P2,3 (a) The E(k) dependence in some material eau be parameterized in the conduc
ID: 2289696 • Letter: P
Question
P2,3 (a) The E(k) dependence in some material eau be parameterized in the conduction band as E(k) = E0-E1 cos ka, where E0 = 22 eV, E1 = 2 eV, a = 10 A, and in the valence band as E(k) = E0 + E1 cos ka, where E0 = 16 eV, E1 = 2 eV, a = 6 A. Determine the effective masses of the electron and the hole at k = 0. Is the material direct or indirect? (b) The E(k) dependence in some other material can be parameterized in the conduction band as E(k)=E0 + E1 cos ka, where E0 = 22 eV, E1 = 2 eV, a=10 A, and in the valence hand as E(k) = E0 + E1 (cos ka)^5/2, where E0 = 14 eV, E1 = 4 eV, a = 5 A. Determine the effective mass of the electron at the minimum in the conduction band energy and the effective mass of the hole at k=0. Is the material direct or indirect?Explanation / Answer
The energy in conduction and valence band are given by;
E(k)=E0-E1 cos ka (in conduction band)
E(k)=E0+E1 cos ka (in valence band)
When k=0 then energy of conduction band is given by;
E(k)=E0-E1 cos00=E0-E1 (As cos 0=1)
E(k)=16 eV-2 eV=14 eV
M1c2=14*1.6*10-19 J
M1(3*108 m/s)2=14*1.6*10-19 J
M1=2.48*10-35 kg
When k=0 then energy of valence band is given by;
E(k)=E0-E1 cos00=E0+E1 (As cos 0=1)
E(k)=16 eV+2 eV=18 eV
M2c2=18*1.6*10-19 J
M2(3*108 m/s)2=14*1.6*10-19 J
M2=3.18*10-35 kg
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