# Radiation Damage

MoreLater - 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 ( 333K ), 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) = \exp( { { ( 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 thinsats. 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-12 Watts per cm^{2}K^{4} is the black-body 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:

Temperature |
Area cm |
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. However, hotter temperatures may accelerate failures, especially around the edges of the cell. We may end up cooking the center at perhaps 175C, and cooking the edges at 150C. We can schedule anneal times when the computation load is low, and we can also interrupt anneals (to be resumed later) when unexpected demand occurs.

The black body radiation at 175C is 4.57W/12.5cm^{2} or 366 mW/cm^{2}. The thermal capacity of silicon is 1.65 Joules/cm^{3}-K or 16.5mJ/cm^{2}-K, so when the heating stops, the silicon cools by 22 degrees per second. Assume that the 12.5cm heated area includes some periphery around a 3 cm diameter disk, with 1cm from the 448K 3cm center disk to the "cold" 333K 7cm edge disk. The area around the inner disk is approximately 100um*10cm. The thermal conductivity of the path is approximately 149W/m-K * 1E-6 m^{2} / 0.02m or 7.5mW/K for a heat flow of 0.8W .

**Please note that the above calculations are based on some pretty dodgy assumptions.** A better analysis will more accurately model horizontal thermal conduction, and start with better numbers for reference rate and temperature and activation energy. The hot spots and temperature gradients should probably be sculpted for maximum reliability. Real empirical measurements will be needed to verify the analysis.

## GaNxAs1-x

GaNxAs1-x has now been demonstrated as a full-spectrum solar cell technology. Moreover as GaN has both high voltage operation and *high radiation resistance*, it may be feasible to purchase Cray Computer Corporation's GaAsfabrication technology (now dormant) and adapt it to GaN with the intention of segmenting each server into:

- GaN digital processing
- GaN power transmission
GaNxAs1-x solar collection

Despite GaN's lower electron mobility than GaAs (and even Si), the higher power available to the digital processing means GaN's higher voltages might be used to compensate. A drawback would be that the higher power consumption of the digital processing would require additional heat dissipation mass on the cold side of the collector.