This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentThis preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: MSE 235 Final Exam April 25, 2006 18 Pages total MSE 235: Materials Physics Prof. Jun Nogami 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. _
__
__
_
__
#4 _
#5 _  MSE 235 Final Exam April 25, 2006 18 Pages total Part 1: short answers 1 oint each 21 oints total 0 Electromagnetic radiation of wavelength 700 nm is called 0 The two types of magnetism that are associated with permanent magnet materials are: and
0 Above the Néel Temperature, an antiferromagnetic material is o In an X Ray spectrum, the MB line corresponds to an energy transition where the electron goes from a state with n: to n:
0 The zincblende structure has atoms in the unit cell.
, e2 1
0 For NaCl, the bonding energy per atom can be approximated by: E = —M 4 —
7178 a Where M is called 0 In magnetic recording the read/write head is made from a (circle one) [HARD / SOFT]
magnetic material, and the recording medium is made from a [HARD / SOFI‘] magnetic material.
0 Paramagnetism is analogous to polarization in a dielectric material.
0 The dielectric constant of silicon is dominated by polarization
0 An example of a hard magnetic material is:
0 An example of a soft magnetic material is: 0 An example of a paramagnetic material is: MSE 235 Final Exam April 25, 2006 18 Pages total 0 A 5 eV electron has a wavelength of (m) [2 pts] 0 A 5 eV photon has a wavelength of (m) [2 pts]  Photons emitted by Ge will be in the portion of the
electromagnetic spectrum. [2 pts] MSE 235 Final Exam April 25, 2006 18 Pages total True / False DDDDDDDDDH
DDDDBDDDEE 1 point each 9 points total Total internal reﬂection can occur in going from a material with a lesser
index of refraction to one with a greater index, For GaAs, the effective mass of holes is less than that for electrons. Energy dissipation is associated with the complex part of the dielectric
constant. A Hall effect measurement allows the determination of both the polarity
and density of charge carriers in a material. The index of refraction is greater than or equal to the square root of the
extreme high frequency dielectric constant. 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 ptype semiconductor, the number of electrons in the conduction
band depends on the temperature in a range near room temperature. The imaginary part of the dielectric constant of a material generally
decreases with decreasing frequency MSE 235 Final Exam April 25, 2006 18 Pages total 1a) A sample of n—type Germanium has the Fermi level at 0.1 eV below the conduction band minimum at 300K. What is the doping level? [5 pts] 1b) What is the hole concentration for this sample? [4 pts] MSE 235 Final Exam April 25, 2006 18 Pages total 1c) Assuming that you want to make a 1000 Ohm cylindrical resistor out of this Ge, with a
diameter of 1 mm, What is the length of this resistor? [5 pts] MSE 235 Final Exam April 25, 2006 18 Pages total 2) Consider a cylindrical capacitor with inner electrode radius a and outer electrode radius b,
usin a dielectric of cross linked polyethl ene (XLPE): Gauss sulface The capacitance is given by:
Dielectric where L is the length of the capacitor. and the electric ﬁeld is given by: V
E(r)= b
rxln — a Properties of XLPE: e, (60 Hz) Dielectric strength (60 Hz) 2a) If the inner electrode has a diameter of 1mm, and the dielectric is 0.1 mm thick, what is the capacitance per unit length? [4 pts] MSE 235 Final Exam April 25, 2006 18 Pages total 2b) What is the maximum operating voltage for this capacitor? [5 pts] 2c) What is the power dissipated by the capacitor per unit length if it is run at 110V at 60 Hz? Assume that you can use the parallel plate capacitor power dissipation equation, and use
the maximum value of the electric ﬁeld at the voltage stated above. [5 pts] MSE 235 Final Exam April 25, 2006 18 Pages total 3 We want to pick the thickness of a diamond coating for a polycarbonate surface that will make it as reﬂective as possible at a wavelength of 600 nm. Assume that the refractive
index of the plastic is 1.58, and that for diamond is 2.39. 3a) What percentage of incident light intensity is reﬂected from the uncoated polycarbonate
surface? [5 pts] 3b) What is the minimum thickness diamond film that will maximize reﬂectivity? [9 pts] MSE 235 Final Exam April 25, 2006 18 Pages total 4 Consider the magnetic properties of Fe given in the table below. (A/m) _(A/m) _g/mol _g/cc 4a) Draw the MH loop, assuming that it is in the form of a parallelogram with vertical sides
(at least for the portion where [H  S H c ). Specify the coordinates of all four corners [5 pts} 10. MSE 235 Final Exam April 25, 2006 18 Pages total 4b) What is the area of the corresponding BH loop? [5 pts] .11 MSE 235 Final Exam April 25, 2006 18 Pages total 4c) How many Bohr magnetons are contributed to the saturation magnetization by each Fe
atom? [4 pt] .12 MSE 235 Final Exam April 25, 2006 18 Pages total 5) We want two consider two alternate strategies for generating light of 9» = 689 nm.
