A method for optimizing process parameters in VCSEL epitaxial wafer manufacturing

Abstract

This invention belongs to the field of semiconductor device manufacturing process control technology, specifically relating to a method for optimizing process parameters in VCSEL epitaxial wafer production. The method includes: constructing a multi-loop PID control system based on process parameters and key quality indicators during VCSEL epitaxial wafer growth; online identification of the ARX model during PID control system operation; calculation of the steady-state process gain matrix characterizing the steady-state causal relationship of the system; identification of the coupling direction based on the sign of the steady-state gain; and calculation of the antagonistic coupling strength factor and the cooperative coupling strength factor. The PID controller gain is then dynamically adjusted to achieve control of the epitaxial wafer growth process. This invention improves the response speed and robustness of each control loop while ensuring the overall stability of the multivariable control system, effectively reducing layer thickness and composition fluctuations caused by parameter drift and strong coupling during VCSEL epitaxial wafer growth, and improving the growth accuracy of the epitaxial wafer.

Description

Technical Field

[0001] This invention relates to the field of semiconductor device manufacturing process control technology. More specifically, this invention relates to a method for optimizing process parameters in VCSEL epitaxial wafer production. Background Technology

[0002] With the rapid development of fields such as optical communication, 3D sensing, and lidar, vertical-cavity surface-emitting lasers (VCSELs) have become key core devices due to their advantages such as low power consumption, high modulation rate, and ease of integration into two-dimensional arrays. Their performance is highly dependent on the growth quality of epitaxial wafers, especially the thickness and compositional uniformity of distributed Bragg mirrors (DBRs) and active quantum well structures. Currently, metal-organic chemical vapor deposition (MOCVD) is the mainstream process for preparing VCSEL epitaxial wafers. This process involves complex physicochemical reactions and requires extremely high precision in controlling process parameters such as temperature and gas flow rate.

[0003] In traditional MOCVD control, multivariable control systems typically employ fixed-parameter PID controllers, with each loop operating independently or linked only through simple feedforward decoupling. However, the epitaxial growth of VCSELs is a dynamic process lasting several hours. During this time, the thermal field distribution, gas flow field, and volatilization characteristics of the MO source within the reaction chamber all change slowly over time. This results in time-varying and nonlinear coupling relationships between the control loops within the system. For example, adjusting the heating power not only affects the wafer temperature but also alters the MO source's decomposition efficiency, thus impacting the growth rate. Conversely, changes in carrier gas flow rate also affect the temperature field by removing heat. If this dynamic coupling is not effectively suppressed, it can easily trigger control oscillations, leading to uneven DBR periodic layer thickness or quantum well compositional deviations, severely impacting device yield. Summary of the Invention

[0004] To address the technical problem that traditional MOCVD fixed PID control cannot handle time-varying nonlinear coupling, leading to uneven VCSEL epitaxial wafer thickness and compositional deviations, which severely affect device yield, this invention provides a method for optimizing VCSEL epitaxial wafer manufacturing process parameters, including:

[0005] Process parameters and key quality indicators during the VCSEL epitaxial wafer growth process are collected. A multi-loop PID control system is constructed based on these parameters and indicators. During the operation of the PID control system, the ARX model is identified online. Based on the identified ARX model, the steady-state process gain matrix, which characterizes the steady-state causal relationship of the system, is calculated. The direction of coupling is identified based on the sign of the steady-state gain in the steady-state process gain matrix, and the antagonistic coupling strength factor and the cooperative coupling strength factor are calculated respectively. The PID controller gain is dynamically adjusted based on the antagonistic coupling strength factor and the cooperative coupling strength factor, and the dynamically adjusted control signal is output to achieve epitaxial wafer growth process control.

[0006] This invention collects process parameters and key quality indicators during the growth of VCSEL epitaxial wafers and constructs a multi-loop PID control system. This system can monitor and control key parameters during the epitaxial wafer growth process in real time. By identifying the ARX model online during the operation of the PID control system, the dynamic characteristics of the reaction chamber that change slowly over time can be continuously tracked. Based on the identified ARX model, the steady-state process gain matrix is ​​calculated. The steady-state gain sign is analyzed to identify the direction of coupling and to calculate the asymmetric coupling strength factor. Based on the antagonistic coupling strength factor and the cooperative coupling strength factor, the PID controller gain is dynamically adjusted. This enables intelligent differentiation of coupling effects and differentiated handling of harmful and beneficial couplings. Thus, while ensuring system stability, the control performance is improved, effectively reducing layer thickness and composition fluctuations caused by parameter drift and strong coupling during the growth process, and improving the growth accuracy and batch consistency of epitaxial wafers.

[0007] Preferably, the process parameters include the MFC setting value of TMGa and the heater power setting value; the key quality indicators include the epitaxial growth rate and the wafer surface temperature.

