A method for designing objective function in temperature control of rapid thermal processing equipment

Abstract

The present invention discloses a method for designing an objective function for temperature control in rapid thermal processing equipment, belonging to the field of semiconductor thermal processing technology. In the rapid thermal processing equipment used, a heating lamp group is divided into multiple lamp zones, and the control voltages of each lamp zone can be independently controlled. The method includes: modifying quadratic performance indicators for state vectors and control vectors to adapt to discrete-time systems, adding a temperature difference term to the quadratic performance indicator to control the temperature difference, and obtaining an objective function; obtaining an optimal control sequence for N future time points through necessary extreme value conditions; and implementing the control voltage vector at the first time point in the optimal control sequence into the temperature control system to adjust the control voltage of the heating lamp group. This method solves the problem of previous control algorithm objective functions lacking consideration of temperature difference factors. It can reduce temperature difference, meet customer requirements for temperature difference indicators, and improve semiconductor process yield and quality.

Description

Technical Field

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

[0002] Rapid Thermal Processing (RTP) is an advanced monolithic wafer heat treatment process, with wafer temperature control being a key core technology. In a typical RTP system, the heating system is the most important component, primarily comprising a heating chamber, magnetic levitation device, halogen lamp, and reflector. The measurement and control system primarily controls temperature, cooling gas flow, and other auxiliary systems. Furthermore, it communicates with a host computer and includes functional units such as a halogen lamp control power amplifier unit, a temperature control board, and a temperature sensor and its signal conditioning transmitter.

[0003] In the existing technology, 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 taking into account the temperature difference. Therefore, it is difficult to simultaneously control the specific conditions of the temperature control result curve, and it is difficult to meet the current high-end semiconductor process requirements for temperature control accuracy. 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, which solves the problem that the temperature control result curve is difficult to control multiple objectives at the same time when using the existing solution, and realizes that the temperature control result curve can simultaneously meet the customer's requirements for various indicators related to temperature and temperature difference.

[0005] According to the technical solution of the present invention, a method for designing an objective function for temperature control in a rapid thermal processing device is provided. The rapid thermal processing device used in the method includes a heating chamber for accommodating a wafer and a temperature control system. The temperature control system includes a heating lamp group for heating the wafer. The heating lamp group is directly opposite the wafer and is divided into multiple lamp zones. The control voltage of each lamp zone can be independently controlled. The wafer is divided into multiple temperature zones. The rapid thermal processing device is also provided with multiple temperature measuring devices to measure the temperature of each temperature zone on the wafer.

[0006] The objective function design method for temperature control of rapid thermal processing equipment includes the following contents:

[0007] 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, resulting in the following objective function:

[0008] ,

[0009] ,in, , i=1…N;

[0010] 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, 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 N time points in and 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;

[0011] 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:

[0012] ;

[0013] Expand J(k) to get:

[0014] ;

[0015] 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.

[0016] Furthermore, in the objective function:

[0017] ,in, , i=1…N;

[0018] ,in, , i=0…N-1;

[0019] ,in, , i=1…N;

[0020] Among them, each element in the Q matrix is ​​the weight of controlling the temperature error of each temperature zone in the N time points after the k moment; each element in the R matrix is ​​the weight of controlling each control voltage in the total N time points of k and thereafter; each element in the S matrix is ​​the weight of controlling each temperature difference in the N time points after the k moment.

[0021] 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; and 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.

[0022] 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.

[0023] 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.

[0024] Furthermore, in the rapid thermal processing equipment, a quartz bracket is provided at the bottom of the heating chamber through a magnetic levitation rotation system, and a support ring is provided on the quartz bracket, which is used to place the chip. The heating lamp group is a halogen tungsten lamp array, which is installed in a reflective cover above the heating chamber.

[0025] Compared with the prior art, the beneficial technical effects of the present invention are as follows:

[0026] 1. The objective function design method for temperature control of rapid thermal processing equipment of the present invention adopts the 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.

[0027] 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

[0028] Figure 1 The diagram is a schematic structural diagram of a heating lamp assembly and a wafer of a rapid thermal processing device provided by the present invention.

[0029] Figure 2a This is a temperature change curve diagram measured by seven temperature measuring devices during the process of rapid thermal processing equipment under the existing technical solution.

[0030] Figure 2b The figure is a temperature variation curve diagram obtained by seven temperature measuring devices during the process of the rapid thermal processing equipment using the method of the present invention.

