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are normally much narrower than the inactive barrier regions. We will analyze the photocurrent caused by intersubband
excitations in a QWIP and consider only the case of positive photoconductivity; the effect of which is to have smaller
resistance against the incident of IR light. Negative photoconductivity is possible, if one has a device with a negative
differential resistance region [6].
THEORETICAL BACKGROUND
QWIPs belong to the category of the so-called photon detectors; the absorption of an infrared photon results
directly in some specific quantum event, such as the photoelectric emission of electrons from a surface, or electronic inter
band transitions in semiconductor materials. Therefore, the output of photon detectors is governed by the rate of absorption
of photons and not directly by the photon energy. Photon detectors typically require cooling down to cryogenic
temperatures in order to get rid of excessive dark current, but in return their general performance is high. QWIPs are most
often used as photo-conductive detectors. In this type of detectors photo-generated charge carriers increase the conductivity
of the device material.
The physical structure of QWIPs is the main key of changing or modulating its characteristics such as dark
current, photocurrent, noise currents, responsivity, and detectivity. Our scope in the following sections is to show to what
extent the physical structure can affect the characteristics of dark, photo and noise currents. The theoretical procedure of
calculations of these currents is based on capture and escape probabilities for the electrons. These probabilities are
dependent on capture, transit, escape, and intersubband relaxation time. However, all these parameters vary from one of
QWIP structures to another. In the condition of designing of an optimum QWIP, we must be careful when we choose
QWIP parameters such as doping density in the well, the mole fraction and the barrier width. This is due to the role that
these parameters can play on determination of the capture and escape probabilities. For these reasons, we are going toevaluate the basic formulas which are very useful in comparing the different structures of QWIP devices.
It is generally assumed that each well in a QWIP can be regarded as a discrete generation-recombination (GR)
noise source. Within this approach, a good agreement between theoretical models and experimental QWIP noise results has
been achieved.
Dark and Photo Currents
A QWIP is a photoconductor. Unlike a photodiode, it does not contain an internal electric field. Thus an external
electric field must be applied across the detector to induce current flow. With the incident optical flux, photoelectrons are
generated in the conduction band. Thus, the conductance of the detector changes with incident flux. Since the detector has
a finite conductance, there will always be a dark current associate with the photocurrent. For effective imaging, the dark
current must be significantly less than the photocurrent.
The dark current in a typical photoconductive QWIP is controlled by the flow of electrons above the barriers, and
by the emission and capture of electrons in the wells [6]. It is the current that flows even without the presence of incident
light. This current is the source of noise that represents the main factor limiting the performance of QWIPs. Figure 1 shows
the dark current paths. In the barrier regions, the current flows in a three-dimensional (3D) fashion, and the current density
is labeled aswhich equals the dark current density . In the vicinity of each well, the emission of electrons from
the well contributes to the dark current. This current, which tends to lower the electron density in the well, must be
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4 Mohamed B. El_Mashade & M. El_Hanash
Impact Factor (JCC): 3.8869 Index Copernicus Value (ICV): 3.0
balanced by the trapping or capture of electronsinto the well, so under steady state = [5] since the dark current
is the same throughout the structure. If we define a trapping or capture probability for an electron traversing a well with
energy larger than the barrier height, we must have
(1)
And the sum of the captured and uncaptured fractions must equal the current in the barrier region, so the escape
current density can be written as
(2)
Where is a 2D electron density which only includes electrons on the upper part (with energy greater than the
barrier height) of the ground state suband and is the scattering time to transfer these electrons from the 2D sub and
to the non confined continuum on top of the barrier. The capture probability is related to the relevant time constants by [6]
(3)
is the capture time of an excited electron back into the well and is the transit time for an electron acrossone quantum well region including the surrounding barriers. Practically, 1 , as is true for
actual devices at operating electric fields, the dark current density will be
(4)
""denotes the drift velocity and is the period length of the multiple quantum well structure, which is the sum
of the well and the barrier width = ! . Thus,
(5)
"A" represents the device area.
Because is a function of temperature and is a function of electric field or applied biasing voltage, so the
dark current is a function of both the bias and the temperature [9]. Figure 2 illustrates the theoretical calculations of three
samples. The main difference between these samples is the doping density in the well . The sample structure consists
of 100 periods of #$%&'(%#)*) quantum wells with well width = +,+ -, barrier thickness
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= ./- and0 = .2. The variation of the dark current, generated by this sample, as a function of the electric
field for different values of operating temperatures is plotted in Figure 3 when the well's doping density is = 1,/ 3
1'4-(. On the other hand, when IR light is incident on the detector, all the dark current paths remain unchanged [6]
as Figure 4 demonstrates.
