Post on 23-Apr-2023
High performances III-Nitride Quantum Dot
infrared photodetector operating at room
temperature
A. Asgari1,2,*
and S. Razi,1
1Photonics-Electronics Group, Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163, Iran 2 School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Crawley, WA
6009, Australia
*asgari@tabrizu.ac.ir
Abstract: In this paper we present a novel long wave length infrared
quantum dot photodetector. A cubic shaped 6nm GaN quantum dot (QD)
within a large 18 nm 0.2 0.8
Al Ga N QD (capping layer) embedded in
0.8 0.2Al Ga N has been considered as the unit cell of the active layer of the
device. Single band effective mass approximation has been applied in order
to calculate the QD electronic structure. The temperature dependent
behavior of the responsivity and dark current were presented and discussed
for different applied electric fields. The capping layer has been proposed to
improve upon the dark current of the detector. The proposed device has
demonstrated exceptionally low dark current, therefore low noise, and high
detectivity. Excellent specific detectivity (D*) up to ~3 × 108 CmHz
1/ 2/W is
achieved at room temperature.
©2010 Optical Society of America
OCIS codes: (250.250) Optoelectronics; (250.0040) Detectors.
References and links
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1. Introduction
The most advanced III-V mid and long wavelength infrared (MWIR and LWIR) detectors, to
date, is the quantum well infrared photodetectors (QWIPs) which utilize intersubband or
subband to continuum transitions in quantum wells [1,2]. QWIPs have demonstrated excellent
imagery performance and also extremely uniformity across a large area, which increases the
pixel operability in a focal plane array without the reliance on correction algorithms needed
for MCT detectors. However, QWIPs require lower operating temperature, owing to their
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14605
higher thermionic emission rates. The operating temperature for QWIPs is lower than for
MCT detectors, because the thermionic emission in MCT, for equivalent device parameters,
is approximately five orders of magnitude less than in a QWIP [3]. Another serious drawback
is the fact that, the n-type QWIPs cannot detect normal incidence radiation, due to the
polarization selection rules [1]. Consequently, QWIPs require the addition of light couplers,
such as surface gratings, which add to the cost and complexity.
Recently, quantum dot infrared photodetectors (QDIPs) have been emerged as a potential
alternative to MCT and QWIPs [4–7]. The advantages of QDIPs, can mainly categorize in
three parts, (i) The three dimensional quantum confinement of the carriers, which results in
the δ -like density of states, and sensitivity to the normal incident radiation, without the use
of a grating or corrugations, as is often done in QWIPs [8–10], (ii) reduced electron-phonon
scattering, so long excited state lifetime, and high current gain [7, 11, 12]. (iii) The QDIP
technology is believed to be promising for high-temperature operations [13, 14].
In order to improve the performance of these detectors, different structures and materials
have been investigated [4–8, 15, 16]. It has been shown that a current blocking layer can be
effectively used to reduce the dark current. Lin et al. [15] and Stiff et al. [9, 17] have reported
QDIPs with a single AlGaAs blocking layer on one side of the InAs/GaAs QD layers. Wang
et al. [4] introduced a thin AlGaAs barrier layer between the InAs QDs. This layer filled the
area between the dots but left the top of the dots uncovered. An improvement in the
detectivity relative to similar devices without this barrier layer has been deduced in these
papers. On the other hand, in the last few years, the III-nitride QDs have been extensively
studied for their potential use in transistors, lasers and light emitting diodes [18–20]. GaN and
its alloys with AlN have strange properties such as larger saturation velocity, wide band gap
and higher thermal stability, in comparison to the usual and prevalent III-V materials. But
unfortunately, they still suffer from a certain lack of knowledge in terms of fundamental
material parameters, and they are in their early stage. Here we tried to investigate special kind
of QDs with these materials. The Eigen functions, Eigen values, oscillator strength and other
physical parameters calculated in the first stage. Then, the detector parameters such as
responsivity and dark current were evaluated precisely, by considering their temperature
dependence. Specific detectivity used as figure of merit, and its peak was calculated at
function of temperatures for different applied bias.
