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| Annealing | == Annealing == |
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| Local high temperature annealing can be performed with localized heaters driven by most of the solar cell. This repairs some kinds of displacement damage. Horizontal thermal conductivity is poor on server-sats. Assuming zero albedo perfect black body surfaces on both sides (the worst case, hardest to heat), the black body radiation power is $ P=2 A \times 5.67E-12 \times T^4 $ where A is the area in square centimeters, P is the power in watts, and T is the temperature in Kelvin. Assuming a power of 4 watts, the heatable areas at various temperatures are : | When radiation-damaged silicon is heated, the interstitials and vacancies become more mobile, and are more likely to recombine. Assume that this process takes 3.1 years - 100 million seconds - at 60C, and the activation energy for defect mobility is 1.3 electron volts, corresponding to a "hotness" temperature of H = 15000K. The speedup factor F as a function of temperature is $ F(T) = e^{ (H/333-H/T)} $ and is shown in the table below. |
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| || Temperature || Area || || 150C || 11.02 cm^2^ || || 200C || 7.04 cm^2^ || || 250C || 4.71 cm^2^ || || 300C || 3.27 cm^2^ || |
Local high temperature annealing can be performed with localized heaters driven by most of the solar cell. This repairs some kinds of displacement damage. Horizontal thermal conductivity is poor on server-sats. Assuming zero albedo perfect black body surfaces on both sides (the worst case, hardest to heat), the black body radiation power is $ P=2 A \sigma T^4 $ where A is the area in square centimeters, P is the power in watts, $\sigma$ = 5.67E-8 is the blackbody constant, and T is the temperature in Kelvin. Sunlight absorption adds $P_0 = $ 0.1366W per square centimeter. This results in an area of $ A = P / ( 2 \sigma T^4 - P_0 ) $ Assuming a power of 4 watts, and a cell area of 176.7 cm^2^, and anneals every month, the heatable areas at various temperatures are: |
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| These temperatures should be adequate to anneal damage in seconds. Addressing individual chips and small sections of the solar cell one by one, a full anneal of a server-sat should take less than an hour. | || Temperature || Area cm^2^ || Speedup || Anneal min || Time Fraction || || 60C || 1408.03 || 1.0E+0 || 209156.80 || 4.77E+0 || || 75C || 134.61 || 7.1E+0 || 310443.30 || 7.08E+0 || || 100C || 48.25 || 1.3E+2 || 47404.53 || 1.08E+0 || || 125C || 27.04 || 1.6E+3 || 6668.81 || 1.52E-1 || || 150C || 17.66 || 1.5E+4 || 1086.64 || 2.48E-2 || || 175C || 12.49 || 1.1E+5 || 210.01 || 4.79E-3 || || 200C || 9.28 || 6.7E+5 || 47.69 || 1.09E-3 || || 225C || 7.13 || 3.3E+6 || 12.52 || 2.86E-4 || || 250C || 5.62 || 1.4E+7 || 3.73 || 8.52E-5 || || 275C || 4.51 || 5.2E+7 || 1.25 || 2.84E-5 || || 300C || 3.68 || 1.7E+8 || 0.46 || 1.05E-5 || The last time is the fraction of the monthly cycle taken up by annealing, addressing individual chips and small sections of the solar cell one by one. An '''anneal temperature of 200C''' means that 0.11% of the monthly cycle is spent annealing rather than computing. '''Please note that the above calculations are based on some pretty dodgy assumptions.''' A better analysis including the small horizontal thermal conduction, better numbers for reference rate and temperature and activation energy, and later some real empirical measurements will be needed. |
Radiation Damage
MORE LATER - problem description.
Annealing
When radiation-damaged silicon is heated, the interstitials and vacancies become more mobile, and are more likely to recombine. Assume that this process takes 3.1 years - 100 million seconds - at 60C, and the activation energy for defect mobility is 1.3 electron volts, corresponding to a "hotness" temperature of H = 15000K. The speedup factor F as a function of temperature is F(T) = e^{ (H/333-H/T)} and is shown in the table below.
Local high temperature annealing can be performed with localized heaters driven by most of the solar cell. This repairs some kinds of displacement damage. Horizontal thermal conductivity is poor on server-sats. Assuming zero albedo perfect black body surfaces on both sides (the worst case, hardest to heat), the black body radiation power is P=2 A \sigma T^4 where A is the area in square centimeters, P is the power in watts, \sigma = 5.67E-8 is the blackbody constant, and T is the temperature in Kelvin. Sunlight absorption adds P_0 = 0.1366W per square centimeter. This results in an area of A = P / ( 2 \sigma T^4 - P_0 ) Assuming a power of 4 watts, and a cell area of 176.7 cm2, and anneals every month, the heatable areas at various temperatures are:
Temperature |
Area cm2 |
Speedup |
Anneal min |
Time Fraction |
60C |
1408.03 |
1.0E+0 |
209156.80 |
4.77E+0 |
75C |
134.61 |
7.1E+0 |
310443.30 |
7.08E+0 |
100C |
48.25 |
1.3E+2 |
47404.53 |
1.08E+0 |
125C |
27.04 |
1.6E+3 |
6668.81 |
1.52E-1 |
150C |
17.66 |
1.5E+4 |
1086.64 |
2.48E-2 |
175C |
12.49 |
1.1E+5 |
210.01 |
4.79E-3 |
200C |
9.28 |
6.7E+5 |
47.69 |
1.09E-3 |
225C |
7.13 |
3.3E+6 |
12.52 |
2.86E-4 |
250C |
5.62 |
1.4E+7 |
3.73 |
8.52E-5 |
275C |
4.51 |
5.2E+7 |
1.25 |
2.84E-5 |
300C |
3.68 |
1.7E+8 |
0.46 |
1.05E-5 |
The last time is the fraction of the monthly cycle taken up by annealing, addressing individual chips and small sections of the solar cell one by one. An anneal temperature of 200C means that 0.11% of the monthly cycle is spent annealing rather than computing.
Please note that the above calculations are based on some pretty dodgy assumptions. A better analysis including the small horizontal thermal conduction, better numbers for reference rate and temperature and activation energy, and later some real empirical measurements will be needed.
MORE LATER