Chapter 4 EXCESS CARRIER IN SEMICONDUCTOR

Example 4_2 pgno: 100

In [1]:
#exa 4.2
Nd =2*10**17
print"Nd = ",Nd,"cmˆ−3" # initializing value of donor concentration .
Er =11.9
print"Er = ",Er # initializing value of relative dielectric constant.
e=1.6*10**-19
print"e = ",e,"columns" # initializing value of charge of electrons .
Eo=8.854*10**-14
print"eo = ",Eo # initializing value of permittivity of free space .
un=1350
print"un = ",un,"cm2/Vs" # initializing value of mobility .
sigma=e*un*Nd
print" conducitivity , sigma=e∗un∗Nd)=",sigma,"S/cm"# calculation
td=((Er*Eo)/sigma)
print"Dielectric releaxation time ,td=((Er∗Eo)/sigma))=",td,"s"# calculation

Nd =  200000000000000000 cmˆ−3
Er =  11.9
e =  1.6e-19 columns
eo =  8.854e-14
un =  1350 cm2/Vs
 conducitivity , sigma=e∗un∗Nd)= 43.2 S/cm
Dielectric releaxation time ,td=((Er∗Eo)/sigma))= 2.43894907407e-14 s

Example 4_3 pgno: 101

In [2]:
#exa 4.3
n=10**15
print"n = ",n,"cmˆ−3" # initializing value of concentration of electrons/cmˆ3.
no =10**10
print"no = ",no,"cmˆ−3" # initializing value of intrinsic concentration of electron .
t=10**-6
print"t = ",t,"s" # initializing value of carrier lifetime .
c=1*10**14
print"Excess electron concentration = ",c,"cmˆ−3" # initializing value of excess electrons concentration .
R=(c/t)
print"electron hole recombination ,R=(c/t))=",R," /cmˆ3s"# calculation,

n =  1000000000000000 cmˆ−3
no =  10000000000 cmˆ−3
t =  1e-06 s
Excess electron concentration =  100000000000000 cmˆ−3
electron hole recombination ,R=(c/t))= 1e+20  /cmˆ3s

Example 4_4 pgno: 101

In [3]:
#exa 4.4
Nd =10**15
print"Nd = ",Nd,"cmˆ−3" # initializing value of donor concentration ..
tn =10*10**-6
print"minority carrier lifetime = ",tn,"s" #initializing value of minority carrier lifetime
no=1.5*10**10
print"no = ",no,"cmˆ−3" # initializing value of electron and hole concentration per cmˆ3.
p=(no**2/Nd)
print"excess carrier concentration ,p=(noˆ2/Nd))=",p,"/cmˆ3"# calculation
R=(p/tn)
print"electron hole generation and recombination rate ,R=(p/t))=",R,"/cmˆ3s"#calculation
t=Nd/R
print"majority carrier concentration ,t=Nd/R)=",t,"s"# calculation .
#the value of majority carrier concentration,t=Nd/R( after calculation ) , is provided wrong in the solution .

Nd =  1000000000000000 cmˆ−3
minority carrier lifetime =  1e-05 s
no =  15000000000.0 cmˆ−3
excess carrier concentration ,p=(noˆ2/Nd))= 225000.0 /cmˆ3
electron hole generation and recombination rate ,R=(p/t))= 22500000000.0 /cmˆ3s
majority carrier concentration ,t=Nd/R)= 44444.4444444 s

Example 4_5 pgno: 101

In [4]:
#exa 4.5
from math import log
Nd =10**16
print"Nd = ",Nd," cmˆ−3" # initializing value of donor concentration .
p=10**6
print"p = ",p," cmˆ−3" # initializing value of minority hole concentration .
no =10**10
print"no = ",no," cmˆ−3" # initializing value of electron and hole concentration per cm ˆ3..
n1 =10**15
print"n∗ = ",n1," cmˆ−3" # initializing value of excess electron carrier concentration(denoted by n∗).
p1=10**15
print"p∗ = ",p1," cmˆ−3" # initializing value of excess hole carrier concentration( denoted by p∗).
KT=0.0259
print"KT = ",KT," eV" # initializing value of multipication of temperature and bolzmann constant .
T=300
print"T = ",T," K" # initializing value of temperature .
Ef_Efi=(log(Nd/no)*KT)
print"Thermal equilibirium fermi level ,( Ef Efi )=(KT∗log(n/no)))=",Ef_Efi," eV"#calculation .
Efn_Efi=log((Nd+n1)/no)*KT
print"Quasi−fermi levels for n−type dopant ,( Efn Efi )=(KT∗log ((n+n∗)/no))=",Efn_Efi," eV"# calculation .
Efi_Efp=log((Nd+p1)/no)*KT
print"Quasi−fermi levels for p−type dopant ,( Efi Efp )=(KT∗log ((p+p∗)/no))=",Efi_Efp," eV"# calculation .
#the answer for Efn Efi , Efi Efp is provided wrong in the book.
#In this question,Nd=(n(used in the formula)).

Nd =  10000000000000000  cmˆ−3
p =  1000000  cmˆ−3
no =  10000000000  cmˆ−3
n∗ =  1000000000000000  cmˆ−3
p∗ =  1000000000000000  cmˆ−3
KT =  0.0259  eV
T =  300  K
Thermal equilibirium fermi level ,( Ef Efi )=(KT∗log(n/no)))= 0.357821723451  eV
Quasi−fermi levels for n−type dopant ,( Efn Efi )=(KT∗log ((n+n∗)/no))= 0.360290257108  eV
Quasi−fermi levels for p−type dopant ,( Efi Efp )=(KT∗log ((p+p∗)/no))= 0.360290257108  eV

Example 4_6 pgno: 102

In [5]:
#exa 4.6
from math import log
Nd =5*10**16
print"Nd = ",Nd,"cmˆ−3" # initializing value of donor ion concentration .
Na=0
print"Na = ",Na,"cmˆ−3" # initializing value of value of acceptor ion concentration .
no=1.5*10**10
print"no =",no,"cmˆ−3" # initializing electron and hole concentration per cmˆ3.
n1 =5*10**14
print"n∗ =",n1,"cmˆ−3" # initializing excess electron carrier concentration .
p1 =5*10**14
print"p∗ =",p1,"cmˆ−3" # initializing excess hole carrier concentration .
KT=0.0259
print"KT =",KT  #initializing value of voltage 
Ef_Efi=(KT*log(Nd/no))
print"thermal equilibrium fermi level ,( Ef Efi )=(KT∗log(n/no)))=",Ef_Efi,"eV" #calculation .
Efn_Efi=log((Nd+n1)/no)*KT
print"Excess carrier concentration ,(Efn Efi)=(KT∗log ((n+n∗)/no))=",Efn_Efi,"eV" # calculation .
Efi_Efp=log((Na+p1)/no)*KT
print"(Ef Efi)=(KT∗log((p+p∗)/no))=",Efi_Efp,"eV"# calculation .

Nd =  50000000000000000 cmˆ−3
Na =  0 cmˆ−3
no = 15000000000.0 cmˆ−3
n∗ = 500000000000000 cmˆ−3
p∗ = 500000000000000 cmˆ−3
KT = 0.0259
thermal equilibrium fermi level ,( Ef Efi )=(KT∗log(n/no)))= 0.389004619083 eV
Excess carrier concentration ,(Efn Efi)=(KT∗log ((n+n∗)/no))= 0.389262332652 eV
(Ef Efi)=(KT∗log((p+p∗)/no))= 0.269730711266 eV