2. Model derivation
To model the device, a cubic shaped 6nm GaN QD within a large 18 nm 0.2 0.8
Al Ga N QD
embedded in 0.8 0.2
Al Ga N layer is assumed. The proposed structure has been shown in Fig. 1.
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14606
Fig. 1. The proposed cubic shaped GaN QD within a large 0.2 0.8
Al Ga N QD.
Five layers with QD density of 24 310Nd m−= are used as active region of the device. We
have assumed the large QDs are very close to each other.
In order to study the electronic structures, different methods have been experienced
[21–24]. The single band method is used in this study. In the frame work of the envelope
function, and the effective mass theory, the Hamiltonian can be written as [22]:
2
*
1( , , ).
2 ( , , )H v x y
m x y
−= ∇ ∇ +ℏ
zz
(1)
In which *m is the electron effective mass and is given by:
( )0.2 0.8
0.8 0.2
*
*
*
, , ,
GaN
Al Ga N
Al Ga N
m in QD
m x y m in capping layer
m in barrier
∗
=
z
(2)
and
( )0
, , .c
inside GaN QDV x y
E else
=
∆z (3)
Wherec
E∆ is the conduction and valance bands discontinuity [25]:
0.7( 6.13 (1 ) 3.42 (1 ) ) ,0
E x x x x E eVc g∆ = × + − × − − − (4)
where x notifies Al molar fraction and is considered 0.2 in our calculations for capping layer
and 0.8 for the barrier.
As the system needs an applied electric field to operate and also has a strong built in
electric field, one has to take into account the total fields effect in the Hamiltonian:
2
*
1( , , ) .
2 ( , , )H v x y e F r
m x y
→ →−= ∇ ∇+ +ℏ
zz
(5)
Where F→
denotes both the external and built in electric fields. It should be mentioned that
III- nitrides in the wurtzite phase have a strong spontaneous and piezoelectric polarization.
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14607
The abrupt variation of the polarization at the interfaces gives rise to large polarization sheet
charges which creates the built-in electric field. Therefore, the optical properties of wurtzite
AlGaN/GaN QDs are affected by the 3D confinement electrons and the strong built-in electric
field. This causes the simulation of the systems extremely challenging task.
The Built in electric field which applied in the equations is [26]:
0
( ).
( )
br d
br tot tot
d
d br br d
L P PF
L Lε ε ε−
=+
(6)
Where ( )br d
ε is the relative dielectric constant of the barrier (dot), /br d
totP is the total
polarization and /br d
L is the width of the barrier and height of the dot.
/ / /
.br d br d br d
tot pie o spP P P= +
z (7)
The Piezoelectric polarization includes: one part induced by the lattice mismatch (ms), and
the other caused by thermal strain (ts): / / /br d br d br d
pie o ms tsP P P= +
z, where
/ 13 0
31 33
33
2( )( )br d
ms
c a aP e e
c a
−= − and 4 23.2 10 /d
tsP c m−= − × [26].
31e and
33e are the
piezoelectric coefficients, 13
c and 33
c are elastic constants, and ‘a’ is the lattice constant of
1x xAl Ga N− and is
o
(0.077 3.189) Aa x= + . (All other material parameters can be found in
[27]).
The spontaneous polarization for 1x x
Al Ga N− is Al molar fraction dependent and is given
by: ( 0.052 0.029)sp
P x= − − .
To solve the Schrödinger equation, assuming that the wave functions are expanded in
terms of the normalized plane waves [22]:
( ) ( ), , , ,
, ,
1, , exp . . . .nx ny n nx ny n nx ny nz
nx ny nx y
x y a i k x k y kL L L
ψ = + +∑z z
zz
z z (8)
wherenx x x x
k k n K= + ,ny y y y
k k n K= + , nz
k k n K= +z z z
and 2
x
x
KL
π= ,
2y
y
KL
π= ,
2K
L
π=z
z
.
,x y z
L L and L are lengths of the unit cell along the x, y and z directions. , ,x y
n n nz are the
number of plane waves along the x, y and z directions respectively.
