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Doping dependent frequency response of MQW infrared photodetector
Accepted Manuscript Doping Dependent Frequency Response of MQW Infrared Photodetector
Aref Billaha, Mukul K. Das, S. Kumar PII:
S0749-6036(16)31328-3
DOI:
10.1016/j.spmi.2017.02.018
Reference:
YSPMI 4830
To appear in:
Superlattices and Microstructures
Received Date:
18 November 2016
Revised Date:
10 February 2017
Accepted Date:
12 February 2017
Please cite this article as: Aref Billaha, Mukul K. Das, S. Kumar, Doping Dependent Frequency Response of MQW Infrared Photodetector, Superlattices and Microstructures (2017), doi: 10.1016/j. spmi.2017.02.018
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ACCEPTED MANUSCRIPT
Doping, MQW, Transit time, Bandwidth, Responsivity
ACCEPTED MANUSCRIPT
Doping Dependent Frequency Response of MQW Infrared Photodetector 1,2,3
Md. Aref Billaha1, Mukul K. Das2, Senior Member, IEEE and S. Kumar3 Dept. of Electronics Engineering, Indian Institute of Technology (ISM) Dhanbad, India. [email protected], [email protected]
Abstract— This work is to study the effect of doping concentration in the active layer on the performance of multiple quantum well (MQW) infrared photodetector based on inter subband transitions. A theoretical model for the photocurrent and hence, responsivity of the detector in frequency domain is developed considering the effect of doping dependent absorption and carrier capture at the hetero-interfaces. Transit time and capture time limited bandwidth of the detector is computed from the frequency dependent photocurrent. Results show that, besides the usual effect of capture time, doping concentration in the active layer has an important effect on the bandwidth and responsivity of the device particularly for high value of capture time. KeywordsResponsivity.
Doping,
I.
MQW,
Transit
time,
have not yet been explored in detail by researchers. Position dependent intensity of infrared radiation is another important aspect needs to be considered for accurate analysis of the performance of the device. Effect of doping concentration on the absorption of inter sub-band transition in AlGaAs/GaAs QWIP has already been studied and reported by the authors elsewhere [29]. In this paper, physics based theoretical model for frequency response of MQW infrared photodetector is developed considering the effect of doping on absorption coefficient, effective band offsets, carrier capture etc. Variation of the performance parameters like responsivity, bandwidth and responsivity-bandwidth product with doping are studied. Rest of the paper is organized as follows. In section II, the detail calculation of the photocurrent and hence, responsivity in frequency domain is described. Simulation results are discussed in section III and finally, in section IV, the conclusion of the study is given.
Bandwidth,
INTRODUCTION
Infrared photodetector has attracted a lot of interest among researchers due to their wide-ranging and rapidly expanding applications such as medical science, military (e.g., navigation, night vision, weapons detection), environment monitoring and free space optical communication [1-2]. Such applications require detector having high sensitivity to the infrared incidence [3-4], low dark current [5-6] and high speed of operation [7]. Quantum well infrared photodetector (QWIP) using inter-subband photo-excitation meets such requirement over conventional detector and it has already been demonstrated by researchers [8-10]. HgCdTe has proved its capability to be used for infrared detector [11]. But, HgCdTe based detector is not preferred, for long wavelength infrared region (LWIR) detection in particular, because of difficulty in controlling material composition of HgCdTe. Moreover, HgCdTe devices are very much sensitive to the defects and surface leakage [11]. Recently, GaAs-based multiple quantum well (MQW) infrared photodetector (IP) is one of the most promising infrared detector because of its wide applications specially in infrared imaging at LWIR [12-15]. It has some other advantages also, like easy wavelength adjustment, high thermal stability etc. [16-19]. Carrier dynamics e.g., capture and escape of carriers into and from the quantum well play important roles for the high frequency performance of such devices. Theoretical and experimental studies on the performance of III-V based AlGaAs/GaAs IP considering those aspects have already been done by researchers in recent times [20-28]. To the best of authors knowledge, some of the important aspects like doping concentration dependent Eigen energy states and hence, wavelength of operation, doping dependent density of states and, hence, absorption coefficient
II.
