Question

Please help with this homework problem please, I would appriciate it very much if you would break me into this. Thank You

Q8) As was discussed in Section 1 b, an expression for the intrinsic carrier concentration in a semiconductor is given by: np = n = N N, exp E kᎢ Where N and N, are the so-called density of states and are given by N = 2 211m ky h- And N = 2 211m kT h For Si (Eg = 1.1 eV) these values can be calculated as: Ne = (5.41 x 1015)*73/2 N = (2.23 x 1015)*73/2 where T is the temperature in Kelvin. (i) Now use Excel (or any other software of your choice) to calculate the intrinsic carrier concentration n of a Si over the temperature range of 10 K to 500 K (do in steps of 10K). (Think carefully of the scale to use for your axes !). Insert your plot of n vs temperature below: (6) Insert Plot (ii) Consider the semiconductors Ge (Eg = 0.7 eV) and GaAs (Eg = 1.4 eV) and assume that the same values of N. and Ny will hold as for Si (not really true !). Calculate approximate values for n; for these two semiconductors at temperatures of 80 K, 300 K and 400 K and compare to the values obtained for Si at these temperatures. Also calculate the expected electrical conductivity of each of the three semiconductors at 300 K. (6) Calculated values for n and o: N; at 80 K Nat 300K Ni at 400 K oat 300 K Semiconductor Si Ge GaAs

Answer 1

: S3 را - Eg Ni at 80k Ne. Nu.e K = 8.618165 , Eg= llev - ESIKT = (5.41X 106). 7.(2.238105.42 T3 - Eglkt 3/2 e 30 12.06 X 10 30 . 12.06 *10 (80)? 8.614105x80 e -159.70 = (6144.42) 102 (6174,12).(033.(4.39 %1670) 36 -35 = 124.019x to. 241.07 x 10 36 -35 : Ni at sok 124.01xto 271.07X10 -1 3 Ni at 3ook e = 19.06% 1030 (300) 8.61710fx300 = (325.62) .109 (325-62).186. (3.10).109 36 42.59 41 103.8 x 10 18 .. Ni at 300k 103.8 * 100 18 Ni at Yook 30 12.06 x 10 .(400) 8.61818 5x400 C 36 - 1.84 x 10 - 31.94 e 36 a 971.84 X10 (1.34). 10-14 23 - 103.4 x 10 23 103.4 x 10 . Ni at Gook

(ii) Ge: KT > 3 e - 0.1 Ni at sok K= 8.61x105, Eg=0. tev Nee Nue = (12.86x1030). I - Eg/KT (2.06*1839) (8013 8.614105480 (6174.73) (133). (6174.12) (0-3) (4:29) (1095) 16-10 e -101.63 450.13 x 10 -10 450.13 x 10 Ni at -0.7 Ni at 300k = (12.0641030) 6380) 3. e 8.61x165x300 36 = 325.62 x 10 27.100 e -12 36 325.62 x 10 x leatxo 553.56x 10 24 24 553.55 x 10 :. Ni at 3ook -0.7 8.61X665x400 e Ni at 400 K = (12.06x1039) (40013 (291.84) (1036) (271,84) (136) (1.48).109 S 20.325 e = 114.2 X 10 :. Ni at 4ook 28 =114.2 X to

(ii) Ga AS: - Eg Nc. No.e Ni at 8ok ст k=8.61kios Ega! 1.40V (s) - Eg/KT e 12.06x1039) 73 (12.06x1039) (80)3 1.4 8.614105x80 33 - 6174.72 X 10 - 203.25 e 26174.72 x 10 89d x 5.36x10 barelles et B 1330.96 x 16 .54 -54 80k - 330.9610 Ni at N; at 300k = (2.06x1039) (300)3. e 1.५ 8.614165x300 36 = 325.62 X 10 54-200 X e 36 -24 325.62 x 10 x 2.894 10 941.04 x 10 12 is Ni at zook 941.04x10 -1.4 at 4ook - (12.0641639) (400) 8.61x 105 x 400 191.84 KIO 36 -40.65 xe 771.84 x 108 x 2.21x10 36 -18 = 170.5810 19 :. Ni at 400k = 180.5x10 P