A method for controlling the temperature of a hot plate to compensate for thermal deformation of a wafer

Abstract

This application discloses a hot plate temperature control method for compensating for wafer thermal deformation, relating to the field of semiconductor manufacturing processes. The method estimates the wafer's thermal deformation in real time using temperature signals from temperature detection units located in different heating areas of the hot plate, and compensates for the heating power of the hot plate based on the estimated thermal deformation. This method can infer the wafer's thermal deformation state in real time using existing temperature detection unit signals on the hot plate without the need for additional complex topography measurement devices, and adjust the hot plate heating power and heating rate accordingly, thereby improving wafer heating uniformity and process stability.

Description

Technical Field

[0001] This application relates to the field of semiconductor manufacturing process technology, and in particular to a method for controlling the temperature of a hot plate to compensate for thermal deformation of a wafer. Background Technology

[0002] In semiconductor manufacturing processes, steps such as soft baking and hard baking in photolithography, as well as pre- and post-processing steps in CVD / ALD, typically involve placing a silicon wafer on a hot plate and heating it to a predetermined temperature to achieve purposes such as photoresist curing, film stabilization, or stress adjustment. As device feature sizes decrease and three-dimensional structures increase, the surface film structure of the wafer becomes increasingly complex. Furthermore, the widespread application of back-side grinding processes has significantly reduced wafer thickness, leading to thermal deformations such as bowl-shaped, saddle-shaped, and composite curvatures during the heating and cooling process. The warpage increases significantly after thinning, resulting in a substantial impact on process yield.

[0003] Existing methods for measuring and compensating warpage include two approaches. One approach uses analytical methods such as the Stoney formula to correlate curvature with thin film stress. However, these methods are only suitable for unidirectional, uniform bowl-shaped warpage and cannot accurately characterize saddle-shaped or complex curvature deformations, making them unsuitable for online control. Another approach uses complex morphology measurement equipment, but this suffers from long measurement times, high costs, and limited resolution of complex warpages. It cannot achieve real-time measurement of each wafer in mass production lines, nor can it provide real-time feedback on warpage status during hot plate heating. Summary of the Invention

[0004] This application provides a hot plate temperature control method, device, medium, and hot plate for compensating for wafer thermal deformation. It can infer the thermal deformation state of the wafer in real time by using the temperature detection unit signal on the hot plate without the need for additional complex topography measurement devices, and adjust the heating power and heating rate of the hot plate accordingly, thereby improving the wafer heating uniformity and process stability.

[0005] In a first aspect, this application provides a method for controlling the temperature of a hot plate for compensating for thermal deformation of a wafer, comprising: After the hot plate is preheated to the hot plate reference temperature and the wafer is placed on the preheated hot plate, the temperature of each heating area is collected by temperature detection units arranged on at least one heating area of ​​the hot plate. Based on the hot plate reference temperature and the temperature of each heating zone, the temperature drop difference of at least one second heating zone relative to the first heating zone is obtained, wherein the heating zone of the hot plate is divided into a first heating zone and at least one second heating zone. At least one thermal deformation amount is determined to characterize the thermal deformation state of the wafer based on the temperature drop difference between at least one second heating region and the first heating region and a pre-calibrated compensation coefficient. Heating power distribution control is performed on each heating zone of the hot plate based on at least one thermal deformation amount and a preset target thermal deformation value.

[0006] Secondly, this application provides a hot plate temperature control device, comprising: Temperature detection units are installed in each heating zone of the hot plate; The control unit is used to execute the hot plate temperature control method provided in the first aspect for compensating for wafer thermal deformation.

[0007] Thirdly, this application provides a hot plate, including a first heating area and at least one second heating area, wherein temperature detection units are respectively arranged on the first heating area and each of the second heating areas, and the hot plate further includes a control unit, which is electrically connected to the temperature detection units and is used to execute the hot plate temperature control method for compensating for wafer thermal deformation provided in the first aspect.

[0008] In an alternative embodiment of the third aspect, the first heating area is located in the central area of ​​the hot plate, and the second heating area is located in the peripheral area of ​​the hot plate. The hot plate is provided with a second heating area, and the temperature detection unit of the second heating area is arranged at a corresponding position near the outer edge of the wafer in the second heating area; Alternatively, the hot plate may be provided with multiple second heating areas, which are arranged at intervals along the circumference. The temperature detection units on the multiple second heating areas are arranged with equal diameters and angles, or at positions with different radii and angles.

[0009] Fourthly, this application provides a computer-readable storage medium storing a computer program, which, when executed by a processor, performs the hot plate temperature control method for compensating for wafer thermal deformation provided in the first aspect.

[0010] The hot plate temperature control method, apparatus, medium, and hot plate for compensating for wafer thermal deformation provided in this application have at least the following beneficial effects: By utilizing temperature signals from temperature detection units located in different heating zones of the hot plate, the thermal deformation of the wafer is estimated in real time. Based on the estimated thermal deformation, the heating power of the hot plate is compensated and controlled. This allows for the real-time inference of the wafer's thermal deformation state using existing temperature detection unit signals on the hot plate, without the need for additional complex topography measurement equipment. The heating power and heating rate of the hot plate are adjusted accordingly, thereby improving wafer heating uniformity and process stability. Furthermore, this application analyzes the thermal conduction response (temperature drop mode) rather than directly relying on a single curvature model and the Stoney formula. Therefore, it is applicable not only to bowl-shaped warpage but also to saddle-shaped and other complex curvature warpages. Attached Figure Description

[0011] The accompanying drawings, which are incorporated in and form part of this specification, illustrate embodiments consistent with this application and, together with the description, serve to explain the principles of this application.