[0008] Preferably, the multi-loop PID control system includes: normalizing the collected process parameters and key quality indicators respectively; constructing loop one, where the process variable is the normalized epitaxial wafer growth rate and the controller output is the normalized MFC setpoint of TMGa; and constructing loop two, where the process variable is the normalized wafer surface temperature and the controller output is the normalized heater power setpoint.

[0009] This invention eliminates dimensional differences between variables by normalizing process parameters and key quality indicators, ensuring all variables are within the same numerical range. This improves the numerical stability and convergence speed of the subsequent online identification algorithm. The two loops constructed in this invention control the epitaxial growth rate and wafer surface temperature, respectively, covering the most critical control requirements in the VCSEL epitaxial process. The normalized control system makes the controller gain parameter settings more intuitive and consistent, avoiding the problem of unbalanced control performance caused by differences in the magnitude of dependent variables. This ensures the overall coordination and stability of the multivariable control system and provides a high-quality data foundation for subsequent coupling analysis and intelligent gain scheduling.

[0010] Preferably, the online identification employs the recursive least squares method.

[0011] Preferably, the steady-state process gain matrix is ​​obtained by taking the limit value of the transfer function matrix at zero frequency, and the transfer function matrix is ​​obtained by performing a Z-transform on the online identified ARX model.

[0012] Preferably, the step of identifying the direction of coupling based on the sign of the steady-state gain in the steady-state process gain matrix, and calculating the antagonistic coupling strength factor and the cooperative coupling strength factor respectively, includes: when Time loop The controller for the loop Coupling gain of process variables and Time loop The controller for the loop The main gain of the process variable When the signs are opposite, it is antagonistic coupling, and the antagonistic coupling strength factor is... The synergistic coupling strength factor is ;when Time loop The controller for the loop Coupling gain of process variables and Time loop The controller for the loop The main gain of the process variable When the symbols are the same, it is cooperative coupling; the strength factor of antagonistic coupling is... The synergistic coupling strength factor is ;in, To prevent hyperparameters with a denominator of zero.

[0013] This invention identifies the direction of coupling by analyzing the sign of steady-state gain, accurately distinguishing between two distinct coupling effects: antagonistic coupling and cooperative coupling. When the coupling gain and the main gain have opposite signs, it is defined as antagonistic coupling; when they have the same sign, it is defined as cooperative coupling. This invention uses a relative coupling strength measurement method, dividing the coupling gain by the main gain to obtain a dimensionless ratio, which serves as the antagonistic coupling strength factor and the cooperative coupling strength factor. This makes systems of different magnitudes comparable, enabling the control system to more reasonably assess the importance of coupling effects and providing a quantitative basis for subsequent differentiated control strategies. It avoids the problem of overly conservative control strategies caused by treating all couplings as harmful interferences.

[0014] Preferably, the dynamic adjustment of the PID controller gain includes: setting a set of reference gain parameters for each loop, including a reference proportional gain, a reference integral gain, and a reference derivative gain; dynamically adjusting the reference proportional gain, reference integral gain, and reference derivative gain according to the antagonistic coupling strength factor and the cooperative coupling strength factor reference gain parameters, respectively, to obtain the actual proportional gain, actual integral gain, and actual derivative gain; wherein, Time loop Actual proportional gain for: , for The adversarial inhibition coefficient at any given time. for The cooperative inhibition coefficient at time t, and ; for Time loop loop The antagonistic coupling strength factor; for Time loop loop The synergistic coupling strength factor.

[0015] This invention sets a reference gain parameter for each loop and dynamically adjusts it based on the adversarial coupling strength factor and the cooperative coupling strength factor, thereby realizing intelligent scheduling of the controller gain. By making the adversarial suppression coefficient greater than the cooperative suppression coefficient, a differentiated coupling processing mechanism is constructed, which strongly suppresses harmful coupling and moderately tolerates beneficial coupling. When adversarial coupling increases, the controller gain decreases significantly, effectively suppressing harmful interference. When cooperative coupling increases, the controller gain decreases slightly, maintaining system stability while making full use of beneficial coupling. While ensuring system stability, the system's response performance is maintained to the maximum extent, effectively solving the problems of control oscillation and slow response caused by coupling effects during VCSEL epitaxial wafer growth.

[0016] Preferably, the method for obtaining the antagonistic inhibition coefficient and the cooperative inhibition coefficient is as follows: Covariance matrix of parameter estimation at time step traces as System stability index at time The parameter estimation covariance matrix is ​​the parameter obtained during online identification of the ARX model; according to System stability index at time and benchmark stability index Obtain the antagonistic inhibition coefficient and the coefficient of synergistic inhibition : , .

