Chapter 3 CARRIER TRANSPORT IN SEMICONDUCTOR

Example 3_1 pgno: 71

In [1]:
#exa 3.1
I=5*10**-3
print "I = ",I," amphere" # initializing value of current flowing through the sample.
B=1*10**-6
print "B= ",B," Tesla" # initializing value of magnetic field .
w=0.01*10**-2
print "w = ",w," m" # initializing value of width of germanium sample .
l=0.1*10**-2
print "l = ",l," m" # initializing value of length of germanium sample .
t=0.001*10**-2
print "t = ",t," m" # initializing value of thickness of germanium sample .
p=10**17
print "p = ",p," atoms/mˆ3" # initializing value of doped acceptor atoms .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
EH=(I*B)/(w*t*p*e)
print "Hall electric field ,EH=(I∗B)/(w∗t∗p∗e)= ",EH," V/m"  # calculation 18 
E=EH*10**-2
print "Hall electric field in centimeter ,EH=(I∗B)/(w∗ t∗p∗e)= ",E," V/cm" # calculation

I =  0.005  amphere
B=  1e-06  Tesla
w =  0.0001  m
l =  0.001  m
t =  1e-05  m
p =  100000000000000000  atoms/mˆ3
e =  1.6e-19  columb
Hall electric field ,EH=(I∗B)/(w∗t∗p∗e)=  312.5  V/m
Hall electric field in centimeter ,EH=(I∗B)/(w∗ t∗p∗e)=  3.125  V/cm

Example 3_2 pgno: 72

In [2]:
#exa 3.2
I=5*10**-3
print "I = ",I," amphere" # initializing value of current flowing through the sample.
B=1*10**-6
print "B= ",B," Tesla" # initializing value of magnetic field .
w=0.01*10**-2
print "w = ",w," m" # initializing value of width of germanium sample .
l=0.1*10**-2
print "l = ",l," m" # initializing value of length of germanium sample .
t=0.001*10**-2
print "t = ",t," m" # initializing value of thickness of germanium sample .
p=10**17
print "p = ",p," atoms/cmˆ3" # initializing value of doped acceptor atoms .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
Rh=(1/(p*e))
print "hall cofficient ,Rh=(1/(p∗e))= ",Rh," cmˆ3/C"# calculation

I =  0.005  amphere
B=  1e-06  Tesla
w =  0.0001  m
l =  0.001  m
t =  1e-05  m
p =  100000000000000000  atoms/cmˆ3
e =  1.6e-19  columb
hall cofficient ,Rh=(1/(p∗e))=  62.5  cmˆ3/C

Example 3_3 pgno: 72

In [3]:
#exa 3.3
I=10*10**-3
print "I = ",I," amphere" # initializing value of current flowing through the sample.
B=10*10**-6
print "B= ",B," Tesla" # initializing value of magnetic field .
w=0.01*10**-2
print "w = ",w," m" # initializing value ofwidth of germanium sample .
l=0.1*10**-2
print "l = ",l," m" # initializing value of length of germanium sample .
t=0.001*10**-2
print "t = ",t," m" # initializing value of thickness of germanium sample .
n=10**16
print "n = ",n," atoms/cmˆ3" # initializing value of doped donor atoms .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
Vh=((I*B)/(n*e*t))
print "Hall voltage ,Vh=((I∗B)/(n∗e∗t)))= ",Vh," V" # calculation

I =  0.01  amphere
B=  1e-05  Tesla
w =  0.0001  m
l =  0.001  m
t =  1e-05  m
n =  10000000000000000  atoms/cmˆ3
e =  1.6e-19  columb
Hall voltage ,Vh=((I∗B)/(n∗e∗t)))=  6.25  V

Example 3_4 pgno: 72

In [4]:
#exa 3.4
I=10*10**-3
print "I = ",I," amphere" # initializing value of current flowing through the sample.
B=10*10**-6
print "B= ",B," Tesla" # initializing value of magnetic field .
w=0.01*10**-2
print "w = ",w," m"  # initializing value of width of germanium sample .
l=0.1*10**-2
print "l = ",l," m" # initializing value of length of germanium sample .
t=0.001*10**-2
print "t = ",t," m" # initializing value of thickness of germanium sample .
p=10**18
print "p = ",p," atoms/cmˆ3" # initializing value of doped donor atoms .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
Yh=((B)/(p*e*t))
print "Hall voltage ,Yh=((B)/(p∗e∗t)))= ",Yh,"ohm" # calculation

I =  0.01  amphere
B=  1e-05  Tesla
w =  0.0001  m
l =  0.001  m
t =  1e-05  m
p =  1000000000000000000  atoms/cmˆ3
e =  1.6e-19  columb
Hall voltage ,Yh=((B)/(p∗e∗t)))=  6.25 ohm

