Chapter1 - Vaccum Tubes and Semiconductors

Example 1.1 Page No. : 6

In [43]:
from __future__ import division
#refer to fig 1.2(c) and given d.c operating points VGKQ=-2 V,VAKQ=250 V,IAQ=-1.2 mA
VAK2=300
print "VAK2 = %0.2f"%(VAK2)," volts" # value of anode voltage2 
VAK1=170
print "VAK1 = %0.2f"%(VAK1)," volts" # value of anode voltage1 
IA2=2*10**(-3)
print "IA2 = %0.4f"%(IA2)," ampere" # value of anode current2
IA1=0*10**(-3)
print "IA1 = %0.4f"%(IA1)," ampere" # value of anode current1
rP=(VAK2-VAK1)/(IA2-IA1)#anode resistance at VGK=VGKQ
print "resistance,rP =(VAK2-VAK1)/(IA2-IA1)=%0.2f"%(rP)," ohm" #calculation
VGK2=-2.5
print "VGK2 = %0.2f"%(VGK2)," volts" # value of grid voltage2 
VGK3=-1.5
print "VGK1 = %0.2f"%(VGK3)," volts" # value of grid voltage1
VAK3=200
print "VAK3 = %0.2f"%(VAK3)," volts" # value of anode voltage1 
u=(VAK2-VAK3)/(VGK2-VGK3)#amplification factor at IA=IAQ
print "amplification factor,u =(VAK2-VAK1)/(VGK2-VGK1)=%0.2f"%(u)," unitless " #calculation
IA4=2.2*10**(-3)
print "IA4 = %0.4f"%(IA4)," ampere" # value of anode current4
IA3=0.5*10**(-3)
print "IA1 = %0.4f"%(IA3)," ampere" # value of anode current1
gm=(IA4-IA3)/(VGK2-VGK3)# transconductance at VAK=VAKQ
print "transconductance,gm =(IAK4-IAK3)/(VGK2-VGK3)=%0.2f"%(gm)," ampere/volt " #calculation
#mistake of negative sign for answers for u(amplification factor) and gm(transconductance)in book

VAK2 = 300.00  volts
VAK1 = 170.00  volts
IA2 = 0.0020  ampere
IA1 = 0.0000  ampere
resistance,rP =(VAK2-VAK1)/(IA2-IA1)=65000.00  ohm
VGK2 = -2.50  volts
VGK1 = -1.50  volts
VAK3 = 200.00  volts
amplification factor,u =(VAK2-VAK1)/(VGK2-VGK1)=-100.00  unitless 
IA4 = 0.0022  ampere
IA1 = 0.0005  ampere
transconductance,gm =(IAK4-IAK3)/(VGK2-VGK3)=-0.00  ampere/volt

Example 1_2 Page No. : 10

In [1]:
d=0.5*10**(-2)
print "d = %0.2f"%(d),"metre" #initializing value of distance b/w plates
l=2*10**(-2)
print "l = %0.2f"%(l),"metre" #initializing value of length of plates
L=20*10**(-2)
print "L = %0.2f"%(L),"metre" #initializing value of distance b/w centre of plates and screen
Va=2000
print "Va = %0.2f"%(Va),"volts" ##initializing value ofanode voltage
Vd=100
print "Vd = %0.2f"%(Vd),"volts" #initializing value of deflecting voltage
m=9.11*10**(-31)
print "m = %0.2e"%(m),"Kg" #mass of electron
q=1.6*10**(-19)
print "q = %0.2e"%(q),"coulomb" #charge on an electron
print "horizontal beam velocity,Vx =(2*Va*q/m)**(0.5) metre/second" #formula
Vx =(2*Va*q/m)**(0.5)
print "horizontal beam velocity,Vx =(2*Va*q/m)**(0.5)= %0.2e"%(Vx)," metre/second" #calculation
print "transit time,t1 =(l/Vx) second" #formula
t1=(l/Vx)
print "transit time,t1 =(l/Vx)= %0.2e"%(t1)," second" #calculation
print "vertical beam velocity,Vy =(q*Vd*l/d*m*Vx) metre/second" #formula
Vy=((q*Vd*l)/(d*m*Vx))
print "vertical beam velocity,Vy =(q*Vd*l/d*m*Vx)= %0.2e"%(Vy)," metre/second" #calculation
print "vertical displacement,D =((l*L*Vd)/(2*d*Va) metre" #formula
D =(l*L*Vd)/(2*d*Va)
print "vertical displacement,D =((l*L*Vd)/(2*d*Va)=%0.2f"%(D)," metre" #calculation
print "sensitivity of CRT,S =(0.5*l*L)/(d*Va) metre/volt" #formula
S =(0.5*l*L)/(d*Va)
print "sensitivity of CRT,S =(0.5*l*L)/(d*Va)=%0.1e"%(S)," metre/volt" #calculation