[0017] This invention utilizes the trace of the parameter estimation covariance matrix as a system stability index. When the system is running stably and the model converges well, the trace of the parameter estimation covariance matrix is ​​small, and vice versa. This invention achieves intelligent perception and response to the system state by comparing the current system stability index with the benchmark stability index and adaptively adjusting the antagonistic suppression coefficient and the cooperative suppression coefficient. When the system stability decreases, both the antagonistic suppression coefficient and the cooperative suppression coefficient will increase, but the growth rate of the antagonistic suppression coefficient is greater than that of the cooperative suppression coefficient, ensuring that the suppression of harmful coupling is always greater than the suppression of beneficial coupling. The adaptive mechanism of the antagonistic suppression coefficient and the cooperative suppression coefficient in this invention enables the control system to intelligently adjust the control strategy according to the real-time process state, optimizing control performance while ensuring stability.

[0018] Preferably, the output of the dynamically adjusted control signal to realize the epitaxial wafer growth process control includes: for each loop, using an incremental PID algorithm, calculating the increment of the controller output based on the dynamically adjusted gain, accumulating the increment to the control signal at the previous moment to obtain the control signal at the current moment, performing inverse normalization on the control signal at the current moment, and sending it to the corresponding actuator of the MOCVD equipment to complete one dynamic adjustment of the growth process.

[0019] Preferably, the method is repeated in each control sampling cycle until the entire epitaxial wafer growth process is completed.

[0020] The beneficial effects of this invention are as follows: By constructing a multi-loop PID control system and using the recursive least squares method to identify the dynamic characteristics of the reaction chamber online, a dimensionless parameter matrix that can reflect the real state of the system in real time is obtained. Based on this, a steady-state gain matrix is ​​obtained based on the online identified ARX model. By analyzing the sign of the steady-state gain matrix, the concepts of antagonistic coupling strength factor and cooperative coupling strength factor are proposed, realizing intelligent identification of antagonistic and cooperative coupling effects. The gain of the PID controller is differentially suppressed by the antagonistic coupling strength factor and cooperative coupling strength factor, realizing strong constraints on harmful couplings and rational utilization of beneficial couplings. Under the premise of ensuring the overall stability of the multivariable control system, the response speed and robustness of each control loop are significantly improved, and the layer thickness and composition fluctuations caused by parameter drift and strong coupling during the growth process are effectively reduced. This greatly improves the growth accuracy and batch consistency of VCSEL epitaxial wafers, providing a reliable technical guarantee for the large-scale production of high-performance VCSEL devices. Attached Figure Description

[0021] Figure 1 This is a flowchart illustrating a method for optimizing VCSEL epitaxial wafer manufacturing process parameters according to the present invention;

[0022] Figure 2 This is a schematic diagram showing the changes in the antagonistic coupling strength factor and the cooperative coupling strength factor of loop 1 to loop 2;

[0023] Figure 3 This is a schematic diagram showing the changes in the antagonistic coupling strength factor and the cooperative coupling strength factor of loop 2 to loop 1;

[0024] Figure 4 This is a schematic diagram illustrating the performance of process variable tracking.

[0025] Figure 5 This is a schematic diagram of the controller output. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some, not all, of the embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] The specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0028] This invention discloses a method for optimizing process parameters in the production of VCSEL epitaxial wafers, referring to... Figure 1 This includes steps S1 to S5:

[0029] S1. Collect process parameters and key quality indicators during the growth of VCSEL epitaxial wafers.

[0030] Specifically, the process parameters include the setpoints of the trimethylgallium (TMGa) mass flow controller (MFC) and the heater power setpoints. The key quality indicators include the epitaxial growth rate and the wafer surface temperature.

[0031] In this embodiment, the process parameters are collected in real time by reading the control system interface of the MOCVD equipment, the epitaxial growth rate is collected in real time by a reflectometer, and the wafer surface temperature is collected in real time by an optical pyrometer in the MOCVD equipment. In this embodiment, the sampling frequency is set to 1Hz, that is, the process parameters and key quality indicators are collected once every 1 second. In other embodiments, the implementer can set the sampling frequency according to the actual implementation situation, such as 0.5Hz, 2Hz or 5Hz.

[0032] It should be noted that the reflectometer obtains growth rate information in real time by monitoring the change in reflectivity of light of a specific wavelength on the wafer surface. In this embodiment, the reflectometer uses a helium-neon laser as the light source with a wavelength of 632.8 nanometers, which has good sensitivity to commonly used VCSEL materials such as GaAs / AlAs. During epitaxial layer growth, due to the difference in refractive index of the materials, the reflectivity will oscillate periodically with the change in film thickness. After each monolayer growth, the reflectivity will exhibit one complete oscillation cycle. By calculating the frequency of the reflectivity oscillation, the real-time growth rate can be accurately obtained. The optical pyrometer measures the intensity of infrared radiation emitted from the wafer surface and converts it into a temperature value according to Planck's radiation law, achieving non-contact temperature measurement. Both the reflectometer and the optical pyrometer are standard configurations of the MOCVD system, providing high-precision, real-time process parameter feedback, providing a reliable data foundation for subsequent process parameter optimization.

