Ramp rate limiter to control stress during ramping

[0002] 1. Field of the Invention

[0003] This invention relates to the control of processes and plants that perform those processes. More specifically, the present invention relates to the limiting of the ramp rate of variable under control in order to control stress in a process or plant.

[0004] 2. Background Information

[0005] In control of a plant or process a control system attempts to ramp up and stabilize to a particular variable under control. In some processes or plants (i.e., systems under control) the ramping process may cause stresses which affect the overall yield of the system. The following description describes an example of a problem where the temperature ramping process in a semiconductor furnace may cause stress on a wafer. It should be noted, however, that such problems may occur in other systems and that the example is meant merely to be illustrative and not limiting.

[0006] FIG. 1 illustrates a graph of the temperatures on a wafer surface in a semiconductor furnace. Line 110 illustrates the setpoint programmed by the user for the desired temperature on a wafer in a semiconductor furnace. Line 120 illustrates the temperature at the center of the wafer and line 130 illustrates the temperature at the edge of the wafer.

[0007] FIG. 2 illustrates a graph of the difference between the temperatures at the edge of the wafer and at the center of the wafer for FIG. 1. Line 210 represents the result of the edge temperature of the wafer minus the center temperature of the wafer (i.e., edge-center temperature).

[0008] FIG. 3 illustrates a graph of the difference between the temperatures at the edge of the wafer and at the center of the wafer plotted as (edge-center) temperature versus wafer temperature. Line 310 illustrates the edge temperature of the wafer minus the center temperature of the wafer (i.e., edge-center). As shown, as the (edge-center) 310 ramps up it stabilizes quickly at a quasi-steady state value and then as the ramp rate slows down (i.e., the ramp rate decreases and the temperature of the furnace/wafer stabilizes as illustrated in FIG. 1) the (edge-center) 310 drops off.

[0009] Also illustrated in FIG. 3 is stress limit curve 320. The (edge-center) difference may put physical stress on the wafer. Too much stress on the wafer may cause slip faults in the crystals of the wafer. Slip faults are cracks in the crystal structure of a wafer. Slip faults can damage the semiconductor devices being manufactured on the wafer, thus reducing the number of working devices on the wafer (i.e., reducing the yield of the entire semiconductor factory).

[0010] The stress limit curve 320 describes an allowable limit. If, at a particular wafer temperature, the (edge-center) temperature 310 is below the stress limit curve 320, slip faults will rarely occur. However, if at any wafer temperature the (edge-center) temperature 310 exceeds the stress limit curve 320, slip faults are much more likely to occur. Therefore, it is desirable to keep the edge-center difference 310 below the stress limit curve 320.

[0011] One current attempt to keep the edge-center difference of the wafer temperature below the stress limit curve is to manually adjust the ramp rate. Manual adjustments are mainly made because it is hard to determine the temperatures at the center and edges of the wafer. In general the temperatures at these areas must be estimated because it is difficult to place an actual measurement device close enough to the center of the wafer or the edge of the wafer to measure the actual temperature of those areas.

[0012] What is needed is a method and system to limit the ramp rate of a variable under control in order to control stress in a process or plant under control.

[0013] The present invention includes a method and system for limiting the ramp rate of a variable under control in order to control stress in a process or plant under control. The present invention takes a limit curve provided by the user and combines that limit curve with a scale factor curve obtained from a model of the system to produce an allowable limit curve. A ramp rate limiter then uses the allowable limit curve to control the ramp rate of the variable under control such that the ramp rate of the variable under control is able to achieve the maximum allowable limit but no more.

[0014] Additional features and benefits of the present invention will become apparent from the detailed description, figures, and claims set forth below.

[0015] The present invention is illustrated by way of example and not limitation in the accompanying figures in which:

[0016] FIG. 1 illustrates a graph of the temperatures on a wafer surface in a semiconductor furnace.

[0017] FIG. 2 illustrates a graph of the difference between the temperatures at the edge of the wafer and at the center of the wafer.

[0018] FIG. 3 illustrates a graph of the difference between the temperatures at the edge of the wafer and at the center of the wafer plotted as (edge-center) temperature versus wafer temperature.

[0019] FIG. 4 illustrates a graph of the (edge-center) difference versus the wafer temperature.

[0020] FIG. 5 illustrates a graph of scale factor versus wafer temperature.

[0021] FIG. 6 illustrates a graph of allowable ramp rate versus wafer temperature.

[0022] FIG. 7 illustrates a block diagram of system according to one embodiment of the present invention.

[0023] FIG. 8 illustrates a flow chart of one embodiment of the present invention.