[0012] Figure 1 A schematic flowchart of a hot plate temperature control method for compensating for wafer thermal deformation provided in an embodiment of this application; Figure 2 This is a schematic diagram of a hot plate heating partition structure provided in an embodiment of this application; Figure 3 This is a schematic diagram showing the temperature of the central heating area, the temperature of the surrounding heating area, the temperature drop difference ΔTdiff, and the estimated thermal deformation w0 over time in the embodiments of this application. Figure 4 This is a schematic diagram of another hot plate heating partition structure provided in an embodiment of this application; Figure 5 This is a schematic diagram of another hot plate heating partition structure provided in an embodiment of this application; Figure 6 This is a schematic diagram of a hot plate provided in an embodiment of this application. Detailed Implementation

[0013] It should be understood that the specific embodiments described herein are merely illustrative of the technical solutions of this application and are not intended to limit this application.

[0014] It should be noted that "multiple" in this application refers to two or more.

[0015] As mentioned in the background section, wafer thinning is used to reduce wafer thickness, improve package thickness, and enhance heat dissipation performance. However, this process can lead to the following issues:

[0016] (1) Due to the different coefficients of thermal expansion (CTE) of each layer of material and the presence of intrinsic stress in the thin film, wafers are prone to significant thermal deformation during heating and cooling. This warpage includes not only bowl-shaped warpage that bends upward or downward as a whole, but also often presents saddle-shaped warpage with two mutually perpendicular directions of curvature and opposite signs, as well as more complex composite curvature morphologies.

[0017] (2) When the wafer is thicker, the overall rigidity is greater, and the warpage caused by the same film stress is smaller. However, when the wafer is thinned to hundreds of micrometers or even thinner by back-side grinding, the same film stress will cause a significant increase in warpage, and the impact of warpage on the process and yield becomes more prominent.

[0018] Traditional approaches often use analytical relationships similar to the Stoney formula to link a single curvature with the average equivalent stress of the thin film. However, the Stoney formula and its variations typically assume that the wafer deformation is a unidirectional uniform curvature, i.e., an approximate bowl-shaped warp. When actual wafers exhibit saddle-shaped or complex curvature deformations, for example, curvatures in different directions on the same wafer may have opposite signs, and the stress state at the same location is no longer in a one-to-one correspondence with the local curvature. Therefore, single curvature models and analytical formulas based on these models cannot accurately characterize actual warpages and are difficult to use for online control.

[0019] Furthermore, most existing wafer warpage measurement equipment uses methods such as optical scanning to measure the overall morphology of the wafer on a dedicated measurement stage and calculate the bow or principal curvature. This type of equipment has the following shortcomings: (1) Long measurement time and high equipment cost; (2) Most assumptions are that the wafer is close to a bowl-shaped warp, and the analysis of saddle-shaped and complex warps is limited; (3) It is difficult to perform real-time measurement on each wafer in a high-speed mass production line; (4) It is impossible to provide real-time feedback on the warpage during the heating process of the hot plate, so as to directly control the heating conditions.

[0020] On the other hand, existing hot plate equipment typically only arranges a small number of temperature sensing units inside or on the surface of the hot plate, using PID control to keep the hot plate temperature tracking the set temperature. This method only controls the "hot plate body temperature" and does not incorporate the contact state between the wafer and the hot plate, or wafer warpage, into the control parameters. When the wafer experiences bow or saddle warping, the actual contact conditions between the center of the hot plate and the surrounding heating areas change as follows: First, heat conduction is enhanced in areas with good contact, resulting in a more significant drop in local hot plate temperature; second, heat conduction is weakened in areas with gaps, so even if the hot plate surface temperature is close to the set value, the wafer body temperature is still lower than other areas. Therefore, even if the hot plate surface appears to have a "uniform temperature," the temperature distribution on the wafer body may be severely uneven, directly affecting the consistency of lithographic linewidth (CD), film thickness uniformity, and stress distribution, thereby reducing device performance and yield.

[0021] Traditional approaches either involve offline warpage simulation using finite element method (FEA) software during the design phase, or offline warpage measurement of a portion of the wafer using dedicated measurement equipment for process evaluation. However, neither of these methods is suitable for real-time warpage estimation and dynamic compensation control during wafer heating using the hot plate's own sensors in mass production.

[0022] Based on this, this application provides a hot plate temperature control method for compensating for wafer thermal deformation, applied in semiconductor manufacturing processes where wafers are heated on a hot plate. This method utilizes temperature detection unit signals located at the center and periphery of the hot plate to estimate the wafer's thermal deformation in real time, and compensates for the heating power and heating rate of the hot plate based on the estimated thermal deformation. It can infer the wafer's thermal deformation state (including combined warpage including bowl-shaped and saddle-shaped warpage) in real time using existing temperature detection unit signals on the hot plate without the need for additional complex topography measurement devices, and adjust the hot plate heating power and heating rate accordingly, thereby improving wafer heating uniformity and process stability.

[0023] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0024] Please see Figure 1 The hot plate temperature control method for compensating for wafer thermal deformation provided in this application includes the following steps: S10: After the hot plate is preheated to the hot plate reference temperature and the wafer is placed on the preheated hot plate, the temperature of each heating area is collected using temperature detection units arranged on at least one heating area of ​​the hot plate.

[0025] In practice, the hot plate is first heated to the predetermined preheating temperature and kept at that temperature for a period of time to allow the hot plate to reach thermal equilibrium. The temperature of the hot plate at this point is then used as the reference temperature of the hot plate.

[0026] Then, a wafer with an initial temperature lower than the hot plate reference temperature (e.g., a 300mm wafer with an initial temperature of approximately 23°C, a 10μm Al metal film on the top, and a 750μm Si substrate on the bottom) is placed on the preheated hot plate. Temperature signals for each heating area are collected by temperature detection units located on the hot plate, and the temperature of each heating area is obtained. When collecting temperature signals for each heating area, continuous sampling can be performed according to a preset sampling period (e.g., 0.1s, sampling frequency ≥10Hz).

[0027] The hot plate contains multiple heating zones, each equipped with a corresponding temperature detection unit. The temperature detection unit can be an independent temperature sensor, such as a thermistor temperature sensor, a thermal sensor array temperature sensor, a MEMS temperature sensor, or a thermal diode temperature sensor, or it can be a temperature sensing probe of a temperature sensor.

[0028] S20, based on the hot plate reference temperature and the temperature of each heating zone, obtain the temperature drop difference of at least one second heating zone relative to the first heating zone, wherein the heating zone of the hot plate is divided into a first heating zone and at least one second heating zone.