[0031] Figure 3 It is a structural schematic diagram of a rapid thermal processing equipment provided by the present invention.

[0032] Figure 4 This is a structural block diagram of a temperature control system of a rapid thermal processing equipment provided by the present invention. DETAILED DESCRIPTION

[0033] To make the objectives, technical solutions, and advantages of the present invention more clear, the technical solutions of the present invention will be clearly and completely described below in conjunction with the accompanying drawings. Obviously, the embodiments described are only some embodiments of the present invention, not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts shall fall within the scope of protection of the present invention.

[0034] 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 and features of the embodiments of the present invention may be combined with each other.

[0035] It should be noted that the concepts of "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.

[0036] It should be noted that the modifications of "one" and "multiple" mentioned in the present invention are illustrative rather than restrictive. Those skilled in the art should understand that unless otherwise clearly indicated in the context, it should be understood as "one or more".

[0037] The present invention provides a method for designing an objective function in temperature control of rapid thermal processing equipment, which solves the problem that the temperature control result curve is difficult to control multiple objectives simultaneously when using existing solutions, and realizes that the temperature control result curve simultaneously meets the customer's requirements for various indicators related to temperature and temperature difference.

[0038] Performance indicators in temperature control methods measure how well a system performs under different control vector functions. Many model-based or optimization-based control methods require specific performance indicators. The content and form of these indicators depend primarily on the control problem's intended task, and different control problems require different performance indicators. For RTP temperature control problems, performance indicators primarily use temperature and the control voltage of the wafer heater (heating lamp).

[0039] Quadratic performance indicators are the most typical among performance indicators. They are expressed as the integral of a quadratic function of the state variable or control variable. Quadratic performance indicators have distinct physical meanings, represent the performance indicator requirements proposed in a large number of practical engineering problems, and are relatively simple to mathematically process. Therefore, they have been widely used in practical engineering problems. Without considering terminal restrictions, the quadratic performance indicator with respect to the state vector and control vector can be defined as:

[0040] ,

[0041] Among them, J is the performance index, expressed in integral form; t0 and tf are the initial and terminal moments respectively; e(t) is the error vector between the system output and the target; u(t) is the control vector; Q(t) is a symmetric non-negative timing variable matrix; R(t) is a symmetric positive timing variable matrix; Q(t) and R(t) are often taken as diagonal matrices, so their symmetry is naturally satisfied.

[0042] 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.

[0043] See also Figure 1 、 Figure 3 、 Figure 4 The rapid thermal processing equipment used in the present invention includes a heating chamber 5 for accommodating a wafer 6 and a temperature control system. The temperature control system includes a heating lamp assembly 1 for heating the wafer 6, with the heating lamp assembly 1 facing the wafer 6. The heating lamp assembly 1 is divided into multiple lamp zones, and the control voltage of each lamp zone can be independently controlled. In other words, the heating power can be controlled separately. The wafer 6 is divided into several temperature zones, and the rapid thermal processing equipment is also equipped with several temperature measuring devices 4 to measure the temperature of each temperature zone on the wafer 6.

[0044] In this invention, the heating lamp and temperature control are both vector quantities, not scalar quantities, because the heating lamp assembly 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. Whether m and n are equal is not strictly limited. In some embodiments, the number of lamp zones and temperature zones is equal, and their positions correspond one-to-one. For example, with three lamp zones and three temperature zones, the control voltages for the three lamp zones L1, L2, and L3 are u1, u2, and u3, and each temperature zone has a temperature measuring device (thermometer), measuring the temperatures T1, T2, and T3. The number and arrangement of the lamp zones and temperature zones can be designed and selected based on actual needs.

[0045] 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; and y(t) is the temperature output vector [T1, T2, T3, ...]. The control vector u(t) is the control voltage vector for the heating lamp. For a system with three temperatures, Q(t) and R(t) are expressed as follows. Approximate expressions for more temperatures are possible, and so on.

[0046] ,

[0047] ;

[0048] 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, where the numerical value reflects the weight of each error component (the error component refers to each element in the error vector) at different times. The second term of the integral function, i.e. 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 strength of the control energy restriction.

[0049] If the objective function is slightly modified to accommodate 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 indicator, where N is the number of discrete time points considered.

[0050] ,

[0051] Among them, k refers to the kth moment;

[0052] If the variables in the above formula are expressed as vectors or matrices, they can be transformed into:

[0053] ;

[0054] 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 it does not consider the temperature difference, it is difficult to accurately control the shape of the temperature curve at the same time.

