{
"metadata": {
"name": "",
"signature": "sha256:0febf6654b4226cea8bd31c369bda102743b50db8084bc6251d5320576f18189"
},
"nbformat": 3,
"nbformat_minor": 0,
"worksheets": [
{
"cells": [
{
"cell_type": "heading",
"level": 1,
"metadata": {},
"source": [
"Chapter6:MICROWAVE FIELD-EFFECT TRANSISTORS"
]
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.1.1:pg-229"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculation of pinch-off voltage\n",
"\n",
"a=0.1*(10**-6) #channel height in m\n",
"Nd=8*(10**23) #Electron Concetration in m-3\n",
"er=11.80 #relative dielectric constant\n",
"es=8.854*(10**-12)*er #permittivity of silicon in F/m\n",
"q=1.6*(10**-19) #charge of electron in C\n",
"Vp=(q*Nd*(a**2))/(2*es) #pinch-off voltage\n",
"\n",
"print\"Pinch-off volatge in(Volts)is=\",round(Vp,2),\"Volts\" #answer is wrong in book \n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pinch-off volatge in(Volts)is= 6.13 Volts\n"
]
}
],
"prompt_number": 1
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.1.2:pg-233"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#(a)Calculate the pinch-off Voltage in Volts\n",
"a=0.2*(10**-4) #channel height in cm\n",
"Nd=1*(10**17) #Electron density in /cm3\n",
"er=11.80 #relative dielectric constant\n",
"es=8.854*(10**-14)*er #permittivity of silicon in F/cm\n",
"q=1.6*(10**-19) #charge of electron in C\n",
"Vp=(q*Nd*(a**2))/(2*es) #pinch-off voltage\n",
"print\"The pinch-off volatge in(Volts)is=\",round(Vp,2),\"V\"\n",
"\n",
"#(b)Calculate the pinch-off current\n",
"un=800 #electron mobility in cm2/V.s\n",
"L=8*(10**-4) #channel length in cm\n",
"Z=50*(10**-4) #channel width in cm\n",
"a=0.2*(10**-4) #channel height in cm\n",
"Nd=1*(10**17) #Electron density in /cm3\n",
"er=11.80 #relative dielectrin constant\n",
"es=8.854*(10**-14)*er #permittivity of silicon in F/cm\n",
"q=1.6*(10**-19) #charge of electron in C\n",
"Ip=(un*(q**2)*(Nd**2)*Z*(a**3))/(L*es) #pinch-off voltage\n",
"Ip=Ip*1000 # in mA\n",
"print\"The pinch-off current in(mA)is=\",round (Ip,2),\"mA\"\n",
"\n",
"#(c)Calculate the built-in voltage\n",
"Nd=1*(10**17) #Electron density in /cm3\n",
"Na=1*(10**19) #hole density in /cm3\n",
"w0=26*(10**-3)*math.log((Nd*Na)/((1.5*(10**10))**2))\n",
"print\"Built-in voltage in(volts)is=\",round(w0,3),\"V\"\n",
"\n",
"#(d) Calculate the drain current\n",
"Vd=10 #drain voltage in volt\n",
"Vg=-1.5 #gate voltage in volt\n",
"Vg=-1*Vg #we take only magnitude\n",
"x=sqrt(((Vd+Vg+round(w0,3))/round(Vp,2))**3)\n",
"x=x*2/3\n",
"y=sqrt(((Vg+round(w0,3))/(round(Vp,2)))**3)\n",
"y=y*2/3\n",
"Id=(Vd/round(Vp,2))-x+y\n",
"Id=round(Ip,2)*Id\n",
"print\"The drain current (mA)is=\",round(Id,2),\"mA\" #answer is wrong in book\n",
"\n",
"#(e) Calculate the saturation drain current at Vg=0\n",
"Vg=-1.5 #gate voltage in volt\n",
"Vg=-1*Vg #we take only magnitude\n",
"x=(Vg+round(w0,3))/(round(Vp,2))\n",
"y=sqrt(((Vg+round(w0,3))/(round(Vp,2)))**3)\n",
"y=y*2/3\n",
"Idsat=(1.0/3)-x+y\n",
"Idsat=round(Ip,2)*Idsat\n",
"print\"The saturation drain current (mA)is=\",round(Idsat,3),\"mA\" #answer is wrong in book\n",
"\n",
"#(f) Calculate the cut-off frequency\n",
"fc=(2*un*q*Nd*(a**2))/(math.pi*es*(L**2));\n",
"fc=fc/(10**9) #in GHz\n",
"print\"The cut-off frequency(Ghz)=\",round(fc,1),\"GHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The pinch-off volatge in(Volts)is= 3.06 V\n",
"The pinch-off current in(mA)is= 9.8 mA\n",
