisfied:
(3)
specifically, for each grid point, substituting the device parameter data of the semiconductor device and the current simulation data corresponding to the grid point into the residual equation (3) to obtain a first residual corresponding to the grid pointSecond residual- >And third residual->. Exemplary, the current simulation residual +.>The following formula is satisfied:
wherein,representing the number of grid points in the semiconductor grid model, < >>For characterising +.>Sum of squares of residuals corresponding to individual grid points, specifically, < >>。
And S140, for each grid point, determining the current conductive concentration of the grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to the grid point, updating the current independent variable of the grid point based on the judgment result of the current conductive concentration and the preset concentration range, and returning to S110.
Specifically, the grid doping concentration is used for representing the doping concentration corresponding to the grid device area to which the grid point belongs. In an alternative embodiment, determining the current conductivity concentration of the grid points based on the grid doping concentration, the current electron concentration, and the current hole concentration corresponding to the grid points includes: and taking the concentration difference value corresponding to the current electron concentration and the current hole concentration as the current difference value concentration, and taking the sum of the current difference value concentration and the grid doping concentration as the current conductive concentration of the grid point.
Wherein, by way of example, the current conductivity concentration satisfies the formula:wherein->Represent the first The>Conductive concentration corresponding to the individual grid points, < >>Indicate->The>Current electron concentration of individual grid points,/->Indicate->The>Current hole concentration of individual grid points,/->Indicate->Grid doping concentration of individual grid points.
In an alternative embodiment, updating the current argument of the grid point based on the determination result of the current conductive concentration and the preset concentration range includes: under the condition that the current conductive concentration meets the preset concentration range, taking the first independent variable as the current independent variable of the grid point; under the condition that the current conductive concentration does not meet the preset concentration range, taking the second independent variable as the current independent variable of the grid point; when the maximum preset conductive concentration in the preset concentration range is smaller than or equal to a preset concentration threshold value, the first independent variable is potential, electron concentration and hole concentration, and the second independent variable is potential, electron quasi-fermi level and hole quasi-fermi level; when the minimum preset conductive concentration in the preset concentration range is greater than or equal to the preset concentration threshold, the first independent variables are the potential, the electron quasi-fermi level and the hole quasi-fermi level, and the second independent variables are the potential, the electron concentration and the hole concentration.
In an alternative embodiment, the preset concentration threshold is preset, and as an example, the preset concentration threshold may be 1, and correspondingly, the preset concentration range may beMay be +.>Of course, the preset concentration range may also be +.>Or->The preset concentration range is not limited herein.
Wherein the preset concentration threshold is used for defining that the iterative solution is based on independent variablesCondition number and iterative solution of Jacobian matrix in process of constructing simulation equation set are based on independent variable +.>The relationship between the condition numbers of the Jacobian matrix in the process of constructing the simulation equation set. Applicants have found that the smaller the condition number of the Jacobian matrix in the iterative solution process, the smaller the condition number of the iterative solution algorithmThe more accurate the convergence direction, the faster the algorithm converges.
The preset concentration threshold value preset in this embodiment can ensure that if the current conductive concentration is less than or equal to the preset concentration threshold value, the independent variableThe condition number of the corresponding Jacobian matrix is smaller than the argument +.>The condition number of the corresponding Jacobian matrix, the argument +_if the current conductivity concentration is greater than the preset concentration threshold>The condition number of the corresponding Jacobian matrix is greater than the argument +.>Condition number of the corresponding jacobian matrix.
Alternatively, the preset concentration range in the present embodiment may ensure that, when the maximum preset conductive concentration in the preset concentration range is less than or equal to the preset concentration threshold, if the current conductive concentration satisfies the preset concentration range, the independent variableThe condition number of the corresponding Jacobian matrix is smaller than the argument +.>Condition number of corresponding Jacobian matrix, independent variable +_if current conductive concentration does not meet preset concentration range>The condition number of the corresponding Jacobian matrix is greater than the argument +.>Condition number of the corresponding jacobian matrix. When the minimum preset conductive concentration in the preset concentration range is greater than or equal to the preset concentration threshold, if the current conductive concentration does not meet the preset concentration rangeEnclose, independent variable->The condition number of the corresponding Jacobian matrix is smaller than the argument +.>Condition number of corresponding Jacobian matrix, independent variable +_if current conductive concentration satisfies preset concentration range>The condition number of the corresponding Jacobian matrix is greater than the argumentCondition number of the corresponding jacobian matrix.
