CN109680329A - Growing method and system are melted based on melting zone height and crystal angle control zone - Google Patents
Growing method and system are melted based on melting zone height and crystal angle control zone Download PDFInfo
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- CN109680329A CN109680329A CN201810837682.XA CN201810837682A CN109680329A CN 109680329 A CN109680329 A CN 109680329A CN 201810837682 A CN201810837682 A CN 201810837682A CN 109680329 A CN109680329 A CN 109680329A
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- C—CHEMISTRY; METALLURGY
- C30—CRYSTAL GROWTH
- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
- C30B13/00—Single-crystal growth by zone-melting; Refining by zone-melting
- C30B13/28—Controlling or regulating
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- C—CHEMISTRY; METALLURGY
- C30—CRYSTAL GROWTH
- C30B—SINGLE-CRYSTAL GROWTH; UNIDIRECTIONAL SOLIDIFICATION OF EUTECTIC MATERIAL OR UNIDIRECTIONAL DEMIXING OF EUTECTOID MATERIAL; REFINING BY ZONE-MELTING OF MATERIAL; PRODUCTION OF A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; SINGLE CRYSTALS OR HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; AFTER-TREATMENT OF SINGLE CRYSTALS OR A HOMOGENEOUS POLYCRYSTALLINE MATERIAL WITH DEFINED STRUCTURE; APPARATUS THEREFOR
- C30B29/00—Single crystals or homogeneous polycrystalline material with defined structure characterised by the material or by their shape
- C30B29/02—Elements
- C30B29/06—Silicon
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- Engineering & Computer Science (AREA)
- Crystallography & Structural Chemistry (AREA)
- Materials Engineering (AREA)
- Metallurgy (AREA)
- Organic Chemistry (AREA)
- Crystals, And After-Treatments Of Crystals (AREA)
Abstract
The invention discloses one kind to melt growing method and system based on melting zone height and crystal angle control zone, radius and angle, upper melting zone height and lower melting zone height, melt volume, melt waist, fusing and the growth rate for establishing non-linear lower-order model prediction polycrystal material and crystal, form the proper trajectory of crystal growth；It is reference with the track, uses fine melt area height hGAnd crystal angleAdjustment adjustment supply voltage UgenWith speed v on polycrystal materialF, control the growth of crystal.The full automation of growing zone-melting monocrystal may be implemented in the present invention, different coil-types, different aimed dias and different machine components can be setup flexibly in the non-linear lower-order model that the present invention designs, and can also directly handle the dynamic change in single crystal growth process.The experience intervention for avoiding operator, can effectively improve the quality of production efficiency and zone melting single-crystal.
Description
Technical field
The invention belongs to study on floating zone silicon technical fields, relate to a kind of molten using melting zone height and crystal angle control zone
The method and system of crystal automatic growth.
Background technique
Currently, expansion shoulder is mainly carried out in the way of diameter using zone-melting process production silicon single crystal, in spite of fixed expansion shoulder work
Skill parameter, but operator can modify according to the experience of itself to shoulder technological parameter is expanded, for example, the increasing of modification heating power
Add the parameters such as the speed of growth of frequency or monocrystalline.It is found by multi-group data comparative analysis, used by different operators
Expand shoulder technological parameter and given expansion shoulder technological parameter is variant, most of operator can be during expanding shoulder to technique
Parameter is modified, and subjectivity is strong, easily occurs dislocation or other situations in single crystal growth process.
Summary of the invention
In order to reduce the experience intervention of operator, improving zone melting single-crystal production efficiency and reduce production cost, this hair
It is bright to propose that melting zone height and crystal angle automation expand the method and system of shoulder, guarantee the growth of dislocation-free single crystal, while can subtract
The participation of few operator, an operator can guard 3 even more zone melting furnaces.
In order to achieve the above objectives, the technical scheme of the present invention is realized as follows:
One kind melting growing method based on melting zone height and crystal angle control zone, establishes non-linear lower-order model prediction
The radius and angle of polycrystal material and crystal, upper melting zone height and lower melting zone height, melt volume, melt waist, fusing and growth
Rate forms the proper trajectory of crystal growth；It is reference with the track, uses fine melt area height hGAnd crystal angleAdjustment
Adjust supply voltage UgenWith speed v on polycrystal materialF, control the growth of crystal.
