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Unformatted text preview: MSE 235/ 320 Final Exam December 7, 2004 15 Pages total MSE 235/320: Materials Physics Prof. Jun Nogami [:1 1 am in MSE 235 1:] 1 am in MSE 320 Print your name, Last name first: Student #: This exam is out of a total of 100 points. Read through the exam in its entirety before
starting, and feel free to do the easier parts ﬁrst. For all numerical problems, assume three signiﬁcant ﬁgures for all numbers given, and give
all answers to this accuracy. Remember to write down the units for each answer. Question Score Part1 (11)
Part 11 (14)
#1 (15)
#2 (15)
#3 (15)
#4 (15)
#5 (15)
Total (100) MSE 235 / 320 Final Exam Part I: short answers December 7, 2004 1 point each 11 points total 15 Pages total Fill in the blanks with a two or three word description of the four features of this MH curve for a ferromagnetic material: Short answer: Orientational polarization is analogous to what form of magnetism? Electromagnetic radiation of wavelength 300 nm is called In a degenerate ntype semiconductor, the Fermi level is Above the Curie Temperature, a ferromagnetic material is In an X Ray spectrum, the LB line corresponds to an energy transition where the electron goes from a state with n: The diamond structure has to n: atoms in the unit cell. MSE 235 / 320 Final Exam December 7, 2004 15 Pages total True / False 1 point each 14 points total The dielectric constant of water is dominated by orientational polarization. The electron drift mobility in an n—type semiconductor decreases with
increasing dopant density. A material with a band gap of greater than 1.77 eV will be optically
transparent. The electron drift mobility in Au will decrease if it is alloyed with a small
amount of Cu. For an ntype semiconductor, the number of electrons in the conduction
band depends on the temperature in a range near room temperature. Minimizing thickness will decrease the voltage at which a capacitor will
breakdown. It is desirable for a soft magnetic material to have large coercivity.
A fenimagnetic material can be used to make a permanent magnet.
In a transformer core, you should use a soft magnetic material A diamagnetic material has a small positive permeability. The relative permeability of a magnetic material is always greater than or
equal to one. The relative permittivity of a dielectric material is always greater than or
equal to one. The index of refraction is greater than or equal to the square root of the low
frequency dielectric constant. DDDDDDDDDDDDDDH
DDDDDDDUDDDDDD. A GaAs LED will emit orange light. MSE 235 / 320 F inal Exam 1a) lb) December 7, 2004 15 Pages total A sample of p—type GaAs has the Fermi level at 0.2 eV above the valence band maximum at 300K. What is the doping level? [6 pts] What are the electron and hole concentrations for this sample? [4 pts] MSE 235 / 320 Final Exam 1c) December 7, 2004 15 Pages total Assuming that you want to make a 1000 Ohm cylindrical resistor out of this GaAs, with a
diameter of 1 mm, what is the length of this resistor? [5 pts] MSE 235/ 320 Final Exam December 7, 2004 15 Pages total 2) We want to design a parallel plate capacitor with C=0.1 nF, using a polymer dielectric
PET
Properties of PET s, (60 Hz) Dielectric strength (60 Hz) 2a) If we choose a thickness of 5 pm for the dielectric, what is the area of the capacitor?
[2 pts] 2b) What is the maximum operating voltage for this capacitor? [2 pts] MSE 235 / 320 Final Exam December 7, 2004 15 Pages total 2c) If we want to use this capacitor at 500 Volts, what is the area of dielectric necessary to
get C=0.1 nF, using the minimum safe thickness of the dielectric at this higher voltage? [5 PtS] 2d) Using the values from 2c), what is the power dissipated by the capacitor if it is run at
110V at 60 Hz? [6 pts] MSE 235/ 320 Final Exam December 7, 2004 15 Pages total 3 We want to design pick the thickness of a diamond coating for a Silicon surface that will
make it as reﬂective as possible at a wavelength of 600 nm. Assume that the refractive
index of Si is 3.5, and that for diamond is 2.39 3a) What percentage of incident light intensity is reﬂected from the uncoated Si surface? [5