S150, determining numerical simulation data of the semiconductor device based on current simulation data corresponding to each grid point.
Specifically, current simulation data corresponding to each grid point is used as numerical simulation data of the semiconductor device.
Fig. 2 is a flowchart of a specific example of a numerical simulation method of a semiconductor device according to an embodiment of the present invention, specifically, before performing a first iterative solving operation, current independent variables corresponding to m grid points, such as grid1, grid2 … grid m, in a semiconductor grid model are independent variables. Based on the current independent variables corresponding to the grid points, constructing the current simulation equation set equences corresponding to the semiconductor device, and executing the +.>And carrying out iterative solving operation for the times to obtain current simulation data corresponding to each grid point respectively. Judging whether the current simulation residual is smaller than a preset residual threshold value, and if so, taking the current simulation data corresponding to each grid point as the numerical simulation data of the semiconductor device.
If not, then for the firstThe individual grid points gridj determine the current electron concentration corresponding to the grid points gridj>Current hole concentration->And grid doping concentration->Whether the current conductivity concentration of the composition is less than 1, if so, the argument +.>As the current argument corresponding to grid point gridj, if greater than or equal to, the argument isAs the current argument for grid point gridj. Judging- >If equal, returning to execute the step of constructing the current simulation equation set Equations corresponding to the semiconductor device based on the current independent variables respectively corresponding to the grid points, if not, executing the grid=grid (j+1), and returning to execute the step of judging the current electron concentration corresponding to the grid points based on the grid>Current hole concentration->And grid doping concentration->A step of composing whether the current conduction concentration is less than 1, wherein 1.ltoreq.L.>≤m。
According to the technical scheme, a current simulation equation set corresponding to the semiconductor device is constructed based on current independent variables corresponding to grid points in a semiconductor grid model of the semiconductor device, in the process of each iteration solving, the current conductive concentration of the grid points is determined based on the grid doping concentration corresponding to the grid points, the current electron concentration and the current hole concentration in current simulation data, and the current independent variables of the grid points are updated based on the judging result of the current conductive concentration and the preset concentration range, until the iteration ending condition is met, the numerical simulation data of the semiconductor device is determined, the problem that the equation set is constructed based on only a single independent variable in the traditional iteration solving algorithm is solved, the accuracy of the numerical simulation result of the semiconductor device is guaranteed, and the algorithm convergence speed requirement of the numerical simulation process of the semiconductor device is met.
Fig. 3 is a flowchart of another numerical simulation method of a semiconductor device according to an embodiment of the present invention, where the method for obtaining the "preset concentration range" in the above embodiment is further refined. As shown in fig. 3, the method includes:
s210, determining a first Jacobian matrix corresponding to the first independent variable and a second Jacobian matrix corresponding to the second independent variable based on device parameter data corresponding to the semiconductor device.
With first argument as argumentThe second argument is the argument +.>As an example. Based on the residual equation set (3) in the above embodiment, the jacobian matrix +_corresponding to the first argument can be obtained>The method comprises the following steps:
by dimensional analysis of the electrostatic poisson equation, it was found that there is a space in lengthSo thatIs true according to the independent variable->And independent variable->The parameter conversion relation between the two parameters can be obtained through numerical derivation, and the following corresponding relation is obtained:
based on the correspondence, the Jacobian matrix corresponding to the first argument can be obtainedThe simplification is as follows:
specifically, the device parameter data corresponding to the semiconductor device is substituted into the Jacobian matrixIn which a first Jacobian matrix can be obtained>。
According to the independent variable And independent variable->Parameter conversion relation between the above-mentioned Jacobian matrix +.>Jacobian matrix corresponding to the second argument can be obtained>The following relationship is satisfied:
wherein,then Jacobian matrix->The method comprises the following steps:
specifically, the device parameter data corresponding to the semiconductor device is substituted into the Jacobian matrixIn which a first Jacobian matrix can be obtained>。
According to the Jacobian matrixAnd Jacobian matrix->The device parameter data at least comprises a unit charge amountPermittivity->、/>Electron mobility->Hole mobility->。
In this embodiment, the device parameter data includes at least two reference doping concentrations, and the reference doping concentrations characterize preset doping concentrations for deduction verification.
S220, for each reference doping concentration, determining a condition data set based on the reference doping concentration, the reference simulation data, the first jacobian matrix, and the second jacobian matrix.
