This is how it looks. It is not exactly a bell curve, but it is pretty decent, in the sense that it is not too squished to the top, nor is it too concentrated at the bottom.

Here are the details of the grading. All the rubrics used for the grading of this exam are listed here.

Part 1 (10 points) : kB T for RT?  26 meV or 25.85 meV.
        100 %: practically perfect
         75 %: missing unit, otherwise correct
         50 %: 1000 times too small an answer.
         50 %: 10 times too large an answer.
         25 %: correct starting formula, but no or little development from it
Part 2 (10 points) : photon wave vector for 1 eV = 1/(1973 Angstrom)
        100 %: practically perfect
         80 %: incorrect unit, otherwise correct
         50 %: correct formula, but did not know where to plug in 1 eV
          0 %: answer missing, or completely incorrect
Part 3p1 (5 points) : KE identified correctly as p^2/(2m), not mc^2 or mc^2 + p^2/(2m)
        100 %: practically perfect
          0 %: answer missing, or completely incorrect
Part 3p2 (5 points) : p^2/(2m) = 1 eV: k = p/hbar; k = 0.512 Angstrom^{-1}
        100 %: practically perfect
         90 %: correct except for a (small) numerical error
         25 %: incorrectly handled formula, no numeric answer
          0 %: answer missing, or completely incorrect
Part 4 (10 points) : Definitions of metal, insulator, semi-metal, semi-conductor
        100 %: practically perfect
         75 %: metal and semi-metal are not distinguished properly
         75 %: practically perfect except for semi-metal
         65 %: semi-metal not described or incorrectly described, semiconductor vaguely described
         50 %: semi-metal and semi-conductor incorrectly defined
Part 5 (10 points) : Degenerate and non-degenerate semi-conductors
        100 %: practically perfect
         75 %: definitions correct but rationale missing
         75 %: rationale good (quantum vs. classical statistics) but definitions in terms of EF pos missing
         60 %: definitions with an error (3kT or O(kT) missing) and rationale missing
          0 %: answer missing, or completely incorrect
Part 6 (10 points) : np = ni pi  = ni^2 --> n = 3.33 x 10^5 cm^{-3}
        100 %: practically perfect
         90 %: correct except for a (small) numerical error
         75 %: missing unit, otherwise correct
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 7a (10 points) : fcc lattice
        100 %: practically perfect
Part 7b (10 points) : Si crystal = two fcc lattices with relative displacement = (a,a,a)/4
        100 %: practically perfect
         95 %: would have been perfect, were it not for some errors in the notation
         90 %: correct except for a (small) numerical error
         90 %: correctly identified tetrahedron motif but did not clearly describe the crystal
         50 %: mentioned "tetrahedron" but did not show it (or incorrectly showed it) or explain the crystal
         50 %: Said "made up of fcc lattices" without specifying the relative displacement.
         33 %: simply said that Si forms an fcc, or things to that effect
         25 %: simply said "cubic structure" with no mor details
          0 %: answer missing, or completely incorrect
Part 7c (10 points) : (4 + 4)/a^3 = 8/a^3
        100 %: practically perfect
         80 %: counting slightly incorrect
         50 %: correct answer but incorrect or missing explanation
         50 %: dimensionally correct, counting incorrect
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 7d (10 points) : (111) plane identification
        100 %: practically perfect
          0 %: answer missing, or completely incorrect
Part 7e (10 points) : (111) plane 2D diagram -- hexagonal lattice
        100 %: practically perfect
         33 %: hexagonal-like diagram with superflous or missing atoms
          0 %: answer missing, or completely incorrect
Part 7f (10 points) : (2 x 4) / (1/2 * sqrt(2)a * sqrt(3/2)a) = 16/(sqrt(3) a^2)
         50 %: numerical error, double counting missing
          0 %: answer missing, or completely incorrect
Part 8a (10 points) : Se is a donor when replacing In or Sb
        100 %: practically perfect
         50 %: Logic OK, Se was mistaken as Si!
Part 8b (15 points) : Se replacing Sb,  E_D = -0.66 meV relative to E_C
         80 %: Derivation partial, answer correct
         70 %: Derviation missing, answer correct
         50 %: Description missing, answer incorrect due to an incorrect Z value used
         50 %: Derivation partial, anwer incorrect
         25 %: correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 8c (12 points) : E_v, E_c, E_D, E_F (T = 0), E_F (T = 300 K), E_i in a diagram
         84 %: All correct except one (EF at T = 0 or EF at T = 300 or missing E_i)
         80 %: incorrect unit, otherwise correct
         67 %: Two of them are incorrect (E_F (T = 0)  and E_i, for example)
         50 %: E_v, E_c, E_i correct, others incorrect
         33 %: E_c and E_v correct.  All others are incorrect.