[0055] In the present invention, a multi-input multi-output discrete linear system described by the state equation is considered:

[0056] ,

[0057] 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.

[0058] 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 and prevent it from being too large. The temperature difference is recorded as D (a vector), and the following objective function is obtained:

[0059] ,

[0060] ,in, , i=1…N;

[0061] ,in, , i=0…N-1;

[0062] ,in, , i=1…N;

[0063] ,in, , i=1…N;

[0064] 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, 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 moment k, u(k) includes the control voltage vectors of a total of N time points at and after moment 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);

[0065] Taking three temperature zones and a certain time point as an example, .

[0066] Q, R, and S are typically chosen as constant diagonal matrices, with Q being the first constant diagonal matrix, R being the second constant diagonal matrix, and S being the third constant diagonal matrix. The values ​​in Q represent the weights assigned to each error component (the error components refer to the elements in the error vector e(k)). Specifically, each element in the Q matrix represents the weight assigned to the temperature error in each temperature zone at N time points after time k. The number of diagonal elements is n×N. Larger values ​​in the matrix indicate a faster and stronger response of the control voltage to the corresponding temperature error. Each element in the R matrix represents the weight assigned to each control voltage at N time points after time 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 values ​​in the matrix represent the strength of the control energy constraint (control energy refers to the control voltage, and energy in this case refers to the electrical energy consumed). Larger values ​​reduce the likelihood of the control voltage increasing, thereby minimizing energy consumption. Each element in the S matrix represents the weight for controlling each temperature difference at N time points after time k. The number of diagonal elements is n×N. The magnitude of the matrix reflects the strength of the restriction on the temperature difference vector D(k). A larger value indicates a faster and stronger response of the control voltage to the temperature difference. The values ​​of these matrix elements are adjustable and can be manually modified by engineers during algorithm testing and product verification to achieve the desired temperature curve.

[0067] It should be noted that in the above objective function, the control voltage at time k can only reflect the effect of temperature error and temperature difference at time k+1. Therefore, the control voltage will be advanced by one time point compared with other variables. That is, the first time point of the control voltage in the performance index is time k+0, and the first time point of the temperature error and temperature difference is time k+1.

[0068] 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, that is, 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.

[0069] Each term 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, the u(k) that minimizes J(k) can be obtained through the necessary conditions for extreme values, namely:

[0070] ;

[0071] Expanding J(k) yields:

[0072] ;

[0073] 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 at and 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)}.

[0074] The temperature control algorithm is in the form of code in the temperature 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 minimum control voltage vector of N cycles. * The “0” in (0) refers to k+0, which corresponds to time k (the current calculation cycle).

[0075] 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 use the new u * (0)For implementation.

[0076] See also Figure 4The temperature control system in the rapid thermal processing equipment also includes a temperature controller and an SCR (silicon control unit) module. The temperature measuring device, temperature controller, SCR module, and heating lamp group are connected in sequence. The temperature measuring device is connected to the heating chamber of the RTP equipment to collect the wafer radiation signal for temperature measurement; the SCR module is connected to the halogen tungsten lamp (heating component) in the heating chamber 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. 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 for the temperature control of the rapid thermal processing equipment is run in the temperature controller in the form of software code.

[0077] 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.

[0078] 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 hexagonal manner similar to concentric circles), and each lamp zone has several heating lamps (bulbs) for uniform heating.

[0079] See also Figure 3In the rapid thermal processing equipment employed in the present invention, the heating chamber 5 (or reaction chamber) is a sealed chamber that provides mounting space for other components. The sides of the heating chamber 5 have gas inlets and outlets. A quartz holder 2 (e.g., a rotating quartz cylinder) is mounted at the bottom of the heating chamber 5 via a magnetic levitation rotation system. A support ring 3 (a silicon carbide support ring) is mounted on the quartz holder 2. The support ring 3 is used to hold a wafer 6, which can rotate about its center in a horizontal plane, ensuring more uniform heating. The bottom of the heating chamber 5 also includes several temperature measuring devices for measuring the wafer temperature, such as pyrometers 4. To prevent any impact on the wafer temperature, non-contact pyrometers, such as fiber optic probes, are used for temperature measurement. The heating lamp assembly 1 is preferably a halogen tungsten lamp array mounted within a reflective cover above the heating chamber 5. Under normal operating conditions, the halogen lamps maintain a temperature range of 600-1650K, with radiated energy concentrated within a wavelength range of 1-5 microns, representing infrared radiation. This high-density arrangement of heat sources significantly improves temperature field uniformity at the mechanical level. The tungsten-halogen lamp array is divided into several groups (i.e., lamp zones) based on radial distance, with each group's lamp power individually controlled. The number of lamp zones typically matches the number of pyrometers, with multiple pyrometers simultaneously measuring the temperature at different radial locations on the wafer to improve temperature uniformity.