As reported in [28], the attraction of the normalized plane wave approach is the fact that
there is no need to explicitly match the wave function, across the boundary of the barrier and
QD. Hence this method is easy to apply to an arbitrary confining potential problem. As more
plane waves are taken, more accurate results are achieved. We used thirteen normalized plane
waves in each direction to form the Hamiltonian matrix (i.e. , ,x y
n n and nz from −6 to 6) and
we formed 2197*2197 matrix. It was found that using more than 13 normalized plane waves
in each direction takes significantly long computational time and only about 1 meV more
accurate energy eigenvalues. By substituting the Eq. (8) in Schrödinger equation,
eigenfunctions and eigenvalues are calculated. The energy Eigenvalues of the considered
structure have been demonstrated in Fig. 2.
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14608
Fig. 2. Energy diagram for the proposed structure and the strongest transition ‘a’.
The transition matrix element, | |if i fr rψ ψ→
=< > can be calculated using obtained wave
functions. In this relation i f
andψ ψ are the initial and final transition states, respectively.
The oscillator strength, if
f , of a given transition is one of the most important factors in the
absorption coefficient ( )α ω and is given by:
( )2
2
2,ifif i f
mf E E r
∗ →
= −ℏ
(9)
where i
E and f
E are the initial and final transition state energy, respectively.
The absorption coefficient can be expressed as [16]:
( )
2
* 22
0
( ) ,d op
i f if
if
N n en n f
m c
πα
εε ω ω
Γ= −
− +Γ
ℏ
ℏ ℏ
(10)
where Γ is the life time broadening which is considered 33 10−× eV . Nd is QD volume
density, op
n is refractive index, 0
ε and ε are the permeability of free space and the medium,
respectively. i
n and f
n are the occupation probabilities of the initial and final states. The
occupation probability can be defined as:
/
,/ /
( ) ( )/
B
B B
E k Tie
niE k T E k T
s te e d f Nd
s tc
ερ ε εε
−=
− − + +∑ ∑ ∫
(11)
where s
E is the quantum dot energy levels, ( )ρ ε is the density of continuum states, B
k is
Boltzmann constant, and t
E is the trap levels. For the low temperatures, 1i
n ≈ and 0f
n ≈
and the specific transition is high, but with increasing the temperature, the carriers
redistributed and the transition decreases.
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14609
Fig. 3. The behavior of absorption vs. the photon energy for different GaN QD sizes at T=77 K
(the QD sizes are Lx=Ly, and Lz=3nm).
Figure 3 indicates the behavior of optical absorption of the structure with different QD
size for the transition indicated as “a” in Fig. 2. It is obvious that by increasing the size of
QD, the peak of the absorption increases and there is a red shift which can be related to
increasing of the oscillator strength, and decreasing of the energy levels difference,
respectively.
As long as there are unoccupied excited states available, the electrons in the lower states
can participate in photon induced intraband transitions. However, with further increasing of
the temperature, the electrons occupy the excited states and consequently the absorption
coefficient decreases and dark current increases. It should be mentioned that the strongest
photonic transitions are usually the ones which are energetically directly above each other,
with an s-symmetry to p-symmetry change and in our calculation the “a” transition not only
are in the range of 8-12 µm, but also is a transition from a state with s-symmetry to p-
symmetry.
3. Results and discussion
The insertion of the capping layer is supposed to change the transport properties of the
carriers. In this paper, we introduce a structure, which has a low dark current and high
responsivity and therefore have a good signal to noise ratio. The main parameters of the
detector which discussed in this paper by details are the device responsivity, dark current and
detectivity.
3.1 Responsivity
The responsivity is one of the most important parameters of the photodetectors and defined as
the ratio of its output electrical signal, either a current out
I or a voltageout
V , to the input
optical signal. It is given by
,e
R gηω
=ℏ
(12)
Where g is the gain and defined as the ratio of the recombination time over the transit time:
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14610
be
Fg
LC
µ=
where Cbe is the quantum mechanical capture rate into the QD excited state. Estimates for the
Cbe in the literatures, are in the range of 11 12~ 10 10− Hz for shallow excited states, which are
reachable by acoustic phonon emission, and is about 10~ 10 Hz for deep levels [16]. µ is the
mobility of the electron, which has been successfully demonstrated in our previous work by
considering all scattering mechanisms, and the effects of temperature and electric fields [29].
