Figure 5.1: LPCVD Multiwafer Furnace—Calculated Temperatures in the Wafer-load Region vs. Position shows a contour plot of calculated temperatures in the wafer load region. This figure includes temperatures beyond the wafer radius that actually correspond to the liner tube, reactor wall, heater and insulation, as well. Figure 5.2: LPCVD Multiwafer Furnace—Calculated Temperatures in the Entrance Region vs. Axial Position shows temperatures for some of these materials in the region between the top/front of the reactor and the wafer load. As expected, the second quartz wall is closer to the heater in temperature than the first quartz wall, and the insulation on the outside of the heater has the lowest temperature. Note that the first segment of the heater is specified to start at 38.45 cm, but there is no grid-point located exactly there, so the heater temperature appears to drop off too early. The use of more gridpoints, with a corresponding increase in computation time, would give a plot closer to the input, but this was deemed sufficient to demonstrate the features of this model. The false-color scale in Figure 5.2: LPCVD Multiwafer Furnace—Calculated Temperatures in the Entrance Region vs. Axial Position makes the temperatures appear very uniform across the wafer load, but the numerical values in the output files show that there is actually enough non-uniformity to affect the deposition rates.
Figure 5.2: LPCVD Multiwafer Furnace—Calculated Temperatures in the Entrance Region vs. Axial Position
The temperature profile file for the LPCVD Furnace model is created in the samples<release_number>\lpcvd_furnace\thermal_analysis folder after running the sample problem. This file, called temp.dat, provides detailed temperature distribution information to the CVD simulation.
The output file for the Thermal Analyzer also provides information about the run and numerical results. The output file contains an echo of the input file at the beginning, and then lists the user-provided initial guess for the temperatures before trying to solve the problem. After finding a solution, it gives information about the temperatures in the entrance region, the exit region, then the wafer load region. Figure 5.3: Part of Thermal Analyzer Output File for the Sample Problem lists an excerpt of the output file that gives the first part of the solution. The results for the wafer temperatures clearly show that the first few wafers near the beginning of the load have lower temperatures than those in the middle of the load, and that the temperature at the ends are also radially less uniform (the edge of the wafer is at gridpoint 6). This is consistent with experiment, where in production a significant number of "pseudo" wafers are always used at the ends of the wafer load. At the end of the output file, the temperatures at the specified thermocouple locations are given.
Detailed numerical results from the solution are also given in the plot file, plot2d_twafer.plt, which is also found in the samples<release_number>\lpcvd_furnace\thermal_analysis folder after running the sample problem. This file was originally formatted to be plotted with the Tecplot software, but is human-readable and could be used by other programs. In this file, the first line is a title line, which is followed by a list of the variables that are included in the file, the radial position, axial position, and wafer temperature. This is followed by blocks of numbers giving the corresponding values, which include header comments identifying the variable and corresponding units.