Further, model foundation and the step of control, include:
S1, model structure design, the dynamical system including nonlinear model and based on model control two parts；
The nonlinear model is using the canonical form of mathematical method optimization problem:
It submits toφ lb≤φ≤φ ub
gi(φ)≤0, i=1 ..., the additional quantity for not waiting constraints
hi(φ)=0, i=1 ..., the equal constraint of quantity
Wherein φoptIt is the optimal vector of design, J is scalar objective function, φ1bIt is the lower limit of design vector, φubDesign
The upper limit of vector, giInequality constraints and hiEquality constraint；The minimum value of objective function is Jopt=J (φopt)；Iteration is from setting
Count vector φoInitial value and target value J (φo) calculating start；If being unsatisfactory for termination condition, pass through mathematical method tune
The vector of whole design, and start new interative computation by calculating corresponding target value J；It is excellent if meeting the condition of convergence
Change and terminates；
Based on model dynamical system control in, use state spatial model, input, output and state be expressed as to
Amount；System mode vector x (t) indicates the state of system at any point in time；It includes measurable amount that system, which exports y (t),；For
Given original state x0With given list entries u (t), state vector x (t) and output vector y are calculated based on model equation
(t) variation；
withx(0)=x 0,
y(t)=h(t,x(t),u(t),Θ)
The model is single order coupled differential system.The time-derivative x (t) of state vector is provided by pattern function f；It is defeated
Function h provides the equation of computing system output y (t) out；Pattern function f and output function h depends on time t, state vector x
(t), input vector u (t) and model parameter vector θ；The variation of state vector x (t) is calculated by using numerical integrating.
S2, model and parameters identification；According to the mathematic sign of variable each in model, process variable parameter is identified,
Including polycrystal material radius RF, polycrystalline charge bar angle [alpha]F, the height h in upper melting zoneF, melting rate vMe, crystal radius RC, crystal angleThe height h in lower melting zoneC, crystalline rate vCr, it is seen that melt volume Vvi, the radius R of melt waistN.Auxiliary variable: melt body
Product Vbo, entire melting zone height hG, polycrystal material length LF, the distance H of polycrystal material frame to coil topF, crystal length LC, crystal frame
To the distance H of inductor bottomC；
S3, setting state estimator；According to the process value of time, crystal length and/or estimation, by reference to trajectory calculation
Reference value；Reference locus is set point that is constant or persistently changing；Cannot parameter measured directly, estimated according to the model of front
These variables are counted, and reflect the variation of these variables；
S4, verification；The step mainly the data of three steps in front are verified, principal security model it is accurate
Property, corresponding controller can be configured after being proved to be successful, and then carry out control experiment；
S5, setting control parameter；This step mainly controls input, output variable and state variable, makes state variable
With output variable close to reference value；
S6, control experiment；This step is mainly to reduce the error of reference value and output valve by adjusting operating value, with reality
The purpose of experiment is now controlled, feedback controller compensation control error e, is the difference between measured value or observation process values and reference value
Value；It is to be realized by the feedback cycle for the process values observed；The reference value that predictive controller is provided according to path generator
Manipulation value is calculated, this can be from empirically (such as using fixed mass (from the experience of growth experiment) or by mathematical model
Equilibrium equation) complete.
S7, control verification.This step is to be preferably minimized error to the check and correction of control experiment.
Further, the recognition methods of process variable parameter described in step S2 includes: to establish measuring system；Measurement system
System is measured using optical method, collects the image of polycrystalline charge bar, melting zone, crystal；It is handled by visual pattern to collection
Image handled, acquisition process variable parameter.
Further, in step S3, for cannot variable measured directly, select Kalman filter estimated；
The variable not directly measured is carried out mathematical formulae conversion according to mathematical model by Kalman filter, to realize estimating for variable
Meter.