"Built-in voltage in(volts)is= 0.937 V\n",
"The drain current (mA)is= -16.86 mA\n",
"The saturation drain current (mA)is= 0.105 mA\n",
"The cut-off frequency(Ghz)= 4.9 GHz\n"
]
}
],
"prompt_number": 41
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.2.1:pg-239"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#calculate Pinch-Off Voltage Of a MESFET\n",
"\n",
"a=0.1*(10**-6) #channel height in meter\n",
"Nd=8*(10**23) #Electron Concetration /m3\n",
"er=13.10 #relative dielectric constant\n",
"es=8.854*(10**-12)*er #permittivity of GaAs in F/m\n",
"q=1.6*(10**-19) #electronic charge in C\n",
"Vp=(q*Nd*(a**2))/(2*es)#pinch-off voltage\n",
"\n",
"print\"Pinch-off volatge in(Volts)is=\",round(Vp),\"V\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pinch-off volatge in(Volts)is= 6.0 V\n"
]
}
],
"prompt_number": 42
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.2.2:pg-244"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"\n",
"#(a) Calculate the pinch-off voltage\n",
"a=0.1*(10**-6) #channel height in meter\n",
"Nd=8*(10**23) #Electron Concetration in /m3\n",
"er=13.1 #relative dielectric constant\n",
"e=8.854*(10**-12)*er #permittivity of GaAs in F/m\n",
"q=1.6*(10**-19) #electronic charge in C\n",
"Vp=(q*Nd*(a**2))/(2*e) #pinch-off voltage\n",
"\n",
"print\"Pinch-off volatge in(Volts)is=\",round(Vp,2),\"V\"\n",
"\n",
"#(b)Calculate the velocity ratio\n",
"un=0.08 #electron mobility in m2/V.s\n",
"vs=2*(10**5) #saturation drift velocity in m/s\n",
"L=14*(10**-6) #channel length in meter \n",
"n=(Vp*un)/(vs*L)\n",
"print\"The velocity ratio is=\",round(n,3)\n",
"\n",
"#(c) Calculate the saturation current at Vg=0\n",
"L=14*(10**-6) #channel length in meter\n",
"Z=36*(10**-6) #channel width in meter\n",
"Ipsat=(q*Nd*un*a*Z*round(Vp,2))/(3*L)\n",
"Ipsat=Ipsat*1000 #in mA\n",
"print\"The saturation current at Vg=0 is=\",round(Ipsat,3),\"mA\"\n",
"\n",
"#(d) Calculate the drain current\n",
"\n",
"Vd=5 #drain voltage\n",
"Vg=-2 #gate voltage\n",
"Vg=-1*Vg\n",
"u=sqrt((Vd+Vg)/Vp)\n",
"p=sqrt((Vg)/Vp)\n",
"Id=(3*((u**2)-(p**2))-2*((u**3)-(p**3)))/(1+(n*((u**2)-(p**2))))\n",
"Id=Id*Ipsat\n",
"print\"The drain current (mA)is=\",round(Id,2),\"mA\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"Pinch-off volatge in(Volts)is= 5.52 V\n",
"The velocity ratio is= 0.158\n",
"The saturation current at Vg=0 is= 4.845 mA\n",
"The drain current (mA)is= 1.26 mA\n"
]
}
],
"prompt_number": 44
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.2.3:pg-247"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#(a) Calculate the cut-off frequency\n",
"gm=0.05 #device transconductance in mho \n",
"Cgs=0.60*(10**-12) #gate source capacitance in Farad\n",
"fco=(gm)/(2*math.pi*Cgs) \n",
"fco=fco/(10**9) #in GHz\n",
"print\"The cut-off frequency(in GHz)is=\",round(fco,2),\"GHz\" \n",
"\n",
"#(b)Calculate the maximum operating frequency\n",
"Rd=450 #drain resistance in ohms\n",
"Rs=2.5 #source-gate resistance in ohms\n",
"Rg=3 #gate metallization resistance in ohms\n",
"Ri=2.5 #input resistance\n",
"fmax=(fco/2)*sqrt(Rd/(Rs+Rg+Ri)) \n",
"print\"The maximum operating frequency(in Ghz)is=\",round(fmax,2),\"GHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The cut-off frequency(in GHz)is= 13.26 GHz\n",
"The maximum operating frequency(in Ghz)is= 49.74 GHz\n"
]
}
],
"prompt_number": 46
