A model is presented for the performance of quantum well infrared photodetectors (QWIPs) utilizing intersubband electron transitions and tunneling injection electrons. The dark current and the responsivity are derived as functions of the QWIP parameters, including the number of the QWs and electric field dependent capture probability in an analytical form.
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Singh, D.P.

Singh, R.P.

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   J. Nano- Electron. Phys. 3 (2011) No1, P. 992-994  2011 SumDU (Sumy State University)   992 PACS number: 42.79.Pw  VARIATION OF QUANTUM WELL INFRARED PHOTODETECTORS PARAMETER WITH AN APPLIED ELECTRIC FIELD   R.P. Singh, D.P. Singh    Department of Physics,   Banaras Hindu University, Varanasi-221005, India   E-mail: ravindra142@gmail.com  A model is presented for the performance of quantum well infrared photodetectors (QWIPs)  utilizing  intersubband  electron  transitions  and  tunneling  injection electrons. The dark current and the responsivity are derived as functions of the QWIP parameters, including the number of the QWs and electric field dependent capture probability in an analytical form.   Keywords: QUANTUM WELL INFRARED PHOTODETECTORS, INTERSUBBAND ELECTRON TRANSITIONS, DARK CURRENT, RESPONSIVITY.  (Received 04 February 2011)  1.  INTRODUCTION  Quantum wells [1] are formed in semiconductors by using very common well material  like  gallium  arsenide  sandwiched  between  two  layers  of  a  barrier material  with  a  wider  bandgap,  i.e.  aluminium  gallium  arsenide.    In  this paper  an  analytical  model  is  developed  for  evaluating  the  performance  of QWIPs in which the electron injection from the emitter into the QW structure is associated with the electron tunneling through the extreme barrier, the aim of  the  paper  is  to  investigate  theoretically  the  QWIP  operation  using  the proposed analytical model [2, 3].We also study the effect of the variation of capture probability[4] with electric field on QWIP operation.  2.  THEORY   2.1  Mathematical description   The  QWIP  under  consideration  comprises  a  QW  structure,  sandwiched between the emitter and collector barriers followed by contact layers heavily doped  by  donors.  Under  the  assumptions  the  model  of  the  QWIP  [5]  is described  by  Poisson  equation  and  an  equation  governing  the  electron balance in the QW structure. These equations can be estimated as,   21 24( ) ( )Nn n ddex nLdx  (1)    ()cd n nPg I je  (2)  Here   is the electrostatic potential, e is the charge of electron,   is the dielectric constant,  n and  d are the electron sheet concentration in      VARIATION OF QUANTUM WELL INFRARED PHOTODETECTORS…993 the  n-th QW and the donor sheet concentration in each well, L = LB + d,  N is number of quantum well, LB is the thickness of barrier and d is the width of well, Pc the electric field dependent capture probability of electron in QW, d(x) is the Dirac d function, gd is the rate of the electron thermo excitation from the QW, j is the density of electron.   Solving the equation (1) under the boundary condition j (x = 0) = 0 and j (x = W) = V we have     ( )( )e x p1e x p1d m dinjdcz j eIjzPh sthéù - å= ×+ êú- êú ëû    where t = jmPc/egd, hd = pħ2 Sd/mkT and I is intensity of light.  2.2  D                     D a r k  c u r r e n t  i s  t h e  t e r m  f o r  t h e  e l e c t r i c a l  o u t p u t  o f  a  d e t e c t o r  i n  t h e absence of input. Under dark condition (I = 0) the simple formula for the dark current density is    ( )exp explnid Btd a r kmcdkT e aEj jEP NE aeh éù - ìü æö = -- íý êú ç÷èø îþ ëû  (3)  where 22B a me a = h is the Bohr radius and  ( ) ( )1 1.5 0.50 22 tF E me p ee-=- h , ε0 is the height of the barrier for the electron in the emitter and eF is their Fermi energy.  2.3  Responsivity   The ratio of the detector output and the detector input is defined as the responsivity. It is given in ampere/watt or volt/watt. At low intensities of the infrared radiation responsivity can be estimated as     ln1 tddEERRNEa éù -=+ êúëû  (4)  Where Rd = esSd/Pcet.  3.  RESULT AND DISCUSSION  In Fig. 1 we have seen that the dark current increase rapidly with electric f i e l d  f o r  s i n g l e  w e l l  b u t  s l o w l y  i n c r e a s e s  f o r  m u l t i q u a n t u m  w e l l s  a n d saturate for higher applied electric field.  I t  i s  c l e a r  f r o m  F i g .  2  t h a t responsivity of a photodetector increases with electric field and saturate from higher electric field. The responsivity of different numbers of well is shown in figure. According to this theory we can say that responsivity is independent upon number of well but dependent upon donor concentration.     994  R.P. SINGH, D.P. SINGH     F  . 1 – Variation of dark current density with electric field     F  . 2 – Variation of dark current density with electric field  4.  CONCLUSION  From this study we conclude that the capture probability has significant effect at low electric field on QWIP parameter and the increasing the number of wells above N = 8 has no significant effect on responsivity and dark current.  REFERENCES 1.  B.F. Levine, J. Appl. Phys. 74, R1 (1993). 2.  K.M.S.V. Bandara, B.F. Levine, R.E. Leibenguth, M.T. Asom, J. Appl. Phys.74, 1826 (1993)  3.  V. Ryzhii, Jpn. J. Appl. Phys. 33, 78 (1994). 4.  M. Kishimoto, K. Sakasai, K. Ara, J. Appl. Phys. 79, 1 (1996). 5.  V. Ryzhii, J. Appl. Phys. 81, 6442 (1997). 