Wherein, the reference simulation data specifically characterizes preset simulation data for deduction verification, and the reference simulation data comprises reference potentialReference electron concentration->And reference hole concentration->。
In this embodiment, the condition data set includes a first condition number corresponding to the first jacobian matrix and a second condition number corresponding to the second jacobian matrix.
In an alternative embodiment, determining the set of condition data based on the reference doping concentration, the reference simulation data, the first jacobian matrix, and the second jacobian matrix comprises: substituting the reference simulation data and the reference doping concentration into a reference Jacobian matrix to obtain a target Jacobian matrix; taking the product corresponding to the norm of the target Jacobian matrix as the reference condition number corresponding to the reference Jacobian matrix; wherein the reference condition number is a first condition number when the reference jacobian matrix is a first jacobian matrix and a second condition number when the reference jacobian matrix is a second jacobian matrix.
According to equation in residual equation set (3)Can get->. A unit charge amount of the semiconductor device>Permittivity->Reference potential，/>Electron mobility->Hole mobilityReference electron concentration->Reference hole concentration->For example, the reference doping concentrations and the reference conduction concentrations formed by the reference simulation data are +.>、1、/>And->。
When (when)When (I)>First condition number->Second condition number->The method comprises the steps of carrying out a first treatment on the surface of the When->When (I)>First condition numberSecond condition number->The method comprises the steps of carrying out a first treatment on the surface of the When->In the time-course of which the first and second contact surfaces,first condition number- >Second condition number->The method comprises the steps of carrying out a first treatment on the surface of the When (when)When (I)>First condition number->Second condition number。
S230, determining a preset concentration range corresponding to the semiconductor device based on the condition data sets corresponding to the reference doping concentrations respectively.
In an alternative embodiment, determining the preset concentration range corresponding to the semiconductor device based on the condition data sets corresponding to the reference doping concentrations respectively includes: determining at least two reference conductive concentrations based on the reference simulation data and the at least two reference doping concentrations, respectively; based on the reference conductive concentrations, performing preset sorting operation on the condition data sets corresponding to the reference doping concentrations respectively to obtain preset sorting results; and determining a preset concentration range corresponding to the semiconductor device based on the preset sequencing result.
In an alternative embodiment, determining a preset concentration range corresponding to the semiconductor device based on the preset sequencing result includes: under the condition that the preset sorting operation is descending sorting, taking the reference conductive concentration corresponding to the condition data set with the last first condition number larger than the second condition number in the preset sorting result as a first conductive concentration, and taking the reference conductive concentration corresponding to the condition data set with the first condition number smaller than or equal to the second condition number in the preset sorting result as a second conductive concentration; under the condition that the preset sorting operation is ascending sorting, taking the reference conductive concentration corresponding to the condition data set with the last first condition number smaller than or equal to the second condition number in the preset sorting result as a first conductive concentration, and taking the reference conductive concentration corresponding to the condition data set with the first condition number larger than the second condition number in the preset sorting result as a second conductive concentration; and determining a preset concentration range corresponding to the semiconductor device based on the first conductive concentration and the second conductive concentration.
As can be seen from the above examples, in the case where the preset sort operation is the descending sort, the first condition number is larger than the second condition number, and the first condition number is smaller than the second condition number as the reference conductive density decreases. In the case where the preset sort operation is an ascending sort, the first condition number is smaller than the second condition number, and the first condition number is larger than the second condition number as the reference conductive density increases.
Taking the above example as an example, the first conductive concentration and the second conductive concentration include 1 and. In one embodiment, specifically, a statistical value corresponding to the first conductive concentration and the second conductive concentration is used as a preset concentration threshold, and a preset concentration range corresponding to the semiconductor device is determined based on the preset concentration threshold.
The statistics may be, for example, a maximum value, a minimum value or an average value, which is not limited herein, and may be specifically set in a user-defined manner according to actual requirements.
In an alternative embodiment, the preset concentration threshold is taken as the largest preset conductive concentration in the preset concentration range, and the minimum value of the reference conductive concentrations smaller than the preset concentration threshold is taken as the smallest preset conductive concentration in the preset concentration range. Taking the above example as an example, if the statistical value is the maximum value, the preset concentration range may be 。
In another alternative embodiment, the preset concentration threshold is taken as the minimum preset conductive concentration in the preset concentration range, and the maximum value of the reference conductive concentrations greater than the preset concentration threshold is taken as the maximum preset conductive concentration in the preset concentration range. Taking the above example as an example, if the statistical value is the maximum value, the preset concentration range may be。
S240, current independent variables corresponding to grid points in a semiconductor grid model of the semiconductor device are obtained, and a current simulation equation set corresponding to the semiconductor device is constructed based on the current independent variables.