          0 %: answer missing, or completely incorrect
Part 8d (13 points) : r = 640 Angstroms
        100 %: practically perfect
         80 %: Derivation partial, answer correct
         60 %: Correct answer, but r was not derived.
         25 %: (nearly) correct starting formula, but no or little development from it
          0 %: answer missing, or completely incorrect
Part 8e (10 points) : High mobility since mass is small
        100 %: practically perfect
         50 %: correct answer, but incorrect reason (low binding energy, e.g.)
          0 %: answer missing, or completely incorrect
Part 8f (10 points) : N_D = 4.8e14 cm^{-3} --> impurity band starts to form
         70 %: N_D was indicated correctly, but the consequence not discussed.
         50 %: correct qualitative statement (hopping) but no quantitative estimate of N_D
          0 %: answer missing, or completely incorrect
Part 9 (10 points) : 1d tight binding band -- k=0 is min (bonding) while k=pi/a is max (anti-bonding).
         50 %: sketched wave functions correctly but did not discuss the reason why the energy is lower or higher.
         50 %: argued based on the epsilon(k), but without explaining why t > 0.
         33 %: argument based on epsilon(k), which is presented incorrectly.
          0 %: answer missing, or completely incorrect
Part 10 (10 points) : Fermi level aligns because there should not be any net particle current.
        100 %: practically perfect
         75 %: Analogy with the pressure equilbriation of two gas systems, but the exact correspondence (p <-> EF, V <-> N) is missing.
         70 %: Good overall argument, but energy = energy (T) only (energy = energy (T,N,V)) and the "chemical potential" was never mentioned.
         60 %: EF will become equalized but without mentioning "chemical potential" or "(free) energy"
         60 %: mentioned chemical potential, but some misconception ("until the concentration is equivalent" e.g.)
         50 %: Definition of the Fermi level approximately correct.  But no discussion regarding the chemical potential nature.
         50 %: described energy and entropy but did not clearly define the chemical potential
         50 %: Gave the correct definition of the Fermi level, or the chemical potential.  No more progress though.
         33 %: Did not mention "chemical potential" and a simple restatement "Fermi levels must be the same" or something like it
         33 %: Did not mention "chemical potential" and expressed misconception "particle flows until the concentration is equal."
          0 %: answer missing, or completely incorrect
Part 11 (10 points) : resistance, conductance, resistivity, conductivity
         80 %: vague or incorrect definitions for two, otherwise perfect
         65 %: vague but correct definitions for two quantities and correct units for all
         50 %: Resistance and resisitivity are good, but not the other two.
         40 %: two good definitions, two vague definitions, no units given.
         40 %: two good definitions and one good unit
         35 %: vague definitions (how easy current flows or something like it) and two units correct
         25 %: no or incorrect definitions, two units correct
         25 %: one good definition, two vague definitions, no units given
         20 %: one good definition, one vague defintion, no units given
         20 %: one unit correct, with incorrect or vague definitions
          0 %: answer missing, or completely incorrect
Part 12 (10 points) : electron mass -- light -- wave + infinite reflections
         95 %: crystal momentum, dispersion relation, and effective mass all good, except not ever mentioning "reflection" or "Bragg diffraction."
         50 %: mentioned the correlation between "energy dispersion/function" and "effective mass"
         50 %: wave nature or "quality very different from free electron" invoked,  but reflected waves (Bragg-diffracted waves) not mentioned
          0 %: answer missing, or completely incorrect
Part 13 (10 points) : hole -- absence of electron of an otherwise filled band -- Hall, or thermo-power
        100 %: practically perfect
         90 %: all good except no mentioning of a "filled band" (or at least a "filled something")
         50 %: good qualitative definition of hole, but no discussion of how to distinguish hole from electron
         33 %: hole is the absence of an electron, with no mentioning of referencing to the filled band and no good valid examples of how to distinguish hole from electron
          0 %: answer missing, or completely incorrect
Part 14 (10 points) : tunneling -- through the Coulumb potential barrier, makes the electron go explore all atoms in a crystal very fast providing a prerequisite condition for conduction
        100 %: practically perfect
         80 %: all good except did not specify the nature of the energy barrier.
         33 %: tunneling is "going through a barrier," with no, or incorrect, explanation of what the barrier is and subsequently why the tunneling is essential for conduction
          0 %: answer missing, or completely incorrect