[0033] S2. Construct a multi-loop PID control system based on process parameters and key quality indicators. During the operation of the PID control system, perform online identification of the ARX model.

[0034] It should be noted that the growth of VCSEL epitaxial wafers is a precise process lasting several hours. During this period, the MOCVD reaction chamber is not a static system. For example, the temperature characteristics of the graphite disk in the reaction chamber will change slightly due to prolonged heating, leading to changes in thermal radiation characteristics; the output flow rate of the metal-organic (MO) source will also experience slight drift due to a decrease in cylinder pressure; the accumulation of deposits on the reaction chamber walls will alter gas flow characteristics; and changes in the growth state of the wafer surface will affect the adsorption and decomposition processes of reactants. These factors all cause slow changes in the dynamic characteristics of the MOCVD reaction chamber, making fixed-model-based control strategies ineffective. Therefore, this invention employs an online identification method to capture the dynamic response within the reaction chamber in real time and accurately compensate for disturbances during the growth process.

[0035] It should be further explained that, in order to avoid inconsistencies in dimensions caused by directly using the collected process parameters and key quality indicators for online identification, which would affect the identification accuracy and control effect, this invention normalizes the collected process parameters and key quality indicators respectively to eliminate the dimensional differences between different data.

[0036] Specifically, each collected process parameter and key quality indicator is linearly normalized, mapping them to a dimensionless interval of [0,1]. In other embodiments, implementers may choose a normalization method, such as standardization, based on the actual implementation situation.

[0037] Furthermore, a multi-loop PID control system is constructed based on the normalized key quality indicators and process parameters, wherein the process variables in loop one are... The controller outputs the normalized growth rate. The MFC setpoint for normalized TMGa; process variables in loop two. The controller outputs the normalized wafer surface temperature. This is the normalized heater power setting.

[0038] During the operation of the PID control system, a multivariate autoregressive exogenous (ARX) model is constructed:

[0039]

[0040] In the formula, , is the output vector of the ARX model. For PID control system The process variables of time loop one, i.e. Time-normalized growth rate For PID control system The process variables of time loop two, i.e. The wafer surface temperature after time-normalization; The regression vector is 8×1, containing historical process variables and historical controller output, specifically... ,in , They are respectively The process variables of loop one and loop two at time points, , They are respectively The process variables of loop one and loop two at time points, , They are respectively The controller outputs of loop one and loop two at specific times. , They are respectively The controller outputs of loop one and loop two at specific times; It is an 8×2 parameter matrix. Based on historical data The predicted value; It is a 2×1 noise vector. This reflects the actual measured value. And the current model Predicted value The prediction error between them.

[0041] Furthermore, the recursive least squares method is used to perform online identification of the ARX model, obtaining the ARX model at each time step. Corresponding parameter matrix And the parameter estimation covariance matrix within the recursive least squares algorithm. The parameter matrix can continuously track the dynamic characteristics that change slowly over time within the reaction chamber, and the parameter estimation covariance matrix can reflect the degree of uncertainty in the model parameter estimation, i.e., the accuracy and reliability of the parameter estimation.

[0042] It should be noted that the ARX model predicts current process variables using historical data. The current growth rate and wafer temperature depend not only on the current TMGa flow rate and heater power, but also on control and process variables from multiple past moments. For example, when the TMGa flow rate is increased, the growth rate does not immediately reach a new stable value but requires a transition period. Similarly, changes in heater power will not be fully reflected in the wafer temperature for some time. The ARX model captures this time delay and dynamic change characteristic. In this embodiment, the ARX model considers the impact of historical data from the previous two moments on the current state. This means that the system simultaneously considers the TMGa flow rate, heater power, growth rate, and wafer temperature data from the two most recent sampling periods to predict the current growth rate and wafer temperature. This allows the model to accurately reflect the dynamic characteristics of the system while avoiding excessive computational burden due to model overcomplexity.

[0043] It should be further noted that recursive least squares is a standard method in the field of system identification, which is based on actual measured values. Compared with the current model Predicted value The prediction error is used to iteratively update the parameter matrix describing the dynamic response of the process. This update process uses a progressively recursive parameter estimation covariance matrix to calculate the optimal correction gain, adjusting the parameter matrix in the direction of reducing prediction error. Furthermore, a forgetting factor is introduced to gradually reduce the influence weight of old data, thereby ensuring that the estimated parameter matrix can continuously track the slowly changing dynamic characteristics within the reaction chamber over time. The forgetting factor assigns higher weight to new data. When the forgetting factor is close to 1, the influence of old data decays slowly, suitable for slow-changing processes. When the forgetting factor is small, the influence of old data decays quickly, suitable for fast-changing processes. In the VCSEL epitaxial growth process, the characteristics of the reaction chamber change relatively slowly; therefore, the forgetting factor is typically set to 0.98-0.99. In this embodiment, the forgetting factor is set to 0.99. In other embodiments, the implementer can set the forgetting factor according to the actual implementation situation.