Example 3_8 pgno: 75

In [5]:
#exa 3.8
from math import sqrt
no=1.5*10**10
print "no = ",no #  initializing value of electron hole per cmˆ3.
n=2*10**16
print "n= ",n # initializing value of number of electrons per cmˆ3.
un =1200
print "un = ",un # initializing value of mobility of n−type carrier .
up =500
print "up = ",up # initializing value of mobility of p−type carrier .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
p=(1/(2*e*no*(sqrt(un*up))))
print "resistivity ,p=(1/(2∗e∗no∗(sqrt(un/up))))= ",p," ohm" # calculation
sigmamin=(1/p)
print "conductivity ,s=(1/p))= ",sigmamin," S /cm" # calculation
sigma=e*no*(un+up)
print "intrinsic conductivity ,sigma=e∗no∗(un+up))= ",sigma," S/cm" # calculation

no =  15000000000.0
n=  20000000000000000
un =  1200
up =  500
e =  1.6e-19  columb
resistivity ,p=(1/(2∗e∗no∗(sqrt(un/up))))=  268957.17682  ohm
conductivity ,s=(1/p))=  3.71806401236e-06  S /cm
intrinsic conductivity ,sigma=e∗no∗(un+up))=  4.08e-06  S/cm

Example 3_10 pgno: 76

In [6]:
#exa 3.10
from math import sqrt
from math import exp
from math import log
po =10**18
print "po = ",po," cmˆ−3" # initializing value of N type doping level .
no=1.5*10**10
print "no = ",no," /cmˆ−3" # initializing value of electron and hole concentration per cmˆ3.
Po =10**17
print "P(o)= ",Po," cmˆ−3" # initializing value of excess hole concentration .
A=0.1
print "A = ",A," cmˆ−2" #  initializing the value of area .
up=300
print "up = ",up," cmˆ2/Vs" # initializing value of mobility of p−type carrier .
t=7*10**-9
print "t = ",t," sec" # initializing value of transit time.
T=300
print "T = ",T,"K" # initializing value of temperature .
Vt=0.0259
print "Vt = ",Vt," eV" # initializing value of thermal voltage at 300K.
x=500*10**-8
print "x = ",x," cm" # initializing value of distance at which difference in fermi level is to calculated .
Dp=(Vt*up)
print "Diffusion cofficient ,Dp=(Vt∗up))= ",Dp," cmˆ2/s" #calculation 
Lp=(sqrt(Dp*t))
print "Diffusion length ,Lp=(sqrt(Dp∗t)))= ",Lp," cm" # calculation
px=(po+(Po*exp(-x/Lp)))
print "Excess charge generated ,p(x)=(po+(P(o)∗exp(−x/Lp) ) )= ",px," cmˆ−3" # calculation
Efi_Efp=(Vt*log(px/no))
print "Fermi level ,Efi Efp=(Vt∗log(p(x)/no)))= ",Efi_Efp," eV" # calculation

po =  1000000000000000000  cmˆ−3
no =  15000000000.0  /cmˆ−3
P(o)=  100000000000000000  cmˆ−3
A =  0.1  cmˆ−2
up =  300  cmˆ2/Vs
t =  7e-09  sec
T =  300 K
Vt =  0.0259  eV
x =  5e-06  cm
Diffusion cofficient ,Dp=(Vt∗up))=  7.77  cmˆ2/s
Diffusion length ,Lp=(sqrt(Dp∗t)))=  0.000233216637485  cm
Excess charge generated ,p(x)=(po+(P(o)∗exp(−x/Lp) ) )=  1.09787888943e+18  cmˆ−3
Fermi level ,Efi Efp=(Vt∗log(p(x)/no)))=  0.469012627899  eV

Example 3_11 pgno: 77

In [7]:
#exa 3.11
from math import exp
A=0.1*10**-4
print "A = ",A," cmˆ2" # initializing value of area .
Dp =7.77*10** -4
print "Dp= ",Dp," cmˆ2/s" # initializing value of diffusion cofficient .
Lp =0.233*10** -5
print "Lp = ",Lp," cm" # initializing value of diffusion length .
x=500*10**-8
print "x = ",x," cm" # initializing value of distance
P=10**17*10**6
print "P(O)−po = ",P # initializing value of P(O)−po
e=1.6*10**-19
print "e = ",e,"column"  # initializing value of charge of electron .
I=(((e*A*Dp*P)/Lp)*exp(-x/Lp))
print "Hole current ,I=(((e∗A∗Dp∗[P(O)−po])/Lp)∗exp(−x/Lp))= ",I,"amphere" # calculation
Q=(e*A*Dp*Lp*P)
print " stored excess hole ,Q=(e∗A∗Dp∗Lp∗P))= ",Q,"C" # calculation
# the value of current(I) given after calculation inthe book is wrong, (as the value of Lp used in the formula while finding value of hole current ( I)at two places is used different).
# I have used the value Lp=0.233∗10ˆ−5 cm

