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{
"metadata": {
"name": "Chapter 9"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": "Semiconducting materials"
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.1, Page number 266"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the number of charge carriers\n\n#Variable declaration\nmew_e=0.36; #mobility of electrons in m^2/Vs\nmew_h=0.14; #mobility of holes in m^2/Vs\nsigma=2.2; #conductivity in ohm-1 m-1\nT=300; #temperature in K\ne=1.6*10**-19; #electron charge in C\n\n#Calculation\nni=sigma/(e*(mew_e+mew_h)); #carrier concentration per m^3\n\n#Result\nprint(\"carrier concentration of an intrinsic semiconductor per m^3 is\",ni);",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('carrier concentration of an intrinsic semiconductor per m^3 is', 2.75e+19)\n"
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.2, Page number 266"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the band gap\n\n#importing modules\nimport math\nimport numpy as np\nfrom __future__ import division\n\n#Variable declaration\nT1=20; #temperature in C\nT2=100; #temperature in C\nsigma_i20=250; #conductivity in ohm-1 m-1\nsigma_i100=1100; #conductivity in ohm-1 m-1\nk=1.38*10**-23;\n\n#Calculation\nT1K=T1+273; #temperature in K\nT2K=T2+273; #temperature in K\nT_1K=T1K**(-1);\nT_2K=T2K**(-1);\nT_1=T_2K-T_1K;\nT_2=T2K/T1K;\nTk=T_1**(-1);\nT_k=(T_2)**(3/2);\n#intrinsic carrier concentration at T1K is ni20 = 2*((2*math.pi*k*m*293)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-Eg/(2*k*293))\n#intrinsic carrier concentration at T2K is ni100 = 2*((2*math.pi*k*m*373)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-Eg/(2*k*373))\n#dividing ni20/ni100 = (293/373)**(3/2)*(math.exp(-Eg/(2*k*293))/math.exp(-Eg/(2*k*373)))\n#ni20/ni100 = (293/373)**(3/2)*math.exp((-Eg/(2*k))((1/293)-(1/373)))\n#sigma_i20/sigma_i100 = (ni20*e*(mew_e+mew_h))/(ni100*e*(mew_e+mew_h)) = ni20/ni100\n#therefore sigma_i20/sigma_i100 = ni20/ni100 = (293/373)**(3/2)*math.exp((-Eg/(2*k))((1/293)-(1/373)))\n#math.exp((-Eg/(2*k))*((1/293)-(1/373))) = (sigma_i20/sigma_i100)*(373/293)**(3/2)\n#by taking log on both sides we get (-Eg/(2*k))*((1/293)-(1/373)) = np.log((sigma_i20/sigma_i100)*(373/293)**(3/2))\n#Eg=2*k*(((1/373)-(1/293))**(-1))*np.log((sigma_i20/sigma_i100)*(373/293)**(3/2))\nEg=2*k*Tk*np.log((sigma_i20/sigma_i100)*T_k); #band gap in J\nEgeV=Eg*6.241*10**18; #converting J to eV\nEgeV=math.ceil(EgeV*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint(\"band gap of the semiconductor in J is\",Eg);\nprint(\"band gap of the semiconductor in eV is\",EgeV);\n\n#answer for band gap in eV given in the book is wrong in the 4th decimal point",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('band gap of the semiconductor in J is', 4.2210259829756855e-20)\n('band gap of the semiconductor in eV is', 0.2635)\n"
}
],
"prompt_number": 3
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.3, Page number 267"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the Hall voltage\n\n#Variable declaration\nI=10**-2; #current in Ampere\nl=100; #length in mm\nd=1; #thickness in mm\nw=10; #breadth in mm\nB=0.5; #magnetic field in Wb/m^2\nRH=3.66*10**-4; #hall coefficient in m^3/C\n\n#Calculation\nw=w*10**-3; #width in m\nVH=(B*I*RH)/w; #hall voltage\nVH=VH*10**4;\n\n#Result\nprint(\"Hall voltage in V is\",VH,\"*10**-4\");",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('Hall voltage in V is', 1.83, '*10**-4')\n"
