Here are the details of the grading. Answers are included here, as are all the rubrics used for the grading of this exam.
Part 1 (7 points) : (c) is incorrect. The law of the junction is valid only in the leading order.
100 %: practically perfect
0 %: answer missing, or completely incorrect
Part 2 (6 points) : (c) Ideal diode equation applies to narrow or wide base.
100 %: practically perfect
0 %: answer missing, or completely incorrect
Part 3 (7 points) : (b) the R-G current.
100 %: practically perfect
0 %: answer missing, or completely incorrect
Part 4 (10 points) : 1 ps (HW7.3; This could be close to ns, but definitely not micro-sec, or ms). Time it takes for majority carriers to screen out charge flucatuation. This time is NOT the Drude relaxation time, while the two relaxation times can be of the same order of magnitude.
80 %: value correct, explanation almost correct (incorrectly invoked "recombination process")
80 %: value partially correct, explanation correct.
75 %: value correct, explanation, while not wrong, is quite insufficient.
50 %: value correct, explanation incorrect.
50 %: value incorrect, explanation correct.
30 %: value partially correct, explanation missing or incorrect.
0 %: answer missing, or completely incorrect
Part 5 (10 points) : D: unit=cm^2/s (QZ 4) and typical value=100 cm^2/s (HW 6.3).
100 %: practically perfect
80 %: A correct equation but unit is derived with a small mistake. Typical value is correct.
70 %: Typical value missing/incorrect. Otherwise, practically perfect.
60 %: Typical value missing. A correct equation but unit is derived with a small mistake.
33 %: A correct equaton involving D given but neither unit nor typical value given/correct.
0 %: answer missing, or completely incorrect
Part 6 (10 points) : Mobility: unit=cm^2/(Vs) (QZ 4) and typical value=1000 cm^2/(Vs) (HW 6.3).
100 %: practically perfect
70 %: Typical value missing/incorrect. Otherwise, practically perfect.
70 %: Unit incorrect, insufficient derivation (but some correct description), correct typical value.
60 %: A correct equation but unit is derived with a small mistake. Typical value is missing/incorrect.
33 %: A correct equaton involving D given but neither unit nor typical value given/correct.
33 %: Unit correct, but no derviation and no typical value.
0 %: answer missing, or completely incorrect
Part 7 (10 points) : Depletion approx: rho (charge density) = N_D - N_A within the depletion region. Physics: p and n small in the depletion region.
100 %: practically perfect
70 %: rho = N_D - N_A not/incorrectly given, but other physics discussions OK.
70 %: No/incorrect physics discussion, but otherwise practically perfect.
65 %: Correct for a step junction. No physics discussion.
33 %: Correct diagram, but no/completely-incorrect discussions.
33 %: Depletion region mentioned, but no definition or physics description.
20 %: One piece of remark that is physically correct, but not really relevant to this question. No other relevant answers.
0 %: answer missing, or completely incorrect
Part 8 (10 points) : T: the minority current is damped as exp(-x/L).
100 %: practically perfect
70 %: Answer correct, but explanation is not enough.
60 %: Answer correct, but no/incorrect explanation.
60 %: Answer incorrect, but some physics discussion correct.
0 %: answer missing, or completely incorrect
Part 9 (10 points) : F: it is good in a region of forward bias (LN 17, slide 10).
100 %: practically perfect
75 %: Said True, incorrectly, but the discussion is very good.
75 %: Correct answer, but the explanation is not correct.
60 %: Correct answer, but the explanation is missing completely.
50 %: Said True, incorrectly, but the discussion has some correct elements.
0 %: answer missing, or completely incorrect
Part 10 (10 points) : True, because minority carriers are not involved.
100 %: practically perfect
80 %: Correct, but the explanation is a bit too vague.
60 %: Correct, but incorrect/missing explanation.
0 %: answer missing, or completely incorrect
Part 11 (10 points) : False, charge goes like sqrt(V-V_A) and so C goes like 1/sqrt(V-V_A), decreasing as it becomes more reverse biased.
100 %: practically perfect
90 %: Correct choice, and the explanation is nearly correct.
80 %: Correct choice, but the explanation is only partially correct.
60 %: Correct, but incorrect/missing explanation.
0 %: answer missing, or completely incorrect
Part 12 (10 points) : True. One factor is the availability of a good insulator (SiO2, HfO2) that works with Si. MOSFET is much more energy efficient.
100 %: practically perfect
80 %: Correct choice, but the explanation is only partially correct.
60 %: Correct, but incorrect/missing explanation.
0 %: answer missing, or completely incorrect
Part 13 (10 points) : True. Forward: G removes backward drift to improve current. Reverse: R adds more carriers.
100 %: practically perfect
80 %: Correct choice, but the reason is correct only for reverse bias.
60 %: Correct, but reasons are not clearly spelled out.
0 %: answer missing, or completely incorrect
Part 14 (10 points) : False. The carriers created by light will be annihilated by RG traps, decreasing the efficiency.
100 %: practically perfect
60 %: Correct, but incorrect/missing explanation.
0 %: answer missing, or completely incorrect
Part 15a (7 points) : 0.49 V
100 %: practically perfect
90 %: correct except for a (small) numerical error
50 %: correct formula, but value quite wrong
0 %: answer missing, or completely incorrect
Part 15b (8 points) : Energy band diagram: (i) metallurgical junction near E_i = E_F, (ii) E_c, E_v, E_i, same shape, (iii) constant E_F, (iv) eV_{bi} is the total amount of band bending.
100 %: practically perfect
80 %: All OK, except eV_{bi} is unclear.
25 %: E_F is constant, but all others are incorrect.
