Modeling and Model Validation for RTP Design
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per unit wavelength interval d0 centered about wavelength X incident per unit solid angle Q from the (0,0) direction, per unit projected normal area of the intercepted surface:
Radiant Power Oi A
n
=
dA cos,0do)d,
(1)
It is more practical to collect incident radiance over the entire hemisphere above the wafer surface and measure spectral irradiance:
Figure 1: Incident spectral radiance L?,i
270tt/2
E; (
Jf
f)= L;,i (k '0,') cos0 sin OdOd4
(2)
0 0
or spectral band irradiance: E
X2
ffE,(X,)dk
(3)
x,
The primary challenge associated with measuring E?, and E is associated with constructing a sensor which possesses a "cosine" response to incident radiance over the range of polar angles 0 of concern to the investigator. Figure 2 and 3 show the spectral and spectral band irradiance sensors developed for this work. [Voltmeter]
P
•
-- Variac
bank
800 Cosi•e(i
Voltmeter ý
I ns E
Detector leads tor leads
. Stainless Tube
Transimped-, Preamnlifier
j
Shutter
Fused Silica Optical Fiber Response V3
I~
T\onj)esedai F3i
Figure 3:
176
386WP 3anc
tube
r-Stainless
Figure 2: Spectral irradiance sensor
lifier A/D board
Spectral band irradiance sensor
Both sensors are based on reversed biased germanium photodiodes. The spectral band irradiance sensor (0.8-1.8gm) provides cosine response to incident radiance up to 500 polar half angle while the spectral irradiance sensor (1.46±0.04gm) provides cosine response out to a 40' polar half angle. Each sensor amplifier outputs a signal voltage proportional to incident photon flux in the pass-band of the device. The voltage output of the spectral irradiance sensor is proportional to EX while the voltage output of the spectral band irradiance sensor is weighted with respect to incident photon wavelength: V = c XEx(k)dk
(4)
X1
RESULTS AND DISCUSSION The sensors were utilized to characterize radial irradiance profiles from the 3 zone RTP chamber shown in Figure 4. Zones A and C in Figure 4 heat the wafer planar surface. Zone A overheats the wafer center while zone C overheats the wafer edge. Proper selection of zone A and C power levels assures nearly uniform heat flux on the wafer planar surface. Zone B is designed to Process Gas Inlet Bankk A Top Bank Top
Proces Position
l# UEdge --•\uP-
....... Bank A •,Total] -- BankBI
Bank C
Bank B
"I, HLower Bank CToa
Quartz Tube
..
I I
I
Pumpine•I,
A
•]
Wafer Entry
.
Pump Line)
Wafer Load
. -.
.
"--
-+
.- . - . -
-.
j
o Radius -----
Position
Figure 4: 3-Zone RTP system and individual zone irradiance profiles provide dynamic wafer edge heat compensation during transients. Zone B heat flux strikes the wafer surface at large incident angle relative to surface normal and thus is de-coupled from planar surface heating. The 3-zone system was designed using a ray trace algorithm to obtain irradiance distributions on the planar wafer surface. These were coupled to a 2-D heat conduction model for temperature distributions in the wafer as discussed in [6]. The numerical approach provided temperatur
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