Method for designing objective function in temperature control of rapid heat treatment equipment

Abstract

The invention discloses an objective function design method in temperature control of rapid heat treatment equipment, and belongs to the technical field of semiconductor heat treatment processes, in the applied rapid heat treatment equipment, a heating lamp group is divided into a plurality of lamp areas, and the control voltage of each lamp area can be independently controlled; the method comprises the following steps: modifying quadratic form performance indexes about a state vector and a control vector to adapt to a discrete time system, and adding a temperature difference item into the quadratic form performance indexes to control the temperature difference to obtain a target function; solving an optimal control sequence of N time points in the future through extreme value necessary conditions; and the control voltage vector of the first time point in the optimal control sequence is applied to the temperature control system so as to adjust the control voltage of the heating lamp group. The method solves the problem that a conventional control algorithm target function lacks consideration of temperature difference factors, can reduce the temperature difference, meets the requirements of customers for temperature difference indexes, and improves the yield and quality of a semiconductor process.

Description

Technical Field

[0001] The invention belongs to the technical field of semiconductor heat treatment process, and in particular relates to an objective function design method in temperature control of rapid heat treatment equipment. Background Art

[0002] Rapid Thermal Processing (RTP) is an advanced single-chip wafer heat treatment process, in which temperature control of single wafer is the most important core technology. In a typical RTP device, the heating system is the most important functional component of the device, which mainly includes a heating cavity, a magnetic suspension device, a halogen lamp and its reflector, etc. The measurement and control system mainly completes the control of temperature, cooling gas and other auxiliary systems. In addition, it has the function of communicating with the host computer, and also includes: halogen lamp control power amplifier unit, temperature control board, temperature sensor and its signal conditioning transmitter and other functional units.

[0003] In the prior art, the objective function in the temperature control algorithm generally specifies temperature and power. In other words, when adjusting the output power of the halogen tungsten lamp, it only considers the power size and the temperature of each area of ​​the chip at the monitoring time, without considering the temperature difference. Therefore, it is difficult to control the specific situation of the temperature control result curve at the same time, and it is difficult to meet the current high-end semiconductor process The precision requirements for temperature control. Summary of the invention

[0004] Based on the technical problems existing in the prior art, the present invention provides an objective function design method for temperature control of rapid thermal processing equipment to solve the problem that the temperature control result curve is difficult to control multiple objectives at the same time when the existing solution is adopted, so as to achieve the temperature control result curve that simultaneously meets the customer's requirements for various indicators related to temperature and temperature difference.

[0005] According to the technical scheme of the present invention, the present invention provides an objective function design method in temperature control of a rapid thermal processing device, wherein the rapid thermal processing device used in the present invention comprises a heating chamber for accommodating a wafer and a temperature control system, wherein the temperature control system comprises a heating lamp group for heating the wafer; the heating lamp group is directly opposite to the wafer, and the heating lamp group is divided into a plurality of lamp zones, and the control voltage of each lamp zone can be controlled independently of each other; the wafer is divided into a plurality of temperature zones, and the rapid thermal processing device is also provided with a plurality of temperature measuring devices to measure the temperature of each temperature zone on the wafer respectively; The objective function design method in the temperature control of the rapid thermal processing equipment includes the following contents: The quadratic performance index of the state vector and the control vector is modified to adapt to the discrete time system, and a temperature difference term is added to the quadratic performance index to control the temperature difference, and the following objective function is obtained: , ,in, , i=1…N; Where k is the time, J(k) is the performance index at the kth time, e(k) is the predicted temperature error vector at N time points after the kth time, and e T (k) is the transposed vector of e(k), Q is the first constant diagonal matrix, u(k) is the control voltage vector of a total of N time points after time k, and the control voltage vector at each moment in u(k) includes the control voltage of each lamp zone at that moment, u T (k) is the transposed vector of u(k), R is the second constant diagonal matrix, D(k) is the temperature difference vector at N time points after time k, D i is the temperature difference at the i-th time point, T 1i To T ni are the temperatures corresponding to the n temperature zones on the chip at the i-th time point, D T (k) is the transposed vector of D(k), S is the third constant diagonal matrix, and N is the number of discrete time points considered; The objective function J(k) can be converted into an expression of u(k); furthermore, at time k, u(k) that minimizes J(k) can be obtained through the necessary conditions for extreme values, namely: ; Expand J(k) to get: ; The u(k) obtained from the above equation is the optimal control u that minimizes J(k). * (k),u * (k) According to the order of time points, it can be expressed as the optimal control sequence {u * (0),u * (1),…u * (N-1)}; the control voltage vector u at the first time point in the optimal control sequence * (0) Implemented into the temperature control system to adjust the control voltage of the heating lamp group.

