TW550647B - System and method to control radial delta temperature - Google Patents

Abstract

A system and method of minimizing stress related to the ramp rate of a variable by limiting the ramp rate as a function of the current value of the variable is provided. More specifically, the present invention provides a system and method of maintaining the radial delta temperature of a semiconductor substrate or other heated body below the crystal slip curve by dynamically controlling the temperature ramp rate during processing.

Description

550647 A7 B7 V. Description of the Invention (1) References to this application before and after related applications request US Patent Application No. 10 / 068,127 filed on February 6, 2002, and March 8, 2002 The priority of the filed case No. 10 / 095,974, of which, by reference in its entirety, is hereby incorporated into the publication of case number 10 / 068,127. FIELD OF THE INVENTION The present invention is generally related to a system and method for minimizing stress related to the slope of a control variable during a process, such as, for example, a semiconductor substrate temperature or a wafer during substrate processing. More specifically, the present invention provides an enhanced system and method for maintaining a radial temperature difference (r D T) of a wafer during processing below an overheating stress curve by controlling the slope of temperature during processing. In the semiconductor industry, temperature uniformity is expected to be achieved in a substrate during a temperature cycle of the substrate. Temperature uniformity is a temperature-triggering step that includes film deposition, oxide growth, and dopant diffusion to provide uniform processing output on the substrate, such as layer thickness, resistivity, and junction depth. In addition, to prevent wafer damage caused by thermal stresses such as distortion, defects, and spar structure slippage, temperature uniformity in the substrate is necessary. BACKGROUND OF THE INVENTION Manufacturing and other processing systems have traditionally deepened and changed one or more of the control variables. The variables include, but are not limited to, temperature, pressure, and gas flow rate. This paper is sized to the Chinese National Standard (CNS) A4 specification (210X297). %)! 5-(Please read the notes on the back before filling in this page)

Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs of the Ministry of Economic Affairs -4- 550647 A7 B7 V. Description of the invention (2) (Please read the notes on the back before filling this page), concentration, tension, voltage, force, and location . The rate at which a control variable changes from a start to a stop is the slope or a derivative of the variable, which is commonly called the slope. For example, the first derivative of slope or position versus time (such as d χ / d t) is velocity. It is often expected that stress will be minimized in a process in which equipment and / or products are exposed to the stress. Excessive stress can result in reduced process efficiency or premature equipment or product failure. In many systems, stress is a function of the slope of one or more control variables. The slope can be reduced to keep the stress below an acceptable threshold. However, unnecessarily severe slope restrictions slow the overall throughput of the program and are not expected. One of the concepts elicited by semiconductor processing systems illustrates examples. It should be noted, however, that slope-related issues are not unique to the applications discussed in detail here. Rather, the example is meant to be illustrative and in no way restrictive. Printed by the Intellectual Property Bureau of the Ministry of Economic Affairs and Consumer Cooperatives. One of the important points in semiconductor and integrated circuit manufacturing is the temperature change and temperature fluctuations experienced by semiconductor wafers during processing. Two important restrictions apply to the heating and cooling of semiconductor wafers: 1) the acceleration and deceleration of the temperature slope cannot be faster than the thermal inertia allowed by the wafer and 2) the temperature difference between the center of the wafer and the outer edge should be maintained enough Small to prevent thermal expansion damage to the wafer. Thermal inertia describes the impedance of a mass that immediately jumps from a steady-state temperature or zero-slope state to a finite non-zero slope and returns to a steady-state state. In these idealized temperature slopes that require heating or cooling, real objects cannot be instantly and infinitely accelerated, decelerated, and decelerated. The acceleration or deceleration of temperature is the second derivative of temperature. As far as the acceleration and deceleration of the position when a mass is stationary, the temperature acceleration and deceleration rate cannot be unlimited. This paper size applies to the Chinese National Standard (CNS) A4 specification (210x297 mm) -5- 550647 A7 ___B7 V. Description of the invention (3) (Please read the precautions on the back before filling this page) In Ruyi Semiconductor Wafer Processing System In a furnace, when heating or cooling from one temperature to another, it is often important to reach the desired setpoint temperature in a minimum amount of time. Traditionally, the furnace will use a controlled linear ramp to move from one temperature setpoint to another. Becoming a linear slope suffers from two shortcomings: the delay in reaching the expected temperature slope by the substrate being heated; and the tendency of the substrate to exceed the expected set point and then oscillate around the set point temperature before reaching a steady state temperature. A solution to this problem is described in the co-examined U.S. Patent Application Nos. 10/0 6 8 and 1 2 7 which use the temperature slope acceleration and mitigation phase which can actually be achieved, which is incorporated herein by reference. . Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs. Due to the internal temperature gradient exceeded in the object, it is also important to limit the maximum temperature slope to protect the negative thermal effects on the object or objects under heating. This is particularly relevant to semiconductor wafer processing systems, in which an important manufacturing point of view is the temperature change and temperature experienced by the semiconductor wafer during processing. In particular, due to excessive heating and cooling relative to the outer edge of one of the wafer's centers, actual and / or chemical damage that may render the wafer unusable or cause early failure of semiconductor wafers manufactured by the wafer is rapidly increasing. During the processing of a heat treatment furnace or similar equipment, the temperature difference between the wafer center and the outer edge is significant. The center temperature difference of the outer edge is called the radial temperature difference, or the radial difference of one T (R D T). This problem particularly affects a batch of furnaces that heat the outside of a stack of wafers. During heating with a radiant heat source such as an impedance heating coil or an exothermic lamp, the outer edge of the wafer is sometimes a few degrees (or even several degrees) hotter than the center of the wafer because radiant heat transfer is greatest at the outer edge of the wafer. Conversely, during cooling, the outer edge is subjected to faster heat loss through radiative cooling ^ Paper size applies Chinese National Standard (CNS) A4 (210X297 mm) -6-550647 A7 B7 V. Description of the invention (4) and therefore Actually cooler than the wafer center. At high temperatures, this R D T can cause crystals to slip on the wafer. (Please read the precautions on the back before filling out this page) Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs It is well known that limiting the temperature slope minimizes the spar slip damage caused by thermal expansion stress on the semiconductor substrate. It is expected that the RD T will be minimized during processing and the overheating stresses occurring on the substrate will be minimized. The temperature slope during processing is a major factor in determining R D T. When the heat applied to the outer edge is not immediately transmitted to the center of the substrate, with a higher slope, the thermal inertia of the substrate during heating can further increase the temperature change between the outer edge and the center. At lower temperatures, because the silicon atom-to-atom bond is stronger and can withstand hotter stress at lower temperatures, larger RDTs can be tolerated without causing overheating stress. Accordingly, it is contemplated to provide a system and method for controlling R D T across the substrate. To avoid exceeding the maximum allowable thermal stress on a wafer, conventional techniques rely on a manual planning sequence with a fixed slope. As mentioned above, because the maximum allowable slope of the thermal stress caused by RDT is to be avoided as a function of temperature, this method prevents the process from being applied at the maximum possible slope during the entire heating or cooling process. Operation. Moreover, this segmented slope profile also results in a slope that exceeds the maximum allowable R D T for a given temperature. It is heated in a discontinuous temperature ramp profile, so it deviates from the ideal maximum slope curve. Therefore, a temperature controlled progressive system and method is needed to manage the slope as a function of body temperature or substrate during heating or cooling. Description of the invention This paper applies the Chinese National Standard (CNS) A4 specification (210X297 mm) -7- 550647 A7 ____B7 V. Description of the invention (c) 5 (Please read the notes on the back before filling this page) An object is to provide an enhanced system and method for limiting the radial temperature difference to a substrate when it is heated by controlling the temperature slope during processing. Specifically, the present invention provides a system and method for controlling a radial temperature difference (R D T) across a substrate using a dynamically changeable temperature slope '. Generally, as the body temperature increases, the temperature slope decreases. More particularly, the present invention provides an enhanced system and method for controlling a radial temperature difference of a heated substrate in a manufacturing process, which process is, but is not limited to, semiconductor wafer processing and equipment. An embodiment of the present invention provides a method for limiting the slope of a variable. Calculate the maximum allowable slope of the variable based on the current set point of the variable. Until the set point below the variable under control is reached, the slope of the variable is greater than the maximum allowable slope. Printed by the Intellectual Property Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs. In another embodiment of the present invention, a temperature control algorithm is used to change the temperature of a body stored in a temperature-controlled furnace