[0044] Thus, at every moment Each of these methods can obtain a dimensionless parameter matrix that is updated in real time and describes the current dynamic characteristics of the reaction chamber. And the parameter estimation covariance matrix, which reflects the uncertainty of model parameter estimation. The parameter matrix defines the ARX model at the current moment, providing a data foundation for subsequent calculations of coupling strength.

[0045] S3. Based on the ARX model identified online, calculate the steady-state process gain matrix that can characterize the steady-state causal relationship of the system. Identify the direction of coupling based on the sign of the steady-state gain in the steady-state process gain matrix, and calculate the antagonistic coupling strength factor and the cooperative coupling strength factor respectively.

[0046] It is important to note that simply treating all inter-loop interactions as harmful interference will lead to an overly conservative control strategy, sacrificing unnecessary system performance. In MOCVD growth, coupling effects have a clear physical directionality. For example, when the growth rate is low and an increase in TMGa flow is needed, if the temperature is also low, the action of increasing heating power in the temperature loop will actually help increase the growth rate by promoting MO source decomposition—this is a beneficial synergistic coupling. Conversely, if the growth rate is high and a decrease in TMGa is needed, the heating action becomes an antagonistic coupling. In the growth of VCSEL epitaxial wafers, especially when growing critical structures such as DBR mirrors or quantum wells, extremely high layer thickness control accuracy is required, typically requiring an error of less than 1%. If the good and bad couplings cannot be distinguished, and synergistic coupling is also treated as interference suppression, the system response will be slow, making it unable to respond promptly to process disturbances; while if antagonistic coupling is not effectively suppressed, control oscillations will occur, causing layer thickness fluctuations. Therefore, to enable the control system to distinguish and differentiate between these two drastically different types of coupling, this invention introduces an antagonistic coupling strength factor and a synergistic coupling strength factor.

[0047] Specifically, based on the ARX model identified online, a dimensionless steady-state process gain matrix that can characterize the steady-state causal relationship of the system is calculated using standard control theory transformation methods. The elements in the steady-state process gain matrix represent the steady-state gain of the controller on the process variables. The diagonal elements in the steady-state process gain matrix are the main gain, representing the controller's direct control capability over the process variables, while the off-diagonal elements are the coupling gain, representing the intensity of the cross-coupling influence of the controller on the process variables.

[0048] It should be noted that the steady-state process gain matrix can be obtained by the limit value of the transfer function matrix at zero frequency. The transfer function matrix is ​​obtained by performing a Z-transform on the ARX model obtained online. Since zero frequency corresponds to the point z=1 in a discrete system, the steady-state process gain matrix is ​​equal to the value of the transfer function matrix at z=1. This is a standard method in control theory and will not be elaborated on here.

[0049] Furthermore, the direction of coupling is identified based on the sign of the steady-state gain in the steady-state process gain matrix, and the antagonistic coupling strength factor and the cooperative coupling strength factor are calculated respectively:

[0050] When the circuit The controller for the loop Coupling gain of process variables AND loop The controller for the loop The main gain of the process variable When the signs are opposite, it is defined as antagonistic coupling, and the antagonistic coupling strength factor is used. Coupling strength factor with synergy They are respectively:

[0051]

[0052]

[0053] When the circuit The controller for the loop Coupling gain of process variables AND loop The controller for the loop The main gain of the process variable When the signs are the same, it is defined as cooperative coupling; antagonistic coupling strength factor. Coupling strength factor with synergy They are respectively:

[0054]

[0055]

[0056] In the formula, for Time loop loop The antagonistic coupling strength factor; for Time loop loop The synergistic coupling strength factor; for The steady-state process gain matrix at time t is the first... Line number The elements of the column represent Time loop The controller for the loop The coupling gain of process variables; for The steady-state process gain matrix at time t is the first... Line number The elements of the column represent Time loop The controller for the loop The main gain of the process variable; This is a preset, extremely small positive number used to prevent the denominator from being zero. In this embodiment, it is set to... In other embodiments, implementers can set the parameters according to the actual implementation situation, but in order to ensure computational stability and not affect the accuracy of the results, Must meet ,Right now It should be much smaller than the absolute value of the minimum main gain that may occur in the system.