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.3.1:pg-251"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#Calculate the Drain Current\n",
"q=1.60*(10**-19) #charge of electron in C\n",
"n=5.21*(10**15) #two-dimensional electron gas density in /m2\n",
"W=150*(10**-6) #gate width in meter\n",
"v=2*(10**5) #electron velocity in m/sec\n",
"Ids=q*n*W*v \n",
"Ids=1000*Ids #in mA\n",
"print\"The drain current in(mA) is=\",int(Ids),\"mA\"\n",
"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The drain current in(mA) is= 25 mA\n"
]
}
],
"prompt_number": 47
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.3.2:pg-253"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#(a) Calculate the conduction band-edge difference between GaAs and AlGaAs\n",
"Ega=1.8 #AlGaAs bandgap in volt\n",
"Egg=1.43 #GaAs bandgap in volt\n",
"AEc=Ega-Egg \n",
"print\"The conduction band-edge difference(in Volt) is=\",AEc,\"V\"\n",
"\n",
"#(b) Calculate the sesitivity of the HEMT\n",
"q=1.6*(10**-19) #charge of electron in C\n",
"Nd=2*(10**24) #donar concentration /m3\n",
"wms=0.8 #metal-semiconductor schottky barrier potential in volt\n",
"Vth=0.13 #threshold voltage in volt\n",
"er=4.43 #AlGaAs dielectric constant\n",
"e=er*(8.854*(10**-12)) \n",
"S=-sqrt((2*q*Nd*(wms-AEc-Vth))/(e)) #sesitivity of the HEMT\n",
"S=S/(10**6) \n",
"S=-1*S\n",
"print\"The sensitivity of the HEMT (mV/nm) is=\",int(round(S)),\"mV/nM\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The conduction band-edge difference(in Volt) is= 0.37 V\n",
"The sensitivity of the HEMT (mV/nm) is= 70 mV/nM\n"
]
}
],
"prompt_number": 48
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.4.1:pg-260"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"import math\n",
"#(a) Calculate the surface potential ws(inv) for strong inversion\n",
"kt=26*(10**-3) \n",
"Na=3*(10**17) #doping concentration in /cm3\n",
"Ni=1.5*(10**10) \n",
"wsinv=2*kt*math.log(Na/Ni) \n",
"print\"The strong potential w(inv) for strong inversion(in volts) is=\",round(wsinv,3),\"V\"\n",
"\n",
"#(b)Calculate the insulator Capacitance\n",
"eir=4 #relative dielectric constant of SiO2\n",
"ei=8.854*(10**-12)*eir #permittivity of SiO2 in F/m\n",
"d=0.01*(10**-6) #insulator depth in meter\n",
"Ci=ei/d \n",
"Ci=Ci*(1000) \n",
"print\"The insulator Capacitance(in mF/m**2) is=\",round(Ci,2),\"mF/m2\"\n",
"\n",
"#(c) Calculate the threshold voltage\n",
"q=1.6*(10**-19) \n",
"Na=3.0*(10**23) \n",
"er=11.8 \n",
"e=8.854*(10**-12)*er #permittivity of SiO2 in F/m\n",
"Vth=wsinv+((2/(Ci*(10**-3)))*sqrt(e*q*Na*(wsinv/2)))\n",
"print\"The threshold voltage(in Volts) is=\",round(Vth,2),\"V\"\n"
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The strong potential w(inv) for strong inversion(in volts) is= 0.874 V\n",
"The insulator Capacitance(in mF/m**2) is= 3.54 mF/m2\n",
"The threshold voltage(in Volts) is= 1.71 V\n"
]
}
],
"prompt_number": 49
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.4.2:pg-262"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#(a)Calculate the insulator capacitance\n",
"eir=3.9 #constant of SiO2\n",
"ei=8.854*(10**-12)*eir #permittivity of SiO2 in F/m\n",
"d=0.05*(10**-6) #insulator thickness in meter\n",
"Ci=ei/d \n",
"print\"The insulator capacitance(in F/m**2) is=\",\"{:.2e}\".format(Ci),\"F/m2\"\n",
"\n",
"#(b)Calculate the saturation drain current\n",
"Z=12*(10**-6) #channel depth in meter\n",
"Vg=5 #gate voltage in volt\n",
"Vth=0.10 #threshold voltage in volt\n",