d = 0.01 metre
l = 0.02 metre
L = 0.20 metre
Va = 2000.00 volts
Vd = 100.00 volts
m = 9.11e-31 Kg
q = 1.60e-19 coulomb
horizontal beam velocity,Vx =(2*Va*q/m)**(0.5) metre/second
horizontal beam velocity,Vx =(2*Va*q/m)**(0.5)= 2.65e+07  metre/second
transit time,t1 =(l/Vx) second
transit time,t1 =(l/Vx)= 7.55e-10  second
vertical beam velocity,Vy =(q*Vd*l/d*m*Vx) metre/second
vertical beam velocity,Vy =(q*Vd*l/d*m*Vx)= 2.65e+06  metre/second
vertical displacement,D =((l*L*Vd)/(2*d*Va) metre
vertical displacement,D =((l*L*Vd)/(2*d*Va)=0.02  metre
sensitivity of CRT,S =(0.5*l*L)/(d*Va) metre/volt
sensitivity of CRT,S =(0.5*l*L)/(d*Va)=2.0e-04  metre/volt

Example 1-3 Page No. : 11

In [2]:
m=9.11*10**(-31)
print "m = %0.2e"%(m)," Kg" #mass of electron
q=1.6*10**(-19)
print "q = %0.2e"%(q)," coulomb" #charge on an electron
B=1.5*10**(-3)
print "B = %0.2e"%(B)+ " wb/m**2" #initializing value of magnetic field
l=5*10**(-2)
print "l = %0.2f"%(l)," metre" #initializing axial length of magnetic field
L=30*10**(-2)
print "L = %0.2f"%(L)," metre" #initializing value of distance of screen from centre of magnetic field
Va=10000
print "Va = %0.2f"%(Va)," volts" ##initializing value of anode voltage
print "horizontal beam velocity,Vx =(2*Va*q/m)**(0.5) metre/second" #formula
Vx =(2*Va*q/m)**(0.5)
print "horizontal beam velocity,Vx =(2*Va*q/m)**(0.5)= %0.2e"%(Vx)," metre/second" #calculation
print "radius,r =(m*Vx)/(B*q) metre" #formula
r =(m*Vx)/(B*q)
print "radius,r =(m*Vx)/(B*q)= %0.2f"%(r)," metre" #calculation
print "deflection,D =(L*l)/r) metre" #formula
D =(L*l)/r
print "deflection,D =(L*l)/r)=%0.2f"%(D)," metre" #calculation

m = 9.11e-31  Kg
q = 1.60e-19  coulomb
B = 1.50e-03 wb/m**2
l = 0.05  metre
L = 0.30  metre
Va = 10000.00  volts
horizontal beam velocity,Vx =(2*Va*q/m)**(0.5) metre/second
horizontal beam velocity,Vx =(2*Va*q/m)**(0.5)= 5.93e+07  metre/second
radius,r =(m*Vx)/(B*q) metre
radius,r =(m*Vx)/(B*q)= 0.22  metre
deflection,D =(L*l)/r) metre
deflection,D =(L*l)/r)=0.07  metre

Example -1.4 Page No. : 12

In [7]:
from math import pi
q=1.6*10**(-19)
print "q = %0.2e"%(q),"coulomb" #charge on an electron
I=10
print "I = %0.2f"%(I),"Ampere" #initializing value of current
r=64.25
print "radius,r = %0.2f"%(r)," mils" #initializing value of radius of wire
def mils2metres(mils):
    metres=(mils*2.54)/(1000*100)
    return metres
r1=mils2metres(r)   
print "r1 = %0.2f"%(r1)," metre"
n=5*10**(28)
print "n = %0.2e"%(n)," electrons/m**3" # electrons concentration in copper
A=(pi*r1**2) #formulae                            
print "cross sectional area,A =(pi*r1**2)= %0.2e"%(A)," square metre" #calculation
v=(I)/(A*q*n)#formulae(I=A*q*n*v)
print "drift velocity,v=(I)/(A*q*n)=%0.2e"%(v)," metre/second" #calculation

 

q = 1.60e-19 coulomb
I = 10.00 Ampere
radius,r = 64.25  mils
r1 = 0.00  metre
n = 5.00e+28  electrons/m**3
cross sectional area,A =(pi*r1**2)= 8.37e-06  square metre
drift velocity,v=(I)/(A*q*n)=1.49e-04  metre/second

