ECE131_2009SPRING_EXAM1__[0]

ECE131_2009SPRING_EXAM1__[0] - ECE 131 Solid State...

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Unformatted text preview: ECE 131 Solid State materials and Devices Spring 09 Test 1 1. a) Give the Miller indices for each of the planes sketched below (21 points): Z z b) Consider the face-centered cubic (fcc) and body-centered cubic (bcc) structures 0 shown below each with lattice constant 10A. Body centered cubic Face centered cubic Calculate the ratio of the surface densities for the (100) plane of the fee to the bee. 2. Assume that the band gap of germanium is temperature independent. (18 points) a) Calculate the intrinsic carrier concentration of germanium at 500K. b) A germanium semiconductor is doped with a donor density of 10'5 cm" and an acceptor density of 1014 cm'3. Calculate the thermal equilibrium electron and hole concentrations at §00K. c) Compare the position of the Fermi energy level of the compensated semiconductor to that of the intrinsic Fermi level at 500K. 3 3. Consider the inﬁnite potential well sketched below. The well is 8 angstroms wide. In regions I and III, the potential, V(x), is inﬁnite; the potential, V(x), in region II is zero. (25 points) V(X) oo 00 I II III X 90 8 A The wave function satisﬁes the time independent Schrodinger’s wave equation: 62w(x) 2m 6x2 + F (E — V(x))|//(x) = 0; m is the mass of the particle trapped in the well. Why are the wave functions is regions I and 111, both zero? Derive the general form of the wave function in region 2. By using the boundary conditions, or otherwise, show that the wave solution in [/2- 0 region II is V(x) =W‘sin(n—8m—C] where x is in A . Show that in this system if the particle trapped in the well is a proton, the energy is quantized to E" = 2.03 x10'2'n2J If INSTEAD, the particle in the well is an electron and the electron drops from the 5‘h to the 4‘h energy level, what is the wavelength of the photon emitted? For gallium arsenide, EC — Ep = 0.28eV at 450K. Calculate (12 points) a) the electron concentration b) the hole concentration Assume that the Fermi energy level of silicon is 1/10 of the band gap above the mid-gap energy level at 300K. Assume that the band gap energy is independent of temperature. (24 points) a) Draw an energy level diagram that includes the conduction band, the valence band, the mid—gap energy and the Fermi energy level. Compute the probability that an energy state in the bottom of the conduction band is occupied by an electron. c) Find the probability that an energy state in the top of the valence band of silicon is empty. Determine the probability that an energy level 0.03 eV above the Fermi energy level in silicon is occupied by an electron at 400K. b) d) Table 13.2 | Conversion factors ' 1 (angstrom) = 10“ cm = 10‘10 m 10‘” femto- = f 1 pm (micron) = 10“ cm 10'‘2 pico- = p ( 1 mil = 10'3 in. = 25.4 um 10‘9 nano- = n 2.54 cm = 1 in. 10-6 ' micro- = u leV = 1.6 x 10’19 J 10" milli- = m 1] =107 erg 10+3 kilo- : k 10” mega- = M 10+9 giga— _ G 10+12 tcra - T Table B.3 I Physical constants _—_—_—_— Avogadro's number NA = 6.02 x 10*” ‘ atoms per gram ; , molecular weight L Boltzmann’s constant k = 1.38 x 10'23 J/K ‘ = 8.62 X 10—5 eV/K Electronic charge e = 1.60 x 10'” C (magnitude) Free electron rest mass mo = 9.11 x 10'“ kg Permeability of free space Mo = 4n x 10'7 H/m ‘; Permittivity of free space so = 8.85 x 10‘14 F/cm 1 = 8.85 x 10''2 F/m Planck’s constant h = 6.625 x 10‘34 J—s = 4.135 x 10'15 eV-s . h g = h = 1.054 x 10-“ 1-5 . Proton rest mass M = 1.67 x 10-27 kg Speed of light in vacuum c = 2.998 x 101° cm/s Thermal voltage (T = 300 K) V. = 5:- = 0.0259 volt : kT = 0.0259 eV IIDIX I System of Units. Conversion Factors. and General Constants Table 13.6 I properties of \$02 and Si3N4 (T r 3 r V - ho most integrated rystal structure _ I _ circuit applications] Atomic or molecular 2.2 x 107-2 1.48 x 1022 density (cm—3) Density (g-cm") 2.2 3.4V Energy gap k9 eV 4.7 e Dielectric constant 3.9 7.5 a 1700 N 1900 Melting point (°C) (c‘3 ) Atomic weight .2809 Crystal structure Diamond Density (g/cm'3) 2.33 Lattice constant (A) 5.43 Melting point (°C) 1415 Dielectric constant 11.7 Bandgap energy (eV) 1.12 Electron afﬁnity. x (volts) 4.01 Effective density of states in 2.8 x 1019 conduction band, 1!; (cm-3) Effective density of states in 1 04 x 10‘9 valence band, N., (cm'3) Intrinsic carrier concentration (cm-3) 1 5 x 10‘0 ' ‘ ’ cmzN-s MoElbggryoﬁt, p... ) 1350 Hole, 44,, 480 m’ 2’ Effective mass mo ’Etecuons m; = 0.98 m,’ = 0.19 Holes mfh = 0.16 "1,1,, = 0.49 Effective mass (density of states) Electrons 1.08 W, mo 0.56 mi Holes (4) ‘ ___L__——————————————————— A, ' :1" ‘ 97 Al ' um arsenide 12.0 3 37 Gallium phosphide 1(9) 8 3.0 A1 mpmpmde 1'35 5137 12.1 4.35 3.37 144.63 Zincblende 532 565 1238 13A L42 407 47x107 7.0x10m 1.8x106 8500 400 0.067 . 0.082 0.45 0067‘ 0.48 l f L64 0082 . 0044 x 028 0.55 l 0.37 Table 13.1 I International system of units* 11 Mass kilogram kg Time second s or sec Temperature kelvin K Current ampere A Frequency hertz Hz 1/s Force newton N kg-m/s2 Pressure pascal Pa N/m2 Energy joule J N-m Power watt W J/s Electric charge coulomb C A-s Potential volt V r J/C Conductance Siemens S A/V Resistance ohm 52 WA Capacitance far-ad F C/V Magnetic ﬂux weber Wb V-s Magnetic ﬂux density tesla T Wb/m2 Inductance ' henry H Wb/A *The cm is the common unit of length and the electron-volt is the common unit of energy (see Appendix F) used in the study of semiconductors. However, the joule and in some cases the meter should be used in most formulas. ...
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ECE131_2009SPRING_EXAM1__[0] - ECE 131 Solid State...

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