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{
"metadata": {
"celltoolbar": "Raw Cell Format",
"name": "",
"signature": "sha256:f5d955431773596849dab1900f3dadd3740eea7cc2816449e90ee1d7309c3fc7"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter 2: Fundamental of Semiconductor Theory"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.1,Page number 43"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"n=1;\n",
"Ne=2*n**2;\n",
"print\"Maximum number of electron in 1st shell is \",Ne; #Result\n",
"n2=2; #shell no\n",
"Ne2=2*n2**2; #shell no\n",
"print\"Maximum number of electron in 2nd shell is \",Ne2; #Result\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Maximum number of electron in 1st shell is 2\n",
"Maximum number of electron in 2nd shell is 8\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.2,Page number 45"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"#Given for silicon for temp 0-400K\n",
"Eg0_Si=1.17; #in eV\n",
"A=4.73*10**-4; #in eV/K\n",
"B=636;\n",
"for i in range(1,9):\n",
" T=50*i; #degree/Kelvin\n",
" Eg_Si=Eg0_Si-(A*T**2)/(B+T);\n",
" print\"Band gap energy of silicon at \",T,\" K is \",round(Eg_Si,3),\"eV \"; #result\n",
"\n",
"#Given for Germanium for temp 0-400K\n",
"print\"\\n\"\n",
"Eg0_Ge=0.7437; #in eV\n",
"A_Ge=4.774*10**-4; #in eV/K\n",
"B_Ge=235;\n",
"for i in range(1,9):\n",
" T=50*i; #degree/Kelvin\n",
" Eg_Ge=Eg0_Ge-(A_Ge*T**2)/(B_Ge+T);\n",
" print\"Band gap energy of germanium at \",T,\" K is \",round(Eg_Ge,3),\"eV \"; #result\n",
"\n",
"\n",
"#Given for GaAs for temp 0-400K\n",
"print\"\\n\"\n",
"Eg0_Ga=1.519; #in eV\n",
"A_Ga=5.405*10**-4; #in eV/K\n",
"B_Ga=204;\n",
"for i in range(1,9):\n",
" T=50*i; #degree/Kelvin\n",
" Eg_Ga=Eg0_Ga-(A_Ga*T**2)/(B_Ga+T);\n",
" print\"Band gap energy of GaAs at \",T ,\"K is \",round(Eg_Ga,3),\"eV\"; #result\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Band gap energy of silicon at 50 K is 1.168 eV \n",
"Band gap energy of silicon at 100 K is 1.164 eV \n",
"Band gap energy of silicon at 150 K is 1.156 eV \n",
"Band gap energy of silicon at 200 K is 1.147 eV \n",
"Band gap energy of silicon at 250 K is 1.137 eV \n",
"Band gap energy of silicon at 300 K is 1.125 eV \n",
"Band gap energy of silicon at 350 K is 1.111 eV \n",
"Band gap energy of silicon at 400 K is 1.097 eV \n",
"\n",
"\n",
"Band gap energy of germanium at 50 K is 0.74 eV \n",
"Band gap energy of germanium at 100 K is 0.729 eV \n",
"Band gap energy of germanium at 150 K is 0.716 eV \n",
"Band gap energy of germanium at 200 K is 0.7 eV \n",
"Band gap energy of germanium at 250 K is 0.682 eV \n",
"Band gap energy of germanium at 300 K is 0.663 eV \n",
"Band gap energy of germanium at 350 K is 0.644 eV \n",
"Band gap energy of germanium at 400 K is 0.623 eV \n",
"\n",
"\n",
"Band gap energy of GaAs at 50 K is 1.514 eV\n",
"Band gap energy of GaAs at 100 K is 1.501 eV\n",
"Band gap energy of GaAs at 150 K is 1.485 eV\n",
"Band gap energy of GaAs at 200 K is 1.465 eV\n",
"Band gap energy of GaAs at 250 K is 1.445 eV\n",
"Band gap energy of GaAs at 300 K is 1.422 eV\n",
"Band gap energy of GaAs at 350 K is 1.399 eV\n",
"Band gap energy of GaAs at 400 K is 1.376 eV\n"
]
}
],
"prompt_number": 12
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.3,Page number 52"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"l=10*10**-3; #in m\n",
"w=2*10**-3; #in m\n",
"h=2*10**-3; #in m\n",
"V=12; #in V\n",
"u_n=0.14; #in m*m/V*s\n",
"u_p=0.05; #in m*m/V*s\n",
"q_n=1.6*10**-19; #in Columbs\n",
"q_p=1.6*10**-19; #in Columbs\n",
"p_i=2.4*10**19; #in columbs\n",
"n_i=2.4*10**19; #in columbs\n",
"E=V/l;\n",
"v_n=E*u_n;\n",
"v_p=E*u_p;\n",
"J_n=n_i*q_n*v_n;\n",
"J_p=p_i*q_p*v_p;\n",
"J=J_n+J_p;\n",
"print\"Electron velocity :vn is \",v_n,\"m/s\"; #result\n",
"print\"Hole velocity :vp is \",v_p/1000,\"km/s\"; #result\n",
"print\"Current density : Jn \",J,\"A/m^2\"; #result\n",
"A=88*10**-6;\n",
"I_T=J*A;\n",
"print\"Total current :I_T is\",round(I_T*1000,4),\"mA\"; #result\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Electron velocity :vn is 168.0 m/s\n",