[0029] The first heating zone serves as a temperature reference zone.

[0030] In practice, the difference between the hot plate reference temperature and the real-time temperature of each heating region is first calculated to obtain the temperature drop of each heating region. Then, the heating regions are classified into a first heating region and a second heating region, with the first heating region set as the temperature reference region of the hot plate. The temperature drop difference between each second heating region and the first heating region is measured using this temperature as a benchmark. This temperature drop difference directly reflects the uneven heat conduction caused by the different contact states between different regions of the wafer and the hot plate during the hot plate heating process, thus characterizing the difference in the degree of thermal deformation in corresponding regions or different directions of the wafer.

[0031] In one embodiment, the temperature drop difference between the second heating region and the first heating region is obtained by calculating the difference between the temperature drop value of the second heating region and the temperature drop difference of the first heating region.

[0032] In another embodiment, based on the difference between the temperature drop value of the second heating region and the temperature drop difference of the first heating region, a first-order low-pass filter can be applied to the difference to obtain the temperature drop difference between the second heating region and the first heating region, so as to reduce the influence of measurement noise.

[0033] S30, at least one thermal deformation amount is determined to characterize the thermal deformation state of the wafer based on the temperature drop difference between at least one second heating region and the first heating region and a pre-calibrated compensation coefficient.

[0034] Optionally, each second heating zone uniquely corresponds to a compensation coefficient. The calibration method for the compensation coefficient includes: The first step is to prepare various wafer samples with different structures (different types of metal films, thicknesses, stacking structures and thicknesses, etc.), and measure the actual thermal deformation w_actual under certain temperature conditions using an external warpage measuring device; The same piece is placed on the hot plate, and the temperature drop difference ΔTdiff_j between each second heating area and the first heating area is obtained by using the calculation method in S20 above. ΔTdiff_j represents the temperature drop difference between the j-th second heating area and the first heating area. When there is only one second heating area, there is only one temperature drop difference ΔTdiff. Regression analysis is performed on w_actual and ΔTdiff to obtain the compensation coefficient K_T corresponding to different wafer types, or regression analysis is performed on the relationship between w_actual and ΔTdiff_j to obtain the compensation coefficient K_Tj corresponding to different wafer types and different second heating regions, and a calibration table is formed.

[0035] During mass production, a portion of wafers can be selected for periodic actual warpage measurements. The measured w_actual_online value is compared with the thermal deformation calculated by the method in this application embodiment, and the deviation is calculated. K_T or K_Tj is updated appropriately based on the deviation to compensate for equipment aging and sensor drift.

[0036] In this embodiment, the thermal deformation state of the wafer is characterized under different scenarios: In the first case, if there is only one second heating region, the temperature drop difference ΔTdiff_f(t) between the second heating region and the first heating region is multiplied by the pre-calibrated compensation coefficient K_T to obtain the thermal deformation amount w0(t) of the wafer. After calibration by an external warpage measurement device, w0(t) can correspond to the equivalent warpage height or equivalent thermal deformation near the first heating region and is used as a representative indicator of wafer warpage. A positive value can represent the average upward arching state of the first heating region (e.g., the central heating region) or the saddle-shaped warpage, while a negative value can correspond to the average downward arching state of the first heating region or the saddle-shaped warpage.

[0037] In the second case, if there are multiple second heating regions, the temperature drop difference between each second heating region and the first heating region is multiplied by its corresponding compensation coefficient to obtain the thermal deformation amount corresponding to each second heating region. Then, the wafer thermal deformation state is characterized using any of the following methods: Method 1: The thermal deformation state of the wafer is characterized by the combined thermal deformation amount corresponding to all the second heating areas of the hot plate, so as to reflect the difference in the degree of thermal deformation in the corresponding areas or different directions of the wafer.

[0038] Method 2: Calculate the arithmetic mean of the thermal deformation amounts corresponding to all the second heating areas of the hot plate to obtain the overall thermal deformation amount, so as to characterize the thermal deformation state of the wafer as a whole.

[0039] The arithmetic mean can be calculated using either a simple arithmetic mean or a weighted average.

[0040] Method 3: Perform two-dimensional surface fitting or interpolation on the thermal deformation amounts corresponding to multiple second heating areas of the hot plate to obtain the thermal deformation distribution on the wafer surface, and characterize the thermal deformation state of the wafer through the thermal deformation distribution.

[0041] Specifically, after obtaining the thermal deformation amount w_j of each second heating zone, w_j is fitted into a two-dimensional surface w(x,y) using methods such as least squares fitting based on the position coordinates (x_j,y_j) of each temperature detection unit, thereby obtaining the thermal deformation distribution. Through this thermal deformation distribution, the thermal deformation amount at each location point of the hot plate can be obtained, thus achieving precise temperature compensation at different locations of the hot plate based on the thermal deformation amount at different locations.

[0042] S40, based on at least one thermal deformation amount and a preset target thermal deformation value, performs heating power distribution control on each heating area of ​​the hot plate.

[0043] In some implementations, control calculations can be performed based on the error between the thermal deformation of at least one second heating zone and the target thermal deformation value to obtain control parameters for adjusting the power distribution of different heating zones of the hot plate. Then, the heating power of different heating zones of the hot plate can be differentiated and controlled based on the control parameters.

[0044] Optionally, the differentiated allocation and control of heating power for different heating zones of the hot plate based on control parameters may include: obtaining the overall heating power of the hot plate; allocating the heating power of each heating zone based on the overall heating power of the hot plate, the control quantity / power correction quantity of each second heating zone / power compensation of each heating zone, to obtain the final heating power of each heating zone, wherein, during the allocation process, the heating power of each heating zone is adjusted by limiting processing, normalization processing, or power compensation deduction so that the sum of the final heating power of each heating zone does not exceed the overall heating power of the hot plate.

[0045] The following describes the implementation of power distribution in conjunction with different partitioned heating structures of the hot plate.