Figure 5.3: Part of Thermal Analyzer Output File for the Sample Problem
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SEARCH: SUCCESS. THE SOLUTION:
AXIAL
POSITION
(CENTIMETERS
FROM WALL QUARTZ WALL QUARTZ WALL HEATER
ENTRANCE) RADIOSITIES TEMPERATURES TEMPERATURES TEMPERATURES
1 3.9300E+00 2.7640E-01 3.8769E+02 3.6836E+02 3.6161E+02
2 1.1790E+01 4.4137E-01 5.3805E+02 5.0752E+02 4.4929E+02
3 1.9650E+01 6.7561E-01 6.0852E+02 5.8375E+02 5.2857E+02
4 2.7510E+01 1.0255E+00 6.6990E+02 6.5214E+02 6.1071E+02
5 3.5370E+01 1.6059E+00 7.3844E+02 7.3160E+02 7.1238E+02
6 4.3230E+01 2.8523E+00 8.2261E+02 8.3746E+02 8.7315E+02
7 5.1090E+01 3.0075E+00 8.4305E+02 8.5368E+02 8.7315E+02
8 5.8950E+01 3.0938E+00 8.5258E+02 8.5990E+02 8.7315E+02
9 6.6810E+01 3.1389E+00 8.5737E+02 8.6298E+02 8.7315E+02
10 7.4670E+01 3.1552E+00 8.5954E+02 8.6457E+02 8.7315E+02
AXIAL
POSITION
(CENTIMETERS WALL
FROM INSULATION
ENTRANCE) TEMPERATURES
1 3.9300E+00 3.2594E+02
2 1.1790E+01 3.8603E+02
3 1.9650E+01 4.3269E+02
4 2.7510E+01 4.7583E+02
5 3.5370E+01 5.2240E+02
6 4.3230E+01 5.7465E+02
7 5.1090E+01 5.8306E+02
8 5.8950E+01 5.8441E+02
9 6.6810E+01 5.8462E+02
10 7.4670E+01 5.8466E+02
JEND = 6.1884E-01
TEND = 2.9600E+02
TENDI = 3.0937E+02
AXIAL
POSITION
(CENTIMETERS
FROM WALL QUARTZ WALL QUARTZ WALL HEATER
EXIT) RADIOSITIES TEMPERATURES TEMPERATURES TEMPERATURES
1 3.9300E+00 2.7633E-01 3.8763E+02 3.6830E+02 3.6155E+02
2 1.1790E+01 4.4130E-01 5.3803E+02 5.0749E+02 4.4926E+02
3 1.9650E+01 6.7554E-01 6.0850E+02 5.8373E+02 5.2855E+02
4 2.7510E+01 1.0255E+00 6.6989E+02 6.5213E+02 6.1070E+02
5 3.5370E+01 1.6059E+00 7.3843E+02 7.3159E+02 7.1237E+02
6 4.3230E+01 2.8523E+00 8.2261E+02 8.3746E+02 8.7315E+02
7 5.1090E+01 3.0075E+00 8.4305E+02 8.5368E+02 8.7315E+02
8 5.8950E+01 3.0938E+00 8.5258E+02 8.5990E+02 8.7315E+02
9 6.6810E+01 3.1389E+00 8.5737E+02 8.6298E+02 8.7315E+02
10 7.4670E+01 3.1551E+00 8.5954E+02 8.6457E+02 8.7315E+02
AXIAL
POSITION
(CENTIMETERS WALL
FROM INSULATION
EXIT) TEMPERATURES
1 3.9300E+00 3.2589E+02
2 1.1790E+01 3.8600E+02
3 1.9650E+01 4.3267E+02
4 2.7510E+01 4.7582E+02
5 3.5370E+01 5.2239E+02
6 4.3230E+01 5.7465E+02
7 5.1090E+01 5.8306E+02
8 5.8950E+01 5.8441E+02
9 6.6810E+01 5.8462E+02
10 7.4670E+01 5.8466E+02
JEND = 6.1878E-01
TEND = 2.9600E+02
TENDI = 3.0929E+02
RADIAL WAFER WAFER WAFER WAFER
POSITION TEMPERATURE TEMPERATURE TEMPERATURE TEMPERATURE
(CENTIMETERS AT AT AT AT
FROM WAFER 78.60 79.08 79.56 80.04
CENTERLINE) CENTIMETERS CENTIMETERS CENTIMETERS CENTIMETERS
1 0.0000E+00 8.4794E+02 8.5512E+02 8.6047E+02 8.6427E+02
2 1.8750E+00 8.4813E+02 8.5537E+02 8.6070E+02 8.6445E+02
