1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
|
{
"metadata": {
"name": "Chapter 8"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": "Conducting materials"
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.1, Page number 231"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the electrical resistivity\n\n#Variable declaration\nm=9.1*10**-31; #mass of the electron in kg\nn=2.533*10**28; #concentration of electrons per m^3\ne=1.6*10**-19;\ntow_r=3.1*10**-14; #relaxation time in sec\n\n#Calculation\nrho=m/(n*(e**2*tow_r));\n\n#Result\nprint(\"electrical resistivity in ohm metre is\",rho);",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('electrical resistivity in ohm metre is', 4.526937967219795e-08)\n"
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.2, Page number 231"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the band gap of semiconductor\n\n#importing modules\nimport math\n\n#Variable declaration\ns=3.75*10**3; #slope\nk=1.38*10**-23;\n\n#Calculation\nEg=2*k*s;\nEg=Eg/(1.6*10**-19); #converting J to eV\nEg=math.ceil(Eg*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint(\"band gap of semiconductor in eV is\",Eg);",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('band gap of semiconductor in eV is', 0.647)\n"
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.3, Page number 231"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the probability of occupation of electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nT=989; #temperature in C\nk=1.38*10**-23;\n#let E-EF be E\nE=0.5; #occupied level of electron in eV\n\n#Calculation\nT=T+273; #temperature in K\nE=E*1.6*10**-19; #converting eV to J\n#let fermi=dirac distribution function f(E) be f\nf=1/(1+math.exp(E/(k*T)));\nf=math.ceil(f*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint(\"probability of occupation of electrons is\",f);",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('probability of occupation of electrons is', 0.011)\n"
}
],
"prompt_number": 4
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.4, Page number 232"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the drift velocity of free electrons\n\n#Variable declaration\nmew_e=0.0035; #mobility of electrons in m^2/Vs\nE=0.5; #electric field strength in V/m\n\n#Calculation\nvd=mew_e*E;\nvd=vd*10**3;\n\n#Result\nprint(\"drift velocity of free electrons in m/sec is\",vd,\"*10**-3\");\n\n#answer given in the book is wrong",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('drift velocity of free electrons in m/sec is', 1.75, '*10**-3')\n"
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.5, Page number 232"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the mobility of electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nA=6.022*10**23; #avagadro number\ne=1.6*10**-19;\nrho=1.73*10**-8; #resistivity of Cu in ohm metre\nw=63.5; #atomic weight \nd=8.92*10**3; #density in kg/m^3\n\n#Calculation\nd=d*10**3;\nsigma=1/rho;\nsigmaa=sigma/10**7;\nsigmaa=math.ceil(sigmaa*10**3)/10**3; #rounding off to 3 decimals\nn=(d*A)/w;\nmew=sigma/(n*e); #mobility of electrons\nmew=mew*10**3;\nmew=math.ceil(mew*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint(\"electrical conductivity in ohm-1 m-1\",sigmaa,\"*10**7\");\nprint(\"concentration of carriers per m^3\",n);\nprint(\"mobility of electrons in m^2/Vsec is\",mew,\"*10**-3\");",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('electrical conductivity in ohm-1 m-1', 5.781, '*10**7')\n('concentration of carriers per m^3', 8.459250393700786e+28)\n('mobility of electrons in m^2/Vsec is', 4.2708, '*10**-3')\n"
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.6, Page number 232"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the fermi energy\n\n#importing modules\nimport math\n\n#Variable declaration\nn=18.1*10**28; #concentration of electrons per m^3\nh=6.62*10**-34; #planck constant in Js\nme=9.1*10**-31; #mass of electron in kg\n\n#Calculation\nX=h**2/(8*me);\nE_F0=X*(((3*n)/math.pi)**(2/3));\nE_F0=E_F0/(1.6*10**-19); #converting J to eV\n\n#Result\nprint(\"Fermi energy in eV is\",E_F0);\n\n#answer given in the book is wrong",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('Fermi energy in eV is', 3.762396978021977e-19)\n"