[0046] Scenario 1: Assuming the heating area of ​​the hot plate contains only one first heating area and one second heating area, the control parameters and power differentiation allocation are determined through the following steps: First, the difference between the target thermal deformation value w_target and the thermal deformation amount w0(t) of the second heating area relative to the first heating area is calculated to obtain the thermal deformation error e_w(t), e_w(t)=w_target−w0(t). Then, the thermal deformation error e_w(t) is calculated using a PI or PID control algorithm to obtain the control quantity u_bow(t) used to adjust the power distribution between the first heating area and the second heating area of ​​the hot plate.

[0047] Then, the average temperature of the hot plate, T_avg(t), is calculated by averaging the temperatures of all heating zones. The difference between the average hot plate temperature T_avg(t) and the target temperature setpoint T_set(t) is then calculated as the temperature error. In the temperature control loop (i.e., temperature PID control), the overall heating power P_tot(t) of the hot plate is obtained using the temperature error as input. Based on the control quantity u_bow(t), the overall heating power P_tot(t) is allocated to the final heating power P_c(t) of the first heating zone and the final heating power P_e(t) of the second heating zone.

[0048] As an example, the final heating power of the first heating zone The final heating power of the second heating zone .

[0049] Scenario 2: Assuming the heating area of ​​the hot plate includes one first heating area and multiple second heating areas, the control parameters and power differentiation allocation can be determined using any of the following methods: Method 1: Calculate the difference between the target thermal deformation value and the arithmetic mean of the thermal deformation values ​​of all second heating regions to obtain the overall thermal deformation error. Perform control calculations on the overall thermal deformation error to obtain a control quantity u_bow(t) for adjusting the power distribution of different heating regions of the hot plate. Then, based on the control quantity u_bow(t), allocate the total heating power P_tot(t) to the first heating region and each of the second heating regions.

[0050] Specifically, u_bow(t) can be allocated to each heating region (including the first heating region and the second heating region) according to a preset allocation weight w_i. Each allocation weight w_i can be determined based on the area, radius position, sensitivity to the warping of the hot plate, historical calibration data, or real-time temperature feedback data of each heating region, and satisfies the following:

[0051] Σw_i=1.

[0052] Therefore, the compensation power of the i-th heating region (first heating region / second heating region) can be expressed as: ΔP_i(t)=w_i×u_bow(t)×P_tot(t).

[0053] Where ΔP_i(t) represents the compensation power of the i-th heating region, and w_i represents the power allocation weight of the i-th heating region.

[0054] The initial target heating power P_i,raw(t) for the i-th heating region can be expressed as: P_i,raw(t)=P_i0(t)+ΔP_i(t).

[0055] Wherein, P_i0(t) is the basic heating power of the i-th heating region, which can be determined based on the region area, radius, heat capacity, or calibration data.

[0056] After obtaining the initial target heating power, the final heating power P_i(t) is obtained through limiting, normalization or power compensation deduction, and it is guaranteed that: ΣP_i(t)≈P_tot(t) or ΣP_i(t)≤P_tot(t).

[0057] In one implementation, each heating zone can be evenly distributed with the same weight; in another implementation, the distribution can be non-uniform based on the radius of each heating zone from the center of the hot plate or the thermal deformation influence coefficient; in a further implementation, the distribution weight w_i can be dynamically corrected based on the feedback value of the temperature detection unit of each heating zone, the deviation between the target thermal deformation value and the actual thermal deformation value.

[0058] Therefore, even if the control quantity u_bow(t) is a total control quantity, multiple independent or semi-independent power outputs of heating zones can be formed through weight allocation, thereby achieving fine compensation control of thermal deformation of the hot plate heating zone.

[0059] Method 2: Calculate the difference between the target thermal deformation value and the thermal deformation of each second heating region to obtain the thermal deformation error of each second heating region. Then, perform control calculations on the thermal deformation errors of each second heating region to obtain the power correction amount of each second heating region. This can be expressed by the formula: e_wj=w_target−w_j, where e_wj represents the thermal deformation error of the j-th second heating region, w_target is the target thermal deformation value, and w_j is the thermal deformation of the j-th second heating region. Then, use a PI or PID control algorithm to calculate the thermal deformation error corresponding to each second heating region to obtain the power correction amount u_j of each second heating region.

[0060] In this application, u_j is the output of the control algorithm corresponding to the j-th second heating zone, not the final heating power. The control unit calculates the actual power correction ΔP_j based on u_j. ΔP_j = K_j × u_j.

[0061] Wherein, K_j is the power correction coefficient for the j-th direction or the j-th second heating region, which can be determined based on the region area, radius position, thermal deformation sensitivity, experimental calibration results, or real-time feedback results.

[0062] In one implementation, the initial target power P_ej,raw(t) of the j-th second heating region can be expressed as: P_ej,raw(t)=P_ej0(t)+ΔP_j(t).

[0063] The initial target power P_c,raw(t) of the first heating region can be expressed as: P_c,raw(t)=P_c0(t).

[0064] Where P_c0(t)=α_c×P_tot(t), P_ej0(t)=α_ej×P_tot(t), and α_c+Σα_ej=1.

[0065] α_c and α_ej can be determined based on the area ratio, radius position, heat capacity, sensitivity to thermal deformation, experimental calibration results, or historical operating data of each heating zone.

[0066] When the areas of each heating region are the same or approximately the same, we can let α_c = α_ej = 1 / N. In this case, Pc0(t) = P_tot(t) / N is only a special case of equal distribution.

[0067] To prevent the total heating power after power correction in each region from exceeding or falling below P_tot(t), the control unit further performs total power constraint processing on the initial target power of each heating region. Specifically, a normalization coefficient λ(t) can be used: λ(t)=P_tot(t) / [P_c,raw(t)+ΣP_ej,raw(t)].

[0068] Therefore, the final heating power P_c(t) of the first heating region can be expressed as: P_c(t) = λ(t) × P_c,raw(t).

[0069] The final heating power P_ej(t) of the second heating region can be expressed as: P_ej(t)=λ(t)×P_ej,raw(t).

[0070] Therefore, it can be guaranteed that: P_c(t)+ΣP_ej(t)=P_tot(t).

