Heat Transfer in Vacuum - Owens Design

Heat Transfer in Vacuum
• Methods of protecting components from heat sources in
vacuum chamber
• How to predict temperature of the components
• Simple 1D heat transfer models for quick design
evaluation
• Project example
Igor Fidelman 9/23/10

What needs to be protected:
• O-rings, plastic parts (limited service temperature)
• Mechanisms ( thermal expansion )
• Chamber walls ( preventing deposition )
• Feedthroughs ( proper function )

Modes of heat transfer: radiation and conduction
(convection: low pressure chambers and frequent pumping/venting )
Methods of protection:
• water cooled chamber walls or baffles,
• increased thermal conductive path
• use of low thermal conductivity materials (quartz,
opaque quartz, ceramics, SST)
• radiation shields
• gas assisted cooling

Opaque quartz
Heat source
O-ring
Water
channel
Clear quartz
Wafer
Cooling gas
Chamber wall
Radiation
shields
Thin wall:
Increased thermal
path

Thermal radiation.
• Wavelength: 0.1 – 100 micrometers
• Black body emits E=s*T^4 (W/m^2)
Stefan-Boltzmann constant s=5.66e-8 (W/m^2*K^4)
• Real body emits E= e*s*T^4 (W/m^2)
e – emissivity (0-1)

Emissivity
Depends on material and surface conditions
SST, polished 0.27-0.29
SST, oxidized 0.53-0.87
Aluminum, polished 0.04-0.09
Aluminum, anodized 0.4-0.6
Opaque quartz 0.92
Alumina 0.9

• Absorptivity, reflectivity, transmissivity
a + r + t = 1

More complications:
Dependence of optical properties on wavelength
Transmittance of 1mm thick clear fused quartz

More complications:
Dependence of optical properties on temperature
Emissivity of 0.725mm Si wafer

More complications:
Spectral distribution of radiation energy.
Maximum energy is emitted at: 2897.6/T(K) microns

More complications:
Reflection – specular, diffusive

Approximation for engineering calculations
• all surfaces are gray: absorptivity = emissivity, does not
depend on wavelength ( rarely exist in real life, many
materials are gray over certain wavelength ranges )
• all surfaces are opaque
• all surfaces are diffusive
• all surfaces are at uniform temperature
Q :=
⎛
⎝
1 − e
1
e ⋅A 1 1
⎡
⎣
( ) 4 − ( T 2 ) 4
σ⋅
T 1
⎞
⎠
+
1
A ⋅F 1 12
+
⎤
⎦
⎛
⎝
1 − e
2
e ⋅A 2 2
⎞
⎠

View Factors
Fraction of energy leaving surface 1 which reaches surface 2

Simple 1D Model
Tw = const
Tl = f (Cv,m)
Liner (top)-Chamber wall
Qr=f (e,T,F,A )
Wafer –
Chamber wall
Qr=f (e,T,F,A )
Qr Wafer-Liner
Qr=f (e,T,F,A )
Heater-Wafer
Qr=f (e,T,F,A )
Tw = f (Cv,m)
Liner (bottom)-
Chamber wall
Qr=f (e,T,F,A )
Th = const

120
115
110
Simple 1D model -results
650
600
550
500
450
400
350
300
250
200
150
100
50
0
0
5
10
15
20
25
30
35
40
45
50
55
60
65
70
T,C
75
80
85
105
100
95
90
time,sec
wafer liner

Taking it a step further
Q radiation
Q convection/conduction
Q radiation
Q convection/conduction
Q conduction
Q radiation
Q convection/conduction
Q radiation
Q convection/conduction

1D Model - Results
base plate
heater
susc. bottom
susceptor 2
susceptor 3
susceptor 4
susc. top
shower head
wafer
temperature, °C
850
840
830
820
810
800
790
780
770
760
750
740
730
720
710
700
690
680
670
660
650
640
630
620
610
600
4990 5000 5010 5020 5030 5040 5050 5060 5070 5080 5090 5100
time, sec

1D Model - Results
base plate
heater
susc. bottom
susceptor 2
susceptor 3
susceptor 4
susc. top
shower head
wafer
temperature, °C
850
840
830
820
810
800
790
780
770
760
750
740
730
720
710
700
690
680
670
660
650
640
630
620
610
600
590
580
570
560
550
5000 5100 5200 5300 5400 5500 5600
time, sec

1D Model - Results
940
920
900
880
860
840
temperature, °C
820
800
780
760
740
720
700
base plate
heater
susc. bottom
susceptor 2
susceptor 3
susceptor 4
susc. top
shower head
wafer
680
660
640
620
600
4900 5000 5100 5200 5300 5400 5500 5600
time, sec

Project example

Problem:
• protect chamber from high energy ion beam
• keep temperature of the shields below 150 deg C
Solution:
Use pure aluminum shields bolted to water cooled Al6061
supports

Project example
SHIELDS

Project example
Cooling
channels
shield

960
930
900
870
840
810
Project example
150
140
130
120
110
100
90
80
70
60
50
40
30
20
10
0
0
30
60
90
120
150
180
210
240
270
300
330
360
390
420
450
480
510
540
570
600
630
660
690
720
780
750
time, sec
sac.plate cool.plate w ater exit T
temperature, C

Conclusions
• Thermal behavior of the chamber components have to be
carefully evaluated when designing a vacuum chamber with a
heat source.
• A simple 1D model allows to quickly estimate steady state and
transient temperature of the parts.