heating chamber from an initial temperature to an end temperature. a way. Temperature data from one or more temperature sensing devices in the heating chamber and a temperature set point are provided as inputs to a temperature control algorithm that controls power delivery to one or more controllable heating elements in the furnace. A maximum allowable temperature slope is calculated as a function of the set-point temperature. Accelerate at a finite acceleration rate from the starting temperature to the temperature setpoint until the calculated maximum allowable temperature slope for the current temperature setpoint is reached. The temperature setpoint is decelerated with a finite deceleration rate until the end temperature is reached, so that the body temperature reaches the end smoothly to set the point temperature, which does not substantially exceed or oscillate around the end temperature. An additional embodiment of the present invention provides a stove, which is in accordance with the above paper size applicable to the Chinese National Standard (CNS) A4 specification (210X297 mm) -8-550647 A7 ______B7_

5. Description of the invention (J 6 abstract method, change the temperature of a body inside the furnace. (Please read the precautions on the back before filling this page) These methods are suitable for various systems that require precise control of program variables. Such variables are as , Temperature set point. Gas flow rate, concentration, pressure, tension, voltage, force, and location. In one illustrative embodiment, the system and method of the present invention are implemented in multiple zones used in a semiconductor process. The following shows a brief description of the present invention and the detailed description of the scope of additional patent applications provided below, and the other objects and advantages of the present invention will become apparent after referring to the illustrations, where: Figure 1 is used in semiconductor manufacturing A simplified diagram of an example of a furnace, wherein the semiconductor can be manufactured using the system and method of the present invention. Figure 2 is a graph of the maximum radial temperature difference of a silicon substrate obtained from Equation 1 versus the temperature of the outer edge of the wafer. Figure 3 is a flowchart illustrating one embodiment of the method of the present embodiment. Figure 4 shows: (i) the set point of the slope, and (ii) the Circle temperature weighted average. Figure 5 printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs indicates (i) the actual center and outer temperature of all zones; (ii) the RDT of all zones; and (iii) according to the present invention The furnace power of each zone over time in an embodiment. Figure 6 illustrates: (i) the weighted average of the center and outer edge temperature (2 1 3 outer edge + 1/3 center) of a semiconductor substrate wafer, usually The weighted average is used to represent the overall wafer temperature; (ii) the RDT of all zones; and (iii) each zone according to an embodiment of the present invention applies the Chinese National Standard (CNS) A4 specification (210 × 297 mm) with the paper size. (%) '-9- 550647 A7 B7 V. Description of the invention (7) The stove electricity printed by time is printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs. Figure 7: (i) shows the close-up of the number, and (ii) shows the root The weighted average is shown in Fig. 8. • (i) The temperature of all zones of 20 ° C / min. The actual pairs of slopes of each zone RD Τ RDT control method 5 pairs of slopes Furnace power 〇 Main components comparison table 1 〇 Stove 1 2 Heater element 1 4 Belt 16 Heating chamber 2 〇 Wafer 2 2 Signal 2 6 Temperature controller 3 0 Temperature control software m πϋ 3 2 Program control software 3 4 tip Point thermocouple 3 6 Shape thermophilic invention Detailed description This paper size applies Chinese National Standard (CNS) A4 specification (210X 297 mm) 5 Wafer temperature shown in the figure Top of the figure According to all zones of an embodiment of the present invention The slope is 5, 10, 15, and the center and outer edge of the wafer; (ii) and (1 1 i) in the absence of the present invention, the zones will become slopes over time (please read the precautions on the back before filling This page) -10- 550647 A7 B7 V. Description of the invention () 8 (Please read the precautions on the back before filling this page) As mentioned above, it is expected to make a radial temperature difference or span, for example, such as a semiconductor substrate or The RDT of the wafer body is minimized to avoid overheating stress or crystal on the body 〃 ,, slippage. The method of the present invention is also generally applicable to any program in which the maximum slope of a control variable is limited so that the stress in a system is minimized. According to an embodiment of the present invention, the R D T is maintained below the superheat stress curve by controlling the temperature slope. This maximum allowable thermal stress curve is a function of temperature. The present invention provides that the maximum temperature slope varies with temperature and maintains the superheat pressure curve below the maximum allowable temperature of the current temperature of the body during heating. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs. At lower temperatures, the body of a semiconductor wafer is less susceptible to overheating stress caused by RDT than at higher temperatures. Because the slope of the temperature in the furnace (as shown in Figure 1) is the main driving factor for determining the RDT, by limiting the maximum allowable temperature slope, the RDT of a body in the furnace during heating or cooling is controlled as a furnace As a function of current temperature. At lower temperatures, larger slopes are allowed. As the temperature rises, the slope gradually decreases. This decreasing temperature slope produces a substantially smooth, continuous temperature profile as a function of time. In this way, the present invention has a variable maximum allowable temperature slope. By controlling the slope in this manner, the present invention minimizes the time required for the body or substrate to climb from one temperature to another without causing excessive stress or injury to the substrate. In one embodiment of the present invention, a method is provided with a limited maximum slope, and a control variable-in this example, temperature-increases or decreases the slope. The invention can be implemented on a semiconductor furnace as illustrated in FIG. The stove 10 in the figure 1 contains a heater element with five individual zones 1 4 This paper size applies the Chinese National Standard (CNS) A4 specification (210X297 mm) " -11-550647 A7 B7 V. Description of the invention (Q) y (please read the precautions on the back before filling out this page), and a heating chamber 16 containing one or more semiconductor substrate wafers 20. A power command or signal 22 is individually controlled in each zone 14. The purpose of the heater element 12 is to heat the wafer 20 to a desired temperature 24. The temperature controller 2 6 with temperature control software 30 and program control software 32 transmits power control signal 2 2 to the stove heater element 12. Although a specific semiconductor furnace 10 having one of five zones 14 is shown, those skilled in the art who understand the system and method of the present invention may use other types of furnaces, and further may use other types of semiconductor equipment or other equipment. Implementation, where other equipment is designed to controllably change the temperature of one body or target from one setpoint temperature to another setpoint temperature. The invention is not limited to the specific examples shown. For example, the present invention can be used in furnaces having different number of zones. Likewise, this can be applied to any other program or system in which the stress is controlled by limiting the slope of a control variable as a function of that variable. In addition, by limiting the slope of one or more variables as a function of those one or more variables, the method can be applied to control stress. In an embodiment of the present invention, printed by an industrial and commercial cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs, the temperature controller 26 includes temperature control software 30. The temperature control software 30 is, for example, built to maintain a control furnace 10 PID control software. Depending on the temperature and the final set point, the set point climb changes and bends during the climb. More specifically, the slope is the slope of the set-point temperature. Because the semiconductor substrate allows a higher RD T, it is less effective at low temperatures (always less than 600 ° C) than at high temperatures (such as in the range of about 60 ° C to 12 0 ° C). Damaged by thermal expansion 'When the temperature is relatively low, the present invention is built so that the set point starts to climb faster. The paper size is applicable to the Chinese National Standard (CNS) A4 specification (210X 297 mm) -12- V. Description of the invention (liter When the temperature rises, the slope becomes slower. Slow. The dynamic function of the present invention. This maximum slope is a function of temperature or a large slope as the temperature. The allowable RDT between the tabs is the number. When the maximum allowable A7 B7, the maximum The RDT is allowed to decrease, so as the temperature of the substrate or wafer increases, the slope used will change the maximum slope more. The current set-point temperature rate can be obtained from a query table of the maximum allowable RDT. Some other planning functions, this function is provided with a best function. Table 1 provides an example temperature of such a look-up table, and the function of a smooth change of the maximum temperature can be obtained by interpolation. Use the ratio determined by experiments. RDT Change to the maximum temperature slope. This proportionality factor can be a constant or it can be a function of temperature itself. For a factor of 30 Omm, it is better to use a rate table of 0.5 ° C per minute per ° C 2RDT, so that it is best to implement The software of the present invention allows the ratio of wafers. These slope tables can be selected in the program recipe using different slopes. In addition, the relationship between temperature and maximum slope can be planned as a series of one or more mathematical functions of temperature The following equation is used to pre-generate the maximum allowable slope as a function of temperature through experiments. This experiment makes the maximum ΔΤ a function of temperature: (Please read the precautions on the back before filling out this page) System ΔΓ 2 .4928 ^ ft ⑴ where f ε / ft is the elongation and E is the young's modulus

E 9 0