S250, performing one-time iterative solution operation on the current simulation equation set to obtain current simulation data corresponding to each grid point respectively; the current simulation data comprises the current electron concentration and the current hole concentration.
S260, judging whether the iteration ending condition is met, if not, executing S270, and if so, executing S280.
S270, for each grid point, determining the current conductive concentration of the grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to the grid point, updating the current independent variable of the grid point based on the judgment result of the current conductive concentration and the preset concentration range, and returning to S240.
S280, determining numerical simulation data of the semiconductor device based on current simulation data corresponding to each grid point.
The S240-S280 in this embodiment are the same as or similar to the S110-S150 shown in fig. 1 in the above embodiment, and the description of this embodiment is omitted here.
According to the technical scheme, a first Jacobian matrix corresponding to a first independent variable and a second Jacobian matrix corresponding to a second independent variable are determined based on device parameter data corresponding to a semiconductor device, and a condition data set is determined based on the reference doping concentration, the reference simulation data, the first Jacobian matrix and the second Jacobian matrix for each reference doping concentration in the device parameter data; the condition data set comprises a first condition number corresponding to the first Jacobian matrix and a second condition number corresponding to the second Jacobian matrix, and a preset concentration range corresponding to the semiconductor device is determined based on the condition data sets corresponding to the reference doping concentrations respectively, so that the problem of large error in manually self-defined preset concentration range setting is solved, the purpose of individually setting the preset concentration ranges matched with different semiconductor devices is achieved, and the accuracy of a simulation result of numerical simulation of the semiconductor device is further improved.
The following is an embodiment of a numerical simulation apparatus for a semiconductor device according to an embodiment of the present invention, which belongs to the same inventive concept as the numerical simulation method for a semiconductor device according to the above embodiment, and details of the numerical simulation apparatus for a semiconductor device, which are not described in detail in the embodiment, may be referred to in the above embodiment.
Fig. 4 is a schematic structural diagram of a numerical simulation apparatus for a semiconductor device according to an embodiment of the present invention. As shown in fig. 4, the apparatus includes: the current simulation equation set determination module 310, the current simulation data solving module 320, the current argument updating module 330 and the numerical simulation data determination module 340.
The current simulation equation set determining module 310 is configured to obtain current independent variables corresponding to grid points in a semiconductor grid model of the semiconductor device, and construct a current simulation equation set corresponding to the semiconductor device based on the current independent variables;
the current simulation data solving module 320 is configured to perform an iterative solving operation on the current simulation equation set to obtain current simulation data corresponding to each grid point respectively; the current simulation data comprise the current electron concentration and the current hole concentration;
The current independent variable updating module 330 is configured to determine, for each grid point, a current conductive concentration of the grid point based on a grid doping concentration, a current electron concentration, and a current hole concentration corresponding to the grid point, and update a current independent variable of the grid point based on a determination result of the current conductive concentration and a preset concentration range;
the numerical simulation data determining module 340 is configured to return to executing the step of constructing the current simulation equation set corresponding to the semiconductor device based on each current argument, until the iteration end condition is satisfied, and determine the numerical simulation data of the semiconductor device based on the current simulation data corresponding to each grid point.
According to the technical scheme, a current simulation equation set corresponding to the semiconductor device is constructed based on current independent variables corresponding to grid points in a semiconductor grid model of the semiconductor device, in the process of each iteration solving, the current conductive concentration of the grid points is determined based on the grid doping concentration corresponding to the grid points, the current electron concentration and the current hole concentration in current simulation data, and the current independent variables of the grid points are updated based on the judging result of the current conductive concentration and the preset concentration range, until the iteration ending condition is met, the numerical simulation data of the semiconductor device is determined, the problem that the equation set is constructed based on only a single independent variable in the traditional iteration solving algorithm is solved, the accuracy of the numerical simulation result of the semiconductor device is guaranteed, and the algorithm convergence speed requirement of the numerical simulation process of the semiconductor device is met.
In an alternative embodiment, the current argument update module 330 comprises:
and the current conductive concentration determining unit is used for taking a concentration difference value corresponding to the current electron concentration and the current hole concentration as a current difference value concentration and taking the sum of the current difference value concentration and the grid doping concentration as the current conductive concentration of the grid points.