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.4, Page number 268"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the concentration of holes and electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nsigma=300; #conductivity in S/cm\nT=300; #temperature in K\nni=1.5*10**10 #carrier concentration per cm^3\nmew_e=1300; #mobility of electrons in cm^2/Vs\nmew_h=500; #mobility of holes in cm^2/Vs\ne=1.6*10**-19; #electron charge in C\n\n#Calculation\nsigma=sigma*10**2; #sigma in S/m\nmew_e=mew_e*10**-4; #mobility of electrons in m^2/Vs\nND=sigma/(e*mew_e); #concentration of electron per m^3\nni=ni*10**6; #carrier concentration per m^3\np=ni**2/ND; #hole concentration per m^3\np=p/10**8;\np=math.ceil(p*10**3)/10**3; #rounding off to 3 decimals\nmew_h=mew_h*10**-4; #mobility of holes in m^2/Vs\nNA=sigma/(e*mew_h); #concentration of hole per m^3\nn=ni**2/NA; #electron concentration per m^3\nn=n/10**7;\n\n#Result\nprint(\"concentration of electron for N-type semiconductor per m^3\",ND);\nprint(\"hole concentration per m^3\",p,\"*10**8\");\nprint(\"concentration of hole for P-type semiconductor per m^3\",NA);\nprint(\"electron concentration per m^3\",int(n),\"*10**7\");",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('concentration of electron for N-type semiconductor per m^3', 1.4423076923076921e+24)\n('hole concentration per m^3', 1.561, '*10**8')\n('concentration of hole for P-type semiconductor per m^3', 3.7499999999999995e+24)\n('electron concentration per m^3', 6, '*10**7')\n"
}
],
"prompt_number": 11
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.5, Page number 269"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To find the type of charge carriers and the carrier concentration\n\n#importing modules\nimport math\n\n#Variable declaration\nRH=-3.68*10**-5; #hall coefficient in m^3/C\ne=1.6*10**-19; #electron charge in C\n\n#Calculation\n#hall coefficient is negative implies charge carriers are electrons\nn=(3*math.pi)/(8*(-RH)*e); #carrier concentration\n\n#Result\nprint(\"charge carriers are electrons\");\nprint(\"carrier concentration per m^3 is\",n);",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "charge carriers are electrons\n('carrier concentration per m^3 is', 2.000844505937792e+23)\n"
}
],
"prompt_number": 13
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.6, Page number 269"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To compare the intrinsic carrier density\n\n#importing modules\nimport math\nfrom __future__ import division\n\n#Variable declaration\nEg1=0.36; #energy gap of 1st material in eV\nEg2=0.72; #energy gap of 2nd material in eV\nT=300; #temperature in K\nmh=9*10**-31;\nme=9*10**-31; \n#given that 2*k*T=0.052; \n#consider X=2*k*T\nX=0.052;\n\n#Calculation\n#intrinsic carrier concentration for A niA = 2*((2*math.pi*k*T*m)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-0.36/(2*k*T))\n#intrinsic carrier concentration for B niB = 2*((2*math.pi*k*T*m)/h**2)**(3/2)*((me*mh)/m**2)**(3/4)*math.exp(-0.72/(2*k*T))\n#dividing niA/niB = math.exp(-0.36/(2*k*T))*math.exp(0.72/(2*k*T))\n#let niA/niB be A\nA = math.exp(-0.36/X)*math.exp(0.72/X);\nA=A/10**3;\nA=math.ceil(A*10**5)/10**5; #rounding off to 5 decimals\n\n#Result\nprint(\"ratio of intrinsic carrier densities of A and B is\",A,\"*10**3\");",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('ratio of intrinsic carrier densities of A and B is', 1.01544, '*10**3')\n"
}
],
"prompt_number": 16
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.7, Page number 270"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the mobility of electrons\n\n#importing modules\nimport math\n\n#Variable declaration\nND=2*10**22; #concentration of electron per m^3\nsigma=112; #conductivity in ohm-1 m-1\ne=1.6*10**-19; #electron charge in C\n\n#Calculation\nmew=sigma/(ND*e); #mobility of electrons \nmew=math.ceil(mew*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint(\"mobility of electrons in m^2/Vs is\",mew);",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('mobility of electrons in m^2/Vs is', 0.035)\n"
}
],
"prompt_number": 17
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.8, Page number 270"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the Hall voltage\n\n#importing modules\nimport math\n\n#Variable declaration\nw=500; #thickness in micrometre\nA=2.5*10**-3; #area of cross section in cm^-2\nIx=1; #current in ampere\nBz=10; #magnetic field in Wb/cm^2\nn=10**16; #donor concentration in m^-3\ne=1.6*10**-19; #electron charge in C\n\n#Calculation\nBz=Bz*10**-4; #magnetic field in Wb/m^2\nw=w*10**-6; #thickness in m\nRH=(3*math.pi)/(8*n*e); #hall coefficient\nVH=(Bz*Ix*RH)/w; #hall voltage\nVH=VH/10**3;\nVH=math.ceil(VH*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint(\"hall voltage in V is\",VH,\"*10**3\");",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('hall voltage in V is', 1.4727, '*10**3')\n"