η is the quantum efficiency and is defined as:
( ) /
( ) /0
( ) ,E F k Tec B
ecE F k Tec B
ec
eL
e
νη α ων ν
−
−
= +
(13)
Here 0
ν is the relaxation rate from the photo excited state to all other states and here
considered 10~ 10 , L is the device length, Eec
is the effective field dependent energy difference
between the photoexcited state and the continuum, ec
ν is phonon assisted escape to
continuum prefactor and expected to have only a weak dependence on the temperature and in
this paper is considered 13~ 10 . The temperature dependent normalized responsivity (R/R0) at
different applied electric field are calculated and plotted in Fig. 4:
( ) /
/ .0 ( )/
0
B
B
E F k Tece
ecR R n Fi E F k Tece
ec
υ
υ υ
− = − +
(14)
Fig. 4. The responsivity of GaN QDIP (the QD sizes are Lx=Ly=10nm and Lz=3nm) as a
function of temperature for different applied electric field.
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14611
Fig. 5. The normalized responsivity of GaN QDIP (the QD sizes are Lx=Ly=10nm and
Lz=3nm) as a function of the external electric field for different temperatures.
As shown in Fig. 4 with increasing the temperature until 100-170K the responsivity
increases and further increasing of the temperature decreases the responsivity. To explain this
effects, as can be deduced from the relation (12), there are two main sources for temperature
dependence of the responsivity; current gain, and quantum efficiency. So, the increasing of
the temperature increases the current gain as well the responsivity. With further increasing the
temperature i
n starts to decreasing, therefore the absorption coefficient and quantum
efficiency decreases and it make a reduction in the responsivity.
Also, the logarithm of the normalized responsivity versus applied fields for different
temperatures has been illustrated in Fig. 5. We have not considered the temperature
dependency of the life time 0
1/ ( )Tν and assumed it as a constant. As shown in this figure,
with increasing the applied electric field the responsivity increases. The reason for this
behavior is that the increasing of the applied bias increases significantly the current gain as
well as the photocurrent.
3.2 Dark current
In the absence of any incident light and the existence of applied fields there is an unwanted
electrical current which is well-known as dark current. At high temperature range, the dark
current originates from thermionic emissions and for low temperatures, sequential resonant
tunneling and phonon-assisted tunneling are probably the dominant components of the dark
curve. This important parameter has been discussed in several articles [4,5,9].
Considering the most important factors dark current could be written as [30]:
3/ 2 1/ 20 / / /
1/ 2/
.(1 )
11(1 )
E k T E eFa E eFa k Tsc B sc sc Bs s
scE eFa k Tsc ss sc B
e be
Ae FN g f e e e edIdark n C w fe be e e
n C
ς ς
ς
µυ
− − −
−
−= ×
−−+
−
∑ (15)
In this relation s
f is the Fermi function for the s'th energy state, A is the illuminated area of
the device, (1 )e
n− is the probability that the state is empty. SC
w is the escape rates between
the band and QD states,
1* 2
2
2e
maς
= ℏ
, and S
g is the density of excited states. Considering
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14612
0
0 (1 )
Ae FNd
I gec sn C
e be
µυ=
−, the logarithm of the normalized dark current
0
darkI
I
versus applied bias
for different temperature has been plotted in Fig. 6. As depicted in figure, at low temperature
the dark current increases rapidly as the bias increases. This can be attributed to the fast
increase of electron tunneling between the QDs. With increasing the bias, the electron density
increases in QD and when a large fraction of the QD states are occupied, further increase in
bias does not significantly alter the electron density. This causes a lowering of the energy
barrier for injected electrons at the contact layers, which results in the nearly exponential
increase of the dark current. Also it should be mentioned that the activation energy decreased
linearly with bias. At high bias, the activation energy is close to ~kT, which resulted in high
dark current even at low temperature.
