Q1) Calculate the intrinsic carrier concentration. ni. at T = 200, 400, and 600 K for (a) silicon, (b)
germanium, and (c) gallium arsenide.
Soln: -we know that,
ni2 =NcNv
T 3 e-Eg/(0.0259(T/300))
300
(a)For silicon,
Substituting value Nc=2.8x1019 cm-3 ,Nv=1.04x1019 cm-3 ,T=200K and Eg=1.12eV
ni2 = (2.8x1019) (1.04x1019) 200
300
3
e-(1.12/ (0.0259(200/300)))
ni2 = (2.8x1019) (1.04x1019) (8/27) (6.75x10-29)
ni2 = 5.83x109
ni =7.6x104 cm-3 ……………... (at T=200K)
at T=400K,
ni2 = (2.8x1019) (1.04x1019) 400
300
3
e-(1.12/ (0.0259(400/300)))
ni2 = (2.8x1019) (1.04x1019) (64/27) (8.22x10-15)
ni2 = 5.67x1024
ni =2.38x1012 cm-3 ……………... (at T=400K)
at T=600K,
ni2 = (2.8x1019) (1.04x1019) 600
300
3
e-(1.12/ (0.0259(600/300)))
ni2 = (2.8x1019) (1.04x1019) (8) (4.07x10-10)
ni2 = 9.49x1029
ni =9.74x1014 cm-3 ……………... (at T=600K)
1
For germanium,
Substituting value Nc=1.04x1019 cm-3 ,Nv=6x1018 cm-3 ,T=200K and Eg=0.67eV
ni2 = (1.04x1019) (6x1018) 200
300
3
e-(0.67/ (0.0259(200/300)))
ni2 = (1.04x1019) (6x1018) (8/27) (1.41x10-17)
ni2 = 2.6x1020
ni =1.612x1010 cm-3 ……………... (at T=200K)
at T=400K,
ni2 = (1.04x1019) (6x1018) 400
300
3
e-(0.67/ (0.0259(400/300)))
ni2 = (1.04x1019) (6x1018) (64/27) (3.75x10-9)
ni2 = 5.55x1029
ni =7.45x1014 cm-3 ……………... (at T=400K)
at T=600K,
ni2 = (1.04x1019) (6x1018) 600
300
3
e-(0.67/ (0.0259(600/300)))
ni2 = (1.04x1019) (6x1018) (8) (2.4x10-6)
ni2 = 1.2x1033
ni =3.47x1016 cm-3 ……………... (at T=600K)
For gallium arsenide,
Substituting value Nc=4.7x1017 cm-3 ,Nv=7x1018 cm-3 ,T=200K and Eg=1.42eV
ni2 = (4.7x1017) (7x1018) 200
300
3
e-(1.42/ (0.0259(200/300)))
ni2 = (4.7x1017) (7x1018) (8/27) (1.9x10-36)
ni2 = 1.87
ni =1.37 cm-3 ……………... (at T=200K)
2
at T=400K,
ni2 = (4.7x1017) (6x1018) 400
300
3
e-(1.42/ (0.0259(400/300)))
ni2 = (4.7x1017) (7x1018) (64/27) (1.39 x10-18)
ni2 = 1.08x1019
ni =3.29x109 cm-3 ……………... (at T=400K)
at T=600K,
ni2 = (4.7x1017) (7x1018) 600
300
3
e-(1.42/ (0.0259(600/300)))
ni2 = (4.7x1017) (7x1018) (8) (1.24x10-12)
ni2 = 3.27x1025
ni =5.72x1012 cm-3 ……………... (at T=600K)
Table showing values of intrinsic carrier concentration(ni) in cm-3 values for different material at
different temperature.
material
silicon
germanium
gallium arsenide
Temp
200K
7.6x104 cm-3
1.612x1010 cm-3
1.37 cm-3
400K
2.38x1012 cm-3
7.45x1014 cm-3
3.29x109 cm-3
600K
9.74x1014 cm-3
3.47x1016 cm-3
5.72x1012 cm-3
3