N -2 ^ is the thermal expansion coefficient of the substrate (silicon in this example), c and η are numerical constants (c = 4.5 × 1014Nm ~~ 2 and η = 2 · 9), and the ruler is Spinzmann ( Boltzmann) constant (k = l. 38x10 23JK — 丄) This paper size is applicable to Chinese National Standard (CNS) A4 specification (210X297 mm) -13- 550647 A7 B7 V. Description of the invention ((Please read the precautions on the back before (Fill in this page) and T is the absolute temperature of the outer edge of the substrate. The thermal gradient is assumed to be the highest under the ghai substrate. This equation is independent of the radius and is therefore applicable to substrates of any size. Figure 2 shows the maximum calculation result ΔΤ. Table 1: Maximum slope query table Temperature set point, ° C Maximum allowable RDT, ° C 600 80 — 700 60 800 44 900 34 — 1000 26 1100 22 1200 18 Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs Fig. 3 illustrates an embodiment of the method of the present invention. Fig. 3 is a flowchart illustrating an embodiment of the method of the present invention. This method starts from step 40 and performs a slope query at step 42. If determined as No 'use the previous setpoint at step 4 4. If decided If yes, then step S 4 6 is to check whether it is time to start slope mitigation. If the decision at step 4 6 is YES, then the method calculates the mitigation rate at step 4 8. If the decision at step 4 6 is no, Then the algorithm confirms whether the slope is currently slowing. In step 50, if the slope is slowing, calculate the set point based on the slowing rate in step 32 and complete the method (step 5 4). In step 5 0 If this paper size applies Chinese National Standard (CNS) A4 specification (210X297 mm) -14- 550647 A7 B7 V. Description of the invention (12) If the slope is not slowed down, go to step 5 6; The interpolation method determines the maximum RDT of the current temperature. And in step 5 and 6, use the (read the precautions on the back before filling this page) scale factor to convert the maximum r DT 値 returned from the lookup table into a maximum slope. 'Query in step 5 8 whether the slope is lower than the maximum slope. If not' then use the maximum slope to calculate the new set point in step 60. If yes' then in step 60 accelerate the slope upwards towards the maximum slope. Section 4 In the figure A graphical illustration of the set point is implemented in practice. Actually, this embodiment of the present invention can be implemented through the following conceptual steps: As explained above, calculate the maximum allowable temperature slope for the current set point temperature and The rate of the maximum allowable slope makes the setpoint temperature a slope. The Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs prints a further embodiment of the present invention to bend the temperature setpoint and increase or accelerate the slope to zero from the initial temperature The slope and then decrease from the maximum slope or slow down the slope to zero at the termination temperature, providing a smooth transition between the steady state (zero slope) of the heating or cooling process and the climbing phase. Slope acceleration reaches maximum and slows down until a finite final set point and actual reach rate minimize the actual bulk temperature oscillations relative to the set point temperature. In a preferred embodiment of the present invention, the temperature gradient is accelerated and slowed with a linear acceleration and mitigation rate (the second derivative of the temperature setpoint with respect to time is a constant). However, non-linear mitigation may be desirable in some cases. The setpoint slope of the feed temperature controller follows the less important of the following: a) The ratio of the RDT to the thermometer and the current setpoint temperature is dynamically based on the Chinese paper standard (CNS) A4 specification (210X297 mm) ) -15- 550647 A7 _______B7 V. Description of the invention (j (please read the notes on the back before filling this page) the maximum allowable slope temperature curve obtained from the number, b) the slope provided by the set point curve, and C ) Can be achieved by the furnace until the set point temperature approaches the maximum slope of the final set point. The setpoint slope is then slowly smoothed to meet the final termination temperature. The method of the present invention sends the wafer to the desired temperature at the fastest possible rate to keep r D T below the slip curve. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs. In this embodiment, the temperature measurement shown in Figure 1 is best using two sets of thermocouples: one or more cusp thermocouples 3 4 and one or more shapes. Thermal coupling 3 6. The cusp thermocouple 34 is closer to the heater element winding (not shown) and responds faster to the control input. The shape thermocouple 36 is closer to the wafer 2 0 ′ and therefore better represents its temperature. The temperature controller 2 6 with temperature control software 30 receives the set point of the expected temperature 2 4 from the program controller 3 2 with the program control software, and reads the measured temperature 38 of the thermocouple. The temperature is measured by a mathematical operation combination of 38, and a control temperature (not shown) for generating an estimated wafer temperature of 20 is generated. The control temperature is preferably a weighted average temperature measured by the cusp thermocouple 34 and the shape thermocouple 36. The weighting is a function of temperature that changes preferentially. The higher the temperature is, the higher the temperature is. In a further preferred embodiment, the mathematical operation combination for measuring temperature 38 also includes one or more temperature compensations. These