[0024] A method and system for a ramp rate limiter to control stress during ramping are disclosed. In the following description, numerous specific details are set forth such as specific equipment, processes, parameters, etc. in order to provide a thorough understanding of the present invention. It will be apparent, however, to one skilled in the art that these specific details need not be employed to practice the present invention. In other instances, well known materials or methods have not been described in detail in order to avoid unnecessarily obscuring the present invention.

[0025] The present invention includes a method and system for limiting the ramp rate of a variable under control in order to minimize stress in a process and/or plant under control. The present invention takes a limit curve provided by the user and combines that limit curve with a scale factor curve obtained from a model of the system to produce an allowable ramp rate curve. A ramp rate limiter then uses the allowable ramp rate curve to limit the ramp rate of the variable under control such that the ramp rate of the variable under control is able to change by the maximum allowable limit but no more.

[0026] It should be noted that although the following description describes ramp rates in terms of temperature on a semiconductor wafer and stress related to a temperature difference on the wafer, the present invention may apply to other ramp rates for example ramp rates with regard to velocity, pressure, gas flow, positioning, etc.

[0027] It should also be noted that the stress may be related to a physical value with units different from the units associated with the variable under control. For example, the variable under control may be a velocity and the stress may be associated with a force. In such an example, the velocity ramp rate would be limited in order to control the force associated with stress in the process or plant under control.

[0028] FIG. 4 illustrates a graph of the edge-center difference versus the wafer temperature. As illustrated in FIG. 4, the edge-center difference is represented as ΔT and the wafer temperature is represented as T. Plotting ΔT versus T creates limit curve 410 for the particular plant under control, for example a semiconductor furnace used to process semiconductor wafers. This limit curve is entered by the user.

[0029] In one embodiment of the present invention the user enters a number of (Temp, ΔT) pairs which, when interpolated, form the curve 410. It should be noted that the user may enter the curve in other ways, for example, using a graphical software tool. It should also be noted that the user enters a limit curve for the particular process being performed and that different processes may have different limit curves.

[0030] It is well known in the field of semiconductor manufacturing that wafer stress is directly related to the wafer edge-center temperature difference. Because of this fact, limiting the wafer edge-center temperature difference will have the effect of limiting the wafer stress.

[0031] FIG. 5 illustrates a graph of scale factor versus wafer temperature. The scale factor relates the actual wafer ramp rate and the edge-center difference. There exists a quasi-steady state approximation such that if the actual ramp rate of the wafer is known and if the scale factor is known, then an approximation of the edge-center difference (ΔT) may be computed. In other words, at each temperature T, the ramp rate multiplied by the scale factor approximately equals the edge-center difference (i.e., ramprate·scalefactor≡ΔT). As illustrated in FIG. 5, scale factor curve 510 may be constant. The scale factor may also vary with temperature. The scale factor curve 510 may be obtained from a mathematical model of the system.

[0032] The user entered curve 410 is then combined with the scale factor curve 510 to create limit curve 610 that represents the allowable ramp rate versus temperature, as illustrated in FIG. 6. Limit curve 610 represents the maximum allowable ramp rate for the system.

[0033] One embodiment of the present invention takes the temperature setpoint programmed by the user, r_requested(t), and produces a setpoint, r_out(t), that does not exceed the allowable limit curve 610. The embodiment operates at a fixed time interval. For the purpose of this description, the time interval is 1. At each time point the embodiment compares the current setpoint that the user is requesting r_requested(t) to the previous output setpoint r_out(t−1). The embodiment then determines whether setting r_out(t) to be r_requested(t) will cause the ramp rate to exceed the allowable limit curve 610. To do this, the embodiment computes the difference [r_requested(t)−r_out(t−1)]. The embodiment also computes a maximum allowable temperature difference r_limit(t) by evaluating the allowable limit curve 610 at temperature r_out(t−1). If the difference [r_requested(t)−r_out(t−1)] is less than r_limit(t), setting r_out(t) equal to r_requested(t) will not exceed the allowable limit r_limit(t). The embodiment then sets r_out(t) equal to r_requested(t). If, however, the difference [r_requested(t)−r_out(t−1)] is greater than the allowable limit r_limit(t), setting r_out(t) equal to r_requested(t) will exceed the allowable limit r_limit(t). To avoid this, the embodiment sets r_out(t) equal to the previous output r_out(t−1) plus the allowable difference r_limit(t).

[0034] It should be noted that the above described embodiment illustrates a case where a positive ramp rate is requested (i.e., r_requested(t) is increasing) and must be limited. It should also be noted that the present invention may be applied in case where a negative ramp rate is requested (i.e., r_requested(t) is decreasing) and must be limited.