Further, melting zone height, polycrystal material and crystal diameter, waist up and down are established by mathematical formulae in the model
Portion, the model for melting volume, fusing and crystalline rate form crystal diameter and crystal angleWith fine melt area height hGLetter
Number stablizes expansion shoulder process by the function；Wherein using melting zone height as reference, the formula of suitable melt waist is obtained
Are as follows:
Wherein: RNFor the radius of melt waist；hFFor the height in upper melting zone；hCFor the height in lower melting zone；RCFor crystal half
Diameter, nhFor application model parameter, nh=-0.9.
The present invention also provides one kind to melt crystal growth system, including measurement based on melting zone height and crystal angle control zone
System, mathematical model system, process planning system and control system；
The measuring system and mathematics model system are used to establish the half of non-linear lower-order model prediction polycrystal material and crystal
Diameter and angle, upper melting zone height and lower melting zone height, melt volume, melt waist, fusing and growth rate form crystal growth
Proper trajectory；
The process planning system and control system are used to the track be reference, use fine melt area height hGAnd crystal
AngleAdjustment adjustment supply voltage UgenWith speed v on polycrystal materialF, control the growth of crystal.
Further, the processing of the measuring system view-based access control model image is established, and is additionally provided with Kalman filter for estimating
Meter cannot variable measured directly.
Further, the mathematical model system includes the identification of related process variable, the foundation of equation and parameter
Identification selects different technological parameters according to the different crystal growth stages based on the feedback control of model.
Compared with prior art, the present invention have it is following the utility model has the advantages that
The present invention may be implemented the full automation of growing zone-melting monocrystal, and the non-linear lower-order model that the present invention designs can be with
Different coil-types, different aimed dias and different machine components is setup flexibly, it is raw can also directly to handle monocrystalline
Dynamic change in growth process.The experience intervention for avoiding operator, can effectively improve the quality of production efficiency and zone melting single-crystal.
Detailed description of the invention
Fig. 1 is the operational process schematic diagram of the feedback controller of the embodiment of the present invention；
Fig. 2 is the Nonlinear Model Predictive Control schematic diagram of the embodiment of the present invention；
Fig. 3 is that the crystal of the embodiment of the present invention expands shoulder schematic diagram；
Fig. 4 is the state-space model schematic diagram of the embodiment of the present invention.
Specific embodiment
It should be noted that in the absence of conflict, the feature in embodiment and embodiment in the present invention can phase
Mutually combination.
The technical scheme adopted by the invention is that predicting the radius of polycrystal material and crystal by establishing non-linear lower-order model
With angle, upper melting zone height and lower melting zone height, melt volume, melt waist, fusing and growth rate, it is raw to form a crystal
Long proper trajectory is reference with the suitable track, controls the growth of crystal.The model prediction accuracy is high, and the time is fast.Certainly
Dynamicization expands during shoulder, which uses fine melt area height hGAnd crystal angleAdjustment adjustment supply voltage UgenWith it is more
Crystalline substance expects upper speed vF, to guarantee that crystalchecked is grown.
The present invention establishes the model of a real-time control crystal growing process, in order to realize the application of the model, this hair
It is bright to create corresponding computer program, including measuring system, mathematical model, process planning and control system.Measuring system
It is the basis that controller calculates, the present invention is based on the processing of visual pattern to establish measuring system；Process of mathematical modeling includes correlation
The identification of process variable, the foundation of equation and parameter identification.This unsteady Model is to be feedback controlled to base with model
Plinth, all stages suitable for crystal growth；Process parameter value is most important to the stable growth of monocrystalline, therefore, according to not
The same crystal growth stage selects different technological parameters；For cannot variable measured directly, the present invention selects Kalman to filter
Wave device estimates these variables.Measuring system, state observer and feedback controller are installed on FZ machine.
The foundation of model of the present invention includes nonlinear model and dynamical system controls two parts, wherein nonlinear model
Type will use mathematics, and the canonical form of optimization problem is
It submits toφ lb≤φ≤φ ub
gi(φ)≤0, i=1 ..., the additional quantity for not waiting constraints
hi(φ)=0, i=1 ..., the equal constraint of quantity
Wherein φoptIt is the optimal vector of design, J is scalar objective function, φ1bIt is the lower limit of design vector, φubDesign
The upper limit of vector, giInequality constraints and hiEquality constraint.The minimum value of objective function is Jopt=J (φopt).Iteration is from setting
Count vector φoInitial value and target value J (φo) calculating start.If being unsatisfactory for termination condition, pass through mathematical method tune
The vector of whole design, and start new interative computation by calculating corresponding target value J.It is excellent if meeting the condition of convergence
Change and terminates.