[0071] In another implementation, the power correction amount ΔP_j of each second heating region can be superimposed and then compensated and subtracted by the first heating region or other non-target heating regions, that is: P_ej(t)=Pc0(t)+ΔP_j(t), P_c(t) = P_tot(t) - ΣP_ej(t).

[0072] When P_c(t) exceeds the allowable power range, the control unit can limit ΔP_j or readjust the allocation weights of each region.

[0073] Therefore, this application does not simply distribute P_tot equally and then directly superimpose u_j, but uses u_j as the power correction amount corresponding to the directional thermal deformation error, and recalculates the final heating power of each heating region under the total power constraint.

[0074] Method 3: Based on the thermal deformation distribution, calculate the thermal deformation w_i=w(x_i,y_i) at the target location point (x_i,y_i) in each heating area, and obtain the error e_wi by subtracting the target deformation value w_target from w_i. Use PI or PID algorithm to calculate the power compensation u_i' for each heating area, and finally allocate the total heating power P_tot as P_i=P_i0+u_i', where P_i represents the heating power at location point (x_i,y_i), and normalization can be used to keep ΣP_i≈P_tot, thereby achieving fine compensation.

[0075] Wherein, P_i0(t) represents the base heating power allocated to position point i or the i-th heating region without the superimposed local thermal deformation compensation amount u_i'(t). In other words, P_i0(t) is the base power initially allocated from the total heating power P_tot(t) according to the preset allocation rules, and u_i'(t) is the local power correction amount superimposed on this base power.

[0076] In one implementation, when the areas of each heating region are the same or approximately the same, P_i0(t) can be calculated using an average distribution method: P_i0(t) = P_tot(t) / N.

[0077] Where N represents the number of locations or heating zones involved in power distribution.

[0078] In another implementation, when the heating areas, radii, or heat capacities of the heating zones differ, P_i0(t) can be calculated using a weighted allocation method: P_i0(t)=α_i×P_tot(t).

[0079] Where α_i is the reference power allocation coefficient of the i-th location point or the i-th heating area, and satisfies: Σα_i=1.

[0080] α_i can be determined based on the area ratio, heat capacity, radius position of the corresponding heating area, correspondence with the target temperature area, experimental calibration results, or historical operating data.

[0081] Furthermore, when the hot plate has one first heating zone and multiple second heating zones, P_tot(t) can be first allocated as the reference heating power P_c0(t) for the first heating zone and the reference heating power P_e0(t) for the second heating zones, and then the heating power of the second heating zones can be redistributed according to the allocation coefficients of each second heating zone. For example: P_c0(t)=α_c×P_tot(t).

[0082] P_ei0(t)=α_ei×P_tot(t).

[0083] Where α_c+Σα_ei=1.

[0084] Finally, the final heating power of the i-th location point or the i-th heating area can be expressed as: P_i(t) = P_i0(t) + u_i'(t), where P_i0(t) = P_c0(t) when the i-th position is the first heating region, and P_i0(t) = P_ei0(t) when the i-th position is the second heating region.

[0085] Furthermore, the control unit can perform limiting, normalization, or power compensation deduction to ensure that the final heating power at each location point or in each heating zone meets the following requirements: ΣP_i(t)≈P_tot(t).

[0086] or: ΣP_i(t)≤P_tot(t).

[0087] In some implementations, the overall heating power of the hot plate is obtained by temperature control calculation (temperature PID control) based on the error between the average temperature of the hot plate and the target temperature setpoint T_set(t) that is dynamically updated during the heating process. Let the rate of change of the target temperature setpoint be the heating rate. When the absolute value of the thermal deformation exceeds a preset thermal deformation limit w_lim (e.g., 50 μm), the heating rate is reduced.

[0088] That is, when |w0|≤w_lim, the basic heating rate R_0 (which is a set value) is used; when |w0|>w_lim, the heating rate is reduced as follows: .

[0089] Where R_0 is the basic heating rate and β is the adjustment coefficient. T_set(t+Δt) is updated based on R(t), thereby reducing thermal stress and temperature non-uniformity when the warpage is too large.

[0090] Optionally, the first heating area is located in the central area of ​​the hot plate, and the second heating area is located in the peripheral area of ​​the hot plate. The hot plate can be divided into a central heating area and a peripheral heating area.

[0091] Alternatively, the heating area of ​​the hot plate can be divided into a central heating area and at least one layer of peripheral heating areas arranged at intervals along the circumference, with each layer having the same number of peripheral heating areas. In this case, the temperature detection units on each peripheral heating area can be arranged in a manner with equal diameter and equal angle. Preferably, power distribution is performed using a power correction method based on the thermal deformation error of each peripheral heating area.

[0092] Alternatively, the hot plate is divided into a central heating area and multiple peripheral heating areas arranged at intervals along the circumference, with different numbers of peripheral heating areas at different levels. In this case, the temperature detection units on each peripheral heating area are positioned at different radii and angles. Preferably, power distribution is performed using a method based on the distribution of wafer thermal deformation to obtain the power compensation amount for each heating area.

[0093] It should be noted that, for cases with multiple surrounding heating areas, the above-mentioned different partitioning structures can all adopt the three heating power differentiation allocation methods provided in Case 2 mentioned above in this application, and are not limited to the preferred implementation methods mentioned in this application.

[0094] The hot plate temperature control method for compensating for wafer thermal deformation provided in this application has the following beneficial effects: (1) This application only uses temperature sensor signals from different heating zones to estimate the thermal deformation of the wafer in real time by the temperature drop difference. No additional optical warpage measurement equipment is required, and warpage-related information can be obtained online during the actual heating process of the wafer.

[0095] (2) This application analyzes the thermal conduction response (temperature drop mode) instead of relying directly on a single curvature model and Stoney formula. Therefore, it is not only applicable to bowl-shaped warpage, but also provides effective compensation for saddle-shaped and other composite curvature warpage. In particular, when using a multi-region, multi-sensor structure, the deformation distribution of the entire wafer can be obtained through two-dimensional fitting, thus achieving more precise control.