pts} 3b) What is the minimum thickness diamond ﬁlm that will maximize reﬂectivity? [10 pts] MSE 235 / 320 Final Exam December 7, 2004 15 Pages total 4 Gd is a ferromagnetic element, with properties given in the table below. T 4a) Estimate the energy loss per unit volume in one circuit of the BH loop, assuming that it
is roughly rectangular in shape [5 pts] 4b) Calculate the saturation magnetization. [5 pts] MSE 235 / 320 Final Exam December 7, 2004 15 Pages total 40) How many Bohr magnetons are contributed to the saturation magnetization by each Gd
atom? [5 pt] 10. MSE 235/ 320 Final Exam December 7, 2004 15 Pages total 5) Consider the electron states in an inﬁnite square well potential. Suppose we want to use
these energy states in a device that will absorb light of a certain frequency. 5a) What is the energy of photons corresponding to a wavelength of 7L = 450 nm? [5 pts]
Please state the answer in units of eV. 5b) Suppose that this photon energy corresponds to the energy spacing between the lowest
two energy states of a one dimensional inﬁnite square well. What is the width of this
well? [10 pts] 11 MSE 235/ 320 Final Exam December 7, 2004 15 Pages total Useful Constants and Equations: Avogadro’s number N A = 6.023 ><1023 atomﬂol
Planck’s constant h = 6.63 ><10'34 J  s = 4.13 ><10~15 eV r 5
Electron Volt 1 eV =1.602 ><10'19 J
Boltzmann’s constant k = 1.38 ><10'23 14mm _ K = 8.62 ><10‘5 “761mm, K
Electron Mass m = 9.11x10'3‘ kg
Electron Charge one electron = 1.602 ><10‘19 Coulomb
J
Ideal gas constant R — kNA — 8.3145 mol K
Permittivity of vacuum 80 = 8.8542x10'12 %
Permeability of vacuum yo = 471: X 10'7 1%”
speed of light c = 3><103 '%
Bohr magneton [3 = 113 = 9.2732 ><10’24 Am2
Equipartition of energy:
1 2kT per degree of freedom for a monatomic ideal gas: average kinetic energy per atom (KE) = 92kT internal energy per mole U = a RT
d 3 J
molar heat capacity Cm = i = — R units [
dT 2 mol K
Electrical properties:
1 R_ L c,_
P —* a  P A  enﬂe
Electromagnetic Radiation:
2
c = iv a) = 275v c = 3 x 108 m/s wavenumber k = 7:!
Photon energy E = hv 2 ha)
Matter Waves
[1 'h
de Broglie: A = — = ———— Where E is kinetic energy
p 2mE .12. MSE 235/320 Final Exam December 7, 2004 15 Pages total Schroedinger’s Wave Equation 2
i V? + W = E‘I’
2m
+51
for nontime dependent potentials, we can write ‘I’(F,t) = 1110') X w(t) Where w(t) = e h
and 1/107 ) satisfies the Time independent Schroedinger’s Equation:
2
—h
——V%+Vw=Ew
2m
. 412 dzy/
In 1D: 5”: dxz +Vlll= Elli
> d
Momentum Operator: [3 = —th in 1D, [’5 = ——jh2—£
7’1sz
for a free electron E versus k = 3——
m 1D Infinite Square Well of width a, O < x < a yr" = A" sin“; ) n = 1, 2, 3, 4, Energies
1227? 2 122 2
E” — Zma2 n . 8ma2 n
Probability Density: P = M2 = ‘P*‘I’
2
Normalization: dV = 1
Heisenberg’s Uncertainty Principle: Ap Ax 2 4L7:
~Z2me4 1 1
One electron atom: En = 880th = (—13.6 eV) Z2(717)
. . . . . 1
FermiDirac Distribution F(E) = W
3 312
Density of States for a 3D Metal Z( E) dE = ﬂagﬂ— JE dE
. h2 3n %
Fermi Energy for a metal. E F = 13. MSE 235/320 Final Exam December 7, 2004 15 Pages total Semiconductors:
Selected semiconductor pro erties at T=300K 
25  NV
. m.
i 25
w 1.04x1025 6.6x102" 2.4x1019 19 O : enuu’e + epuh ntype a: 3I2
E —E
n=Ncexp:‘———( CkT 10] N =2£2m£kTJ P'type * 3'2
p: NV eXE{_.(EF—EQ] Nv = kT n =n2=NN ex ~531
p i c v Capacitance C =% Parallel Plate Capacitor A
C = 808, E dielectric . . . __ _12 F
Perm1tt1v1ty of vacuum 80 — 8.8542 x 10 A" Polarizability
P=N%$ 1
s, =1+—Nae
8 0 Power dissipated per unit volume Wvol : (27V)£2808r’ tan6 way 3 m .14. MSE 235/ 320 Final Exam December 7, 2004 15 Pages total Magnetism Permeability of vacuum #0 = 47: X 10'7 11%” Bohr magneton ﬁ = ,uB = 9.2732 X 10—7“4 %
In vacuum I; = itall
In a medium E =u0urﬁ= #0031 + M)=uo(l+ zmﬁl
Optical Properties
index of refraction n = J;
2 speed of light in a medium v= . . A.
wavelength 1n a medium A = J n
reﬂection and transmission at normal incidence:
in going from 111 to n2 2
r=n1—”2 R H2=(ni"n2) T: 4nan R+T=1
"1+n2 .15 ...
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This note was uploaded on 04/28/2008 for the course MSE 235 taught by Professor Nogami during the Fall '04 term at University of Toronto.
 Fall '04
 NOGAMI

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