[0006] Furthermore, in the objective function: ,in, , i=1…N; ,in, , i=0…N-1; ,in, , i=1…N; Among them, each element in the Q matrix is ​​the weight of controlling the temperature error of each temperature zone at N time points after moment k; each element in the R matrix is ​​the weight of controlling each control voltage at a total of N time points at moment k and thereafter; each element in the S matrix is ​​the weight of controlling each temperature difference at N time points after moment k.

[0007] Furthermore, the temperature control system in the rapid thermal processing equipment also includes a temperature controller and an SCR module; the temperature measuring device, the temperature controller, the SCR module, and the heating lamp group are connected in sequence; the objective function design method in the temperature control of the rapid thermal processing equipment runs in the temperature controller in the form of software code.

[0008] Furthermore, the temperature controller calculates u * The control voltage of each lamp zone represented by (0) is sent to the SCR module in the form of a percentage, where the percentage refers to the percentage of the rated voltage of the heating lamp; the SCR module applies the voltage to each lamp zone according to the percentage, so the voltage and brightness of each lamp zone are adjusted according to the temperature controller, thereby adjusting the temperature of each temperature zone on the chip to form a closed-loop control.

[0009] Furthermore, the heating lamp group is divided into a plurality of lamp zones in a concentric circle manner, and each lamp zone has a plurality of heating lamps.

[0010] Furthermore, in the rapid thermal processing equipment, a quartz bracket is provided at the bottom of the heating chamber through a magnetic suspension rotation system, a support ring is provided on the quartz bracket, the support ring is used to place the wafer, and the heating lamp group is a halogen tungsten lamp array, which is installed in a reflective cover above the heating chamber.

[0011] Compared with the prior art, the beneficial technical effects of the present invention are as follows: 1. The objective function design method for temperature control of rapid thermal processing equipment of the present invention adopts a method of adding a temperature difference term to the quadratic performance index of the control algorithm to control the temperature difference, which solves the problem of lack of consideration of the temperature difference factor in the objective function of the previous control algorithm and ensures the uniformity of the chip temperature.

[0012] 2. The objective function design method for temperature control of rapid thermal processing equipment of the present invention can reduce the temperature difference, meet the customer's requirements for temperature difference indicators, improve the yield and quality of semiconductor processes, and better realize semiconductor processes with higher temperature control accuracy requirements. BRIEF DESCRIPTION OF THE DRAWINGS

[0013] Figure 1 The invention discloses a schematic diagram of the structure of a heating lamp assembly and a wafer of a rapid thermal processing device provided by the invention.

[0014] Figure 2aIt is a temperature variation curve diagram measured by 7 temperature measuring devices during the process of rapid thermal processing equipment under the existing technical solution.

[0015] Figure 2b The temperature variation curve diagram is obtained by using seven temperature measuring devices during the process of the rapid heat treatment equipment using the method of the present invention.

[0016] Figure 3 It is a structural schematic diagram of a rapid thermal processing equipment provided by the present invention.

[0017] Figure 4 The present invention provides a structural block diagram of a temperature control system for rapid thermal processing equipment. DETAILED DESCRIPTION

[0018] In order to make the purpose, technical solution and advantages of the present invention clearer, the technical solution of the present invention will be clearly and completely described below in conjunction with the drawings of the present invention. Obviously, the described embodiments are part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0019] It should also be noted that, for ease of description, only the parts related to the invention are shown in the drawings. In the absence of conflict, the embodiments of the present invention and the features in the embodiments can be combined with each other.

[0020] It should be noted that the concepts such as "first" and "second" mentioned in the present invention are only used to distinguish different devices, modules or units, and are not used to limit the order or interdependence of the functions performed by these devices, modules or units.

[0021] It should be noted that the modifications of "one" and "plurality" mentioned in the present invention are illustrative rather than restrictive, and those skilled in the art should understand that, unless otherwise clearly indicated in the context, it should be understood as "one or more".