In an alternative embodiment, the current argument update module 330 comprises:
a current independent variable updating unit, configured to take the first independent variable as a current independent variable of the grid point when the current conductive concentration meets a preset concentration range;
under the condition that the current conductive concentration does not meet the preset concentration range, taking the second independent variable as the current independent variable of the grid point;
when the maximum preset conductive concentration in the preset concentration range is smaller than or equal to a preset concentration threshold value, the first independent variable is potential, electron concentration and hole concentration, and the second independent variable is potential, electron quasi-fermi level and hole quasi-fermi level; when the minimum preset conductive concentration in the preset concentration range is greater than or equal to the preset concentration threshold, the first independent variables are the potential, the electron quasi-fermi level and the hole quasi-fermi level, and the second independent variables are the potential, the electron concentration and the hole concentration.
In an alternative embodiment, the apparatus further comprises:
the Jacobian matrix determining module is used for determining a first Jacobian matrix corresponding to a first independent variable and a second Jacobian matrix corresponding to a second independent variable based on device parameter data corresponding to a semiconductor device; wherein, the device parameter data comprises at least two reference doping concentrations;
a condition data set determining module for determining a condition data set based on the reference doping concentration, the reference simulation data, the first jacobian matrix, and the second jacobian matrix for each reference doping concentration; the condition data set comprises a first condition number corresponding to a first Jacobian matrix and a second condition number corresponding to a second Jacobian matrix;
the preset concentration range determining module is used for determining the preset concentration range corresponding to the semiconductor device based on the condition data sets corresponding to the reference doping concentrations respectively.
In an alternative embodiment, the condition data set determining module is specifically configured to:
substituting the reference simulation data and the reference doping concentration into a reference Jacobian matrix to obtain a target Jacobian matrix;
taking the product corresponding to the norm of the target Jacobian matrix as the reference condition number corresponding to the reference Jacobian matrix;
Wherein the reference condition number is a first condition number when the reference jacobian matrix is a first jacobian matrix and a second condition number when the reference jacobian matrix is a second jacobian matrix.
In an alternative embodiment, the preset concentration range determination module includes:
a reference conductivity concentration determining unit for determining at least two reference conductivity concentrations based on the reference simulation data and the at least two reference doping concentrations, respectively;
the preset sequencing result determining unit is used for executing preset sequencing operation on the condition data sets corresponding to the reference doping concentrations respectively based on the reference conductive concentrations to obtain preset sequencing results;
and the preset concentration range determining unit is used for determining the preset concentration range corresponding to the semiconductor device based on the preset sequencing result.
In an alternative embodiment, the preset concentration range determining unit is specifically configured to:
under the condition that the preset sorting operation is descending sorting, taking the reference conductive concentration corresponding to the condition data set with the last first condition number larger than the second condition number in the preset sorting result as a first conductive concentration, and taking the reference conductive concentration corresponding to the condition data set with the first condition number smaller than or equal to the second condition number in the preset sorting result as a second conductive concentration;
Under the condition that the preset sorting operation is ascending sorting, taking the reference conductive concentration corresponding to the condition data set with the last first condition number smaller than or equal to the second condition number in the preset sorting result as a first conductive concentration, and taking the reference conductive concentration corresponding to the condition data set with the first condition number larger than the second condition number in the preset sorting result as a second conductive concentration;
and determining a preset concentration range corresponding to the semiconductor device based on the first conductive concentration and the second conductive concentration.
The numerical simulation device of the semiconductor device provided by the embodiment of the invention can execute the numerical simulation method of the semiconductor device provided by any embodiment of the invention, and has the corresponding functional modules and beneficial effects of the execution method.
Fig. 5 is a schematic structural diagram of an electronic device according to an embodiment of the present invention. The electronic device 10 is intended to represent various forms of digital computers, such as laptops, desktops, workstations, servers, blade servers, mainframes, and other appropriate computers. Electronic equipment may also represent various forms of mobile devices, such as personal digital assistants, cellular telephones, smartphones, wearable devices (e.g., helmets, eyeglasses, watches, etc.), and other similar computing devices. The components shown herein, their connections and relationships, and their functions, are meant to be exemplary only, and are not meant to limit implementations of the inventions described and/or claimed herein.