[0096] (3) By dynamically adjusting the power distribution of different heating areas of the hot plate using the estimated thermal deformation, the temperature uniformity of the wafer surface can be significantly improved, the consistency of lithography linewidth, film thickness uniformity and stress distribution uniformity can be enhanced, and the device performance and yield can be improved.

[0097] (4) When the warpage is detected to be too large, this application automatically reduces the heating rate, which can effectively reduce the temperature gradient and stress gradient, reduce the probability of thermal stress-related defects such as wafer cracking and film peeling, and improve process reliability.

[0098] (5) This application makes full use of the existing temperature sensor and heater on the hot plate. Warpage compensation control can be achieved by upgrading the software and control logic. There is no need to add complex physical measurement devices. The hardware modification is small, and it has good engineering feasibility and cost advantages.

[0099] The following describes several embodiments of the present invention in detail, taking the first heating area as the central heating area and the second heating area as the peripheral heating area, with reference to the accompanying drawings. Those skilled in the art should understand that these embodiments are for illustrative purposes only and are not intended to limit the scope of protection of the present invention.

[0100] Example 1: 3mm AlN hot plate + two temperature detection units + two heating zones

[0101] In this embodiment: The hot plate is made of AlN material, approximately 3mm thick, and large enough to support a 300mm wafer; the hot plate contains a heater in the central heating area and a ring heater in the peripheral heating area. For example... Figure 2 As shown, a temperature sensor is positioned near the center of the hot plate, directly below or near the center of the wafer; another temperature sensor is positioned near the outer edge of the hot plate to detect the temperature of the surrounding heated area. The control unit is electrically connected to the heater and temperature sensors described above, and is used to execute the hot plate temperature control method for compensating for wafer thermal deformation provided in this embodiment of the application.

[0102] Before the process begins, the control unit drives the heater to heat the hot plate to a preheating temperature T_pre, for example, 110°C, and records this temperature as the hot plate reference temperature Tp0 when the plate is in thermal equilibrium. Subsequently, a 300mm wafer with an initial temperature of approximately 23°C is placed on the hot plate. The wafer consists of an upper Al metal film of 10μm and a lower Si substrate of 750μm.

[0103] During the instant of wafer placement and for a short period thereafter, the control unit reads Tc(t) and Te(t) at a sampling period of 0.1s, calculates ΔTc(t), ΔTe(t), and their difference ΔTdiff(t) = ΔTe − ΔTc, and obtains ΔTdiff_f(t) through a first-order low-pass filter. Using a pre-calibrated compensation coefficient K_T, ΔTdiff_f(t) is converted into thermal deformation w0(t) = K_T · ΔTdiff_f(t), which serves as a representative quantity of the wafer warpage. Figure 3 As shown, Figure 3 This is a schematic diagram showing the temperature of the central heating area, the temperature of the surrounding heating area, the temperature drop difference ΔTdiff, and the estimated thermal deformation w0 over time.

[0104] The control unit sets a target thermal deformation value w_target (e.g., 0 μm), calculates e_w(t) = w_target − w0(t), and obtains the power distribution control quantity u_bow(t) through a PI or PID algorithm. Simultaneously, based on the temperature error e_T(t) between the current target temperature setpoint T_set(t) and the average temperature of the hot plate T_avg(t) = (Tc + Te) / 2, the control unit uses a temperature control algorithm to calculate the overall heating power P_tot(t).

[0105] Finally, the control unit allocates P_tot(t) as follows: P_c(t)=P_tot(t)·(0.5+u_bow(t)); P_e(t)=P_tot(t)·(0.5−u_bow(t)); These are used to drive the center heater and the peripheral heater, respectively. When a warpage is detected to tend to convex upwards or concave downwards at the center, the control unit can determine the sign and magnitude of u_bow(t) based on the pre-calibrated correspondence between the thermal deformation direction and the power compensation direction, thereby creating a corresponding differentiated power distribution between the center heating area and the peripheral heating area.

[0106] In addition, when |w0(t)| exceeds the preset threshold w_lim, the control unit reduces the heating rate R(t), thereby reducing thermal stress and temperature non-uniformity.

[0107] Example 2: Four-zone hot plate + four temperature detection units (directional warpage compensation)

[0108] In this embodiment, as Figure 4 As shown, the hot plate is divided into: a central heating zone and three peripheral heating zones arranged at approximately 120° intervals along the circumference. Temperature sensors are installed in the central heating zone and the three peripheral heating zones. The control unit calculates the temperature drop difference between each peripheral heating zone and the central heating zone. ΔTdiff1=ΔTe1−ΔTc, ΔTdiff2=ΔTe2−ΔTc, ΔTdiff3=ΔTe3−ΔTc; The directional thermal deformation amounts w1, w2, and w3 are calculated using their respective compensation coefficients K_T1, K_T2, and K_T3. The control unit can obtain the overall w0 based on the average value of w1, w2, and w3, or it can directly calculate the power correction amounts u1, u2, and u3 for each region based on the directional errors e_w1=w_target−w1, and distribute the overall power P_tot as P_c, P_e1, P_e2, and P_e3 to achieve directional compensation for the asymmetric warpage (including the saddle component).

[0109] Example 3: 16-zone hot plate + multiple temperature detection units + two-dimensional warpage compensation

[0110] In this embodiment, as Figure 5 As shown, the hot plate has 16 heating zones inside, including one central heating zone and 15 peripheral heating zones located at different radii and angles. Each heating zone is equipped with a temperature sensor.

[0111] The control unit calculates the difference ΔTdiff_j between the temperature drop at each temperature sensor position j and the center temperature, and calculates the local thermal deformation w_j using the compensation coefficient K_Tj. Based on the temperature sensor's position coordinates (x_j, y_j), the control unit uses methods such as least squares fitting to fit w_j into a two-dimensional surface w(x, y), thereby obtaining the overall warpage distribution of the wafer.

