Analysis of a quantum well structure optical integrated device
This paper demonstrates theoretical modeling of a quantum well structure optical integrated device. The constituent devices of the developed structure are a Quantum Well Infrared Photodetector (QWIP) to detect the optical infrared signal, a Heterojunction Phototransistor (HPT) to amplify the signal,...
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Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України
2017
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| Cite this: | Analysis of a quantum well structure optical integrated device / Sh.M. Eladl, M.H. Saad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 204-209. — Бібліогр.: 11 назв. — англ. |
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| author | Eladl, Sh.M. Saad, M.H. |
| author_facet | Eladl, Sh.M. Saad, M.H. |
| citation_txt | Analysis of a quantum well structure optical integrated device / Sh.M. Eladl, M.H. Saad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 204-209. — Бібліогр.: 11 назв. — англ. |
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| description | This paper demonstrates theoretical modeling of a quantum well structure optical integrated device. The constituent devices of the developed structure are a Quantum Well Infrared Photodetector (QWIP) to detect the optical infrared signal, a Heterojunction Phototransistor (HPT) to amplify the signal, and a Light Emitting Diode (LED) to emit this signal in a visible form. The model is based on the transient behavior of the constituent parts of the structure. The dominant pole approximation scheme is used to reduce its transfer function. The convolution theorem is used to get the overall transient response of the device under consideration. All interesting parameters concerning the transient response, rise time, and output derivatives are theoretically investigated. The results show that the overall transient behavior, output derivative, and rise time of the considered structure are approximately the same as those of the constituent device possessing the lowest cutoff frequency. This type of model can be applied with high sensitivity in the upconversion of infrared or far infrared range for image signal processing.
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| first_indexed | 2026-03-21T13:44:50Z |
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Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 204-209.
doi: https://doi.org/10.15407/spqeo20.02.204
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
204
PACS 07.57.Kp, 85.35.Be, 85.60.Dw, 85.60.Jb
Analysis of a quantum well structure optical integrated device
Sh.M. Eladl and M.H. Saad
Radiation Eng. Dept., 3 Ahmed Elzomor St., NCRRT,
P.O. Box 29, Nasr City, Atomic Energy Authority,
Cairo, Egypt
Abstract. This paper demonstrates theoretical modeling of a quantum well structure
optical integrated device. The constituent devices of the developed structure are a
Quantum Well Infrared Photodetector (QWIP) to detect the optical infrared signal, a
Heterojunction Phototransistor (HPT) to amplify the signal, and a Light Emitting Diode
(LED) to emit this signal in a visible form. The model is based on the transient behavior
of the constituent parts of the structure. The dominant pole approximation scheme is used
to reduce its transfer function. The convolution theorem is used to get the overall
transient response of the device under consideration. All interesting parameters
concerning the transient response, rise time, output derivatives are theoretically
investigated. The results show that the overall transient behavior, output derivative, and
rise time of the considered structure are approximately the same as the constituent device
possessing the lowest cutoff frequency. This type of model can be applied with high
sensitivity in the up conversion of infrared or far infrared range for image signal
processing.
Keywords: quantum well infrared photodetector, heterojunction phototransistor, light
emitting diode, quantum well structure, optical integrated device.
Manuscript received 19.11.16; revised version received 05.04.17; accepted for
publication 14.06.17; published online 18.07.17.
1. Introduction
For optical image processing applications, it is necessary
to focus on devices and components that can detect, pro-
cess, and transmit information with great adaptability
and better efficiency [1]. An effective scheme is deve-
loped by integrating of Quantum Well Infrared Photo-
detector (QWIP) and a Light Emitting Diode (LED) to
be used as a pixel detector to far or middle infrared
radiation with near infrared or visible output, the
structure with this scheme is called as up converter [2].
The QWIP is applied for under IR light
illumination where its resistance decreases, which yields
the voltage drop across the LED to increase and,
therefore, an increase in the output intensity. This device
is thus an IR converter [3, 4]. When a forward bias
voltage is applied, recombination between the photo-
current electrons from the detector side and the injected
holes take place giving rise to an intensified light in the
LED side.
To improve the quantum efficiency of the up
converter, a bottom mirror for the infrared detector side
and a resonant cavity for the emitting side are
introduced. In this way, the quantum efficiency could be
5–6-fold increased, and the contrast transfer function is
even better in comparison with that of the conventional
structure [5]. Other theoretical and experimental
investigations for conversion from mid infrared to
visible LED (MIR type-I LEDs) were developed.