"vs=1.70*(10**5) #electron velocity in m/s\n",
"Idsat=Z*round(Ci,6)*(Vg-Vth)*vs\n",
"Idsat=Idsat*1000 #in mA\n",
"print\"The saturation drain current(in mA) is=\",round(Idsat,2),\"mA\"\n",
"\n",
"#(c)Calculate the transconductance in the saturation region\n",
"Z=12*(10**-6) #channel depth in meter\n",
"vs=1.70*(10**5) #electron velocity in m/s\n",
"gmsat=Z*Ci*vs \n",
"gmsat=gmsat*10**3\n",
"print\"the transconductance in the saturation region(in millimhos) is=\",round(gmsat,2),\"millimhos\" \n",
"\n",
"#(d)Calculate the maximum operating frequency in the saturation region\n",
"vs=1.70*(10**5) \n",
"L=4*(10**-6) #channel length in meter\n",
"fm=vs/(2*math.pi*L) \n",
"fm=fm/(10**9) #in GHz\n",
"print\"The maximum operating frequency in the saturation region(in GHz) is=\",round(fm,2),\"GHz\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The insulator capacitance(in F/m**2) is= 6.91e-04 F/m2\n",
"The saturation drain current(in mA) is= 6.91 mA\n",
"the transconductance in the saturation region(in millimhos) is= 1.41 millimhos\n",
"The maximum operating frequency in the saturation region(in GHz) is= 6.76 GHz\n"
]
}
],
"prompt_number": 50
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.6.1:pg-278"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"# Calculate the power dissipation per bit\n",
"n=3 #number of phases \n",
"f=10*(10**6) #clock frequency in Hertz\n",
"V=10 #applied voltage in volts\n",
"Qmax=0.04*(10**-12) #maximum stored charges in Coulomb\n",
"p=n*f*V*Qmax \n",
"p=p*(10**6) #in mW\n",
"print\"The power dissipation per bit(micro watt)is=\",int(p),\"micro Watt\""
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The power dissipation per bit(micro watt)is= 12 micro Watt\n"
]
}
],
"prompt_number": 51
},
{
"cell_type": "heading",
"level": 2,
"metadata": {},
"source": [
"Eg6.6.2:pg-279"
]
},
{
"cell_type": "code",
"collapsed": false,
"input": [
"#(a)Calculate the insulator capacitance\n",
"eir=3.9 #insulator relative dielectric constant\n",
"ei=8.854*(10**-12)*eir #permittivity of material in F/m\n",
"d=.15*(10**-6) #insulator thickness in meter\n",
"Ci=ei/d \n",
"Ci=Ci*(10**5) \n",
"print\"The insulator capacitance(in nF/cm**2) is =\",int(round(Ci)),\"nF/cm2\" \n",
"\n",
"#(b)Calculate the maximum stored charges per well\n",
"Nmax=2*(10**12) #electron density in /cm2\n",
"q=1.6*(10**-19) #charge of electron in C\n",
"A=.5*(10**-4) #insulator cross-section in cm2\n",
"Qmax=Nmax*A*q \n",
"Qmax=Qmax*(10**12) #in pC\n",
"print\"The maximum stored charges per well(picocoulombs)is=\",int(Qmax),\"pC\"\n",
"\n",
"#(c) Calculate the required applied gate voltage\n",
"Nmax=2*(10**12) \n",
"q=1.6*(10**-19) \n",
"Vg=(Nmax*q)/(Ci*10**-9) \n",
"print\"The required applied gate voltage(in Volts) is=\",int(round(Vg)),\"V\"\n",
"\n",
"#(d)Calculate the clock frequency\n",
"P=.67*(10**-3) #power dissipation allowable per bit in Watt\n",
"n=3 \n",
"f=P/(n*Vg*Qmax*(10**-12)) \n",
"f=f/(10**6) #in MHz\n",
"print\"The clock frequency(in MHz) is=\",int(f),\"MHz\" "
],
"language": "python",
"metadata": {},
"outputs": [
{
"output_type": "stream",
"stream": "stdout",
"text": [
"The insulator capacitance(in nF/cm**2) is = 23 nF/cm2\n",
"The maximum stored charges per well(picocoulombs)is= 16 pC\n",
"The required applied gate voltage(in Volts) is= 14 V\n",
"The clock frequency(in MHz) is= 1 MHz\n"
]
}
],
"prompt_number": 58
}
],
"metadata": {}
}
]
}