Problems (Lecture 13) Hall effect. Two types of charge carriers Derive the magnetoresistance and Hall coefficient formul

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Problems Lecture 13 Hall Effect Two Types Of Charge Carriers Derive The Magnetoresistance And Hall Coefficient Formul 1 (60.31 KiB) Viewed 57 times

Problems (Lecture 13) Hall effect. Two types of charge carriers Derive the magnetoresistance and Hall coefficient formulas for a semicon- ductor which has both types of charge carriers, electrons and holes (with the concentrations, effective masses and scattering times, respectively, n, m, T and | mh, Th). Answers: Pax - po np(6+1) PO (nb +pj* + (-p?lwer)?žW.7)?, RH 1 nba - p + (n - p)(wcT) ec (nb + p)2 + (n - p)(W.T)2 Here po is the resistivity at the zero magnetic field, we = eB/cm is the electron cyclotron frequency, b = An/Hp Hm = et/m and My = en/m) are the electron and hole mobilities. Hints and intermediate expressions. Components of the conductivity tensor are sums of the partial components, which correspond to electron and hole contributions, о е оп, ки +ор, их, Oyr = Onyx + py: een (wet) Onyx B 1+ (wc7)? ест WAT 00= B 1+ ( WT) ecp Open = B 1+ (wch) آل انها ecpwc.6.7) pyx = B 1+ (web) 10 10" 10 10" -Si: B 10" 10 1.2 E 1.0 0.8 -Si: B H,eV) 0.6 0.4 0.2 0.0 10 1000 100 T (K) Figure 4: Temperature dependencies of the hole concentration and chemical po- tential for p-silicon (NA = 105 cm , = 45.6 meV; the temperature dependence of the energy gap E,(T) E (0) -7°/T + ), E (0) = 1.17 V, a 4.73 10+ V/K 8636 K is taken into account)