As shown in fig. 5, the electronic device 10 includes at least one processor 11, and a memory, such as a Read Only Memory (ROM) 12, a Random Access Memory (RAM) 13, etc., communicatively connected to the at least one processor 11, in which the memory stores a computer program executable by the at least one processor 11, and the processor 11 may perform various suitable actions and processes according to the computer program stored in the Read Only Memory (ROM) 12 or the computer program loaded from the storage unit 18 into the Random Access Memory (RAM) 13. In the RAM 13, various programs and data required for the operation of the electronic device 10 may also be stored. The processor 11, the ROM 12 and the RAM 13 are connected to each other via a bus 14. An input/output (I/O) interface 15 is also connected to bus 14.
Various components in the electronic device 10 are connected to the I/O interface 15, including: an input unit 16 such as a keyboard, a mouse, etc.; an output unit 17 such as various types of displays, speakers, and the like; a storage unit 18 such as a magnetic disk, an optical disk, or the like; and a communication unit 19 such as a network card, modem, wireless communication transceiver, etc. The communication unit 19 allows the electronic device 10 to exchange information/data with other devices via a computer network, such as the internet, and/or various telecommunication networks.
The processor 11 may be a variety of general and/or special purpose processing components having processing and computing capabilities. Some examples of processor 11 include, but are not limited to, a Central Processing Unit (CPU), a Graphics Processing Unit (GPU), various specialized Artificial Intelligence (AI) computing chips, various processors running machine learning model algorithms, digital Signal Processors (DSPs), and any suitable processor, controller, microcontroller, etc. The processor 11 performs the respective methods and processes described above, such as the numerical simulation method of the semiconductor device provided in the above-described embodiment.
In some embodiments, the numerical simulation method of the semiconductor device provided in the above embodiments may be implemented as a computer program, which is tangibly embodied in a computer-readable storage medium, such as the storage unit 18. In some embodiments, part or all of the computer program may be loaded and/or installed onto the electronic device 10 via the ROM 12 and/or the communication unit 19. When the computer program is loaded into the RAM 13 and executed by the processor 11, one or more steps of the numerical simulation method of the semiconductor device described above may be performed. Alternatively, in other embodiments, the processor 11 may be configured to perform the numerical simulation method of the semiconductor device in any other suitable way (e.g. by means of firmware).
Various implementations of the systems and techniques described here above may be implemented in digital electronic circuitry, integrated circuit systems, field Programmable Gate Arrays (FPGAs), application Specific Integrated Circuits (ASICs), application Specific Standard Products (ASSPs), systems On Chip (SOCs), load programmable logic devices (CPLDs), computer hardware, firmware, software, and/or combinations thereof. These various embodiments may include: implemented in one or more computer programs, the one or more computer programs may be executed and/or interpreted on a programmable system including at least one programmable processor, which may be a special purpose or general-purpose programmable processor, that may receive data and instructions from, and transmit data and instructions to, a storage system, at least one input device, and at least one output device.
The computer program for implementing the numerical simulation method of a semiconductor device of the present invention may be written in any combination of one or more programming languages. These computer programs may be provided to a processor of a general purpose computer, special purpose computer, or other programmable data processing apparatus, such that the computer programs, when executed by the processor, cause the functions/acts specified in the flowchart and/or block diagram block or blocks to be implemented. The computer program may execute entirely on the machine, partly on the machine, as a stand-alone software package, partly on the machine and partly on a remote machine or entirely on the remote machine or server.
In the context of the present invention, a computer-readable storage medium may be a tangible medium that can contain, or store a computer program for use by or in connection with an instruction execution system, apparatus, or device. The computer readable storage medium may include, but is not limited to, an electronic, magnetic, optical, electromagnetic, infrared, or semiconductor system, apparatus, or device, or any suitable combination of the foregoing. Alternatively, the computer readable storage medium may be a machine readable signal medium. More specific examples of a machine-readable storage medium would include an electrical connection based on one or more wires, a portable computer diskette, a hard disk, a Random Access Memory (RAM), a read-only memory (ROM), an erasable programmable read-only memory (EPROM or flash memory), an optical fiber, a portable compact disc read-only memory (CD-ROM), an optical storage device, a magnetic storage device, or any suitable combination of the foregoing.
To provide for interaction with a user, the systems and techniques described here can be implemented on an electronic device having: a display device (e.g., a CRT (cathode ray tube) or LCD (liquid crystal display) monitor) for displaying information to a user; and a keyboard and a pointing device (e.g., a mouse or a trackball) through which a user can provide input to the electronic device. Other kinds of devices may also be used to provide for interaction with a user; for example, feedback provided to the user may be any form of sensory feedback (e.g., visual feedback, auditory feedback, or tactile feedback); and input from the user may be received in any form, including acoustic input, speech input, or tactile input.
