Pressure control in high vaccum multichamber system

01/01/1997

Pressure control in a high vacuum multichamber system

Won Ick Jang, Jong Hyun Lee, Jong Tae Baek, Semiconductor Division, Electronics and Telecommunications Research Institute, Yusong, Taejon, South Korea

We have implemented a fast precision pressure control system for the transport chamber of a high vacuum multichamber process tool used in advanced semiconductor fabrication. To overcome the typically slow response of mass flow controllers (MFCs), we adjusted the starting time and the tuning constants using the Ziegler-Nichols method.

A comparison of pressure control techniques, including motor speed control, throttle valve control, and gas ballast control for plasma/LPCVD systems was reported in 1982 [1]. In 1986, the transfer function and optimized control parameters were calculated leading to a new controller design with downstream pressure control [2]. An adaptive adjustment is necessary to avoid excessive overswing or slow response to changes of the pressure setpoint. Previous studies typically operated between 1-1000 mtorr, and these methods are widely used for deposition, etching, and sputtering of thin films in device fabrication.

As devices become more complex and dimensions become smaller, however, contamination and native oxide formation due to atmospheric exposure may pose an increased threat to yield. Recently, a series of advanced semiconductor processes have been integrated via "cluster tools" - multichamber systems with a central transport module [3]. Cluster tools have reduced fabrication costs and extended equipment cycles.

Wafers are transported from process to process under high vacuum; it is therefore necessary to precisely control the pressure in a molecular flow range. The main problems are the large time delay caused by the typically slow response of the MFCs and the removal of overswing for the pressure setpoint.

In our present work, we have developed a new pressure control technique using the Ziegler-Nichols tuning method to provide good estimates of the controller settings for the multichamber system. Practical tests with the new pressure controller on real high vacuum systems were performed and found to agree with theoretical analysis.

Figure 1. Configuration of the high vacuum multichamber system.

Experimental

Figure 1 shows the configuration of an experimental apparatus for a high vacuum multichamber system [4]. Each processing module is mechanically and electrically independent and has its own vacuum and control system. There are rectangular slot valves between modules for vacuum isolation, operating at an acceptable pressure difference of 22.5 mtorr. The vacuum system of the transport module is composed of an ion gauge, a convectron gauge, isolation valves, a turbo-drag pump with its electronic drive, vacuum valves, a diaphragm pump, and a throttle valve with its controller.

The control system of the high vacuum multichamber system is composed of a cluster tool controller (CTC), transport module controller (TMC), and process module controllers (PMCs). These are interconnected via an Ethernet cable network. The CTC commands and schedules the TMC and PMCs and interacts with the operators. The TMC performs all the jobs related to wafer and cassette movements by controlling the robot, aligner, cassette elevators, and various valves. Each PMC is dedicated to its own process module, such as metal and oxide etchers.

Figure 2. Schematic of the pressure control system of the transport chamber.

Figure 2 illustrates a typical pressure control system for the transport chamber. It includes the chamber volume, a pressure sensor, a pressure controller, a MFC, and a pump. To control the flow rate of nitrogen gas, the TMC calculates the proportional-integral-differential (PID) controller output by comparing a user-supplied setpoint signal and a voltage signal from the ion gauge. Then MFC power is supplied by the MFC control board. The inlet pressure of nitrogen gas is maintained at about 40 psi. In Fig. 3, we can see from the characteristic curves of the MFC for nitrogen gas that the MFC has a dead time of 1 sec and takes 4 sec to stabilize to within ?2% for setpoints at 20% (lower curves) and 100% (top curves) of the full scale.

Figure 3. Characteristic curves of the MFC for nitrogen gas. The top curves correspond to data for setpoints at 100% of the full scale. The lower curves represent data for setpoints at 20% of the full scale.

Theoretical background

Theoretical analysis. In order to design vacuum and pressure control systems, we must use the theory of vacuum technology for various components between the process chamber and vacuum pump. The variables and constants used are summarized and defined in the table.