A =  1e-05  cmˆ2
Dp=  0.000777  cmˆ2/s
Lp =  2.33e-06  cm
x =  5e-06  cm
P(O)−po =  100000000000000000000000
e =  1.6e-19 column
Hole current ,I=(((e∗A∗Dp∗[P(O)−po])/Lp)∗exp(−x/Lp))=  6.24054720884 amphere
 stored excess hole ,Q=(e∗A∗Dp∗Lp∗P))=  2.896656e-10 C

Example 3_12 pgno: 77

In [8]:
#exa 3.12
I=2*10**-3
print "I = ",I," amphere" # initializing value of current flowing through the sample.
B=1000*10**-4
print "B= ",B," Tesla" # initializing value of magnetic field .
w=0.2*10**-3
print "w = ",w," mm" # initializing value of width of sample .
l=2*10**-3
print "l = ",l," m"  # initializing value of length of sample .
t=0.02*10**-3
print "t = ",t," m" # initializing value of thickness of sample .
Vaa=10
print "Vaa = ",Vaa," V" # initializing value of applied voltage .
Vh = -10*10** -3
print "Vh = ",Vh," V" # initializing value of hall voltage .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
n=((I*B)/(e*t*Vh))
print "electron concentration ,n=((I∗B)/(e∗t∗Vh))= ",n," mˆ−3" # calculation
un=(I*l/(e*abs(n)*Vaa*w*t))
print "mobility ,un=(I∗L/(e∗n∗Vaa∗w∗t))= ",un," mˆ2/Vs" # calculation

I =  0.002  amphere
B=  0.1  Tesla
w =  0.0002  mm
l =  0.002  m
t =  2e-05  m
Vaa =  10  V
Vh =  -0.01  V
e =  1.6e-19  columb
electron concentration ,n=((I∗B)/(e∗t∗Vh))=  -6.25e+21  mˆ−3
mobility ,un=(I∗L/(e∗n∗Vaa∗w∗t))=  0.1  mˆ2/Vs

Example 3_14 pgno: 78

In [9]:
#exa 3.14
print "ND x = ((10ˆ17) −(10ˆ18∗x))"  # donor concentration in an N type semiconductor
print "differentiating above equation with resprct to x"
print "d[ND x]/dx = (−10ˆ18) cmˆ−4"
print "now, electric field is given by "
print "E x = −(VT/ND x)∗(d[ND x]/dx) = (0.0259∗10ˆ18)/((10ˆ15) −(10ˆ18∗x))" # equation for electric field
print "for x = 0" 
x=0
E_x = (0.0259*10**18)/((10**15) -(10**18*x))
print "E x = ",E_x,"V/cm"
print "for x = 1∗10ˆ−4 cm"
x = 1*10**-4
E_x = (0.0259*10**18)/((10**15) -(10**18*x))
print "E x = ",E_x,"V/cm"

ND x = ((10ˆ17) −(10ˆ18∗x))
differentiating above equation with resprct to x
d[ND x]/dx = (−10ˆ18) cmˆ−4
now, electric field is given by 
E x = −(VT/ND x)∗(d[ND x]/dx) = (0.0259∗10ˆ18)/((10ˆ15) −(10ˆ18∗x))
for x = 0
E x =  25.9 V/cm
for x = 1∗10ˆ−4 cm
E x =  28.7777777778 V/cm

Example 3_17 pgno: 81

In [10]:
#exa 3.17
from math import sqrt
Nd =10**17
print "Nd = ",Nd," /cmˆ3" # initializing value of donor concentration .
Na=0
print "Na= ",Na,"/cmˆ3"  # initializing value of acceptor concentration .
no=1.8*10**6
print "no = ",no," /cmˆ3" # initializing value of electron and hole concentration per cmˆ3.
E=5
print "E = ",E," V/cm" # initializing value of electric field .
un=7500
print "un = ",un," cmˆ2/s" # initializing value of mobility .
n1=10**17
print "n1= ",n1," cmˆ−3" # initializing value of impurity concentration .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
n=(-(Na-Nd)+sqrt((Na-Nd)**2+4*no))/2
print "Electron concentration ,n=(−(Na−Nd)+sqrt ((Na−Nd)ˆ2+4∗no))/2)= ",n," cmˆ−3"  #calculation
p=(no**2/n)
print "Hole concentration ,p=(noˆ2/n))= ",p," cmˆ−3"  # calculation
Jdrift=n1*un*e*E
print "Drift current density , Jdrift=n1∗un∗e∗E)= ",Jdrift," A/cmˆ2" # calculation