Variation of quantum well infrared photodetectors parameter with an applied electric field

SocioEconomic Challenges Journal (Sumy State University)

 
 
 
J. Nano- Electron. Phys. 
3 (2011) No1, P. 992-994 
 2011 SumDU 
(Sumy State University) 
 
 
992 
PACS number: 42.79.Pw 
 
VARIATION OF QUANTUM WELL INFRARED PHOTODETECTORS 
PARAMETER WITH AN APPLIED ELECTRIC FIELD  
 
R.P. Singh, D.P. Singh 
 
 Department of Physics, 
 Banaras Hindu University, Varanasi-221005, India
 
 E-mail: ravindra142@gmail.com 
 
A model is presented for the performance of quantum well infrared photodetectors 
(QWIPs) utilizing intersubband electron transitions and tunneling injection 
electrons. The dark current and the responsivity are derived as functions of the QWIP 
parameters, including the number of the QWs and electric field dependent capture 
probability in an analytical form.  
 
Keywords: QUANTUM WELL INFRARED PHOTODETECTORS, INTERSUBBAND 
ELECTRON TRANSITIONS, DARK CURRENT, RESPONSIVITY. 
 
(Received 04 February 2011) 
 
1. INTRODUCTION 
 
Quantum wells [1] are formed in semiconductors by using very common well 
material like gallium arsenide sandwiched between two layers of a barrier 
material with a wider bandgap, i.e. aluminium gallium arsenide.  In this 
paper an analytical model is developed for evaluating the performance of 
QWIPs in which the electron injection from the emitter into the QW structure 
is associated with the electron tunneling through the extreme barrier, the aim 
of the paper is to investigate theoretically the QWIP operation using the 
proposed analytical model [2, 3].We also study the effect of the variation of 
capture probability[4] with electric field on QWIP operation. 
 
2. THEORY  
 
2.1 Mathematical description  
 
The QWIP under consideration comprises a QW structure, sandwiched 
between the emitter and collector barriers followed by contact layers heavily 
doped by donors. Under the assumptions the model of the QWIP [5] is 
described by Poisson equation and an equation governing the electron 
balance in the QW structure. These equations can be estimated as, 
 
 
2
12
4
( ) ( )
N
n n d
d e
x nL
dx
 (1) 
 
 ( )
c
d n n
P
g I j
e
 (2) 
 
Here  is the electrostatic potential, e is the charge of electron,  is the 
dielectric constant, n and d are the electron sheet concentration in 
 
 
 
 VARIATION OF QUANTUM WELL INFRARED PHOTODETECTORS…993 
the n-th QW and the donor sheet concentration in each well, 
L = LB + d, N is number of quantum well, LB is the thickness of 
barrier and d is the width of well, Pc the electric field dependent 
capture probability of electron in QW, d(x) is the Dirac d function, gd 
is the rate of the electron thermo excitation from the QW, j is the 
density of electron. 
 Solving the equation (1) under the boundary condition j (x = 0) = 0 and j 
(x = W) = V we have  
 
 
( )
( )
exp 1
exp 1
dm d
inj
d c
zj e I
j z
P
h s
t h
é ù- å= × +ê ú-ê úë û
  
 
where t = jmPc/egd, hd = pħ2 Sd/mkT and I is intensity of light. 
 
2.2 Dark current density 
 
Dark  current  is  the  term  for  the  electrical  output  of  a  detector  in  the  
absence of input. Under dark condition (I = 0) the simple formula for the 
dark current density is 
 
 
( )
exp exp
ln
i d B t
dark m
c d
kT ea E
j j E
P NE a
e hé ù- ì üæ ö= - -í ýê úç ÷è øî þë û
 (3) 
 
where 2 2Ba mea= h is the Bohr radius and ( ) ( )
11.50.5
0 2 2t FE m ep e e
-
= - h , 
ε0 is the height of the barrier for the electron in the emitter and eF is their 
Fermi energy. 
 
2.3 Responsivity  
 
The ratio of the detector output and the detector input is defined as the 
responsivity. It is given in ampere/watt or volt/watt. At low intensities of 
the infrared radiation responsivity can be estimated as   
 
 
ln
1 td
d
E E
R R
NE
aé ù-= +ê ú
ë û
 (4) 
 
Where Rd = esSd/Pcet. 
 
3. RESULT AND DISCUSSION 
 
In Fig. 1 we have seen that the dark current increase rapidly with electric 
field  for  single  well  but  slowly  increases  for  multiquantum  wells  and  
saturate for higher applied electric field. It  is  clear  from  Fig.  2  that  
responsivity of a photodetector increases with electric field and saturate 
from higher electric field. The responsivity of different numbers of well is 
shown in figure. According to this theory we can say that responsivity is 
independent upon number of well but dependent upon donor concentration. 
 
 
 
 
994 R.P. SINGH, D.P. SINGH  
 
 
Fig. 1 – Variation of dark current density with electric field 
 
 
 
 
Fig. 2 – Variation of dark current density with electric field 
 
4. CONCLUSION 
 
From this study we conclude that the capture probability has significant 
effect at low electric field on QWIP parameter and the increasing the 
number of wells above N = 8 has no significant effect on responsivity and 
dark current. 
 
REFERENCES 
1. B.F. Levine, J. Appl. Phys. 74, R1 (1993). 
2. K.M.S.V. Bandara, B.F. Levine, R.E. Leibenguth, M.T. Asom, J. Appl. Phys.74, 
1826 (1993)  
3. V. Ryzhii, Jpn. J. Appl. Phys. 33, 78 (1994). 
4. M. Kishimoto, K. Sakasai, K. Ara, J. Appl. Phys. 79, 1 (1996). 
5. V. Ryzhii, J. Appl. Phys. 81, 6442 (1997). 


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Variation of quantum well infrared photodetectors parameter with an applied electric field

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