3 3.7500E+00 8.4870E+02 8.5614E+02 8.6139E+02 8.6497E+02
4 5.6250E+00 8.4973E+02 8.5752E+02 8.6255E+02 8.6582E+02
5 7.5000E+00 8.5110E+02 8.5942E+02 8.6394E+02 8.6677E+02
6 1.4750E+01 8.6417E+02 8.6492E+02 8.6575E+02 8.6658E+02
7 1.6250E+01 8.6921E+02 8.6975E+02 8.7024E+02 8.7069E+02
8 2.1150E+01 8.7315E+02 8.7315E+02 8.7315E+02 8.7315E+02
9 2.5300E+01 5.8466E+02 5.8466E+02 5.8466E+02 5.8466E+02
RADIAL WAFER WAFER WAFER WAFER
POSITION TEMPERATURE TEMPERATURE TEMPERATURE TEMPERATURE
(CENTIMETERS AT AT AT AT
FROM WAFER 80.52 81.00 81.48 81.95
CENTERLINE) CENTIMETERS CENTIMETERS CENTIMETERS CENTIMETERS
1 0.0000E+00 8.6690E+02 8.6871E+02 8.6996E+02 8.7082E+02
2 1.8750E+00 8.6703E+02 8.6880E+02 8.7002E+02 8.7087E+02
3 3.7500E+00 8.6740E+02 8.6906E+02 8.7020E+02 8.7099E+02
4 5.6250E+00 8.6799E+02 8.6946E+02 8.7047E+02 8.7117E+02
5 7.5000E+00 8.6863E+02 8.6989E+02 8.7076E+02 8.7137E+02
6 1.4750E+01 8.6736E+02 8.6809E+02 8.6874E+02 8.6933E+02
7 1.6250E+01 8.7108E+02 8.7142E+02 8.7170E+02 8.7194E+02
8 2.1150E+01 8.7315E+02 8.7315E+02 8.7315E+02 8.7315E+02
9 2.5300E+01 5.8466E+02 5.8466E+02 5.8466E+02 5.8466E+02
RADIAL WAFER WAFER WAFER WAFER
POSITION TEMPERATURE TEMPERATURE TEMPERATURE TEMPERATURE
(CENTIMETERS AT AT AT AT
FROM WAFER 82.43 82.91 83.39 83.87
CENTERLINE) CENTIMETERS CENTIMETERS CENTIMETERS CENTIMETERS
1 0.0000E+00 8.7143E+02 8.7185E+02 8.7216E+02 8.7238E+02
2 1.8750E+00 8.7146E+02 8.7187E+02 8.7217E+02 8.7239E+02
3 3.7500E+00 8.7154E+02 8.7193E+02 8.7221E+02 8.7242E+02
4 5.6250E+00 8.7166E+02 8.7202E+02 8.7227E+02 8.7246E+02
5 7.5000E+00 8.7180E+02 8.7211E+02 8.7234E+02 8.7251E+02
6 1.4750E+01 8.6984E+02 8.7030E+02 8.7069E+02 8.7103E+02
7 1.6250E+01 8.7215E+02 8.7232E+02 8.7246E+02 8.7258E+02
8 2.1150E+01 8.7315E+02 8.7315E+02 8.7315E+02 8.7315E+02
9 2.5300E+01 5.8466E+02 5.8466E+02 5.8466E+02 5.8466E+02
RADIAL WAFER WAFER WAFER WAFER
POSITION TEMPERATURE TEMPERATURE TEMPERATURE TEMPERATURE
(CENTIMETERS AT AT AT AT
FROM WAFER 84.35 84.83 85.31 85.79
CENTERLINE) CENTIMETERS CENTIMETERS CENTIMETERS CENTIMETERS
1 0.0000E+00 8.7255E+02 8.7267E+02 8.7276E+02 8.7283E+02
2 1.8750E+00 8.7255E+02 8.7267E+02 8.7276E+02 8.7284E+02
3 3.7500E+00 8.7257E+02 8.7269E+02 8.7277E+02 8.7284E+02
4 5.6250E+00 8.7260E+02 8.7271E+02 8.7279E+02 8.7285E+02
5 7.5000E+00 8.7263E+02 8.7273E+02 8.7281E+02 8.7287E+02
6 1.4750E+01 8.7133E+02 8.7159E+02 8.7181E+02 8.7200E+02
7 1.6250E+01 8.7267E+02 8.7275E+02 8.7282E+02 8.7288E+02
8 2.1150E+01 8.7315E+02 8.7315E+02 8.7315E+02 8.7315E+02
9 2.5300E+01 5.8466E+02 5.8466E+02 5.8466E+02 5.8466E+02
.....