}
],
"prompt_number": 18
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.7, Page number 233"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the concentration of free electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nE_F0=5.5; #fermi energy in eV\nh=6.63*10**-34; #planck constant in Js\nme=9.1*10**-31; #mass of electron in kg\n\n#Calculation\nE_F0=E_F0*1.6*10**-19; #converting eV to J\nn=((2*me*E_F0)**(3/2))*((8*math.pi)/(3*h**3));\n\n#Result\nprint(\"concentration of free electrons per unit volume of silver per m^3 is\",n);\n\n#answer given in the book is wrong\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('concentration of free electrons per unit volume of silver per m^3 is', 4.603965704817037e+52)\n"
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.8, Page number 233"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the probability of an electron\n\n#importing modules\nimport math\n\n#Variable declaration\nEg=1.07; #energy gap of silicon in eV\nk=1.38*10**-23;\nT=298; #temperature in K\n\n#Calculation\nEg=Eg*1.6*10**-19; #converting eV to J\n#let the probability of electron f(E) be X\n#X=1/(1+exp((E-Ef)/(k*T)))\n#but E=Ec and Ec-Ef=Eg/2\nX=1/(1+math.exp(Eg/(2*k*T)))\n\n#Result\nprint(\"probability of an electron thermally excited is\",X);",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('probability of an electron thermally excited is', 9.122602463573379e-10)\n"
}
],
"prompt_number": 21
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.9, Page number 234"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the fermi energy and temperature\n\n#importing modules\nimport math\n\n#Variable declaration\nk=1.38*10**-23;\nm=9.1*10**-31; #mass of the electron in kg\nvf=0.86*10**6; #fermi velocity in m/sec\n\n#Calculation\nEfj=(m*vf**2)/2;\nEf=Efj/(1.6*10**-19); #converting J to eV\nEf=math.ceil(Ef*10**3)/10**3; #rounding off to 3 decimals\nTf=Efj/k;\nTf=Tf/10**4;\nTf=math.ceil(Tf*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint(\"fermi energy of metal in J is\",Efj);\nprint(\"fermi energy of metal in eV is\",Ef);\nprint(\"fermi temperature in K is\",Tf,\"*10**4\");\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('fermi energy of metal in J is', 3.3651800000000002e-19)\n('fermi energy of metal in eV is', 2.104)\n('fermi temperature in K is', 2.4386, '*10**4')\n"
}
],
"prompt_number": 24
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.10, Page number 234"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the Lorentz number\n\n#Variable declaration\nsigma=5.82*10**7; #electrical conductivity in ohm^-1m^-1\nK=387; #thermal conductivity of Cu in W/mK\nT=27; #temperature in C\n\n#Calculation\nT=T+273; #temperature in K\nL=K/(sigma*T);\n\n#Result\nprint(\"lorentz number in W ohm/K^2 is\",L);\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('lorentz number in W ohm/K^2 is', 2.2164948453608246e-08)\n"
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 8.11, Page number 235"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the electrical conductivity, thermal conductivity and Lorentz number\n\n#importing modules\nimport math\n\n#Variable declaration\nm=9.1*10**-31; #mass of the electron in kg\ne=1.6*10**-19;\nk=1.38*10**-23;\nn=8.49*10**28; #concentration of electrons in Cu per m^3\ntow_r=2.44*10**-14; #relaxation time in sec\nT=20; #temperature in C\n\n#Calculation\nT=T+273; #temperature in K\nsigma=(n*(e**2)*tow_r)/m;\nsigmaa=sigma/10**7;\nsigmaa=math.ceil(sigmaa*10**4)/10**4; #rounding off to 4 decimals\nK=(n*(math.pi**2)*(k**2)*T*tow_r)/(3*m);\nK=math.ceil(K*100)/100; #rounding off to 2 decimals\nL=K/(sigma*T);\n\n#Result\nprint(\"electrical conductivity in ohm^-1 m^-1 is\",sigmaa,\"*10**7\");\nprint(\"thermal conductivity in W/mK is\",K);\nprint(\"Lorentz number in W ohm/K^2 is\",L);\n\n#answer for lorentz number given in the book is wrong\n",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('electrical conductivity in ohm^-1 m^-1 is', 5.8277, '*10**7')\n('thermal conductivity in W/mK is', 417.89)\n('Lorentz number in W ohm/K^2 is', 2.4473623172034308e-08)\n"
}
],
"prompt_number": 29
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