Simulation results show that a good control of the
optical wavelength and efficient confinement for carrier
in the active region is obtained if a MQW active region
in the structure design is included [6]
The improvement of selectivity inherent to these
devices can be made by using quantum well infrared
photodetectors having a resonator (R-QWIP). The
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 204-209.
doi: https://doi.org/10.15407/spqeo20.02.204
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
205
benefit of resonances is to increase the quantum
conversion efficiency [7-9]. These detectors will convert
the far infrared light signal to be amplified by HBT
which derive a visible Light Emitting Diode (LED).
The input infrared light signal is applied to the
developed quantum well structure as it is converted to
photo-excited carriers by the Quantum Well Infrared
Photodetector (QWIP); the HBT is used to amplify the
QWIP output electric signal; and the LED is driven by
this output amplified signal transferred from the HBT
and radiates an intensified light of near infrared or
visible range. The dynamic response of this structure
was analyzed being based on the frequency response of
its constituent devices [9].
This paper focuses on examining the closest
constituent device of the developed structure to its exact
dynamic behavior. The pole approximation scheme and
convolution theorem are two useful methods to complete
this issue, this analysis is important for designing and
deeper understanding this type of structure.
The paper is organized as follows: formulation of
the specified parameters that describes the transient
response, derivative, and rise time is presented in
Section 2. The generated curves as results are outlined
and discussed in Section 3. Finally, conclusion of this
work and an important note to continue the research of
this subject have been discussed in Section 4.
2. Theoretical analysis
The schematic layer structure of the device under study
is shown in Fig. 1. To understand the transient response
of the device version under study, it is important to
investigate the transient response of each element that
constitutes it. The recognition of the characteristic
equation describing the overall transient response
becomes available when the transient response equation
of each element is known.
Fig. 1. Schematic structure of an integrated QWIP-HBT-LED
pixel.
The relative overall frequency response can be
obtained from [10] as follows:
( ) ( )
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ω
ω
+⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ω
ω
+⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ω
ω
+
=
=
ηηη
ω
=ω
LEDHBTQWIP
LEDHBTQWIP
111
1
jjj
S
R
. (1)
The transfer function of the QWIP-HBT-LED
structure has three distinct real roots, it is possible to use
useful approximations to reduce the model to the first
order system. The most common way to do that is to use
the dominant pole approximation scheme. This method
is applied to the transfer function in the form of
frequency, time or Laplace domain. The dominant pole
of the structure means the one that is closer to the origin
on Pole-Zero Map which means the slowest pole. This
method is restricted to the examination of the transient
response and can’t be applied to calculate the bandwidth
of the structure. The dominant pole approximation
scheme can be applied as
( )
( )
( )
( )
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎪
⎪
⎪
⎨
⎧
ω<ω<ω
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ω
ω
+
=ω
ω<ω<ω
⎟⎟
⎠
⎞
⎜⎜
⎝
⎛
ω
ω
+
=ω
ω<ω<ω
⎟
⎟
⎠
⎞
⎜
⎜
⎝
⎛
ω
ω
+
=ω
=ω
QWIPHBTLED
LED
LED
QWIPLEDHBT
HBT
HBT
LEDHBTQWIP
QWIP
QWIP
for
1
1
for
1
1
for
1
1
j
R
j
R
j
R
R
(2)
where ηQWIP, ηHBT, and ηLED are the conversion
efficiency of QWIP, HBT, and LED, respectively. Also,
ωQWIP, ωHBT, and ωLED are the cutoff frequency of QWIP,
HBT, and LED, respectively.
Let R1(t), R2(t), and R3(t) be the relative transient
responses at the output side of QWIP, HBT, and LED,
respectively. The convolution among them is also a
function of time and is denoted by [11].
If the input light is assumed as a unit step time
signal, the convolution theorem is applied to the
constituent devices as
( ) ( ) ( ) ( ) ( ),1 QWIP
QWIP
0
1
QWIP
0
t
t
edRtUtRtR ω−−=λλλ−== ∫
(3)
where U(t – λ) is a unit step input signal delayed by time
λ and RQWIP (λ) is RQWIP (t) at time λ.