5a) The first strategy is to use a bulk semiconductor of the correct bandgap. Assuming that in the GaxAl(1_x)As system, the band gap scales linearly with composition from Eg = 1.42 eV
for GaAs to Eg = 2.16 eV for AlAs, what is the appropriate value of x? [7 pts] .13. MSE 235 Final Exam April 25, 2006 18 Pages total 5b) The second approach is to use a AlAs / GaAs / AlAs quantum well structure. Assume that
we can approximate the quantized valence band and conduction band states as infinite
quantum wells, with the zero of electron energy at the conduction band minimum of
GaAs, and the zero of hole energy at the valence band maximum of GaAs, then if we
want to use the transition between the n=1 hole and electron states to give l = 689 nm
photons, what is the appropriate width of this well? [7 pts] in .14. MSE 235 Final Exam April 25, 2006 18 Pages total Useful Constants and Equations: , _ 23 t
Avogadro 3 number NA — 6.023 x10 a 0m%nol
Planck’s constant h = 6.63 x10“34 J ~ s = 4.13 ><10‘15 eV  s
Electron Volt 1 eV =1.602 x 10‘” J
Boltzmann’s constant k = 1.38 x10‘23 J/awm , K = 8.62 ><10‘5 0761mm. K
Electron Mass m = 9.11><10_31 kg
Electron Charge one electron = 1.602 x 10—19 Coulomb
J
Ideal gas constant R — kNA — 8.3145 mol K
Permittivity of vacuum 80 = 8.8542x10'12 1%"
Permeability of vacuum [.10 = 47: X 10—7 %
speed of light c = 3x108 ”/S
Bohr magneton 13 = #8 = 9.2732 ><10’24 Am2 Equipartition of energy: ékT per degree of freedom for a monatomic ideal gas:
3
average kinetic energy per atom (KE) = 2 kT
3 internal energy per mole = 2— RT
d U 3 . J
molar heat capacity Cm = — = — R umts
dT 2 mol K
Electrical properties:
 l R  £— 0'  en
p — O _ p A _ nue
Electromagnetic Radiation:
2
c = iv a) =2n'v c = 3 x 108 m/s wavenumber k = 7’75
Photon energy E = hv = 7160
Matter Waves
h h
d B lie: )L = — = — Where E is kinetic ener
e ro g p m gy 15 MSE 235 Final Exam April 25, 2006 18 Pages total Schroedinger’s Wave Equation 2
i V211l + W = E‘I’
2m
_,.2
for nontime dependent potentials, we can write ‘I’(F,t) = w(F) >< w(t) where w(t) = e h and w(F) satisfies the Time independent Schroedinger’s Equation:
2 iV2w+ Vw = Ey/
2m . —h2 dﬁy
"11D: Ew+Vw=Ew
» d
Momentum Operator: f7 = th in 1D, 13 = —jh2;
1'1sz
for a free electron E versus k E = 2
m 1D Inﬁnite Square Well of width a, 0 < x < a VI" = A" sin(ﬂc:E ) n = 1, 2, 3, 4, Energies
hzrc2 2 h2 2
E" — 2ma2 n _ 8ma2 n
Probability Density: P = [‘142 = ‘P*‘P
2
Normalization: II‘PI dV = 1
h
Heisenberg’s Uncertainty Principle: Ap Ax 2 E
~sze4 1 1
One electron atom: En = 85:th [715] = (—13.6 eV)ZZ(;2)
F ' D' D' t 'b ' F  1
erml irac lS r1 utlon (E) — 1+ e(EEF)IkT
4 L3 2 3”
Density of States for a 3D Metal Z(E) dE = ”—(h3—ml— JE dB
1’;2 3n %
Fermi Energy for a metal. E F = %(§) 16. MSE 235 Final Exam April 25, 2006 18 Pages total Semiconductors:
Selected semiconductor ro  erties at T=300K t =—— /
e n
GaAs 142 0850 1.2504x10 6.246x1o 24x10” 0390 0190 éi: np = ni
:4 3’2
Ev _ E 271mg kT
41M 44 W J
(EF _ Ev) 271m; kT 3'
p N ex kT NV = 2 hz
—N —E—3
"1):"? MN ex —k—T
 _ Q
Capac1tance C  7
Parallel Plate Capacitor
C= 808,;1 dielectric
Permittivity of vacuum 80 = 8.8542 X 10—12 %
Polarizability
1
P=Nae£ 8r=1+_—Nae 8 0 Power dissipated per unit volume anI = (W)£2808r' tan6 Way 3 m .17.. MSE 235 Final Exam April 25, 2006 Magnetism Permeability of vacuum [to = 471: X 10‘7 hym Bohr magneton B = ,LLB = 9.2732X104'4 % In vacuum E = no}? In a medium E =pmurl§= [40(131 + M)=uo(1+ 1,31;
Optical Properties index of refraction n = J; speed of light in a medium v =% wavelength in a medium 1 = %’ reﬂection and transmission at normal incidence: in going from 111 to 112 2
=m R: 2:21:22; T: 4%
r ”idr12 H (711+n2)2 (n1+nz)2 13. 18 Pages total R+T=l ...
View
Full Document
 Fall '04
 NOGAMI

Click to edit the document details