[0080] Temperature control indicators for rapid thermal processing generally include temperature and temperature differential. Temperature indicators refer to the overall need for multiple temperatures to meet customer-specified requirements, such as heating rate, overshoot, and steady-state error. Temperature differential indicators refer to the difference between individual temperatures, typically the difference between the highest and lowest temperatures at the same moment.

[0081] 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 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.

[0082] In RTP applications, some processes require that the product wafers be free of contamination from impurity gases during heating, thus requiring a high degree of vacuum. The vacuum pumping system typically utilizes a single-stage or two-stage vacuum pump, depending on the specific vacuum level required.

[0083] Certain processes require gas protection, or high-temperature nitriding, oxidation, etc. Therefore, the system must provide multiple atmosphere sources simultaneously, such as argon, nitrogen, and oxygen. Each gas is controlled on and off by a switching 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 between 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 first evacuate the chamber and then introduce the set gas. This requires the coordination of software design to achieve.

[0084] In order to ensure that the wafers are not contaminated when they are taken and placed, a two-degree-of-freedom manipulator is used to perform the operations of taking and placing the wafers.

[0085] In most system applications, the vast majority of processes have strict requirements for the wafer temperature profile, requiring both rapid heating and cooling. Cooling can be achieved simply and effectively by introducing either low-temperature or room-temperature gas, with the type of gas varied depending on the specific process requirements. For safety reasons, cooling water circulates through the heating chamber walls.

[0086] The method of the present invention is a key software module in the independently developed temperature control algorithm. It can be applied to different types of equipment. Currently, the main application equipment includes RTA, IDP and IDP Plus. The difficulty of the temperature control algorithm includes:

[0087] 1. Strong coupling relationship. Silicon wafers are large in size, and there is a strong coupling relationship between the multi-temperature zone controls, which makes it difficult to quickly and uniformly control the temperature.

[0088] 2. High adaptability requirements. RTP equipment processes are diverse and require very high algorithm adaptability. Often, an algorithm is required to perform well under various temperatures, pressures, heating rates, and various structural sheets.

[0089] 3. High control accuracy is required. 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.

[0090] 4. Nonlinear control: In model-based design, the nonlinearity, time-varying nature, and delay of temperature control systems increase the difficulty of modeling.

[0091] After the method of the present invention is applied to the system, the temperature difference can be significantly reduced. Figure 2a 、 2b As shown in the figure, 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, it can be seen that the temperature difference is reduced from 5.2°C to 2.3°C after optimization.

[0092] 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 for the control rate. Therefore, the situation of considering system constraints is not covered by the present invention.

[0093] 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 temperature control accuracy requirements.

[0094] 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 various embodiments of the present invention.

Claims

1. A method for designing an objective function in temperature control of a rapid thermal processing equipment, characterized in that: The rapid thermal processing equipment used therein includes a heating chamber for accommodating wafers and a temperature control system. The temperature control system includes a heating lamp group for heating the wafers. The heating lamp group is directly opposite the wafers and is divided into multiple lamp zones. The control voltage of each lamp zone can be controlled independently. The wafer is divided into several temperature zones. The rapid thermal processing equipment is also equipped with several temperature measuring devices to measure the temperature of each temperature zone on the wafer. The objective function design method for temperature control of 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, resulting in the following objective function: ， ,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 N time points in and 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 in the N time points after the k moment; each element in the R matrix is ​​the weight of controlling each control voltage in the total N time points of k and thereafter; each element in the S matrix is ​​the weight of controlling each temperature difference in the N time points after the k moment.

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 several lamp zones in a concentric circle manner, and each lamp zone has several 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 set at the bottom of the heating chamber through a magnetic levitation rotation system. A support ring is set on the quartz bracket for placing the wafer. The heating lamp group is a halogen tungsten lamp array, which is installed in a reflective cover above the heating chamber.

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