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 204-209.
doi: https://doi.org/10.15407/spqeo20.02.204
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
206
If the unit input light is inputted to HBT, the
individual relative time response for HBT can be get as
( ) ( ) ( ) ( )t
t
edRtUtR HBT1HBT
0
HBT
0
ω−−=λλλ−= ∫ , (4)
where RHBT (λ) is RHBT (t) at time λ.
At the output side of HBT, one can get
( ) ( ) ( ) ( ) ( ) λλλ−=⋅= ∫ dRtRtRtRtR
t
HBT
0
1HBT12 . (5)
The above equation is calculated as
( )
{ }HBTQWIP
QWIPHBTQWIPHBT
HBTQWIP
2
1
ω−ω− ω−ω−ω+ω×
×
ω−ω
=
ee
tR
.
(6)
If the unit input light is inputted to LED, the
individual relative time response for LED can be get as
( ) ( ) ( ) ( )t
t
edRtUtR LED1LED
0
LED
0
ω−−=λλλ−= ∫ . (7)
At the end of the LED part, the relative response of
the output signal is calculated as
( ) ( ) ( ) ( ) ( ) λλλ−=⋅= ∫ dRtRtRtRtR
t
LED
0
2LED2 , (8)
where RLED (λ) is RLED (t) at time λ.
Then
( )
( )
( )
( )
( )
⎪
⎪
⎪
⎪
⎪
⎭
⎪
⎪
⎪
⎪
⎪
⎬
⎫
⎪
⎪
⎪
⎪
⎪
⎩
⎪
⎪
⎪
⎪
⎪
⎨
⎧
ωω−ω
ωω
−
−ωω−
−ωω+ωω−
−ωω+ωω−
−ωω−ωω+
+ωω−ωω
=
ω−
ω−
ω−
ω−
t
t
t
t
e
e
e
e
tR
LED
QWIP
HBT
HBT
HBTQWIP
2
LED
HBTQWIP
LED
2
HBT
LED
2
HBTHBT
2
LED
QWIP
2
LEDQWIP
2
HBT
QWIP
2
LEDLED
2
QWIP
HBT
2
QWIPLED
2
QWIP
, (9)
where
( )( ) .
1
QWIPLEDLEDQWIPQWIPHBTLEDHBT
2
HBT
0
ω−ωωω+ωω−ωω−ω
=R
(10)
The final state of transient response of the structure
can be expressed as
( ) .1lim
LED
2
HBTHBT
2
LED
QWIP
2
LEDQWIP
2
HBT
LED
2
QWIPHBT
2
QWIP
0 =
⎪
⎪
⎭
⎪⎪
⎬
⎫
⎪
⎪
⎩
⎪⎪
⎨
⎧
ωω+ωω−
−ωω+ωω−
−ωω+ωω−
==
∞→
RtRR
tf
(11)
The derivative of the transient response of the
device is expressed by ( )tR
dt
d , which is a measure of
the device speed, this quantity can be expressed as:
( )
( )
( )
( )
( )
⎪
⎪
⎪
⎪
⎭
⎪⎪
⎪
⎪
⎬
⎫
⎪
⎪
⎪
⎪
⎩
⎪⎪
⎪
⎪
⎨
⎧
ωω−ω
ωωω
+
+ωω+
+ωωω+
+ωωω
=
ω−
ω−
ω−
ω−
t
t
t
t
e
e
e
e
RtR
dt
d
LED
QWIP
HBT
HBT
HBTQWIP
2
LED
HBTQWIPLED
LED
2
HBT
HBTQWIP
2
LED
HBTLED
2
QWIP
0 . (12)
The rise time of the considered structure is the time
needed for the signal to reach the final value Rf. By using
the approximation where ωHBT is the lowest cutoff
frequency, the rise time is expressed as:
( )
( ) ⎪⎭
⎪
⎬
⎫
⎪⎩
⎪
⎨
⎧
ωω−ωωηηη
+
×
×
ω
−
=
QWIP
2
HBTHBT
2
QWIPLEDHBTQWIP
HBT
1
ln
1
fRH
T
,
(13)
where
.LED
2
HBTHBT
2
LEDQWIP
2
LED
QWIP
2
HBTLED
2
QWIPHBT
2
QWIP
ωω+ωω−ωω+
+ωω−ωω+ωω−=H
(14)
3. Results and discussions
The device parameters used in the following calculations
are as follow, ωQWIP = 1 GHz, ωHBT = 0.1 GHz,
ωLED = 1.2 GHz and ηQWIP ηHBT ηLED = 1. The input
infrared radiation is assumed as a step function in time.