[0112] For each heating region i, the control unit calculates the thermal deformation w_i=w(x_i,y_i) at the center position (x_i,y_i) of its corresponding region, compares it with the target deformation value w_target to obtain the error e_wi, and uses PI or PID algorithm to calculate the power compensation u_i of each heating region. Finally, the overall power P_tot is allocated as P_i=P_i0+u_i, and can be normalized to keep ΣP_i≈P_tot, thereby achieving fine compensation for the two-dimensional warpage.

[0113] This application also provides a hot plate temperature control device, including at least one temperature detection unit and a control unit. The temperature detection unit is disposed on the heating area of ​​the hot plate. The hot plate includes multiple heating areas, and at least one temperature detection unit is disposed in each heating area. Each temperature detection unit is connected to the control unit via wired or wireless means. The control unit is used to execute the hot plate temperature control method for compensating for wafer thermal deformation provided in the above embodiments.

[0114] like Figure 6 As shown, this application embodiment also provides a hot plate 100, including a first heating area and at least one second heating area. Temperature detection units are respectively arranged on the first heating area and each of the second heating areas. The temperature detection unit arranged on the first heating area is a first temperature detection unit 10a, and the temperature detection unit arranged on the second heating area is 10b. The hot plate also includes a control unit, which is electrically connected to the temperature detection unit and is used to execute the hot plate temperature control method for compensating for wafer thermal deformation provided in the above embodiment.

[0115] The first heating zone is located in the center of the hot plate, and the second heating zone is located in the peripheral area of ​​the hot plate.

[0116] The hot plate is provided with a second heating area, and the second temperature detection unit is arranged in the corresponding position of the second heating area near the outer edge of the wafer; Alternatively, the hot plate may be provided with multiple second heating zones, which are arranged at intervals along the circumference. The second temperature detection units on the multiple second heating zones are arranged with equal diameters and angles, or at positions with different radii and angles.

[0117] like Figure 4As shown, a temperature sensor (i.e., a temperature detection unit) can be installed at the center of the central heating area 1, and a temperature sensor can be installed at the center of the peripheral heating areas 2, 3, and 4 respectively. The temperature sensors installed in the peripheral heating areas 2, 3, and 4 are arranged in the radial direction of the hot plate and have the same diameter and angle.

[0118] like Figure 5 As shown, the hot plate can be divided into a central heating area 1 located in the center and 15 peripheral heating areas 2, 3, ... 15, and the temperature sensors arranged in the 15 peripheral heating areas 2, 3, ... 15 can be arranged at different radii and different angle positions.

[0119] This application provides a computer-readable storage medium having computer-readable program instructions (i.e., a computer program) stored thereon. These computer-readable program instructions are used to execute the hot plate temperature control method for compensating for wafer thermal deformation provided in the above embodiments. The computer-readable storage medium provided in this application may be, for example, a USB flash drive, but is not limited to, electrical, magnetic, optical, electromagnetic, infrared, or semiconductor systems, devices, or any combination thereof. More specific examples of computer-readable storage media may include, but are not limited to: electrical connections with one or more wires, portable computer disks, hard disks, random access memory (RAM), read-only memory (ROM), erasable programmable read-only memory (EPROM or flash memory), optical fibers, portable compact disk read-only memory (CD-ROM), optical storage devices, magnetic storage devices, or any suitable combination thereof. In this embodiment, the computer-readable storage medium may be any tangible medium containing or storing a program that can be used by or in conjunction with an instruction execution system, system, or device. Program code contained on a computer-readable storage medium can be transmitted using any suitable medium, including but not limited to: wires, optical fibers, RF (Radio Frequency), etc., or any suitable combination thereof. The aforementioned computer-readable storage medium may be contained within an electronic device; or it may exist independently, not assembled into an electronic device.

[0120] Computer program code for performing the operations of this application can be written in one or more programming languages ​​or a combination thereof, including object-oriented programming languages ​​such as Java, Smalltalk, and C++, and conventional procedural programming languages ​​such as the "C" language or similar programming languages. The program code can be executed entirely on the user's computer, partially on the user's computer, as a standalone software package, partially on the user's computer and partially on a remote computer, or entirely on a remote computer or server. In cases involving remote computers, the remote computer can be connected to the user's computer via any type of network—including a local area network (LAN) or a wide area network (WAN)—or can be connected to an external computer (e.g., via the Internet using an Internet service provider).

[0121] The flowcharts and block diagrams in the accompanying drawings illustrate the architecture, functionality, and operation of possible implementations of systems, methods, and computer program products according to various embodiments of this application. In this regard, each block in a flowchart or block diagram may represent a module, segment, or portion of code containing one or more executable instructions for implementing a specified logical function. It should also be noted that in some alternative implementations, the functions indicated in the blocks may occur in a different order than those indicated in the drawings. For example, two consecutively indicated blocks may actually be executed substantially in parallel, and they may sometimes be executed in reverse order, depending on the functions involved. It should also be noted that each block in the block diagrams and / or flowcharts, and combinations of blocks in the block diagrams and / or flowcharts, can be implemented using a dedicated hardware-based system that performs the specified function or operation, or using a combination of dedicated hardware and computer instructions. Modules described in the embodiments of this application can be implemented in software or hardware. The names of modules do not, in some cases, constitute a limitation on the unit itself.

[0122] The readable storage medium provided in this application is a computer-readable storage medium that stores computer-readable program instructions (i.e., a computer program) for executing the above-described method for controlling the temperature of a hot plate to compensate for wafer thermal deformation. Compared with the prior art, the beneficial effects of the computer-readable storage medium provided in this application are the same as those provided in the above embodiments, and will not be repeated here.

[0123] The above are only some embodiments of this application and do not limit the patent scope of this application. All equivalent structural transformations made under the technical concept of this application and using the content of this application specification and drawings, or direct / indirect applications in other related technical fields, are included in the patent protection scope of this application.