[0022] The present invention provides an objective function design method for temperature control of rapid thermal processing equipment, which solves the problem that the temperature control result curve is difficult to control multiple objectives at the same time when the existing solution is adopted, and realizes that the temperature control result curve simultaneously meets the customer's requirements for various indicators related to temperature and temperature difference.

[0023] The performance index in the temperature control method is a standard to measure the working quality of the system under different control vector functions. Among the many control methods, many model-based or optimization control methods require the specification of performance indicators. The content and form of the performance index mainly depend on the task to be completed by the control problem. Different control problems have different performance indicators. The performance indicators of the RTP temperature control problem mainly use the temperature and the control voltage of the wafer heating device (heating lamp).

[0024] Among the performance indicators, the quadratic performance indicator is the most typical one, which is expressed as the integral of the quadratic function of the state variable or the control variable. Since the quadratic performance indicator has a distinct physical meaning, represents the performance indicator requirements proposed in a large number of practical engineering problems, and is relatively simple in mathematical processing, it has been widely used in practical engineering problems. Without considering the terminal restrictions, the quadratic performance indicator with respect to the state vector and the control vector can be defined as: , Among them, J is the performance index, expressed in integral form; t0 and tf are the initial time and the terminal time respectively; e(t) is the error vector between the system output and the target; u(t) is the control vector; Q(t) is the symmetric non-negative timing variable matrix; R(t) is the symmetric positive timing variable matrix; Q(t) and R(t) are often taken as diagonal matrices, then their symmetry is naturally satisfied.

[0025] This type of control problem is: for a linear system, determine the optimal control u * (t), so that the quadratic performance index is minimized. In terms of practical engineering applications, the performance index reflects the performance requirements of complex control systems.

[0026] See also Figure 1 , Figure 3 , Figure 4 The rapid thermal processing equipment used in the present invention includes a heating chamber 3 for accommodating a wafer 6 and a temperature control system. The temperature control system includes a heating lamp group 1 for heating the wafer 6. The heating lamp group 1 is directly opposite to the wafer 6. The heating lamp group 1 is divided into a plurality of lamp zones. The control voltage of each lamp zone can be controlled independently of each other. In other words, the heating power can be controlled separately. The wafer 6 is divided into a plurality of temperature zones. The rapid thermal processing equipment is also provided with a plurality of temperature measuring devices 4 to measure the temperature of each temperature zone on the wafer 6.

[0027] The control of the heating lamp and temperature in the present invention is a vector rather than a scalar because the heating lamp group is divided into multiple lamp zones, and the wafer is also divided into multiple temperature zones. The number of lamp zones is m, and the number of temperature zones is n. There is no strict restriction on whether m and n are the same. In some embodiments, the number of lamp zones and temperature zones is the same and the positions correspond one to one. Taking three lamp zones and three temperature zones as an example, the control voltages of the three lamp zones L1, L2, and L3 are u1, u2, and u3, and each of the three temperature zones has a temperature measuring device (thermometer), and the measured temperatures are T1, T2, and T3. The number and setting of lamp zones and temperature zones can be designed and selected according to needs in actual applications.

[0028] For the RTP temperature control problem, e(t)=z(t)-y(t), where e(t) is the error vector between the system output and the target, specifically the temperature output error vector; z(t) is the desired output vector; y(t) is the temperature output vector [T1, T2, T3, ...]. The control vector u(t) is specifically the control voltage vector of the heating lamp. Taking a system with three temperatures as an example, Q(t) and R(t) are expressed as follows. There are more approximate expressions for more temperatures, and so on.

[0029] , ; Regarding the quadratic performance index of the state vector and the control vector, the first term of the integral function, that is, e T (t)Q(t)e(t), is used to limit the size of the error vector e(t); Q(t) is usually selected as a diagonal matrix, in which the numerical value reflects the weight of each error component (error component refers to each element in the error vector) at different times. The second term of the integral function, that is, u T (t)R(t)u(t) reflects the restriction on the control voltage vector u(t) of the heating lamp to prevent excessive energy consumption or drastic energy fluctuations; R(t) is usually selected as a diagonal matrix, in which the numerical value reflects the intensity of the restriction on the control energy.

[0030] If the objective function is slightly modified to adapt to discrete-time systems, the control problem becomes how to determine the optimal control sequence {u(0), u(1), … u(N-1)} to minimize the following quadratic performance index, where N is the number of discrete time points considered.