It should be mentioned that the proposed structure has a very low dark current in
comparison to the structures introduced in Ref [16, 30, 31]. It can be deduced from the
relations, where the high values for Cbe not only will decrease the gain, but also the dark
current. So, structures with high densities of QDs might be useful and have a better
performance in suppressing the dark current effects. Having high densities of QDs has
another benefit. It gives hope to engineering the band structure in order to enhance the
tunneling of the photoexcited carriers from the large dots (capping layer). Therefore we can
have high barriers in order to suppress the thermionic term in dark current without having
presentiment about collecting the photoexcited carriers.
Fig. 6. The dark current vs. external electric field for GaN QDIP (the QD sizes are
Lx=Ly=10nm and Lz=3nm) at different temperatures.
3.3 Detectivity
The detectivity is one of the most important factors of detectors and is considered as figure of
merit in most of the literatures. Specific detectivity, is defined as
.R A fresponsivity A
Dnoise i
Nf
∆×∗= =
∆
(16)
In this relation N
i is the noise current and defines as 4i eI g fN d
= ∆ , f∆ is the band width
frequency and we considered it ~ 1 .
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14613
As mentioned before, with increasing the temperature the dark current increases, thus the
responsivity decreases and these behaviors will affect the detectivity. For a given applied bias
and temperature, the responsivity in our proposed structure lower than the other structures
without capping layer. On the other hand, the dark current is much lower in our proposed
structure. This may because an enhancement in impact ionization, which is enabled by the
increased operating voltage that results from the lower dark current [15].Consequently, a net
improvement in the signal to noise ratio is expected. The specific detectivity as function of
temperature for different applied bias are shown in Fig. 7.
The results are representative of high values for specific detectivity in compared to
structures which have been studied previously. Xuejun Lu et al reported in [32], Peak specific
photodetectivity D* of 93.8 10× 1/ 2 /cmH Wz and 81.3 10× 1/ 2 /cmH Wz at the detector
temperature T = 78K and T = 170 K, respectively. Zhengmao Ye give an account that for the
photoresponse peaked at 6.2 mm and 77 K for −0.7 V bias, the responsivity was 14 mA/W
and the detectivity, was 1010 1/ 2 /cmH Wz [33]Bhattacharya et all, reported the some deal
high detectivity, about 6 1/28.6 10 /cmH W× z , in 17 mµ wave length for 300k temperature
[34] and in the other work they reported 9 * 1/2 116 10 ( / ) 10D CmH W× ≤ ≤z for
temperatures100 200K T K≤ ≤ [18,22]. Here we present appropriate results in comparison
and the device which introduced has a good potential to be compared with the structures, have
been presented in [34,35].
Fig. 7. The peak of specific detectivity versus temperature for GaN QDIP
(the QD sizes are Lx=Ly=10, and Lz=3nm) in applied bias of 1 V.
4. Conclusion
As stated in this paper and detailed in numerous publications, owing to their unique material
characteristics, III-N QDIPs have the potential for superior performance as infrared detectors
in the LWIR. In this article we report on the photodetector characteristics related to QDIPs.
The amount of the dark current which calculated is exceptionally perfect and the specific
detectivity of the devise is appreciable in high temperatures, even room temperature.
Therefore the proposed structure will be considered a proper alternative to the mature
technologies that have been widely deployed. The structure studied is sufficiently general, so
covers a large rang of possible device types. Due to better 3-D confinement of carriers,
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14614
operating in higher temperatures was observed. High density of QDs was suggested to solve
the collecting difficulties of the carriers. Also the results indicate that there is hope for band
structure engineering for further improve of the detector parameters at high temperatures.
#127291 - $15.00 USD Received 20 Apr 2010; revised 27 May 2010; accepted 15 Jun 2010; published 23 Jun 2010(C) 2010 OSA 5 July 2010 / Vol. 18, No. 14 / OPTICS EXPRESS 14615