"Hole velocity :vp is 0.06 km/s\n",
"Current density : Jn 875.52 A/m^2\n",
"Total current :I_T is 77.0458 mA\n"
]
}
],
"prompt_number": 14
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.4,Page number 53"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"n_i=2*10**17; #electron/m*m*m\n",
"p=5.7*10**20; #holes/m*m*m\n",
"u_n=0.14; #in m*m/V*s\n",
"u_p=0.05; #in m*m/V*s\n",
"q_n=1.6*10**-19; #in Columbs\n",
"q_p=1.6*10**-19; #in Columbs\n",
"n=(n_i)**2/p;\n",
"print\"Electron :n is \",\"{0:.3e}\".format(n),\"electrons \"; #result\n",
"n=7*10**13\n",
"P=(n*u_n*q_n)+(p*u_p*q_p);\n",
"print\"Conductivity :P is \",round(P,4),\"S/m \"; #result\n",
"# answer misprinted\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Electron :n is 7.018e+13 electrons \n",
"Conductivity :P is 4.56 S/m \n"
]
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.5,Page number 55"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"NA=10**22; #acceptors/m*m*m\n",
"ND=1.2*10**21; #donors/m*m*m\n",
"T=298; #in Kelvin\n",
"k=1.38*10**-23; #Boltzman Constant in J/K\n",
"q=1.6*10**-19; #charge of electron in C\n",
"Vt=k*T/q; #thermal voltage in V\n",
"print\" VT is \",Vt*1000,\"mV\"; #result\n",
"n_i=2.4*10**17; #carrier/m**3 for silicon \n",
"VB=Vt*log(NA*ND/n_i**2); #barrier voltage in V\n",
"print\" Barrier Voltage of Silicon VB is \",round(VB*1000,4),\"mV\"; #result\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" VT is 25.7025 mV\n",
" Barrier Voltage of Silicon VB is 492.3224 mV\n"
]
}
],
"prompt_number": 19
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.6,Page number 56"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"Is=0.12; #in pAmp\n",
"V=0.6; #in V\n",
"T=293; #in Kelvin\n",
"k=1.38*10**-23; #Boltzmann's Constant in J/K\n",
"q=1.6*10**-19; # charge of electron in C\n",
"Vt=k*T/q; #thermal voltage\n",
"print\"VT(20 deg Cel) is \",round(Vt,4),\"V\"; #result in book is misprint\n",
"T1=373; #in Kelvin\n",
"n=1.25;\n",
"Vt1=k*T1/q; #thermal voltage\n",
"print\"VT(100 deg Cel) is \",round(Vt1,4),\"V\";\n",
"I=Is*(math.e**(V/(n*Vt1))-1); #forward biasing current in mircoA\n",
"print\"I(100 deg Cel) is \",round(I/10**6,4),\"microampere\"; #result\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"VT(20 deg Cel) is 0.0253 V\n",
"VT(100 deg Cel) is 0.0322 V\n",
"I(100 deg Cel) is 0.3622 microampere\n"
]
}
],
"prompt_number": 22
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.7,Page number 56"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"Is=100; #in nAmp \n",
"Ts=100; #in Kelvin\n",
"I_s=Is*10**-9*2**(Ts/10); #I_s will be in nm \n",
"print\" I(100 deg Cel) is \",I_s*10**6,\"microampere\"; #converted to microA from nm\n",
"# wrong calculation in the book\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
" I(100 deg Cel) is 102.4 microampere\n"
]
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Example 2.8,Page number 59"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"\n",
"#given\n",
"\n",
"Br_Si=1.79*10**-15; #Recombination coefficient for Si\n",
"Br_Ge=5.25*10**-14; #Recombination coefficient for Ge\n",
"Br_GeAs=7.21*10**-10; #Recombination coefficient for GeAs\n",
"Br_InAs=8.5*10**-11; #Recombination coefficient for InAs\n",
"P_N=2*10**20; #per cubic cm\n",
"\n",
"T_Ge=1/Br_Ge/P_N; #radiative minority carrier lifetime\n",
"print\"T_Ge is \",round(T_Ge/10**-6,4),\"micro-s\"; #result\n",
"\n",
"T_Si=1/Br_Si/P_N; #radiative minority carrier lifetime\n",
"print\"T_Si is \",round(T_Si/10**-6,4),\"micro-s\"; #result\n",
"\n",
"T_InAs=1/Br_InAs/P_N; #radiative minority carrier lifetime\n",
"print\"T_InAs is \",round(T_InAs/10**-12,4),\"ps\"; #result\n",
"\n",
"T_GeAs=1/Br_GeAs/P_N; #radiative minority carrier lifetime\n",
"print\"T_GeAs is \",round(T_GeAs/10**-12,4),\"ps\"; #result\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"T_Ge is 0.0952 micro-s\n",
"T_Si is 2.7933 micro-s\n",
"T_InAs is 58.8235 ps\n",
"T_GeAs is 6.9348 ps\n"
]
}
],
"prompt_number": 25
}
],
"metadata": {}
}
]
}
|