[0031] , Among them, k refers to the kth moment; If the variables in the above formula are expressed as vectors or matrices, they can be transformed into: ; In summary, the objective function in the temperature control algorithm generally specifies temperature and power. The physical meaning of the quadratic performance index is to minimize the control deviation as much as possible and limit the control energy. It can guarantee the final temperature and power, but because the temperature difference is not considered, it is difficult to accurately control the shape of the temperature curve at the same time.

[0032] In the present invention, a multi-input multi-output discrete linear system described by a state equation is considered: , Where x(k) is the state vector at the kth moment, the system input u(k) is the control voltage vector, the system output y(k) is the temperature vector, x(k+1) is the state vector at the k+1th moment, A is the system matrix, B is the input matrix, and C is the output matrix.

[0033] The present invention modifies the conventional quadratic performance index of the state vector and the control vector to adapt to the discrete time system, and adds a temperature difference term to the quadratic performance index to control the temperature difference to prevent the temperature difference from being too large. The temperature difference is recorded as D (a vector), and the following objective function is obtained: , ,in, , i=1…N; ,in, , i=0…N-1; ,in, , i=1…N; ,in, , i=1…N; Where k is the time, J(k) is the performance index at the kth time, e(k) is the predicted temperature error vector at N time points after the kth time, and e T (k) is the transposed vector of e(k), u(k) is the control voltage vector of a total of N time points at and after time k, u(k) includes the control voltage vectors of a total of N time points at and after time k, and the control voltage vector at each moment includes the control voltage of each lamp zone at that moment, u T (k) is the transposed vector of u(k), D(k) is the temperature difference vector at N time points after time k (the temperature difference target is 0), and each element in D(k) is the difference between different temperatures. i is the temperature difference at the i-th time point, T 1i To T ni are the temperatures corresponding to the n temperature zones on the chip at the i-th time point, D T (k) is the transposed vector of D(k); Take three temperature zones and a certain time point as an example. .

[0034] Q, R, and S are usually selected as constant diagonal matrices, Q is the first constant diagonal matrix, R is the second constant diagonal matrix, and S is the third constant diagonal matrix. The numerical value in Q reflects the weight of each error component (the error component refers to each element in the error vector e(k)). Specifically, each element in the Q matrix is ​​the weight of controlling the temperature error of each temperature zone at N time points after moment k. The number of diagonal elements is n×N. The larger the value in the matrix, the faster and stronger the control voltage reacts to the corresponding temperature error. Each element in the R matrix is ​​the weight of controlling each control voltage at a total of N time points after moment k. The number of diagonal elements is m×N, where m is the number of control voltages (i.e., the number of lamp zones). The numerical value in the matrix reflects the intensity of the control energy restriction (control energy refers to control voltage, and energy here refers to the consumed electrical energy). The larger the value, the less likely the control voltage is to increase, thereby reducing energy consumption. Each element in the S matrix is ​​the weight of controlling each temperature difference at N time points after time k. The number of diagonal elements is n×N. The value in the matrix reflects the intensity of limiting the temperature difference vector D(k). The larger the value, the faster and stronger the control voltage reacts to the temperature difference. The values ​​of the above matrix elements are adjustable values, and engineers can manually modify them during the algorithm testing and product verification stages to obtain the ideal temperature curve.

[0035] It should be noted that in the above objective function, the control voltage at the kth moment can only reflect the effect of temperature error and temperature difference at the k+1th moment. Therefore, the control voltage will be one time point ahead of other variables, that is, the first time point of the control voltage in the performance index is the k+0 moment, and the first time point of the temperature error and temperature difference is the k+1 moment.

[0036] In the above objective function, all items on the right side of the equal sign are in vector or matrix form; the temperature difference term is the third term in the integral, i.e., D T (k)SD(k). This control problem is how to determine the optimal control sequence {u * (0),u * (1),…u * (N-1)} minimizes the quadratic performance index, where N is the number of discrete time points considered.

[0037] Each item in the objective function J(k) is related to u(k) and can be converted into an expression of u(k). Therefore, at time k, u(k) that minimizes J(k) can be obtained through the necessary conditions for extreme values, namely: ; Expanding J(k) yields: ; The u(k) obtained from the above equation is the optimal control u that minimizes J(k). * (k),u * The elements contained in (k) are the optimal control sequences of each light zone at a total of N time points after time k, so the number of elements is m×N. * (k) According to the order of time points, it can be expressed as the optimal control sequence {u * (0),u * (1),…u * (N-1)}.