If the pressure is low enough for molecular flow, the gas flow, Q, at the chamber can be expressed by the following equation:

The total gas flow, QG, resulting from the various sources in a chamber is

where the Qs are defined in the table

A viscous gas is characterized by the Knudsen number, Kn, which is simply the ratio of the mean free path to a characteristic dimension of the system, for example, the diameter of the exhaust tube. At very low pressures, where the mean free path is much larger than the dimensions of the vacuum enclosure, molecule-wall collisions dominate gas behavior. In this "molecular flow" region, the value of Kn must satisfy the condition:

where l = the mean free path and D = the diameter of the exhaust tube (16 cm)

For air at ambient temperature, the simple formula

can be used, where P = the average pressure (torr) in the chamber and l is expressed in cm [5]

Using Eqns. 3 and 4, the condition for molecular flow is therefore simply P <3.125?10-4 torr. The initial pressure values have thus been limited to the range 1?10-4 to 5?10-5 torr where it is possible to pump down the process module process pressure within 10 sec.

Assuming the quantities of Qleak, Qm, and Q0 in Eqn. 2 are negligible, the relation between the throughput and the flow rate of the gas is empirically determined by the pressure-rise method:

Qp = DP V/ tu [torr l/sec] = 0.0127 V`(5)

where V = the volume of the chamber, V` = the volumetric flow rate, and tu = the unit of time

In the above equation, 1 sccs is defined as 1/60 sccm, or 0.76 torr l/sec. From these equations, we can establish the governing equation for wafer transportation in the molecular flow range:

(The table contains definitions of the variables.) The time required, t, for lowering the pressure in the chamber from Pi to P has two solutions, depending on the value of Qp:

Qp = constant

If Qp is a constant, one can generate the equation for the time required to reduce the pressure by integrating Eqn. 6 utilizing the variable separation method as shown in the following equations:

where Pi = the value of the initial pressure in the chamber

Pressure values calculated using Eqn. 7 can then be compared to experimental values to determine the validity of the modification of the experimental method.

Qp = f(t)

If Qp changes with time, one can obtain the equation for the time required to reduce the pressure at the chamber by rewriting Eqn. 6. We can rewrite Qp as

where Qi = the initial gas throughput

w = a variable index

After introducing Eqn. 8 into Eqn. 6,

This is a nonhomogeneous first-order linear differential equation. The general solution can be represented as follows [6]:

Because the initial condition states that P = Pi at t = 0, the constant C6 can be obtained from Eqn. 11:

Figure 4. The pressure variations vs. time for various constant values of Qp.

After a period t, the pressure reaches the value P as follows:

Using different values of the index w, the results from Eqn. 13 can be compared to the results from the modified experiment. (Figs. 7 and 9 in the "Results and discussion" section show the agreement between the theoretical and experimental pressure values as functions of time.)

Control algorithm. Generally, the control system is divided into three parts. The first part detects the physical properties, such as gas pressure, to be controlled. The second part calculates the controller output, based on the pressure error (or the difference between the system`s setpoint and actual measured pressure). It is the weighted sum of the error, the integral of the error with time, and the rate of change in error. The last part of the control system uses this output to control actual properties such as chamber pressure.

A continuous time equation for pressure controller output is

where

O(t) = controller output as a function of time

E(t) = pressure error as a function of time = setpoint pressure - measured pressure

K = proportional controller gain = 100/proportional band

Ti = integrating time constant = 1
eset

Td = derivative time constant = rate

The proportional band (or 100/K) is the area around the setpoint pressure where the controller is actually controlling the process. If the controller gain is too high, the proportional gain will be too narrow, resulting in oscillations around the setpoint. If it is too low, the system may take a long time to settle around the setpoint. The integral term acts to eliminate this offset and stabilize the system. The integrating time is the inverse of the reset, which periodically redefines the output requirements at the setpoint until the measured pressure and the setpoint pressure are equal. This reset (integrating) time constant must be larger than the process response. Oscillations will result if it is too high, and the pressure may take a long time to settle at the setpoint if it is too low. The derivative (rate) portion of O(t) is used to compensate for phase lags introduced from the changing measurements. By shifting the proportional band on a slope change of the pressure, the derivative inhibits the more rapid changes in an attempt to prevent overshooting or undershooting the pressure.