compensations can be static or dynamic. In one example, static compensation is used to correct the temperature difference between the temperature of the control body and the temperature of the thermocouple during wafer or other heating. These compensations can be determined experimentally using wafers with thermal coupling as the instrument. Based on the control algorithm and the input control and setpoint temperatures, the temperature controller 26 determines the amount of power to be applied to each zone of the stove heater element 12. When a slope is specified, the setpoint will climb at the selected rate. Applicable to the Chinese National Standard (CNS) A4 specification (210X297 mm) on a paper scale -16- 550647 A7 B7 V. Description of the invention (j (Please read the notes on the back before filling in this. I) In the preferred embodiment The set point bends smoothly to the final set point near the end of the set point climbing phase. The slope decreases linearly during the set point bending toward the final set point. The curved temperature set point is preferentially used at the end of the slope. However, this It is also advantageously applied to the beginning of the slope, 'to avoid large shocks in electricity demand. Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs, when the maximum temperature slope is climbed under the method of the present invention, the immediate temperature set point does not The temperature controller commonly used in the p ID system immediately jumps to the final set point. Instead, it accelerates the set point at a finite and achievable rate until it reaches the maximum achievable slope of the zone and the set point, Or the maximum allowable slope of the current temperature, where the current temperature is derived from the product of the maximum allowable RD T of the current setpoint temperature in Table 1 and the scaling factor The maximum allowable temperature slope as a function of the current setpoint temperature is the product of the function of the radial temperature difference versus temperature and the proportionality factor. The function of RDT on temperature is set as a mathematical operation relationship, or as in the previous embodiment. The description is set as a look-up table. If a look-up table is used, the software is built to obtain the maximum allowable RD T by interpolation at the temperature point where the column 値 is not provided. Set the maximum allowable RD T at a specified temperature Converted to a maximum allowable slope, the proportionality factor as a function of temperature may be constant or it may be a function of temperature. In an additional embodiment, a system is also provided in which the method of the present invention is used to control the temperature control furnace Slope of the set-point temperature in another embodiment. In another embodiment, a system is provided in which the method of the present invention is combined with the temperature control described in the co-examined US Patent Application No. 10 / 068,127. The method, on the whole, applies the Chinese National Standard (CNS) A4 specification (210X297 mm) by referring to the paper size. -17- 550647 A7 ____ B7 V. Description of the invention (15) The test is based on this publication. (Please read the precautions on the back before filling out this page.) Experimental use of a furnace similar to the one shown in Figure 1 and the use of thermally coupled wafers (The semiconductor wafer with a built-in thermocouple, which provides temperature data of different wafer regions) The system and method of the present invention perform several tests. Figures 4 to 7 show the temperature of the wafer using the thermocouple as an instrument. Data and electric power transmission to the furnace that illustrate the experiment. In this experiment, the temperature slope is linearly accelerated and decelerated and the maximum slope is controlled to maintain the RDT below the maximum allowable thermal stress curve. In these cases, thermal coupling will be used as an appliance The wafer was heated from 600 ° C to 95 ° C. Figure 5 is a map of the data collected in this experiment, indicating: (i) the actual center and outer temperature of all zones; (1 i) the RDT 値 of all zones; and (iii) each zone follows Stove power of time. Figure 6 (i) shows the weighted average of the center and outer edge temperature of the wafer with thermal coupling as the instrument in this experiment (2/3 outer edge + 1/3 center), and Figure 7 shows the fifth middle slope surface Close-up on top and weighted average of all zones. Printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs In another experiment, the system and method of the present invention was implemented using a rapid vertical processing (R V P) type furnace with five zones as shown in FIG. 1. Figure 4 shows the setpoints with a slope, plus the weighted average of the wafer temperature measured across all zones. This figure shows how the actual wafer temperature fits the temperature setpoint curve. Fig. 8 shows the results of a linear slope test in which the slope is not controlled by the present invention. Except for bending on the top of the slope, the set point is based on the paper standard applicable to the Chinese National Standard (CNS) A4 ^ see the grid (210X297 mm) '-18- 550647 A7 _B7 V. Description of the invention (j