In the dynamical system control based on model, it is as shown in Figure 4 that state-space model can be used.Input, output and
State is expressed as vector.System mode vector x (t) indicates the state of system at any point in time.System output y (t) includes can
The amount of measurement.For given original state x0With given list entries u (t), can based on model equation calculate state to
Measure the variation of x (t) and output vector y (t).
withx(0)=x 0,
y(t)=h(t,x(t),u(t),Θ)
The model is single order coupled differential system.The time-derivative x (t) of state vector is provided by pattern function f.It is defeated
Function h provides the equation of computing system output y (t) out.Pattern function f and output function h depends on time t, state vector x
(t), input vector u (t) and model parameter vector θ.It can be come by using numerical integrating (such as 4 rank Runge-Kutta)
Calculate the variation of state vector x (t).
Fig. 2 gives the sketch for the modern control system that one is made of the generator of reference locus, prediction and feedback control
Device processed, it is specified that equipment and state estimator.According to the process value (such as crystal diameter) of time, crystal length and/or estimation, lead to
It crosses path generator and calculates reference value (such as crystal diameter and melting zone height).Reference locus can be constant or persistently change
Set point.This model is related to more variable, have it is some can directly measure, and certain variables cannot directly measure (such as:
Melting rate, crystalline rate), it needs to estimate these variables according to the model of front, and reflect the variation of these variables.
The present invention reduces the error of reference value and output valve by adjusting operating value, to realize the purpose of control experiment.
Feedback controller compensation control error e, this is the difference between measured value (or observation process values) and reference value.This is to pass through sight
What the feedback cycle of the process values observed was realized.Predictive controller calculates manipulation according to the reference value that path generator provides
Value.This can from empirically (from the experience of growth experiment) or pass through mathematical model (such as equilibrium equation using fixed mass)
To complete.
In the present invention, the recognition methods of the process variable includes: that measuring system is established in the processing of view-based access control model image, is surveyed
Amount system mainly measured using optical method, by visual pattern handle obtain polycrystalline charge bar, melting zone, crystal it is several
A parameter.The camera processor of computer end dress handles the image of collection, to obtain model parameter.Known by measuring system
Other process variable；For cannot variable measured directly, select Kalman filter estimated.Kalman filter is according to number
It learns model and some variables not directly measured is subjected to mathematical formulae conversion, to realize the estimation of variable.Such as melting rate,
Crystalline rate etc..
Substantially the system of non-linear lower-order model gives the work of different machines component, different coil-types and different-diameter
Skill condition, the model may be implemented automation area and melt process.Melting zone height, polycrystal material and crystal up and down are established by mathematical formulae
Diameter, waist, the model for melting volume, fusing and crystalline rate, form crystal diameter and crystal angle φCWith fine melt area height
hGFunction, by the function make expand shoulder process stablize.Wherein, in order to overcome the problems, such as the measurement of melt waist, by fine melt area height
Spend hGIt is applied in automation as auxiliary quantity, to obtain suitable melt waist.It can come using melting zone height as reference
To suitable melt waist, relationship of the following equation between melt waist and melt height.
Note: application model parameter nh=-0.9.
It is the feedback controller operational process based on model as shown in Figure 1, describes the feedback controller based on model
Task sequence includes mainly 7 steps, is respectively: model structure design, model and parameters identification, setting state estimator, school
It tests, control parameter, control experiment and verification is set.
It is that in the past and the comparison of the following nonlinear model control forecasting, past model is without reference to line, pre- as shown in Figure 2
The limitation of range and control range is surveyed, following nonlinear model has control range H in terms of input controlu, forecasting system shape
There is estimation range to limit H in terms of statepWith reference line r, illustrate that nonlinear model is more accurate than past prediction.
As shown in figure 3, some parameters are identified in figure.