The first set of curves shown in Fig. 2a represents the
transient behavior of the developed structure where ωHBT
is chosen to be the smallest cutoff frequency. The solid
line curve represents the exact response and the dotted
line curve corresponds to the first order dominant pole
approximation concerning HPT, while the dashed line
curve corresponds to the first order dominant pole
approximation for LED, and the dashed dotted line
indicates the QWIP approximation. It is clear from the
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 204-209.
doi: https://doi.org/10.15407/spqeo20.02.204
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
207
figure the exact response of the considered structure is in
close with the first order HPT response, this is because
ωb = 0.1 GHz is close to zero in the pole-zero map than
ωQWIP and ωLED as in Fig. 2b.
Fig. 3 shows variation of the output derivative with
time (which measures the speed of the output changes)
at the three approaches of the constituent devices. It is
clear that the cutoff frequency of the device plays a
major role in determining the response speed, since the
large value of cutoff frequency yields the device to
arrive to its final state quickly unlike those with a
smaller value. The output derivative concerning both
QWIP and LED decreases with time, while nearly
increases with time as regarding HPT and all the
structure. The decrease with time for both QWIP and
LED is caused by their higher cutoff frequencies, which
helps to reduce the arrival time to their final state. The
output derivative concerning HPT is similar to the output
derivative of all structure due to the closest HPT pole to
zero than the other concerning both QWIP and LED as
in Fig. 2b.
Fig. 2a. Relative transient response for constituent devices
approximation and exact response at ωb = 0.1 GHz.
Pole-Zero Map
Real Axis (seconds -1)
Im
ag
in
ar
y
A
xi
s
(s
ec
on
ds
-1
)
-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.120.240.380.50.640.76
0.88
0.97
0.120.240.380.50.640.76
0.88
0.97
0.20.40.60.811.2
Fig. 2b. P-Z Map for ωHBT = 0.1 GHz, ωQWIP = 1 GHz,
ωLED = 1.2 GHz.
Fig. 3. Output derivative for constituent devices approximation
and exact response at ωb = 0.1 GHz.
When there is no negative pole close to zero as in
Fig. 4a, there is no similarity in response among the
constituent devices with the response of all the structure.
This fact is clear in Fig. 4b, where the cutoff frequencies
concerning QWIP, HBT, and LED are close to each
other so they have the same and close behavior.
-1.4 -1.2 -1 -0.8 -0.6 -0.4 -0.2 0
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
0.120.240.380.50.640.76
0.88
0.97
0.120.240.380.50.640.76
0.88
0.97
0.20.40.60.811.2
Pole-Zero Map
Real Axis (seconds -1)
Im
ag
in
ar
y
A
xi
s
(s
ec
on
ds
-1
)
Fig. 4a. P-Z Map for ωHBT = 1.1 GHz, ωQWIP = 1 GHz,
ωLED = 1.2 GHz.
Fig. 4b. Relative transient response for constituent devices
approximation and exact response at ωb = 1.1 GHz.
Closest pole to zero
Time t, ns
O
ut
pu
t d
er
iv
at
iv
e,
n
s-1
QWIP Approximation
HBT Approximation
LED Approximation
Exact
QWIP Approximation
HBT Approximation
LED Approximation
Exact
Time t, ns
R
el
at
iv
e
re
sp
on
se
, R
(t
)
No pole close to zero
R
el
at
iv
e r
es
po
ns
e,
R
(t
)
Time t, ns
QWIP Approximation
HBT Approximation
LED Approximation
Exact
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 204-209.
doi: https://doi.org/10.15407/spqeo20.02.204
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
208
Also, the output derivative itself exihibits a
similar and close behavior as concerning QWIP, HBT,
and LED due to their nearby cutoff frequencies as clear
in Fig. 5. It is shown from the figure the output
derivative increases with time because it takes larger
time to reach its final value due to the overall delay time
through the layers of QWIP, HBT, and LED.
The final state value depends on the quantum
efficiencies of QWIP, HBT, and LED, where it is
assumed to be ηQWIP ηHBT ηLED = 1 in the proposed
model. When this final value increases the device needs
more time to catch it, hence the rise icreases as
illustrated in Fig. 6. It is shown that the cutoff frequency
plays a major role in controlling the rise time, also the
rise time behavior for HBT is again in close proximity to
the rise time behavior of all the structure. If the value of
cutoff frequency of HBT is increased to close the cutoff
frequency for both QWIP and LED, the rise time
behavior of the overall structure is quitely different from
the other constituent devices as illustrated in Fig. 7.
