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Unformatted text preview: Quiz #7: Solid-state Physics April 14, 2008
Problem 1 SOLUTIONS GaN is a semiconductor with the band gap Eg = 3.5 eV. Will it be n- or p-type after doping with Mg? Explain why. Draw a band diagram for this case and for T = 300 K with appropriate labels. Include the dopant level and the Fermi level. Shade the regions occupied with electrons. It will be p-type when Mg (II group) replaces Ga (III group) atoms (source of free holes). Notation is MgGa. Band diagram:
E p-type GaN
EC electrons EA EF EV x At T = 300 K there will be no electrons in the conduction band (because EC-EA >> kT, see FermiDirac function) and there will be some concentration of holes in the valence band. Problem 2 When the n-type GaAs sample with sizes lwt = 8mm3mm0.2mm is placed in a magnetic field B = 2 T, and a current I = 5 mA flows along its length l, a Hall voltage of 1 mV is measured across its width w. Find the concentration of free carriers in this sample (in units cm-3). Also, draw a picture of this sample with indicated directions of I, B, FB, v, and the Hall voltage polarity. Assume that B points into the page and I flows from right to left.
5 10-3 A ( 2 T ) IB ne = = = 3.13 1023 m -3 or 3.13 1017 cm -3 -19 -4 -3 qtVH 1.6 10 C 2 10 m 1 10 V ( ( )( ) )( ) Note: In SI system, [T] =[V][s]/[m2]. 1 m3 = 106 cm3 1/(1m3) = 10-6 1/(1cm3). Thickness is 0.2 mm = 210-4 m. Explanation: Since semiconductor is n-type, + + + + + + + + + + + + + main charge carriers are electrons in conduction Bin v(e-) band. The electrons, as negative particles, flow in direction opposite to the current direction. The FB - - - - - - - - - - - - - side where they are deflected will be negatively charged. I
FB = qvB (use left hand for electron ) ...
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