[0038] The temperature control algorithm is in the form of code in the temperature control controller, and is performed in a fixed cycle, for example, once every 0.01 seconds. Therefore, an optimal control sequence is calculated in each calculation cycle. The meaning of this optimal control sequence is: based on the current calculation cycle, the objective function in the next N calculation cycles can take the smallest N cycle control voltage vector. * The “0” in (0) refers to k+0, which corresponds to time k (the current calculation cycle).

[0039] Therefore, in the current calculation cycle, it is only necessary to change the control vector u at the first time point in the optimal control sequence * (k) is implemented in the temperature control system to adjust the control voltage of the heating lamp group, and the values ​​at other time points are discarded. When the next calculation cycle comes, a new u is calculated based on the system state of the next calculation cycle. * (k), also using the new u * (0)For implementation.

[0040] See also Figure 4 The temperature control system in the rapid thermal processing equipment also includes a temperature controller and an SCR (silicon controlled rectifier) ​​module. The temperature measuring device, the temperature controller, the SCR module, and the heating lamp group are connected in sequence. The temperature measuring device is connected to the heating cavity of the RTP equipment to collect the radiation signal of the chip for temperature measurement; the SCR module is connected to the halogen tungsten lamp (heating component) of the heating cavity of the RTP equipment to output voltage to the halogen tungsten lamp to control the heating power of the halogen tungsten lamp. The temperature controller is used for data processing and implementation of control algorithms, etc. It receives the temperature measured by the temperature measuring device, and adjusts the signal output to the SCR module through the algorithm to achieve control of the heating power. The objective function design method in the temperature control of the rapid thermal processing equipment runs in the temperature controller in the form of software code.

[0041] More specifically, the process of implementing the control vector in the system is as follows: u calculated by the temperature controller *The control voltage of each lamp zone represented by (0) is sent to the SCR module in the form of a percentage, where the percentage refers to the percentage of the rated voltage of the heating lamp; the SCR module applies the voltage to each lamp zone according to the percentage, so the voltage and brightness of each lamp zone are adjusted according to the temperature controller, thereby adjusting the temperature of each temperature zone on the chip to form a closed-loop control.

[0042] In the preferred embodiment, please refer to Figure 1 The heating lamp group (or heating lamp array) is divided into several lamp zones in a concentric circle manner (or a concentric hexagon manner similar to concentric circles), and each lamp zone has several heating lamps (bulbs) for uniform heating.

[0043] See also Figure 3 In the rapid thermal processing equipment used in the present invention, the heating chamber 5 (or reaction chamber) is a closed chamber and provides installation positions for other components. The side of the heating chamber 5 has a gas inlet / outlet. The bottom of the heating chamber 5 is provided with a quartz bracket 2 (such as a rotating quartz cylinder) through a magnetic suspension rotation system. A support ring 3 (silicon carbide support ring) is provided on the quartz bracket 2. The support ring 3 is used to place a wafer 6. The wafer 6 can rotate around its center in a horizontal plane to make the heating effect more uniform. The bottom of the heating chamber 5 is also provided with a number of temperature measuring devices for measuring the temperature of the wafer, such as a pyrometer 4. In order to prevent the temperature of the wafer from being affected, a non-contact pyrometer is used for temperature measurement, such as a fiber optic probe. The heating lamp group 1 is preferably a halogen tungsten lamp array, which is installed in a reflective cover above the heating chamber 5. Under normal working conditions, the temperature of the halogen tungsten lamp is in the range of 600-1650K, and the radiation energy is concentrated in the wavelength range of 1-5 microns, which belongs to infrared radiation. This high-density arrangement of heat sources can improve the uniformity of the temperature field to a high degree at the level of mechanical structure. The halogen tungsten lamp array is divided into several groups (i.e., forming lamp zones) according to the radial distance, and the power of each group of lamps can be controlled separately. The number of lamp zones is generally consistent with the number of pyrometers, and multiple pyrometers simultaneously measure the temperature at different radial positions of the wafer to improve the temperature uniformity.