The systems and techniques described here can be implemented in a computing system that includes a background component (e.g., as a data server), or that includes a middleware component (e.g., an application server), or that includes a front-end component (e.g., a user computer having a graphical user interface or a web browser through which a user can interact with an implementation of the systems and techniques described here), or any combination of such background, middleware, or front-end components. The components of the system can be interconnected by any form or medium of digital data communication (e.g., a communication network). Examples of communication networks include: local Area Networks (LANs), wide Area Networks (WANs), blockchain networks, and the internet.
The computing system may include clients and servers. The client and server are typically remote from each other and typically interact through a communication network. The relationship of client and server arises by virtue of computer programs running on the respective computers and having a client-server relationship to each other. The server can be a cloud server, also called a cloud computing server or a cloud host, and is a host product in a cloud computing service system, so that the defects of high management difficulty and weak service expansibility in the traditional physical hosts and VPS service are overcome.
It should be appreciated that various forms of the flows shown above may be used to reorder, add, or delete steps. For example, the steps described in the present invention may be performed in parallel, sequentially, or in a different order, so long as the desired results of the technical solution of the present invention are achieved, and the present invention is not limited herein.
The above embodiments do not limit the scope of the present invention. It will be apparent to those skilled in the art that various modifications, combinations, sub-combinations and alternatives are possible, depending on design requirements and other factors. Any modifications, equivalent substitutions and improvements made within the spirit and principles of the present invention should be included in the scope of the present invention.
Claims (8)
1. A numerical simulation method of a semiconductor device, comprising:
acquiring current independent variables corresponding to grid points in a semiconductor grid model of a semiconductor device, and constructing a current simulation equation set corresponding to the semiconductor device based on the current independent variables;
performing one-time iterative solving operation on the current simulation equation set to obtain current simulation data corresponding to each grid point respectively; the current simulation data comprise current electron concentration and current hole concentration;
For each grid point, determining the current conductive concentration of the grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to the grid point, and updating the current independent variable of the grid point based on the judgment result of the current conductive concentration and the preset concentration range;
returning to execute the step of constructing a current simulation equation set corresponding to the semiconductor device based on each current independent variable until the iteration end condition is met, and determining the numerical simulation data of the semiconductor device based on the current simulation data respectively corresponding to each grid point;
the determining the current conductive concentration of the grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to the grid point comprises:
taking a concentration difference value corresponding to the current electron concentration and the current hole concentration as a current difference value concentration, and taking the sum of the current difference value concentration and the grid doping concentration as a current conductive concentration of the grid points;
the updating the current independent variable of the grid point based on the judging result of the current conductive concentration and the preset concentration range comprises the following steps:
Under the condition that the current conductive concentration meets a preset concentration range, taking a first independent variable as the current independent variable of the grid point;
taking a second independent variable as the current independent variable of the grid point under the condition that the current conductive concentration does not meet the preset concentration range;
when the maximum preset conductive concentration in the preset concentration range is smaller than or equal to a preset concentration threshold, the first independent variable is potential, electron concentration and hole concentration, and the second independent variable is potential, electron quasi-fermi level and hole quasi-fermi level; when the minimum preset conductive concentration in the preset concentration range is greater than or equal to a preset concentration threshold, the first independent variables are potential, electron quasi-fermi level and hole quasi-fermi level, and the second independent variables are potential, electron concentration and hole concentration.
2. The method according to claim 1, wherein the method further comprises:
determining a first Jacobian matrix corresponding to a first independent variable and a second Jacobian matrix corresponding to a second independent variable based on device parameter data corresponding to the semiconductor device; wherein the device parameter data comprises at least two reference doping concentrations;
Determining, for each reference doping concentration, a set of condition data based on the reference doping concentration, reference simulation data, a first jacobian matrix, and a second jacobian matrix; the condition data set comprises a first condition number corresponding to the first Jacobian matrix and a second condition number corresponding to the second Jacobian matrix;
and determining a preset concentration range corresponding to the semiconductor device based on the condition data sets corresponding to the reference doping concentrations respectively.