Example 1_5 Page No. : 12

In [3]:
A=10*10**(-6)
p1=10**(-4)
p2=10**(3)
p3=10**(10)
l=1*10**(-2)# #initializations
print "cross sectional area,A =%0.2e"%(A),"merer square" 
print "resitivity(rho),p1 =%0.2e"%(p1)," ohm-m"
print "resitivity(rho),p2 =%0.2f"%(p2)," ohm-m"
print "resitivity(rho),p3 =%0.2e"%(p3)," ohm-m"
print "conductor length,l =%0.2f"%(l)," metre"
print " resistance for copper,R = p1*l/A = %0.2f"%(p1*l/A),"ohm" #calculations for copper
print " resistance for silicon,R = p2*l/A = %0.2e"%(p2*l/A),"ohm" #calculations for silicon
print " resistance for glass,R = p3*l/A = %0.2e"%(p3*l/A),"ohm" #calculations for glass

cross sectional area,A =1.00e-05 merer square
resitivity(rho),p1 =1.00e-04  ohm-m
resitivity(rho),p2 =1000.00  ohm-m
resitivity(rho),p3 =1.00e+10  ohm-m
conductor length,l =0.01  metre
 resistance for copper,R = p1*l/A = 0.10 ohm
 resistance for silicon,R = p2*l/A = 1.00e+06 ohm
 resistance for glass,R = p3*l/A = 1.00e+13 ohm

Example 1_6 Page No. : 16

In [4]:
ni = 1.45*10**10 #initializations
nV = 5*10**22 #initializations
un = 1500 #initializations
up = 475#initializations
T = 300 #initializations
I=10**(-6)
print "I = %0.2e"%(I),"Ampere" #initializing value of current
A=(50*10**(-4))**2# l=0.5 #initializations
q=1.59*10**(-19) #charge on an electron
print "intrinsic charge concentration,ni = %0.2e"%(ni)," /centimetre cube"
print "silicon atoms concntration, nV = %0.2e"%(nV)," /centimetre cube "

print "electron mobility,un = %0.2f"%(un)," cm.sq/V-s"
print "hole mobility,up = %0.2f"%(up),"cm.sq/V-s"
print "temperature,T = %0.2f"%(T),"K"
print "q = %0.2e"%(q),"coulomb" #charge on an electron
print "cross sectional area,A =%0.2e"%(A),"cm square" 
print "conductor length,l =%0.2f"%(l),"cm"
N=nV/ni
print "relative concentration,N =nV/ni= %0.2e"%(N)," silicon atoms per electron -hole pair" #calculation
sigma=(1.59*10**(-19)*(1.45*10**10)*(1500+475))
print "intrinsic conductivityi,sigma =(1.59*10**(-19)*(1.45*10**10)*(1500+0475))= %0.2f"%(sigma)," (ohm-cm)**-1" #calculation
pi =(1/sigma)#formulae
print "resitivity(rho),pi =(1/sigma)=%0.2e"%(pi)," ohm-cm" #calculation
R=(2.22*10**5*0.5)/0.000025
print " resistance for silicon,R =((2.22*10**5*0.5)/0.000025) = %0.2e"%(R)," ohm" #calculations for silicon
V=I*R
print " voltage drop,V =I*R = %0.2f"%(V)," V" #calculations 

I = 1.00e-06 Ampere
intrinsic charge concentration,ni = 1.45e+10  /centimetre cube
silicon atoms concntration, nV = 5.00e+22  /centimetre cube 
electron mobility,un = 1500.00  cm.sq/V-s
hole mobility,up = 475.00 cm.sq/V-s
temperature,T = 300.00 K
q = 1.59e-19 coulomb
cross sectional area,A =2.50e-05 cm square
conductor length,l =0.01 cm
relative concentration,N =nV/ni= 3.45e+12  silicon atoms per electron -hole pair
intrinsic conductivityi,sigma =(1.59*10**(-19)*(1.45*10**10)*(1500+0475))= 0.00  (ohm-cm)**-1
resitivity(rho),pi =(1/sigma)=2.20e+05  ohm-cm
 resistance for silicon,R =((2.22*10**5*0.5)/0.000025) = 4.44e+09  ohm
 voltage drop,V =I*R = 4440.00  V