[0044] The temperature control indicators of rapid heat treatment process generally include temperature and temperature difference. The temperature indicator refers to the overall need of multiple temperatures to meet the various requirements specified by the customer, such as heating rate, overshoot, and steady-state error. The temperature difference indicator refers to the numerical difference between each temperature. Generally, the difference between the highest temperature and the lowest temperature at the same time is used as the temperature difference indicator.

[0045] As a more specific supplementary explanation, rapid thermal processing is an advanced single-chip wafer heat treatment process. The typical RTP heating system mainly includes a heating chamber, a magnetic levitation device, a halogen tungsten lamp and its reflector, etc. The measurement and control system mainly completes the closed-loop control of temperature, the control of cooling gas and the control functions of other auxiliary systems. In addition, it also has the function of communicating with the host computer, and also includes: halogen tungsten lamp control power amplifier unit, temperature control board, temperature sensor and its signal conditioning transmitter and other functional units.

[0046] In RTP applications, some processes require that the product sheet is not contaminated by impurity gases during the heating process, so a higher vacuum degree needs to be provided. The vacuum system is usually implemented with a single-stage or two-stage vacuum pump according to the specific vacuum degree requirements.

[0047] Some processes require gas protection, or high-temperature nitriding, oxidation, etc. Therefore, the system must provide multiple atmosphere sources at the same time, such as argon, nitrogen, and oxygen. Each gas is controlled by a switch valve, and a pressure regulating valve is installed on a single pipeline near the entrance of the heating chamber to control the pressure of the atmosphere. Generally, when switching different gases, it is necessary to exhaust the residual gas in the original closed chamber. Therefore, before switching the input gas, it is necessary to evacuate the chamber first, and then introduce the set gas. This requires software design to achieve this.

[0048] In order to ensure that the wafer is not contaminated when it is taken and placed, a two-degree-of-freedom robot is used to perform the operation of taking and placing the wafer.

[0049] In the application of the system, most processes have strict requirements on the temperature curve of the wafer, so not only fast heating but also fast cooling is required. The method of introducing low-temperature gas or normal temperature gas can be used to simply and effectively achieve cooling, and the type of gas introduced may be different according to the specific process requirements. In addition, for safety reasons, the heating chamber wall is cooled by cooling water circulation.

[0050] The method of the present invention is a key software module in the main body of the independently developed temperature control algorithm, which can be applied to different types of equipment. The main application equipment currently includes RTA, IDP and IDP Plus. The difficulties of the temperature control algorithm include: 1. Strong coupling relationship. The silicon wafer is large in size, and there is a strong coupling relationship between the multi-temperature zone controls, which makes it difficult to quickly and evenly control the temperature.

[0051] 2. High adaptability requirements. RTP equipment has a wide variety of processes and requires high algorithm adaptability. An algorithm is often required to perform well under a variety of temperatures, pressures, heating rates, and a variety of structural pieces.

[0052] 3. High control accuracy requirements. Indicators such as temperature difference and overshoot are often strictly required, and the heating time needs to be customized, which brings difficulties to the selection of control schemes and parameter settings.

[0053] 4. Nonlinear control: In model-based design, the nonlinearity, time-varying, and delay of the temperature control system increase the difficulty of modeling.

[0054] When the method of the present invention is applied to the system, the temperature difference can be significantly reduced. Figure 2a , 2b As shown, there are 7 temperatures in the system, where the horizontal axis is the temperature measurement time and the vertical axis is the temperature. By comparison, the temperature difference is reduced from 5.2°C to 2.3°C after optimization.

[0055] It should be noted that if the input and output constraints of the system are considered in the optimization problem, the solution cannot obtain an analytical expression of the control rate. Therefore, the situation of considering system constraints is not covered by the present invention.

[0056] In summary, the objective function design method for temperature control of rapid thermal processing equipment of the present invention adopts a method of adding a temperature difference term to the quadratic performance index of the control algorithm to control the temperature difference, which solves the problem of lack of consideration of the temperature difference factor in the objective function of the previous control algorithm and ensures the temperature uniformity of the chip; and the objective function design method for temperature control of rapid thermal processing equipment of the present invention can reduce the temperature difference, meet the customer's requirements for temperature difference indicators, improve the yield and quality of semiconductor processes, and better realize semiconductor processes with higher requirements for temperature control accuracy.