Nd =  100000000000000000  /cmˆ3
Na=  0 /cmˆ3
no =  1800000.0  /cmˆ3
E =  5  V/cm
un =  7500  cmˆ2/s
n1=  100000000000000000  cmˆ−3
e =  1.6e-19  columb
Electron concentration ,n=(−(Na−Nd)+sqrt ((Na−Nd)ˆ2+4∗no))/2)=  1e+17  cmˆ−3
Hole concentration ,p=(noˆ2/n))=  3.24e-05  cmˆ−3
Drift current density , Jdrift=n1∗un∗e∗E)=  600.0  A/cmˆ2

Example 3_18 pgno: 82

In [11]:
#exa 3.18
from math import sqrt
Nd=0
print "Nd = ",Nd," /cmˆ3" # initializing value of donor concentration .
Na =10**17
print "Na= ",Na," /cmˆ3" # initializing value of acceptor concentration .
no=1.8*10**6
print "no = ",no," /cmˆ3" # initializing value of electron and hole concentration per cmˆ3.
E=10
print "E = ",E," V/cm" # initializing value of electric field .
un=200
print "un = ",un," cmˆ2/s" # initializing value of mobility 
p1=10**17
print "p1= ",p1," cmˆ−3" # initializing value of impurity concentration .
e=1.6*10**-19
print "e = ",e," columb" # initializing value of charge of electron .
p=-(-(Na-Nd)-sqrt((Na-Nd)**2+4*(no**2)))/2
print "Electron concentration ,p=−(−(Na−Nd)−sqrt ((Na−Nd)**2+4∗(no**2)))/2= ",p," cmˆ−3" # calculation
n=(no**2/p)
print "Hole concentration ,n=(noˆ2/p))= ",n,"cmˆ−3"  # calculation
Jdrift=p1*un*e*E
print "Drift current density , Jdrift=n1∗un∗e∗E)= ",Jdrift," A/cmˆ2" # calculation

Nd =  0  /cmˆ3
Na=  100000000000000000  /cmˆ3
no =  1800000.0  /cmˆ3
E =  10  V/cm
un =  200  cmˆ2/s
p1=  100000000000000000  cmˆ−3
e =  1.6e-19  columb
Electron concentration ,p=−(−(Na−Nd)−sqrt ((Na−Nd)**2+4∗(no**2)))/2=  1e+17  cmˆ−3
Hole concentration ,n=(noˆ2/p))=  3.24e-05 cmˆ−3
Drift current density , Jdrift=n1∗un∗e∗E)=  32.0  A/cmˆ2

Example 3_19 pgno: 82

In [12]:
#exa 3.19
D=120
print "D = ",D," A/cmˆ2" # initializing value of drift current density .
E=5
print "E = ",E," V/cm" # initializing value of electric field .
e=1.6*10**-19
print "e = ",e,"columb" # initializing value of charge of electron .
p=(D/(450*e*E))
print "thermal equilibrium value of hole concentration ,p=(D/(450∗ e∗E)))= ",p," /cmˆ3" # calculation

D =  120  A/cmˆ2
E =  5  V/cm
e =  1.6e-19 columb
thermal equilibrium value of hole concentration ,p=(D/(450∗ e∗E)))=  3.33333333333e+17  /cmˆ3

Example 3_20 pgno: 83

In [13]:
#exa 3.20
Nd =5*10**16
print "Nd = ",Nd," /cmˆ3" # initializing value of donor concentration .
A=50*10**-8
print "A= ",A," cmˆ2" # initializing value of area .
l=0.2
print "l = ",l," /cm" # initializing value of length .
E=10
print "E = ",E," V" # initializing value of electric field .
up=1100
print "un = ",up," cmˆ2/s" # initializing value of mobility .
p=5*10**16
print "p= ",p," /cmˆ−3" # initializing value of impurity concentration .
e=1.6*10**-19
print "e = ",e,"columb" # initializing value of charge of electron .
I=(p*up*e*E*A)/l
print "Current through the bar,I=(p∗up∗e∗E∗A)/l)= ",I,"A"  # calculation

Nd =  50000000000000000  /cmˆ3
A=  5e-07  cmˆ2
l =  0.2  /cm
E =  10  V
un =  1100  cmˆ2/s
p=  50000000000000000  /cmˆ−3
e =  1.6e-19 columb
Current through the bar,I=(p∗up∗e∗E∗A)/l)=  0.00022 A