Claims

1. A hot plate temperature control method for compensating for thermal distortion of a wafer, characterized by, include: After the hot plate is preheated to the hot plate reference temperature and the wafer is placed on the preheated hot plate, the temperature of each heating area is collected by temperature detection units arranged on at least one heating area of ​​the hot plate. Based on the hot plate reference temperature and the temperature of each heating zone, the temperature drop difference of at least one second heating zone relative to the first heating zone is obtained, wherein the heating zone of the hot plate is divided into a first heating zone and at least one second heating zone. At least one thermal deformation amount is determined to characterize the thermal deformation state of the wafer based on the temperature drop difference between at least one second heating region and the first heating region and a pre-calibrated compensation coefficient. Heating power distribution control is performed on each heating zone of the hot plate based on at least one thermal deformation amount and a preset target thermal deformation value.

2. The hot plate temperature control method for compensating for wafer thermal deformation as described in claim 1, characterized in that, The determination of at least one thermal deformation amount for characterizing the wafer's thermal deformation state based on the temperature drop difference between at least one second heating region and the first heating region, and a pre-calibrated compensation coefficient, includes: If there is only one second heating region, the temperature difference between the second heating region and the first heating region is multiplied by a pre-calibrated compensation coefficient to obtain the thermal deformation of the wafer. If there are multiple second heating regions, the temperature drop difference between each second heating region and the first heating region is multiplied by its corresponding compensation coefficient to obtain the thermal deformation amount corresponding to each second heating region. The thermal deformation state of the wafer can be characterized using any of the following methods: The thermal deformation state of the wafer is characterized by the combined thermal deformation amounts corresponding to all the second heating zones of the hot plate. The arithmetic mean of the thermal deformation amounts corresponding to all the second heating areas of the hot plate is calculated to obtain the overall thermal deformation amount to characterize the thermal deformation state of the wafer. Two-dimensional surface fitting or interpolation is performed on the thermal deformation amounts corresponding to multiple second heating regions of the hot plate to obtain the thermal deformation distribution on the wafer surface, and the thermal deformation distribution is used to characterize the thermal deformation state of the wafer.

3. The hot plate temperature control method for compensating for wafer thermal deformation as described in claim 2, characterized in that, The compensation coefficient is pre-calibrated and stored based on the material type and thickness of the upper metal film on the wafer; And / or, the first heating area is located in the central area of ​​the hot plate, and the second heating area is located in the peripheral area of ​​the hot plate.

4. The hot plate temperature control method for compensating for wafer thermal deformation as described in claim 2, characterized in that, The method of controlling the heating power distribution of each heating zone of the hot plate based on at least one thermal deformation amount and a preset target thermal deformation value includes: Based on the error between the thermal deformation of at least one second heating zone and the target thermal deformation value, control calculations are performed to obtain control parameters for adjusting the power distribution of different heating zones of the hot plate. The heating power of different heating zones of the hot plate is allocated and controlled differently based on the control parameters.

5. The hot plate temperature control method for compensating for wafer thermal deformation as described in claim 4, characterized in that, The control calculation based on the error between the thermal deformation of at least one second heating zone and the target thermal deformation value yields control parameters for adjusting the power distribution of different heating zones of the hot plate, including: When a second heating zone exists on the hot plate, the thermal deformation error is obtained based on the difference between the target thermal deformation value and the second heating zone, and the control quantity is obtained based on the thermal deformation error. When there are multiple second heating zones, the control parameters can be determined using any of the following methods: The overall thermal deformation error is obtained by calculating the error between the arithmetic mean of the thermal deformation of all second heating zones and the target thermal deformation value. The overall thermal deformation error is then used to obtain the control quantity for adjusting the power distribution of different heating zones of the hot plate. Alternatively, the error between the thermal deformation of each second heating region and the target thermal deformation value can be calculated to obtain the thermal deformation error of each second heating region. The thermal deformation error of each second heating region can be controlled and calculated to obtain the power correction amount of each second heating region. Alternatively, for each heating zone, the thermal deformation amount of the target location point of each heating zone is determined based on the thermal deformation distribution, and control calculations are performed based on the error between the thermal deformation amount of the target location point of each heating zone and the target deformation value, so as to obtain the power compensation amount of each heating zone. And / or, the differentiated allocation of heating power to different heating zones of the hot plate based on control parameters includes: Obtain the overall heating power of the hot plate; The heating power of each heating zone is allocated based on the overall heating power of the hot plate and the control parameters to obtain the final heating power of each heating zone; The final heating power of each heating zone is determined based on the reference heating power of the corresponding heating zone and the power compensation amount determined by the control parameters. Furthermore, during the allocation process, the heating power of each heating zone is adjusted through amplitude limiting, normalization, or power compensation deduction so that the sum of the final heating power of each heating zone does not exceed the overall heating power of the hot plate.

6. The hot plate temperature control method for compensating for wafer thermal deformation as described in claim 5, characterized in that, The overall heating power of the hot plate is obtained by temperature control calculation based on the error between the average temperature of the hot plate and the target temperature setpoint that is dynamically updated during the heating process. The rate of change of the target temperature setpoint is the heating rate. When the absolute value of the thermal deformation is greater than the preset thermal deformation limit, the heating rate is reduced.

7. A hot plate temperature control device, characterized in that, include: Temperature detection units are installed in each heating zone of the hot plate; The control unit is used to perform the hot plate temperature control method for compensating for wafer thermal deformation as described in any one of claims 1 to 6.

8. A hot plate, characterized in that, The hot plate includes a first heating area and at least one second heating area. Temperature detection units are respectively arranged on the first heating area and each of the second heating areas. The hot plate also includes a control unit, which is electrically connected to the temperature detection units and is used to execute the hot plate temperature control method for compensating for wafer thermal deformation as described in any one of claims 1 to 6.

9. The hot plate as described in claim 8, characterized in that, The first heating area is located in the central area of ​​the hot plate, and the second heating area is located in the peripheral area of ​​the hot plate; The hot plate is provided with a second heating area, and the temperature detection unit of the second heating area is arranged at a corresponding position near the outer edge of the wafer in the second heating area; Alternatively, the hot plate may be provided with multiple second heating areas, which are arranged at intervals along the circumference. The temperature detection units on the multiple second heating areas are arranged with equal diameters and angles, or at positions with different radii and angles.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, performs the hot plate temperature control method for compensating for wafer thermal deformation as described in any one of claims 1 to 6.

Images