}
],
"prompt_number": 23
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.9, Page number 271"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To find the ratio between conductivity of intrinsic semiconductor\n\n#importing modules\nimport math\nfrom __future__ import division\nimport numpy as np\n\n#Variable declaration\nEg=1.2; #energy gap in eV\nT1=300; #temperature in K\nT2=600; #temperature in K\nk=1.38*10**-23;\n\n#Calculation\nT_1=T1**(-1);\nT_2=T2**(-1);\nT=T_1-T_2;\nEg=Eg*1.602*10**-19; #Eg in J\n#sigma_300=ni300*e*(mew_e+mew_h)\n#sigma_600=ni600*e*(mew_e+mew_h)\n#sigma_600/sigma_300 = ni600/ni300\n#ni600/ni300 =((T2/T1)**(3/2))*math.exp(-Eg/(2*k*T2))*math.exp(Eg/(2*k*T1));\n#ni600/ni300 =((T2/T1)**(3/2))*math.exp((Eg/(2*k))*T;\n#let ni600/ni300 be X\nX=((T2/T1)**(3/2))*math.exp((Eg/(2*k))*T);\n\n\n#Result\nprint(\"ratio between the conductivity of material is\",int(X));\n\n#answer given in the book is wrong",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('ratio between the conductivity of material is', 311270)\n"
}
],
"prompt_number": 25
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.10, Page number 272"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the intrinsic carrier concentration\n\n#importing modules\nimport math\n\n#Variable declaration\nsigma=10**-6; #electrical conductivity in ohm-1 m-1\nmew_e=0.85; #electron mobility in m^2/Vs\nmew_h=0.04; #hole mobility in m^2/Vs\ne=1.6*10**-19; #electron charge in C\n\n#Calculation\nni=sigma/(e*(mew_e+mew_h)); #intrinsic carrier concentration\nni=ni/10**12;\nni=math.ceil(ni*10**4)/10**4; #rounding off to 4 decimals\n\n#Result\nprint(\"intrinsic carrier concentration per m^3 is\",ni,\"*10**12\");",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('intrinsic carrier concentration per m^3 is', 7.0225, '*10**12')\n"
}
],
"prompt_number": 27
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": "Example number 9.11, Page number 272"
},
{
"cell_type": "code",
"collapsed": false,
"input": "#To calculate the density of impurity atoms and concentration of minority carriers\n\n#importing modules\nimport math\n\n#Variable declaration\nrho_p=10; #resistivity of p-type Si in ohm cm\nrho_n=10; #resistivity of n-type Si in ohm cm\nmew_e=1350; #electron mobility in cm^2/Vs\nmew_h=480; #hole mobility in cm^2/Vs\nni=1.5*10**10; #carrier concentration in cm^-3\ne=1.6*10**-19; #electron charge in C\n\n#Calculation\nrho_p=rho_p*10**-2;#resistivity of p-type Si in ohm m\nsigma_p=1/rho_p; #electrical conductivity\nmew_h=mew_h*10**-3;\nNA=sigma_p/(e*mew_h); #acceptor concentration\nni=ni*10**6; #carrier concentration in m^-3\nn=ni**2/NA; #concentration of minority carriers in m^-3\nn=n/10**12;\nn=math.ceil(n*10**4)/10**4; #rounding off to 4 decimals\nrho_n=rho_n*10**-2; #resistivity of n-type Si in ohm m\nsigma_n=1/rho_n; #electrical conductivity\nmew_e=mew_e*10**-3;\nND=sigma_n/(e*mew_e); #donor concentration\np=(ni**2)/ND; #concentration of minority carriers in m^-3\np=p/10**12;\np=math.ceil(p*10**3)/10**3; #rounding off to 3 decimals\n\n#Result\nprint(\"donor concentration per m^3 is\",ND);\nprint(\"concentration of minority carriers per m^3\",p,\"*10**12\");\nprint(\"acceptor concentration per m^3 is\",NA);\nprint(\"concentration of minority carriers per m^3 is\",n,\"*10**12\");",
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": "('donor concentration per m^3 is', 4.6296296296296284e+19)\n('concentration of minority carriers per m^3', 4.861, '*10**12')\n('acceptor concentration per m^3 is', 1.3020833333333331e+20)\n('concentration of minority carriers per m^3 is', 1.7281, '*10**12')\n"
}
],
"prompt_number": 33
},
{
"cell_type": "code",
"collapsed": false,
"input": "",
"language": "python",
"metadata": {},
"outputs": []
}
],
"metadata": {}
}
]
}
|