Let us now turn our attention to the photocurrent to show to what extent its presence can affect the behavior of the
QWIP detector. There is a direct photoemission of electrons from the well, and this, of course, contributes to the observed
photocurrent in the collector. The photoconductive gain is a result of the extra current injection from the contact necessary
to balance the loss of electrons from the well due to photoemission. The amount of the extra injection must be sufficiently
large in such a way that its fraction trapped in the well equals the direct photoemission current. The total photocurrent
consists of contributions from the direct photoemission and the extra current injection [10]. The photoemission current
directly ejected from one well is
(6)
where is the rate of incident photons, the superscript (1) indicates quantities for one well, is the escape
time, 5% is the intersubband relaxation time, 6 7 6' is the total absorption quantum efficiency, is the
number of wells, and 89is the escape probability for an excited electron from the well is.
The derivation of Eq. (6) is straight-forward from a rate equation consideration which relates the rate of change of
the number of excited electrons % to the other system parameters as:
(7)
As shown in Figure 3, for each well, the injection current :;
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Impact Factor (JCC): 3.8869 Index Copernicus Value (ICV): 3.0
(10)
Shot(Generation-Recombination) Noise Current
The basic principle of photodiode operation is when photons strike photodiode surface, they generate free
electrons and the movement of free electrons results in a measurable current. Shot noise in the current is due to the
statistical nature of the generation of the free electrons. In given time interval, there will be random fluctuations in the
number of free electrons generated as the photons strike that surface. These fluctuations will follow Poisson statistics,
which tells us the uncertainty in the number of events"", that occur in a given time interval is given simply by the square
root of, or =>. During a measuring time interval of?@, the number of events (creation of free electrons), is given
by:
(11)
A represents the external circuit current. Shot noise current is based on Poisson statistics, so the standard
deviation of the current is
(12)
where?B = 1*.?@denotes the measurement's bandwidth.
In the above formula, it is assumed thatC;
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(16)
So the total fluctuations in the dark current can be calculated by adding Eqs. (15) and (16).
(17)
Because := : C;
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(22)
In the above formula, JKis the dark-to-noise current ratio. Substituting C
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(27)
Substituting C.
CONCLUSIONS
Thanks to their wavelength diversity and to their excellent uniformity, QWIP detectors emerge as potentialcandidates for many practical applications; especially in the very long wavelength infrared (VLWIR) spectral domain.
This paper is concerned with calculating all different currents that are generated by several sources of noise. These currents
include dark, shot noise, thermal noise, and photocurrent component. From our calculations, it is noted that the absorption
6 is directly proportional to N while C;
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4. M. Z. Tidrow and W. R. Dyer, "Quantum We11 Infrared Focal Plane Arrays for Ballistic Missile Defense and
Space Applications", RTO SET Symposium on Space-Based Observation Technology, held on the Island of
Samos, Greece, 16-18 October 2000, pp.29-1_29-6.
5.
Levine, B.F, "Quantum-well infrared photodetector" J. Appl. Phys. 74, R1R81 (1993).
6. Harald Schneider and Hui Chun Liu, "Quantum Well Infrared Photodetectors Physics and Applications",
Springer-Verlag Berlin Heidelberg 2007.
7.
K. K. Cho, "Detection wavelength of quantum well infrared photodetectors", J. Appl. Phys. 73 (lo), May 1993.
8. N. Sclar, "Properties of doped silicon and germanium infrared detectors", Prog. Quant. Electr. 9, 149-257
(1984).
9.
Thomas R. Hickey, "TEMPERATURE DEPENDENCE OF DARK CURRENT IN QUANTUM WELL INFRARED
DETECTORS", NAVAL POSTGRADUATE SCHOOL, Monterey, California,June 2002.
10. V. D. Shadrin, V. V. Mitin, and V. A. Kochelapb, "Photoconductive gain and generation-recombination noise in
quantum well infrared photodetectors", J. Appl. Phys. 77 (4), February 1995.
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Robert H. Kingston, "Optical Sources, Detectors, and Systems Fundamentals And Applications", by ACADEMIC
PRESS, INC.1995.
12. L. Li D. Y. Xiong J. Wen Q. C. Weng, "An equivalent circuit model for the long-wavelength quantum well
infrared photo-detectors", Opt Quant Electron, (2013), Vol. 45, pp. 649656.
APPENDICES
Figure 1: The Dark Current Paths
Figure 2:Dark Current Density Plots with Applied Field for Different Doping Densities in the Wel
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Figure 3:Dark Current Density Plots with Applied Field for Different Temperatures
Figure 4: The Dark Current Paths and the Collected Total Photocurrent
Figure 5: The Equivalent Circuit of Photoconductive (QWIP)
Figure 6: Dependence of JKon Number of Quantum Wells
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Figure 7: Dependence of JdKon Number of Quantum Wells