Input variable: generator power Pgen, upper speed vFWith lower speed vC。
State variable: polycrystal material radius RF, polycrystalline charge bar angle [alpha]F, the height h in upper melting zoneF, melting rate vMe, crystal half
Diameter RC, crystal angleThe height h in lower melting zoneC, crystalline rate vCr, it is seen that melt volume Vvi, the radius R of melt waistN.It is auxiliary
Help variable: melt volume Vbo, entire melting zone height hG, polycrystal material length LF, the distance H of polycrystal material frame to coil topF, crystal
Length LC, the distance H of crystal frame to inductor bottomC。
The foregoing describe the contents such as basic principles and main features of the invention and embodiment, but the present invention is not by upper
The limitation for stating implementation process, under the premise of not departing from invention thought and range, the present invention can also have various changes and modifications.
Therefore, unless this changes and improvements are departing from the scope of the present invention, they should be counted as comprising in the present invention.
Claims (8)
1. one kind melts growing method based on melting zone height and crystal angle control zone characterized by comprising establish non-thread
Property the lower-order model prediction polycrystal material and radius and angle of crystal, upper melting zone height and lower melting zone height, melt volume, melt waist
Portion, fusing and growth rate form the proper trajectory of crystal growth；It is reference with the track, uses fine melt area height hGWith
Crystal angleAdjustment adjustment supply voltage UgenWith speed v on polycrystal materialF, control the growth of crystal.
2. it is according to claim 1 a kind of based on the molten growing method of melting zone height and crystal angle control zone, it is special
Sign is that model foundation includes: with the step of control
S1, model structure design, the dynamical system including nonlinear model and based on model control two parts；
The nonlinear model is using the canonical form of mathematical method optimization problem:
It submits toφ lb≤φ≤φ ub
gi(φ)≤0, i=1 ... adds the quantity for not waiting constraints
hi(φ)=0, i=1 ..., the equal constraint of quantity
Wherein φoptIt is the optimal vector of design, J is scalar objective function, φlbIt is the lower limit of design vector, φubDesign vector
The upper limit, giInequality constraints and hiEquality constraint；The minimum value of objective function is Jopt=J (φopt)；Iteration is sweared from design
Measure φoInitial value and target value J (φo) calculating start；If being unsatisfactory for termination condition, set by mathematical method adjustment
The vector of meter, and start new interative computation by calculating corresponding target value J；If meeting the condition of convergence, optimize end
Only；
In the dynamical system control based on model, use state spatial model, input, output and state are expressed as vector；System
The state of state vector x (t) expression system of uniting at any point in time；It includes measurable amount that system, which exports y (t),；For given
Original state x0With given list entries u (t), state vector x (t) and output vector y's (t) are calculated based on model equation
Variation；
y(t)=h(t,x(t) t,u(t),θ)
The model is single order coupled differential system.The time-derivative x (t) of state vector is provided by pattern function f；Export letter
Number h provide the equation of computing system output y (t)；Pattern function f and output function h depend on time t, state vector x (t),
Input vector u (t) and model parameter vector θ；The variation of state vector x (t) is calculated by using numerical integrating.
S2, model and parameters identification；According to the mathematic sign of variable each in model, process variable parameter is identified, including
Polycrystal material radius RF, polycrystalline charge bar angle [alpha]F, the height h in upper melting zoneF, melting rate vMe, crystal radius RC, crystal angleUnder
The height h in melting zoneC, crystalline rate vCr, it is seen that melt volume Vvi, the radius R of melt waistN.Auxiliary variable: melt volume Vbo,
Entire melting zone height hG, polycrystal material length LF, the distance H of polycrystal material frame to coil topF, crystal length LC, crystal frame to induction
The distance H of device bottomC；
S3, setting state estimator；According to the process value of time, crystal length and/or estimation, referred to by reference to trajectory calculation
Value；Reference locus is set point that is constant or persistently changing；Cannot parameter measured directly, this is estimated according to the model of front
A little variables, and reflect the variation of these variables；
S4, verification；The step mainly verifies the data of three steps in front, the accuracy of principal security model,
Corresponding controller can be configured after being proved to be successful, and then carry out control experiment；
S5, setting control parameter；This step mainly controls input, output variable and state variable, makes state variable and defeated
Variable is close to reference value out；
S6, control experiment；This step is mainly to reduce the error of reference value and output valve by adjusting operating value, to realize control
The purpose of experiment is made, feedback controller compensation control error e, is the difference between measured value or observation process values and reference value；
It is to be realized by the feedback cycle for the process values observed；Predictive controller is counted according to the reference value that path generator provides
Manipulation value is calculated, this can be from empirically (such as using the flat of fixed mass (from the experience of growth experiment) or by mathematical model
Weighing apparatus equation) it completes.