[0057] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention, rather than to limit it. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art should understand that they can still modify the technical solutions described in the aforementioned embodiments, or make equivalent replacements for some of the technical features therein. However, these modifications or replacements do not deviate the essence of the corresponding technical solutions from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for designing an objective function in temperature control of a rapid thermal processing device, characterized in that: The rapid thermal processing equipment used in the invention comprises a heating chamber for accommodating a wafer and a temperature control system, wherein the temperature control system comprises a heating lamp group for heating the wafer; the heating lamp group is directly opposite to the wafer, and the heating lamp group is divided into a plurality of lamp zones, and the control voltage of each lamp zone can be controlled independently of each other; the wafer is divided into a plurality of temperature zones, and the rapid thermal processing equipment is also provided with a plurality of temperature measuring devices for measuring the temperature of each temperature zone on the wafer respectively; The objective function design method in the temperature control of the rapid thermal processing equipment includes the following contents: The quadratic performance index of the state vector and the control vector is modified to adapt to the discrete time system, and a temperature difference term is added to the quadratic performance index to control the temperature difference, and the following objective function is obtained: ， ,in, , i=1…N; Where k is the time, J(k) is the performance index at the kth time, e(k) is the predicted temperature error vector at N time points after the kth time, and e T (k) is the transposed vector of e(k), Q is the first constant diagonal matrix, u(k) is the control voltage vector of a total of N time points after time k, and the control voltage vector at each moment in u(k) includes the control voltage of each lamp zone at that moment, u T (k) is the transposed vector of u(k), R is the second constant diagonal matrix, D(k) is the temperature difference vector at N time points after time k, D i is the temperature difference at the i-th time point, T 1i To T ni are the temperatures corresponding to the n temperature zones on the chip at the i-th time point, D T (k) is the transposed vector of D(k), S is the third constant diagonal matrix, and N is the number of discrete time points considered; The objective function J(k) can be converted into an expression of u(k); furthermore, at time k, u(k) that minimizes J(k) can be obtained through the necessary conditions for extreme values, namely: ； Expand J(k) to get: ； The u(k) obtained from the above equation is the optimal control u that minimizes J(k). * (k),u * (k) According to the order of time points, it can be expressed as the optimal control sequence {u * (0),u * (1),…u * (N-1)}; the control voltage vector u at the first time point in the optimal control sequence * (0) Implemented into the temperature control system to adjust the control voltage of the heating lamp group.

2. The objective function design method for temperature control of rapid thermal processing equipment according to claim 1, characterized in that: In the objective function: ,in, , i=1…N; ,in, , i=0…N-1; ,in, , i=1…N; Among them, each element in the Q matrix is ​​the weight of controlling the temperature error of each temperature zone at N time points after moment k; each element in the R matrix is ​​the weight of controlling each control voltage at a total of N time points at moment k and thereafter; each element in the S matrix is ​​the weight of controlling each temperature difference at N time points after moment k.

3. The objective function design method for temperature control of rapid thermal processing equipment according to claim 2, characterized in that: The temperature control system in the rapid thermal processing equipment also includes a temperature controller and an SCR module; the temperature measuring device, the temperature controller, the SCR module, and the heating lamp group are connected in sequence; the objective function design method in the temperature control of the rapid thermal processing equipment runs in the temperature controller in the form of software code.

4. The objective function design method for temperature control of rapid thermal processing equipment according to claim 3, characterized in that: u calculated by the temperature controller * The control voltage of each lamp zone represented by (0) is sent to the SCR module in the form of a percentage, where the percentage refers to the percentage of the rated voltage of the heating lamp; the SCR module applies the voltage to each lamp zone according to the percentage, so the voltage and brightness of each lamp zone are adjusted according to the temperature controller, thereby adjusting the temperature of each temperature zone on the chip to form a closed-loop control.

5. The objective function design method for temperature control of rapid thermal processing equipment according to any one of claims 1 to 4, characterized in that: The heating lamp group is divided into a plurality of lamp zones in a concentric circle manner, and each lamp zone has a plurality of heating lamps.

6. The objective function design method for temperature control of rapid thermal processing equipment according to any one of claims 1 to 4, characterized in that: In the rapid thermal processing equipment, a quartz bracket is arranged at the bottom of the heating chamber through a magnetic suspension rotating system, a support ring is arranged on the quartz bracket, the support ring is used to place the wafer, and the heating lamp group is a halogen tungsten lamp array, which is installed in a reflective cover above the heating chamber.

Images