The Ziegler-Nichols PID tuning criteria [7] provide a good first guess of the controller settings K, Ti, and Td using the setpoint, lag time, and rising slope of the controller response. The values settings K, Ti, and Td are then calculated to be:

where Gr = the fastest rising slope of the open loop response

Lt = the lag time of the response

The rise rate is the maximum measured rate of change divided by the magnitude of the input step. These values are then used to hold the pressure at the setpoint.

The closed loop control implements Ziegler-Nichols PID control and the output is a weighted sum of the current and last three errors. A discrete equation [8] is applied as follows:

O(t) = K0 E(t) + K1 E(t - 1) + K2 E(t - 2) + K3 E(t - 3)(16)

The values of the constants, K0, K1, K2, and K3 are calculated by the TMC using the measured lag time, rise rate of the open loop system, and the sampling period Ts:

(See the table for definitions of a, b, c, and y.)

The sampling time is adjusted to allow sufficient feedback from the MFC. The input parameter is the voltage signal of the ion gauge, at a range of 0-10 V for corresponding pressures of 10-10 to 1 torr. The output parameter is the voltage signal of the MFC, ranging from 0-5 V for flow rates of 0-5 sccm.

Results and discussion

Figure 5. Pressure variations as a function of time for various values of Gr, Lt, and Ts at a transport pressure of 5?10-5 torr.

Qp = constant. To determine the full range of the MFC, we calculated the pressure vs. time for several constant values of Qp using Eqn. 7. Figure 4 gives the pressure variations as a function of time when the flow rates of nitrogen gas are Qp = 0, 0.3, 1.5, and 3 sccm. We can see that the maximum admissible flow rate of the mass flow controller should be 5 sccm for wafer transportation.

In preliminary experiments, most results are classified into three types with overshoot, undershoot, or saturation with respect to the pressure setpoint. Several results are compared with conventional methods. Figure 5 shows pressure variations as a function of time for various parameters of Gr, Lt, and Ts. The transport vacuum is 5?10-5 torr and the initial pressure of the transport chamber is 2.2?10-6 torr. As the lag time decreases, the response of the MFC becomes faster. We also observed an overswing phenomena of both overshoot and undershoot for the referenced pressure. The overshoot appears while adjusting the rise time and the sampling period, but gradually disappears by increasing the lag time (Eqn. 15). The best observed settling time is about 20 sec, at pressures within approximately ?1.0% of the setpoint. The corresponding rise rate, lag time, and sampling period are 0.02 torr/sec, 0.25 sec, and 0.4 sec, respectively.

Figure 6. Comparison for pressure variations by the conventional and modified experimental methods at a transport pressure of 5?10-5 torr. On applying the modified method, the settling time improved to about 8 sec.

From Fig. 3, we conclude that the settling time for the pressure to settle within 2% of a setpoint is about 4 sec, including a delay of 1 sec. We have thus developed a modified experiment with the pressure control starting 4 sec after an initial gas load. Figure 6 represents pressure variations in the conventional and modified experiments. On applying the modified experimental method, the settling time dramatically improved to about 8 sec, at pressures within approximately ?1.0% of the setpoint. At a transport vacuum of 5?10-5 torr, the rise rate is 0.02 torr/sec, the lag time is 0.25 sec, the sampling period is 0.5 sec, and the initial gas load of the nitrogen is 1 sccm. The settling time for the modified method is enhanced above 75 % when compared to the conventional method.

Qp = f(t). Using the same conditions, we calculated pressure variations with time for the index w, which varies from -1 to 0.05 (Fig. 7). By varying w, different values of P(t) (Eqn. 13) can be obtained. In the experiments, the TMC calculates O(t) by comparing a user-supplied setpoint signal and a voltage signal from an ion gauge.

Figure 7. Pressure variations with time for various values of the index w at a transport pressure of 5?10-5 torr and Qi = 1.457 sccm.

As shown in Fig. 7, the experimental result using O(t) to control the experimental pressure agrees with the theoretical result P(t) at w = -1. Since we ignored the residual gas remaining from leakage, outgassing, and permeation in the calculations, there were some differences between the actual and theoretical values. Due to the delay time of the MFC, the pressure gradient of the theoretical results is steeper than that seen in the experiment. The pressure for both cases, however, becomes constant within about 9 sec.

Figure 8. Comparison for pressure variations by the conventional and modified experimental methods at a transport pressure of 1?10-4 torr.