S7, control verification.This step is to be preferably minimized error to the check and correction of control experiment.
3. it is according to claim 2 a kind of based on the molten growing method of melting zone height and crystal angle control zone, it is special
Sign is that the recognition methods of process variable parameter described in step S2 includes: to establish measuring system；Measuring system utilizes optical
Method measures, and collects the image of polycrystalline charge bar, melting zone, crystal；It is handled to the image of collection by visual pattern
Reason, acquisition process variable parameter.
4. one kind according to claim 2 or 3 melts growing method based on melting zone height and crystal angle control zone,
Be characterized in that, in step S3, for cannot variable measured directly, select Kalman filter estimated；Kalman filtering
The variable not directly measured is carried out mathematical formulae conversion according to mathematical model by device, to realize the estimation of variable.
5. it is according to claim 1 a kind of based on the molten growing method of melting zone height and crystal angle control zone, it is special
Sign is, in the model by mathematical formulae establish up and down melting zone height, polycrystal material and crystal diameter, waist, fusing volume,
The model of fusing and crystalline rate forms crystal diameter and crystal angleWith fine melt area height hGFunction, pass through the function
Stablize expansion shoulder process；Wherein using melting zone height as reference, the formula of suitable melt waist is obtained are as follows:
Wherein: RNFor the radius of melt waist；hFFor the height in upper melting zone；hCFor the height in lower melting zone；RCFor crystal radius, nhFor
Application model parameter, nh=-0.9.
6. one kind melts crystal growth system based on melting zone height and crystal angle control zone, which is characterized in that including measuring system,
Mathematical model system, process planning system and control system；
The measuring system and mathematics model system be used to establish non-linear lower-order model prediction polycrystal material and crystal radius and
Angle, upper melting zone height and lower melting zone height, melt volume, melt waist, fusing and growth rate, form the conjunction of crystal growth
Suitable track；
The process planning system and control system are used to the track be reference, use fine melt area height hGAnd crystal angleAdjustment adjustment supply voltage UgenWith speed v on polycrystal materialF, control the growth of crystal.
7. it is according to claim 6 a kind of based on the molten crystal growth system of melting zone height and crystal angle control zone, it is special
Sign is, the processing of the measuring system view-based access control model image is established, be additionally provided with Kalman filter for estimate cannot be direct
The variable of measurement.
8. it is according to claim 6 a kind of based on the molten crystal growth system of melting zone height and crystal angle control zone, it is special
Sign is that the mathematical model system includes the identification of related process variable, the foundation of equation and the identification of parameter with model
Feedback control based on, different technological parameters is selected according to the different crystal growth stages.
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Cited By (1)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN118315002A (en) * | 2024-06-03 | 2024-07-09 | 华侨大学 | Ternary semiconductor material epitaxial growth numerical simulation method |
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| EP0821082A1 (en) * | 1996-06-27 | 1998-01-28 | Wacker Siltronic Gesellschaft für Halbleitermaterialien Aktiengesellschaft | Process and apparatus for controlling the growth of a crystal |
| CN1425808A (en) * | 2001-12-12 | 2003-06-25 | 中国科学院物理研究所 | Remote control crystal growing device and its control method |
| WO2014033212A1 (en) * | 2012-08-30 | 2014-03-06 | Forschungsverbund Berlin E.V. | Model predictive control of the zone-melting process |
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Cited By (2)
| Publication number | Priority date | Publication date | Assignee | Title |
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| CN118315002A (en) * | 2024-06-03 | 2024-07-09 | 华侨大学 | Ternary semiconductor material epitaxial growth numerical simulation method |
| CN118315002B (en) * | 2024-06-03 | 2024-10-11 | 华侨大学 | Ternary semiconductor material epitaxial growth numerical simulation method |
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Application publication date: 20190426 |