[0057] When coupling gain When the absolute value increases, or The main gain also increases accordingly, indicating an enhanced coupling strength; when the main gain... When the absolute value increases, or A decrease indicates enhanced main loop control capability and weakened relative coupling effects. During VCSEL epitaxial growth, when deposit accumulation in the reaction chamber leads to changes in the gas flow field, the coupling gain may increase, at which point the intensity factor... , It will increase accordingly to accurately reflect changes in coupling strength, for example, when and hour, This indicates that the coupling effect is 20% of the main control effect; while when and hour, This indicates that the coupling effect is 10% of the main control effect.

[0058] Therefore, at every moment Characterization circuits can be obtained. loop The antagonistic coupling strength factor of interference properties and intensity and synergistic coupling strength factor .

[0059] For example, Figure 2 This is a schematic diagram showing the changes in the antagonistic coupling strength factor and the cooperative coupling strength factor of loop 1 to loop 2; Figure 3 This is a schematic diagram showing the changes in the antagonistic coupling strength factor and the cooperative coupling strength factor of loop 2 to loop 1.

[0060] S4. Dynamically adjust the PID controller gain based on the adversarial coupling strength factor and the cooperative coupling strength factor.

[0061] It is important to note that when growing critical layers such as DBRs or quantum wells, which require extremely high precision, any antagonistic couplings that could lead to fluctuations in layer thickness or composition must be strictly suppressed. Simultaneously, to ensure growth efficiency and rapid response to setpoint changes, beneficial synergistic couplings should be tolerated or even utilized to a certain extent. In VCSEL epitaxial wafer production, dozens or even hundreds of DBR layers typically need to be grown, with each layer's thickness requiring nanometer-level precision, usually 10-30 nm. If antagonistic couplings are not effectively suppressed, layer thickness fluctuations will accumulate, causing reflectivity to deviate from the design value. Conversely, excessive suppression of synergistic couplings will slow down the system response, making it unable to adjust in time to disturbances such as changes in MO source pressure, similarly affecting layer thickness control precision.

[0062] It is particularly important to note that while synergistic coupling is generally beneficial, over-reliance on it can lead to drastic fluctuations in the system when coupling relationships change. For example, if increasing heating power in the temperature loop happens to help improve the growth rate, a sudden interruption in the MO source supply will cause this synergistic coupling to disappear, and if the controller gain is too high, the system will struggle to stabilize. Therefore, suppressing synergistic coupling to a certain extent can improve the system's robustness and ensure stability even when coupling relationships change. This invention therefore constructs an asymmetric gain adjustment mechanism capable of intelligently distinguishing between good and bad coupling and implementing differentiated suppression, achieving both strong constraints on harmful couplings and rational utilization of beneficial couplings.

[0063] Specifically, for each loop Set a set of reference gain parameters ,in It represents the reference proportional gain, reflecting the instantaneous response strength of the controller to errors; This represents the reference integral gain, reflecting the controller's ability to eliminate accumulated errors; It represents the reference differential gain, reflecting the controller's ability to respond to the rate of change of error.

[0064] During online control, based on the antagonistic coupling strength factor and synergistic coupling strength factor The reference gain parameter is dynamically adjusted asymmetrically. In this embodiment, a proportional gain is used. The following is a description of the dynamic adjustment process, using an example:

[0065] Time loop The actual proportional gain satisfies the expression:

[0066]

[0067] In the formula, for Time loop The actual proportional gain; The reference proportional gain; for The adversarial inhibition coefficient at any given moment; for The cooperativity inhibition coefficient at time step; It is a natural exponential function; for Time loop loop The antagonistic coupling strength factor; for Time loop loop The synergistic coupling strength factor; For loop The total degree of external confrontation received; For loop The overall degree of external cooperation received.

[0068] The antagonistic inhibition coefficient reflects the strength of the system's inhibition of harmful couplings; a larger value indicates stronger inhibition of antagonistic couplings. The cooperative inhibition coefficient reflects the system's tolerance for beneficial couplings; a smaller value indicates higher tolerance for cooperative couplings. The setting of the antagonistic inhibition coefficient and the cooperative inhibition coefficient must follow... The principle, due to Greater than When the circuit When the action is identified as being subject to adversarial interference from other loops, its actual proportional gain will be due to This factor is drastically suppressed, causing its regulatory action to quickly become mild; while when it is subjected to cooperative interference, the actual proportional gain will only be affected by... However, it was slightly suppressed. Overall external antagonism. Representing a circuit The sum of the antagonistic coupling effects from other loops reflects the influence of other loops on the loop. The degree of interference with the target; overall external coordination Representing a circuit The sum of the effects of cooperative coupling from other loops reflects the influence of other loops on the loop. The degree of assistance to the target, the overall external confrontation, and the overall external cooperation jointly determine the loop. The appropriate level of control measures to be taken at this moment, when When the value increases, the antagonistic coupling strengthens. Significantly reduced; when As the size increases, the synergistic coupling strengthens. Slightly reduced. For example, when the antagonistic coupling strength increases from 0 to 1, if ,but from Reduce to That is, it decays to 13.5% of the baseline value; while when the cooperative coupling strength increases from 0 to 1, if ,but from Reduce to That is, it decays to 60.7% of the baseline value.

