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Instructions Answer each of the exam problems shown below o…

Instructions Answer each of the exam problems shown below on your printed answer sheet. Write your answers clearly. For problems 2-5, to receive credit or partial credit, you must show your work. Draw a box around your final answer.  Problem 1 Question 1a (2 points) For a nondegenerate semiconductor, what is the probability that a state in the valence band is empty? 1−f0=e(E−EF)/kBT{“version”:”1.1″,”math”:”\(1-f_0 = e^{(E-E_F)/k_BT}\)”} 1−f0=e(EF−E)/kBT{“version”:”1.1″,”math”:”\(1-f_0 = e^{(E_F-E)/k_BT}\)”} 1−f0=e(EF+E)/kBT{“version”:”1.1″,”math”:”\(1-f_0 = e^{(E_F+E)/k_BT}\)”} 1−f0=e−(EF+E)/kBT{“version”:”1.1″,”math”:”\(1-f_0 = e^{-(E_F+E)/k_BT}\)”} 1−f0=eEF/kBT{“version”:”1.1″,”math”:”\(1-f_0 = e^{E_F/k_BT}\)”} Question 1b (2 points) What is the mathematical statement of space charge neutrality? n=p{“version”:”1.1″,”math”:”\(n = p\)”} n=ND{“version”:”1.1″,”math”:”\(n = {N_D}\)”} n=ND+−NA−{“version”:”1.1″,”math”:”\(n = N_D^ +  – N_A^ – \)”} n+NA−=p+ND+{“version”:”1.1″,”math”:”\(n + N_A^ –  = p + N_D^ + \)”} n+NA−+p+ND+=0{“version”:”1.1″,”math”:”\(n + N_A^ –  + p + N_D^ +  = 0\)”} Question 1c (2 points) Consider Si doped with Boron (NA=1015cm−3,EA−EV=0.045eV){“version”:”1.1″,”math”:”({N_A} = {10^{15}}\;{\rm{c}}{{\rm{m}}^{{\rm{ – 3}}}}, {E_A} – {E_V} = 0.045\;{\rm{eV}})”}. Where is the Fermi level located at T=600K{“version”:”1.1″,”math”:”\(T = 600K\)”}?  (Hint: ni(600K)=4×1015cm−3{“version”:”1.1″,”math”:”\({n_i}\left( {600\;{\rm{K}}} \right) = 4 \times {10^{15}}\;{\rm{c}}{{\rm{m}}^{{\rm{ – 3}}}}\)”}) Near the middle of the band gap. In the upper half of the band gap. In the lower half of the band gap. Below EC{“version”:”1.1″,”math”:”\(E_C\)”} and above ED{“version”:”1.1″,”math”:”\(E_D\)”}. Above EC{“version”:”1.1″,”math”:”\(E_C\)”}. Question 1d (2 points) Which of the following statements describes a semiconductor in the freeze-out region?  ND+ND{“version”:”1.1″,”math”:”\(N_D^ +  > {N_D}\)”} ND+≈ni{“version”:”1.1″,”math”:”\(N_D^ +  \approx {n_i}\)”} ND+≈NC{“version”:”1.1″,”math”:”\(N_D^ +  \approx {N_C}\)”} Question 1e (2 points) What is the Fermi window? The energies for which f1(E)=f2(E)=1{“version”:”1.1″,”math”:”\({f_1}\left( E \right) = {f_2}\left( E \right) = 1\)”}. The energies for which f1(E)=f2(E)=0{“version”:”1.1″,”math”:”\({f_1}\left( E \right) = {f_2}\left( E \right) = 0\)”}. The energies for which f1(E)f2(E){“version”:”1.1″,”math”:”\({f_1}\left( E \right) > {f_2}\left( E \right)\)”}. The energies for which f1(E){“version”:”1.1″,”math”:” \({f_1}\left( E \right)\) “}and f2(E){“version”:”1.1″,”math”:”\({f_2}\left( E \right)\)”} are different. Question 1f (2 points) Particles diffuse down a concentration gradient. What is the force that pushes them down the concentration gradient? A gradient in temperature. A gradient in doping density. A gradient in electrostatic potential. A gradient in particle concentration. There is no force that pushes the particles. Question 1g (2 points) Which of the following corresponds to low level injection in an N-type semiconductor?   (The equilibrium minority hole concentration is p0{“version”:”1.1″,”math”:”\({p_0}\)”} and Δp=p−p0{“version”:”1.1″,”math”:”\(\Delta p = p – {p_0}\)”}  is the excess hole  concentration under nonequilibrium conditions.) Δp>>p0,Δp>>n0{“version”:”1.1″,”math”:”\(\Delta p > > {p_0},\Delta p > > {n_0}\)”} Δp>>p0,Δp

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