Fig. 5. Output derivative for constituent devices approximation
and exact response at ωb = 1.1 GHz.
Fig. 6. Rise time versus final state Sf ωb = 0.1 GHz.
Fig. 7. Rise time versus final state Sf at ωb = 1.1 GHz.
4. Conclusion and future work
Analytical modeling concerning the temporal behavior
of a quantum well structure optical integrated device has
been developed in this paper. The structure contains a
quantum well infrared photodetector to detect the signal,
a heterojunction phototransistor for amplifying, and a
light emitting diode for emitting visible light range. This
modeling is based on applying dominant pole
approximation scheme and convolution theorem. The
analytical expressions concerning all identities of
transient response are determined. The results show that
the transient behavior of the developed structure is in
close proximity with the constituent device which has
the smallest cutoff frequency. The quantum efficiency of
any constituent device causes an enhancement in the
transient response. Also, the constituent device with a
higher cutoff frequency has no effect on both the rise
time and the output derivative of the device. As a future
extension to this study, the use of a resonant cavity to
modeling this device is planned to show the effect of all
interesting parameters on its dynamic behavior.
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Time t, ns
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ut
pu
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iv
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QWIP Approximation
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Exact
Semiconductor Physics, Quantum Electronics & Optoelectronics, 2017. V. 20, N 2. P. 204-209.
doi: https://doi.org/10.15407/spqeo20.02.204
© 2017, V. Lashkaryov Institute of Semiconductor Physics, National Academy of Sciences of Ukraine
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|
| id | nasplib_isofts_kiev_ua-123456789-214931 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1560-8034 |
| language | English |
| last_indexed | 2026-03-21T13:44:50Z |
| publishDate | 2017 |
| publisher | Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України |
| record_format | dspace |
| spelling | Eladl, Sh.M. Saad, M.H. 2026-03-04T12:52:31Z 2017 Analysis of a quantum well structure optical integrated device / Sh.M. Eladl, M.H. Saad // Semiconductor Physics Quantum Electronics & Optoelectronics. — 2017. — Т. 20, № 2. — С. 204-209. — Бібліогр.: 11 назв. — англ. 1560-8034 PACS: 07.57.Kp, 85.35.Be, 85.60.Dw, 85.60.Jb https://nasplib.isofts.kiev.ua/handle/123456789/214931 https://doi.org/10.15407/spqeo20.02.204 This paper demonstrates theoretical modeling of a quantum well structure optical integrated device. The constituent devices of the developed structure are a Quantum Well Infrared Photodetector (QWIP) to detect the optical infrared signal, a Heterojunction Phototransistor (HPT) to amplify the signal, and a Light Emitting Diode (LED) to emit this signal in a visible form. The model is based on the transient behavior of the constituent parts of the structure. The dominant pole approximation scheme is used to reduce its transfer function. The convolution theorem is used to get the overall transient response of the device under consideration. All interesting parameters concerning the transient response, rise time, and output derivatives are theoretically investigated. The results show that the overall transient behavior, output derivative, and rise time of the considered structure are approximately the same as those of the constituent device possessing the lowest cutoff frequency. This type of model can be applied with high sensitivity in the upconversion of infrared or far infrared range for image signal processing. en Інститут фізики напівпровідників імені В.Є. Лашкарьова НАН України Semiconductor Physics Quantum Electronics & Optoelectronics Analysis of a quantum well structure optical integrated device Article published earlier |
| spellingShingle | Analysis of a quantum well structure optical integrated device Eladl, Sh.M. Saad, M.H. |
| title | Analysis of a quantum well structure optical integrated device |
| title_full | Analysis of a quantum well structure optical integrated device |
| title_fullStr | Analysis of a quantum well structure optical integrated device |
| title_full_unstemmed | Analysis of a quantum well structure optical integrated device |
| title_short | Analysis of a quantum well structure optical integrated device |
| title_sort | analysis of a quantum well structure optical integrated device |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/214931 |
| work_keys_str_mv | AT eladlshm analysisofaquantumwellstructureopticalintegrateddevice AT saadmh analysisofaquantumwellstructureopticalintegrateddevice |