[0069] In one embodiment, the antagonistic inhibition coefficient Cooperative inhibition coefficient The settings are configured by the implementers based on the actual implementation situation, for example... , .

[0070] In another embodiment, the covariance matrix is ​​estimated based on the parameters. Obtain resistance inhibition coefficient and the coefficient of synergistic inhibition , specifically:

[0071] Will Covariance matrix of parameter estimation at time step traces as System stability index at time It should be noted that the trace of a matrix is ​​the sum of the n elements on the main diagonal of the matrix, which can effectively reflect the degree of uncertainty in the estimation of model parameters. When the system is running stably and the model converges well, The trace size is relatively small; conversely, when the system oscillates or is subjected to unknown disturbances, the model parameters are difficult to converge. The trace will increase significantly, therefore this invention utilizes parameter estimation of the covariance matrix. The stability of a system is described by its traces.

[0072] From the historical database, several batches of successful epitaxial wafer growth records that were rated as high-quality and with stable growth processes were selected. The average value of the system stability index of all selected growth records at all times was calculated, and this average value was used as the benchmark stability index. It should be noted that the criterion for judging the stability of the growth process is that the tracking error between the actual measured value and the set value of the key quality indicators in the historical batch records is maintained within a preset minimum tolerance range during the growth time, for example, the error is less than 2%. The key quality indicators include epitaxial wafer growth rate, wafer surface temperature, etc.

[0073] according to System stability index at time In addition to the benchmark stability index, the adversarial suppression coefficient is obtained. and the coefficient of synergistic inhibition :

[0074]

[0075]

[0076] in, for The adversarial inhibition coefficient at any given moment; for The cooperativity inhibition coefficient at time t, express System stability indicators at any given time; This represents the baseline stability index.

[0077] It should be noted that, due to ,and Through mathematical analysis, it can be seen that when hour, This constant condition ensures that the antagonistic inhibition coefficient is always greater than the cooperative inhibition coefficient. However, when system stability decreases, Increase and They will all increase, but The growth rate is greater than This ensures that the suppression of harmful couplings is always greater than the suppression of beneficial couplings. For example, when hour, ,when hour, ,when hour, When the system is unstable, adversarial coupling is more strongly suppressed, while cooperative coupling is only moderately suppressed. This achieves strict suppression of harmful coupling and moderate tolerance of beneficial coupling, enabling the control system to maintain rapid response to process disturbances while ensuring stability.

[0078] It should be noted that, for loops Its integral gain and differential gain It will also be dynamically adjusted in the same proportion:

[0079]

[0080]

[0081] in, for Time loop The actual integral gain; The baseline integral gain; for Time loop The actual differential gain; The base differential gain; The coefficient of resistance inhibition; This represents the synergistic inhibition coefficient.

[0082] This invention employs an asymmetric gain adjustment mechanism to ensure differentiated handling of couplings with different properties in the control system. Adverse coupling is strongly suppressed, while cooperative coupling is only moderately suppressed, thus maximizing system response performance while ensuring system stability. During VCSEL epitaxial growth, the coupling relationship changes when deposits accumulate in the reaction chamber, leading to variations in gas flow characteristics. For example, in the early stages of growth, temperature may have a relatively small impact on the growth rate. At a relatively small size, the controller gain is high, and the system response is fast. As the reaction proceeds, deposit accumulation leads to changes in the gas flow field, and the effect of temperature on the growth rate intensifies. Increasing the controller gain moderately reduces system stability, but it does not decrease as drastically as in adversarial coupling, thus maintaining a rapid response capability to process disturbances.

[0083] S5 outputs dynamically adjusted control signals to control the epitaxial wafer growth process.

[0084] Specifically, for each loop, a standard incremental PID algorithm is used, based on the actual operating gain. Calculate the increment of the dimensionless controller output. , will increase Accumulated signal from the previous time step Above, control signals are obtained. .

[0085] Furthermore, the dimensionless control signals calculated from all loops are inversely normalized using the normalization transformation process employed in step S1, restoring them to actual setpoints with physical units. These setpoints are then sent to the corresponding actuators of the MOCVD equipment, such as the various MFCs and heater power supplies, completing a dynamic adjustment of the growth process. The inverse normalization process involves... The dimensionless signal within the interval is converted back to its original physical unit.

[0086] Repeat S1 to S5 in each control sampling cycle until the entire epitaxial wafer growth process is completed.

