Previous Midterm and solution

# Previous Midterm and solution - EE2 Midterm Examination...

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Unformatted text preview: EE2 Midterm Examination Prof. H. R. Fetterman 02/8/07 Please do all work on separate sheets la.For the indicated planes ﬁnd the Miller indices. Please Show your work. 1 1b. In the Figure 2 below an electron is in a one dimensional box with the ‘1’: wavefunction corresponding to an energy of 4 eV. What is the energy in the state corresponding to WI: ? What is the lowest possible energy for an electron is this box? Figure 2 let An energy band is approximated by the expression: Eur] = (haw/2mg} -~ Ak4 Using the condition that vg m 0 at k = n/a calculate A. Also calculate 111* when k = O and k a ﬁle, . What is the value of k for which vg is maximum? 2a. Using the equations for p and pi write an expression for the difference between the Fermi level (EF) and the intrinsic Fermi energy (E3) in p type material. Explain the following Figure 3; Nd {c314} 1032 10B 1314 1015 1016 1917 1018 be. 1012 1913 1014 1015 1036 1017 3618 1 N“ {cm—‘1') 2b. Write the expression for charge neutrality keeping both terms ND and NA. Now solve the resulting quadratic equation to find an expression for 11. Show that in a compensated n type (large ND and N A] the minority hole concentration : Pa = nag I 11:: = 1112/ (Na) - NA) 20. Explain why As is a donor in Si materia} and why Ga is a acceptor in Si material. Now explain what would happen if Si atoms were introduced into GaAs material. In terms of the donor atoms estimate their ionization energy if the dielectric constant of the material is A and the effective mass of an electron is O.Bme. 26923.“ = “LAP/h 3a. Using the density of state function 2(1)) = 4Ldp/ h in 1 dimension ﬁnd the average p at ‘1‘ = 0 in terms of pr . Now derive an expression for the average value of 132. What is the average kinetic energy based upon this value? 31:). Convert the density of electrons, per unit volume, Z(p)dp to a function of energy Z(E)ciE in. 1 ‘dimension. Now derive the total number of electrons (:1), per unit length, in a metal as a function of the Fermi energy at '1‘ a 0. Write an expression for the Fermi energy as a function of 11. How would the Fermi Energy change if the effective mass was reduced by a factor of 2? 3c. Finally, please explain the following diagrams in Figure 4, with equations, in no more than three sentences each. 4N states 0 eiecirons 6N states \ 2N electrons n 2 h‘ electrons 4N states 4N eieclrons 2N states 2N electrons Electron energy —-—-—h» n = l 2 eiectrons A B Maximum kinetic energy, me (‘J 1 i Frequency, :2 E Incidem monpchromuilc light Phome lecimn kineiic energy m T in r; rmmww.‘.m.....n UT 47; vmmﬁ m6 = RE) Emma “NE A 2va f j I f ( )d "‘ ., , d i *av " f N ' 290) dp m 87502 (If? V/h3 N ' 2,13 3 V), V: 0 V3! v3? Vt v3: “y. 87: v 1 3 ﬂ __ L E I: ‘m 11% == 3600?? 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