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ece340Fall03HW5sol - ECE 340 Homework V Fall 2003 Due...

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ECE 340 Homework V Fall 2003 Due: Wednesday, September 24, 2003 Solution: 30 points total 1. An p-type Si sample with N a = 2x10 16 /cm 3 is steadily illuminated such that g op = 10 21 EHP/cm 3 -s. If τ n = τ p =1 μs for the excitation, calculate the separation in the quasi-Fermi levels, (F n -F p ). Draw a band diagram such as Fig. 4-11. Solution: (a) 15 3 1 10 op n p g cm δ δ τ = = = × , therefore indeed low level injection 15 3 0 1 10 n n n cm δ = + = × 16 3 0 2.1 10 p p p cm δ = + = × 0.0259ln 0.288 n i i n F E eV n = = 0.0259ln 0.366 i p i p E F eV n = = 0.654 n p F F eV = 2. (a) A Ge bar 0.1 cm long and 100 μm 2 in cross-sectional area is doped with 1x10 17 /cm 3 gallium. Find the current at 300 K with 10 V applied. Repeat for a Ge bar 1 μm long assuming that the saturation thermal velocity of electrons in Ge is about 10 7 cm/s. (b) Upon a steady illumination uniform excess carriers are generated in the Ge bar. Assume that τ n = τ p = 1 μs for the excitation. Estimate the optical generation rate of EHPs per second required to increase the current by 10% in part (a).
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