[0087] For example, Figure 4This is a schematic diagram of the process variable tracking performance, showing the dynamic tracking of the actual measured values ​​of the two process variables, growth rate and temperature, to their respective set values. Even when the set values ​​change abruptly or when the system has coupling and time-varying characteristics, the process variables growth rate and temperature can quickly and smoothly track the new set values. Figure 5 This is a schematic diagram of the controller output.

[0088] This achieves precise control of the process parameters within the MOCVD reaction chamber.

Claims

1. A method for optimizing process parameters for the production of VCSEL epitaxial wafers, characterized in that The application relates to a method for controlling a growth process of a VCSEL epitaxial wafer. Process parameters and key quality indexes during the growth process of the VCSEL epitaxial wafer are collected; A multi-loop PID control system is constructed according to the process parameters and the key quality indexes; During the operation of the PID control system, an ARX model is identified online, and a steady-state process gain matrix capable of representing a steady-state causal relationship of the system is calculated according to the identified ARX model; The sign of a steady-state gain in the steady-state process gain matrix is identified to determine a coupling direction, and an antagonistic coupling strength factor and a synergistic coupling strength factor are calculated, including: When the coupling gain of the process variable of the loop controlled by the controller of the loop is positive and the primary gain of the process variable of the loop controlled by the controller of the loop is positive , the coupling is antagonistic, and the antagonistic coupling strength factor is , and the synergistic coupling strength factor is ; when the coupling gain of the process variable of the loop controlled by the controller of the loop is negative and the primary gain of the process variable of the loop controlled by the controller of the loop is negative , the coupling is synergistic, and the antagonistic coupling strength factor is , and the synergistic coupling strength factor is ; wherein, is a hyperparameter to prevent the denominator from being zero; The PID controller gain is dynamically adjusted based on the antagonistic coupling strength factor and the synergistic coupling strength factor, and a dynamically adjusted control signal is output to realize the growth process control of the epitaxial wafer; The dynamic adjustment of the PID controller gain comprises: A set of reference gain parameters, including a reference proportional gain, a reference integral gain and a reference derivative gain, are set for each loop; the reference proportional gain, the reference integral gain and the reference derivative gain are dynamically adjusted according to the antagonistic coupling strength factor and the synergistic coupling strength factor reference gain parameters respectively to obtain actual proportional gain, actual integral gain and actual derivative gain; wherein, The actual proportional gain of the loop at time t is The antagonistic inhibition coefficient at time t is The synergistic inhibition coefficient at time t is ; ; The antagonistic coupling strength factor of the loop against the loop at time t is The synergistic coupling strength factor of the loop against the loop at time t is ​​​​​​​​​​ 2. The method of claim 1, wherein the method is characterized by: The process parameters include an MFC set value of TMGa and a heater power set value; and the key quality indexes include an epitaxial wafer growth rate and a wafer surface temperature.

3. The method of claim 2, wherein the method further comprises: The multi-loop PID control system is constructed, including: The collected process parameters and key quality indexes are normalized respectively; loop one is constructed, and a process variable is a normalized epitaxial wafer growth rate, and a controller output is a normalized MFC set value of TMGa; loop two is constructed, and a process variable is a normalized wafer surface temperature, and a controller output is a normalized heater power set value.

4. The method of claim 1, wherein the method is characterized by: The online identification adopts a recursive least square method.

5. The method of claim 1, wherein the method is characterized by: The steady-state process gain matrix is obtained through a limit value of a transfer function matrix at zero frequency, and the transfer function matrix is obtained through Z transformation of the identified ARX model.

6. The method of claim 1, wherein the method is characterized by: The antagonistic inhibition coefficient and the synergistic inhibition coefficient are obtained by: Will Covariance matrix of parameter estimation at time step traces as System stability index at time The parameter estimation covariance matrix is ​​the parameter obtained during online identification of the ARX model; according to System stability index at time and benchmark stability index Obtain the antagonistic inhibition coefficient and the coefficient of synergistic inhibition : , .

7. The method of claim 1, wherein the method further comprises: determining a plurality of process parameters for the VCSEL epitaxial wafer production process; and selecting a process parameter from the plurality of process parameters. The output of the dynamically adjusted control signal to realize the growth process control of the epitaxial wafer comprises: For each loop, an incremental PID algorithm is adopted, an increment of a controller output is calculated according to the dynamically adjusted gain, the increment is accumulated to a control signal at a previous moment to obtain a control signal at a current moment, the control signal at the current moment is de-normalized, and is sent to a corresponding actuator of a MOCVD device to complete a dynamic adjustment of the growth process.

8. The method of claim 1, wherein the method is characterized by: The method is repeatedly executed in each control sampling period until the entire epitaxial wafer growth process is completed.

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