0 %: answer missing, or completely incorrect
Part 15c (7 points) : E, V sketch: E is piecewise linear, and V is piecewise quadratic.
100 %: practically perfect
90 %: Qualitatively OK, but E is not linear enough, and V is not quadratic enough.
50 %: E is not OK. V is OK.
50 %: E is OK. V is not.
50 %: E has wrong sign. V is partially OK.
0 %: answer missing, or completely incorrect
Part 15d (7 points) : ln n = ln n_i + (E_F - E_i) / (kT), ln p = ln n_i - (E_F - E_i) / (kT)
100 %: practically perfect
90 %: All OK, except that ln n and ln p are piece-wise linear (incorrectly).
80 %: Correct formulas, but ln n and ln p swapped.
60 %: Formulas not OK (incorrect treatment of log), but plots are OK.
50 %: Correct formulas, but plots not OK.
0 %: answer missing, or completely incorrect
Part 15e (7 points) : Potential Energy: shaped like the negative of band bending (hole). Kinetic energy: 0 at far n side, and shaped like the band bending (hole).
100 %: The problem had an error (correction: p side --> n side). Everyone gets 100 %.
Part 15f (7 points) : No current in the quasi-neutral region, away from the depletion region. J_{p,diff}: from p to n, large near the p side depletion region. J_{p,drift} = - J_{p,diff}.
100 %: practically perfect
80 %: No current in the quasi-neutral region, and J_diff = - J_drift. But J_drift is not maximum on the p side of the depletion region.
60 %: No current in the quasi-neutral region, but inside the depletion region, currents are not correct.
60 %: J_diff = - J_drift but not correct in details.
0 %: answer missing, or completely incorrect
Part 15g (7 points) : Within the depletion region: np = n_i^2 exp (V_A/(kT)), n=n_i exp((F_N-E_i)/(kT)), p=p_i exp((E_i-F_P)/(kT)) --> F_N - F_P = V_A; In the quasi-neutral regon (n): F_N = "E_F" and F_P approaches "E_F" exponentially within distance L_P. Similarly, in the quasi-neutral p region.
100 %: practically perfect
90 %: All seems well, except that F_N (n) - F_P (p) = 0.2 eV is not noted.
60 %: Correct for the depletion region.
25 %: correct starting formula, but no or little development from it
0 %: answer missing, or completely incorrect
Part 16a (6 points) : G_L tau_p (derived from the minority carrier diffusion eq; see HW 8.4a)
100 %: practically perfect
75 %: Correct equation, correct solution, but the final answer is missing.
60 %: Wrote the correct solution without explaining it.
30 %: Simply wrote down the solution but it is incorrect (like G_L / tau_p).
25 %: correct starting formula, but no or little development from it
0 %: answer missing, or completely incorrect
Part 16b (6 points) : n_i^2 (exp (e beta V) - 1) / N_D due to the law of the junction (HW 8.4)
100 %: practically perfect
90 %: missing "e" or "q" in the exponent.
60 %: Additional RG term, not valid within the ideal diode theory.
0 %: answer missing, or completely incorrect
Part 16c (6 points) : G_L tau_n
100 %: practically perfect
75 %: Correct equation, correct solution, but the final answer is missing.
30 %: Simply wrote down the solution but it is incorrect (like G_L / tau_n).
25 %: correct starting formula, but no or little development from it
0 %: answer missing, or completely incorrect
Part 16d (6 points) : n_i^2 (exp (e beta V) - 1) / N_A due to the law of the junction (just like in HW 8.4)
100 %: practically perfect
60 %: Additional RG term, not valid within the ideal diode theory.
0 %: answer missing, or completely incorrect
Part 16e (6 points) : I = Ideal diode current - e G_L A (L_n + L_p) (cf. HW 8.4 -- the only difference is that )
100 %: practically perfect
80 %: Solution worked out correctly, except that current is dependent on x (incorrectly).
80 %: Correct, except the spurious term ("W") included, not correct within the ideal diode theory.
40 %: Ideal current included, but no/incorrect photo-voltaic current.
25 %: correct starting formula, but no or little development from it
0 %: answer missing, or completely incorrect
Part 16f (5 points) : Just like in HW8.4c.
100 %: practically perfect
75 %: Everything OK, except that I and V are swapped.
60 %: Shift of the curve in the wrong direction.
50 %: Only the ideal current part.
0 %: answer missing, or completely incorrect
Part 16g (5 points) : Plugin V = IR (or V_A = IR) into the ideal diode current part.
100 %: practically perfect
95 %: would have been perfect, were it not for (numerical) mistakes accumulated from previous part(s)
50 %: Ideal diode equation only.
0 %: answer missing, or completely incorrect
Part 16h (5 points) : Load (I < 0, V > 0; the "4-th quadrant" op), open circuit (I = 0, V > 0), short circuit (I < 0, V = 0).
100 %: practically perfect
35 %: Got one of them right.
0 %: answer missing, or completely incorrect
Part 16i (5 points) : V -> V - R_s I, and so shift the graph to the left but on a sliding scale as I changes (open circuit voltage not affected).
100 %: practically perfect
70 %: Shift to the left but including the open circuit point as well (incorrectly).
60 %: Unclear plot, but seems to have a correct idea.
50 %: Unclear plot.
50 %: Shift to the left but the open circuit point is shifted and the short circuit point is not shifted (both incorrectly).
0 %: answer missing, or completely incorrect
Part 17 (20 points) : Too much electron current between BC, degrading gamma. Still amplifying but with less efficiency.
100 %: practically perfect
50 %: Correct idea of the current flow overall, but did not discuss gamma at all, and incorrectly discussed EC.
0 %: answer missing, or completely incorrect