Figure 9. Pressure variations with time for various values of the index w at a transport pressure of 1?10-4 torr and Qi = 2.915 sccm.

Figure 8 shows pressure variations in the conventional and modified experiments, all with a transport vacuum of 1?10-4 torr. Optimum tuning constants in the modified method include a rise rate of 0.02 torr/sec, a lag time of 0.15 sec, a sampling period of 0.5 sec, and an initial gas load of 2.1 sccm. In this case, the settling time is about 9 sec, at pressures within about ?0.5% of the reference pressure. The maximum variation of the pressure is 1.0?10-4 torr, which is the same as the desired output. Under the same conditions, we can see that the modified method surpassed the conventional method in settling time. Figure 9 shows pressure variations with time as the index w changes from -0.1 to 0.03. At a transport vacuum of 1?10-4 torr, the experimental result also agrees with the theoretical result of w = -0.03.

To reduce contamination levels, it is advantageous to open and close the rectangular slot valve when the process chamber is operating at a higher pressure. For wafer transportation, we observed that a lower pressure of 5?10-5 torr in the transport chamber of the cluster tool prevented backstreaming of process gases from the process chambers into the transport chamber.

Conclusion

In this study, we have developed a pressure control system for the multichamber system and evaluated its performance. The control algorithm is based on the Ziegler-Nichols method that considers the weighted sum of the current and last three errors. We obtained relatively fast pressure control by adjusting the starting time and the tuning constants in the control loop algorithm, while taking into account the typically slow response of MFC. This pressure control system can also prevent backstreaming of various contaminants from the transport chamber into the process chambers. Cross-contamination between modules may be reduced by allowing wafers to be transferred at precisely controlled vacuum pressure.n

References

1. W.R. Clark, J.J. Sullivan, "Comparison of Pump Speed Control Techniques for Pressure Control in Plasma/LPCVD Systems," Solid State Technol., p. 105, March 1982.

2. R. Fischer, "Downstream Pressure Control: Calculation of the Transfer Function and Optimization of Control Parameters Leading to a New Controller Design," J.Vac. Sci. Technol., Vol. A 4, No. 3, p. 314, May/June 1986.

3. M.E. Bader, R.P. Hall, G. Strasser, "Integrated Processing Equipment," Solid State Technol., Vol. 33, No. 5, pp. 149-154, May 1990.

4. J. H. Lee, et al., "Development of a MESC-compliant Cluster Tool," Solid State Technol.,Vol. 38, No. 10, p. 93-97, October 1995.

5. A. Roth, Vacuum Technology, North-Holland Publishing Co., Ch. 3, 2nd ed., 1976.

6. E. Kreyszig, Advanced Engineering Mathematics, p. 22, John Wiley and Sons, 3rd ed., 1972.

7. J. R. Leigh, Applied Digital Control; Theory, Design & Implementation, p. 130, Prentice Hall International Ltd., 2nd ed., 1992.

8. N. Mohsenlan, Techware Corp., private communication, January 1995.

WON ICK JANG received his BS and MS degrees in mechanical engineering from Kyungpook National University in 1982 and 1984, respectively. He has been involved in the development of semiconductor process equipment since he joined ETRI, where his current focus is process integration and vacuum technology. Semiconductor Division, ETRI, Yusong P.O. Box 106, Taejon, 305-600, South Korea; ph 82/42-860-6256, fax 82/42-860-6108, e-mail [email protected].

JONG HYUN LEE received his BS degree in mechanical engineering from Seoul National University in 1981, and his MS and PhD degrees in mechanical engineering from Korea Advanced Institute of Science and Technology in 1983 and 1985, respectively. He has been a team leader in the development of cluster tools and wafer steppers for semiconductor fabrication since joining ETRI; his field of interest is microelectromechanical systems (MEMS) and microlithography technology.

JONG TAE BAEK received his BS degree in metallurgical engineering from Hanyang University in 1980, and his MS and PhD degrees in materials science and engineering from Korea Advanced Institute of Science and Technology in 1982 and 1996, respectively. Since joining ETRI, he has researched semiconductor process technology, and is currently head of the process and equipment section. His field of interest is advanced unit process and measurement technology for semiconductor fabrication