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MidtermSolutions230

MidtermSolutions230 - Name Student ID ECE230A Midterm-1...

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Name: Student ID: ECE230A Midterm -1 ALLOWED: Open book, note, and homeworks. Scientific or programmable calculators. NOT ALLOWED: Laptop computers, internet/e-mail access, discussions. 1. (30 pts) Consider a two-level system at thermal equilibrium. The concentration of particles N = 10 18 cm -3 . There are 10 19 cm -3 states at each energy level. (a) (10 pts) Assuming E 2 =1.1eV, E 1 =1.0 eV, T= 300K, find N 1 and N 2 if the system obeys Boltzman statistics. ( k B T = 0.026 eV). N 1 and N 2 are the carrier concentrations at each level. According to Boltzman Statistics ? ~ ? −? / ?? ? 1 ? 2 = ? −? 1 / ?? ? −? 2 / ?? ? 1 ? 2 = ? ( ? 1 −? 2 )/ ?? ? 1 = ? 2 ? ( ? 1 −? 2 )/ ?? − − − − − − − (1) ? = ? 1 + ? 2 − − − − − (2) Using (1) and the given values we get 10 18 = ? 2 ( ? .1 0.026 + 1) ? 2 = 2.09 𝑋 10 16 ?? 3 ? 1 = 9.8 𝑋 10 17 ?? 3
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Name: Student ID: (b) (20 pts) Find the Fermi level and N 1 and N 2 if the particles are Fermions. (Hint: You may need to do approximations as needed to simplify the mathematics in finding E f .) For Fermions ? ~ ?? . ?? ??????
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