Linear becomes ramped. Figure 8 shows the actual wafer center and outer edge temperatures in all zones with the following slopes: 5, 10, 15 & 2 0 t m i η _ 1. Part (i i) of FIG. 8 represents the RDT of the wafer and part (i i i) represents the applied power as a function of time. As shown in Figure 8, increasing the slope in the absence of RDT-type slope control leads to a larger RD T than the observers in Figures 4 and 5 using the method of the present invention. The system and method of the present invention provide the expected performance . For the purposes of illustration and description, the preceding descriptions of specific embodiments and examples of the present invention have been presented, and although the present invention has been described with some previous examples, it should not be interpreted as being limiting. It is not intended to be exhaustive or to limit the invention to the precise form disclosed. In view of the above teachings, obviously many modifications, examples, and changes are possible. It is expected that the scope of the present invention shall include the general scope published as such, the scope of patent applications appended hereto, and their equivalents. (Please read the precautions on the back before filling out this page) Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs This paper applies the Chinese National Standard (CNS) A4 specification (210X297 mm) -19-

Claims (1)

550647 A8 B8 C8 D8 VI. Patent application scope 1 1. A method for limiting the slope of a variable, including the following steps: Calculate the maximum allowable slope of the variable's current value; and (Please read the precautions on the back before filling this page) Restrictions The slope of the variable is such that it does not exceed the maximum allowable slope of 02. The method of item 1 in the scope of patent application, wherein the variable is a set point temperature of a body during heating. 3. The method according to item 2 of the patent application, wherein the body under heating is one or more semiconductor substrates. 4. The method of claim 3, wherein the maximum allowable slope is a function of the maximum radial temperature difference to a wafer at a current temperature. 5. A method for changing the temperature of a body contained in a heating chamber of a temperature-controlled furnace from an initial temperature to an ending temperature using a temperature control algorithm, including the following steps: From one or more temperatures in the heating chamber The induction device and a temperature set point provide temperature data as input to the temperature control algorithm, which controls the power transmission to one or more controllable heating elements in the furnace; printed by the Consumer Cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs Calculate a maximum allowable temperature slope as a function of temperature; accelerate the temperature set point from the starting temperature at a finite acceleration rate until the maximum allowable temperature slope is reached for the current temperature set point; and a finite The slowdown rate decelerates the temperature setpoint until the termination temperature is reached, so that the body temperature smoothly reaches the termination setpoint temperature without substantial overshoot or oscillating around the termination temperature. This $ Zhang scale is applicable to the Zhongguanjia Standard (CNS) A4 ^ (21GX297 mm) '-20- 550647 A8 B8 C8 D8 C, patent application scope 2 6 · If the method of patent application scope No. 5 method, which can be controlled The heating element is selected from the group consisting of a radiation heat lamp and a heating coil. (Please read the precautions on the back before filling out this page) 7. If the method of the scope of patent application is No. 5, wherein the temperature sensing device is one or more thermocouples, A controlled heating element provides one or more temperatures. 8. The method according to item 7 of the scope of patent application, wherein a control temperature is an input of the temperature control algorithm, and the control temperature is a mathematical operation combination of the one or more thermocouple temperatures. 9. The method according to item 8 of the patent application, wherein the control temperature is further defined to have a known compensation from the thermocouple temperature. 10. The method according to item 9 of the scope of patent application, wherein the temperature compensation is static compensation, and the static compensation corrects the control temperature difference between the body temperature and the thermocouple temperature. 1 1 · The method of claim 5 in which the body is a semiconductor substrate. 1 2 · —A temperature control stove for changing the temperature of a body, including: printed by a consumer cooperative of the Intellectual Property Bureau of the Ministry of Economic Affairs, a heating chamber containing one or more controllable heating elements, and one or more temperature sensing devices ; And a temperature controller constructed to implement method 1 of the scope of patent application. 1 3. — A temperature-controlling stove for changing the temperature of a body, comprising: a heating chamber containing one or more controllable heating elements, and one or more paper sizes applicable to China's national 梂 f (CNS) A4 specification ( (210X297) -21-8 8 8 8 ABCD 550647 VI. Patent application range 3 Multiple temperature sensing devices; and a temperature controller that is constructed to implement the fifth method of the patent application range. (Please read the precautions on the back before filling out this page) Printed by the Consumer Cooperatives of the Intellectual Property Bureau of the Ministry of Economic Affairs This paper size applies to China National Standard (CNS) A4 (210X297 mm) -22-