[0035] FIG. 7 illustrates a block diagram of a system according to one embodiment of present invention. As illustrated in FIG. 7, the system 700 includes a device under control (or plant) 710, controller 720, and ramp rate limiter (limiter) 730. The requested setpoint, r_requested(t) 740, is input into the limiter 730. Limiter 730 produces a limiter value, r_out(t) 750, and inputs r_out(t) 750 into controller 720. The controller 720 and plant 710 together produces r_actual(t) 760 which is the actual value of the variable under control that is realized in the plant 710.

[0036] FIG. 8 illustrates a flow chart of one embodiment of the present invention. It should be noted that the flow chart of FIG. 8 is merely meant to be demonstrative and that the steps included in the flow chart may follow many other orders and not just the order illustrated.

[0037] At step 810, the user enters a limit curve 410 mapping ΔT versus T. The user determines this limit curve as described above with regard to FIG. 4.

[0038] At step 820, a scale factor curve 510 is obtained. The scale factor curve 510 is obtained from a model that is associated with the system 700 as is described above with regard to FIG. 5.

[0039] At step 830, the maximum allowable ramp rate limit curve 610 is produced. Limit curve 610 is produced from the combination if the user limit curve 410 and the scale factor curve 510 as described above with regard to FIG. 6. At step 840, an allowable limit r_limit(t) is computed by evaluating the allowable limit curve 610 at temperature r_out(t−1).

[0040] At step 850, it is determined if the difference between the current setpoint requested by the user r_requested(t) and the previous setpoint produced by the limiter r_out(t−1) is greater that the allowable r_limit(t) (i.e., if [r_requested(t)−r_out(t−1)]>r_out(t) ). If the difference [r_requested(t)−r_out(t−1)] is less than r_limit(t), the limiter sets the output value r_out(t) equal to r_requested(t) at step 860. If the difference [r_requested(t)−r_out(t−1)] is not less than r_limit(t), the limiter sets the output value r_out(t) equal to r_out(t)×r_limit(t) at step 870.

[0041] in one embodiment of the present invention steps 830, 840, 850, and 860 or 870 are performed on an ongoing basis at each time point during the operation of the system. In the embodiment described above, the time interval between time points is 1, however other embodiments may operate at time intervals different from 1. In addition, the time interval between time points need not be the same for all time points.

[0042] It should be noted that the comparisons may be made as “less than”, “greater than”, “less than or equal to”, “greater than or equal to”, etc. and that the embodiment described above is meant merely to be exemplary and not limiting. It should also be noted that the comparison given above is just one example of a comparison that may be made to determine which value to select for r_out(t). For example, if the time intervals are different from 1, a different comparison would be used in step 850.

[0043] Additionally, it should be noted that although the example given in the above description discusses the ramp rate as being the temperature ramp rate of a semiconductor furnace, the ramp rate may be for many other variables under control such as the ramp rate of flow (for example in a semiconductor deposition chamber), the ramp rate of velocity (for example of a car), etc.

[0044] Further, it should also be noted that the stress may be related to a physical value with units different from the units associated with the variable under control. For example, the variable under control may be a velocity and the stress may be associated with a force. In such an example, the velocity ramp rate would be limited in order to control the force associated with stress in the process or plant under control.

[0045] Still further, it should be noted that although the above description discusses the present invention in terms of the setpoint of a single variable under control, the present invention may be used in systems with setpoints for multiple variables under control. In the multivariable case, a separate curve (shown in FIGS. 4,5, and 6) is determined for each variable under control. A separate ramp rate limiter 730 is implemented for each setpoint. Each individual ramp rate limiter may operate independently. The ramp rate limiters may also be linked together. For example, if one limiter sets its r_out(t)=r_out(t−1)+r_limit(t), the other limiters may also set their outputs r_out(t) in a similar fashion.

[0046] Yet further, the embodiment described above may be modified to yield other embodiments of the invention that limit ramp rates to control stress. For example, step 840 of FIG. 8 may be modified so that r_limit(t) is determined from the value of r_actual(t) and the allowable ramp rate curve. In another example, step 840 may be modified so that r_limit(t) is determined from an estimate of r_actual(t) and the allowable ramp rate curve. In yet another example, the controller 720 of FIG. 7 might take a ramp rate rather than a setpoint as input. In such an example, the ramp rate limiter 730 would use the user-entered limit curve and the scale factor curve to directly limit the ramp rate input to the controller.

[0047] Thus, a method and system for a ramp rate limiter to control stress during ramping have been described. Although specific embodiments, including specific equipment, processes, and parameters have been described, various modifications to the disclosed embodiments will be apparent to one of ordinary skill in the art upon reading this disclosure. Therefore, it is to be understood that such embodiments are merely illustrative of and not restrictive on the broad invention and that this invention is not limited to the specific embodiments shown and described.