3. The method of claim 2, wherein the determining the set of condition data based on the reference doping concentration, the reference simulation data, the first jacobian matrix, and the second jacobian matrix comprises:
substituting the reference simulation data and the reference doping concentration into a reference Jacobian matrix to obtain a target Jacobian matrix;
taking the product corresponding to the norm of the target Jacobian matrix as the reference condition number corresponding to the reference Jacobian matrix;
wherein the reference condition number is a first condition number when the reference jacobian matrix is a first jacobian matrix, and a second condition number when the reference jacobian matrix is a second jacobian matrix.
4. The method according to claim 2, wherein determining the preset concentration range corresponding to the semiconductor device based on the condition data sets corresponding to the reference doping concentrations, respectively, comprises:
determining at least two reference conductive concentrations based on the reference simulation data and at least two reference doping concentrations, respectively;
based on the reference conductive concentrations, performing preset sorting operation on the condition data sets corresponding to the reference doping concentrations respectively to obtain preset sorting results;
and determining a preset concentration range corresponding to the semiconductor device based on the preset sequencing result.
5. The method of claim 4, wherein determining a predetermined concentration range corresponding to the semiconductor device based on the predetermined ordering result comprises:
under the condition that the preset sorting operation is descending sorting, taking the reference conductive concentration corresponding to the condition data set with the last first condition number larger than the second condition number in the preset sorting result as a first conductive concentration, and taking the reference conductive concentration corresponding to the condition data set with the first condition number smaller than or equal to the second condition number in the preset sorting result as a second conductive concentration;
Under the condition that the preset sorting operation is ascending sorting, taking the reference conductive concentration corresponding to the condition data set with the last first condition number smaller than or equal to the second condition number in the preset sorting result as a first conductive concentration, and taking the reference conductive concentration corresponding to the condition data set with the first condition number larger than the second condition number in the preset sorting result as a second conductive concentration;
and determining a preset concentration range corresponding to the semiconductor device based on the first conductive concentration and the second conductive concentration.
6. A numerical simulation apparatus of a semiconductor device, comprising:
the system comprises a current simulation equation set determining module, a current simulation equation set determining module and a current simulation equation set determining module, wherein the current simulation equation set determining module is used for acquiring current independent variables corresponding to grid points in a semiconductor grid model of a semiconductor device respectively and constructing a current simulation equation set corresponding to the semiconductor device based on the current independent variables;
the current simulation data solving module is used for executing one iteration solving operation on the current simulation equation set to obtain current simulation data corresponding to each grid point respectively; the current simulation data comprise current electron concentration and current hole concentration;
The current independent variable updating module is used for determining the current conductive concentration of each grid point based on the grid doping concentration, the current electron concentration and the current hole concentration corresponding to the grid point, and updating the current independent variable of the grid point based on the judging result of the current conductive concentration and the preset concentration range;
the numerical simulation data determining module is used for returning to execute the step of constructing a current simulation equation set corresponding to the semiconductor device based on each current independent variable until the iteration ending condition is met, and determining the numerical simulation data of the semiconductor device based on the current simulation data corresponding to each grid point respectively;
wherein, the current argument updating module comprises:
a current conductivity concentration determining unit, configured to use a concentration difference value corresponding to the current electron concentration and the current hole concentration as a current difference value concentration, and use a sum of the current difference value concentration and the grid doping concentration as a current conductivity concentration of the grid point;
a current independent variable updating unit, configured to use a first independent variable as a current independent variable of the grid point when the current conductive concentration meets a preset concentration range;
Taking a second independent variable as the current independent variable of the grid point under the condition that the current conductive concentration does not meet the preset concentration range;
when the maximum preset conductive concentration in the preset concentration range is smaller than or equal to a preset concentration threshold, the first independent variable is potential, electron concentration and hole concentration, and the second independent variable is potential, electron quasi-fermi level and hole quasi-fermi level; when the minimum preset conductive concentration in the preset concentration range is greater than or equal to a preset concentration threshold, the first independent variables are potential, electron quasi-fermi level and hole quasi-fermi level, and the second independent variables are potential, electron concentration and hole concentration.
7. An electronic device, the electronic device comprising:
at least one processor; and
a memory communicatively coupled to the at least one processor; wherein,
the memory stores a computer program executable by the at least one processor to enable the at least one processor to perform the numerical simulation method of the semiconductor device of any one of claims 1-5.
8. A computer readable storage medium, characterized in that the computer readable storage medium stores computer instructions for causing a processor to implement the numerical simulation method of the semiconductor device of any one of claims 1-5 when executed.
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