Example 1_7 Page No. : 20

In [5]:
ni = 1.45*10**10 #initializations
nV = 5*10**22 #initializations
un = 1500 #initializations
up = 0475#initializations
T = 300 #initializations
I=10**(-6)
print "I = %0.2e"%(I),"Ampere" #initializing value of current
A=(50*10**(-4))**2# l=0.5 #initializations
q=1.59*10**(-19) #charge on an electron
print "intrinsic charge concentration,ni = %0.2e"%(ni)," /centimetre cube"
print "silicon atoms concntration, nV = %0.2e"%(nV)," /centimetre cube "

print "electron mobility,un = %0.2f"%(un)," cm.sq/V-s"
print "hole mobility,up = %0.2f"%(up)," cm.sq/V-s"
print "temperature,T = %0.2f"%(T)," K"
print "q = %0.2f"%(q),"coulomb" #charge on an electron
print "cross sectional area,A =%0.2f"%(A)," cm square" 
print "conductor length,l =%0.2f"%(l)," cm"
nD=nV/10**6#formulae
print "donor concentration,nD= nV/10**6=%0.2f"%(nD)," /cm.cube" #calculation
nn=nD#formulae
print "resulting mobile electron concentration,nn= nD=%0.2e"%(nn)," /cm.cube" #calculation
pn= ni**2/nD#formulae
print "resulting hole concentration,pn= ni**2/nD=%0.2e"%(pn)," /cm.cube" #calculation
sigma=q*nD*un#formulae
print "n-type semiconductor conductivity,sigma=q*nD*un= %0.2f"%(sigma)," (ohm-cm)**-1" #calculation
pn =(1/sigma)
print "doped silicon resitivity(rho),pn =(1/sigma)=%0.2f"%(pn)," ohm-cm" #calculation
R=(0.084*0.5)/A
print " resistance for silicon,R =((0.084*0.5)/A) = %0.2f"%(R)," ohm" #calculations for silicon
V=I*R
print " voltage drop,V =I*R = %0.2e"%(V)," V" #calculations 

I = 1.00e-06 Ampere
intrinsic charge concentration,ni = 1.45e+10  /centimetre cube
silicon atoms concntration, nV = 5.00e+22  /centimetre cube 
electron mobility,un = 1500.00  cm.sq/V-s
hole mobility,up = 317.00  cm.sq/V-s
temperature,T = 300.00  K
q = 0.00 coulomb
cross sectional area,A =0.00  cm square
conductor length,l =0.01  cm
donor concentration,nD= nV/10**6=50000000000000000.00  /cm.cube
resulting mobile electron concentration,nn= nD=5.00e+16  /cm.cube
resulting hole concentration,pn= ni**2/nD=4.20e+03  /cm.cube
n-type semiconductor conductivity,sigma=q*nD*un= 11.93  (ohm-cm)**-1
doped silicon resitivity(rho),pn =(1/sigma)=0.08  ohm-cm
 resistance for silicon,R =((0.084*0.5)/A) = 1680.00  ohm
 voltage drop,V =I*R = 1.68e-03  V

Example 1_8 Page No. : 22

In [6]:
q=1.59*10**(-19) #charge on an electron
print "q = %0.2e"%(q),"coulomb" #charge on an electron
d=0.037
print "dimension of semiconductor,d=%0.2f"%(d)," cm"
A=(d**2) #area formulae for square shaped semiconductor
print "cross sectional area,A =d**2=%0.2e"%(A)," cm square" 
x=10**(-4)
print "thickness,x =%0.2e"%(x)," cm"
x0=0
print "thickness,x0 =%0.f"%(x0)," cm"
p=9.22*10**(15)#
print "hole concentration at x,p= %0.2e"%(p)," /cm-cube" #calculation
p0=0#
print "hole concentration at x0,p0= %0.f"%(p0)," /cm-cube" #calculation
dp=(p-p0)#formulae
dx=(x-x0)#formulae
print " change in concentration at ,dp= %0.2e"%(dp)," /cm-cube" #calculation
print "change in thickness,dx= %0.2e"%(dx)," cm" #calculation
(dp/dx)==(p-p0)/(x-x0)#formulae
print " slope,(dp/dx) =(p-p0)/(x-x0)=%0.2e"%(dp/dx)," holes/cm-cube" #calculation
Dp=12
print "hole diffusion constant,Dp= %0.2f"%(Dp)," cm-sq/s" #calculation
Ip=A*q*Dp*(dp/dx)
print " hole diffusion current,Ip =A*q*Dp*(dp/dx)=%0.2f"%(Ip)," ampere" #calculation

q = 1.59e-19 coulomb
dimension of semiconductor,d=0.04  cm
cross sectional area,A =d**2=1.37e-03  cm square
thickness,x =1.00e-04  cm
thickness,x0 =0  cm
hole concentration at x,p= 9.22e+15  /cm-cube
hole concentration at x0,p0= 0  /cm-cube
 change in concentration at ,dp= 9.22e+15  /cm-cube
change in thickness,dx= 1.00e-04  cm
 slope,(dp/dx) =(p-p0)/(x-x0)=9.22e+19  holes/cm-cube
hole diffusion constant,Dp= 12.00  cm-sq/s
 hole diffusion current,Ip =A*q*Dp*(dp/dx)=0.24  ampere