DEVICE STRUCTURE AND EQUATION OF THE MODEL
Schematic structure of GaAs/AlxGa1-xAs MQW infra-red photodetector, considered in our analysis, is shown in Fig.1. It is formed by alternate layer of GaAs well and AlxGa1-xAs barrier on semi-insulating GaAs substrate. GaAs layer is considered to be the active layer and is doped with Si donors. Barrier layer of AlxGa1-xAs is considered to be the un-doped. Width of the GaAs top and bottom contact layers are considered as 0.7µm and 0.5µm respectively and are doped with 2 x 1018 cm-3 Si donors. On incidence of light on the device, carriers are generated and these photogenerated carriers, after transport through several hetero-interfaces, are collected by the contacts. Now, the normal incidence is not capable to cause inter sub-band transitions in quantum well structure as per the selection rule. So, the light is assumed to be incident on the detector at an angle () of 45° with the growth axis (z) as shown in Fig.1. Moreover, it is important to mention here that width of the well and barrier layers, doping in the well and mole fraction of Al (x) are chosen in such a way that there exist only one bound state and one quasi-bound state in the well. Under this condition, the highest energy state is almost aligned with top of the barrier. To determine the high frequency response of the device, it is important to consider the aspects of carrier transport including its capture and escape at each of the heterointerfaces. Fig. 2 illustrates the mechanism of carrier transport within the device. In our model, we have assumed that at
1
ACCEPTED MANUSCRIPT steady state, the carriers (only electrons here) are injected from emitter to the first quantum well by tunneling due to high electric field. Out of these injected carriers, some are captured into the bound state and rest of them is transported into the next barrier. Now, photo excitation of electrons is only process of escape of electrons from bound state to quasi-bound state. Capture and escape of carriers occur at each hetero-interface and capture probability entirely depends on the capture lifetime of electrons which is assumed to be same for all wells. But, photo-excitation and hence, escape is position dependent. Intensity of the incident infrared radiation is considered to be decayed exponentially with z. Although the electrons are generated in all wells at the same time due to the incident radiation, photo-generated electrons from different wells arrive at contact layers in different times depending on the position of the well where they are generated. Continuity of the drift current across the multiple quantum wells in the steady state condition is provided by the electron injection from the emitter contact layer which has already mentioned in the beginning of this section. It may be mentioned here that the escape of the carrier due to thermionic emission is negligible since the device is considered to be operating at low temperature.
i-AlxGa1-xAs
N+-GaAs (Collector)
AlxGa1-xAs
N-GaAs M
z direction 2 LB
Lw
1 45°
L1
N+-GaAs (Emitter)
z=0
Substrate
hν Fig. 1: Schematic layer structure of a GaAs/AlxGa1-xAs MQW infrared photodetector. 1,2….M shows the number of QWs. Widths of the well and the barrier layer are respectively denoted as Lw and LB .
Considering the above facts theoretical model for frequency response of the device is developed as follows. Injected electron current density (je) from emitter to the first QW depends on the applied bias and doping concentration in the emitter layer and is given as [30]
je jm e
Et Ee
(1)
where, jm is the maximum emitter current density which is generally dependent on the doping concentration. This can be estimated from the equation governed by jm~qN3d,eF where q is the charge of an electron, N3d,e is the doping concentration of the emitter, F is the electron Fermi velocity, Et is the characteristic tunneling electric field for the emitter barrier, Ee is the electric field in the emitter barrier with z 0 0 and
z W
Fig. 2: Schematic diagram of the conduction band where carrier transport processes are illustrated.
nqw t
applied bias voltage). Ee can be expressed as [30]
nqw
Nd
tr j nqw I q cap
(3)
where, cap is the capture lifetime of electrons, tr is the transit time of electrons, is the photo-excitation cross section, j is the current density, I is the intensity of the incident photon infrared radiation. The term I and nqw are expressed as
V , (here, is the electrostatic potential and V is the
Ee E MEd 1
(2)
nqw ( z , t ) nqw,0 nqw ( z , t ) and I ( z , t ) I 0 I ( z , t )
where, E is the average electric field, E=V/W, where W is the total length of the MQW photodetector i.e. W=(M+1)L (here, L is the length of one quantum well period i.e. L=LB+Lw and M is the number of quantum wells), Nd is the doping sheet concentration which can be calculated from the relationship Nd=NLW (here, N is the doping concentration in the active layer), nqw is the electron sheet concentration in the QW, and Ed 2 qN d æ , where æ is dielectric constant. Value of æ
where, nqw,0 is the steady state electron sheet concentration, I0 is the steady state value of intensity of infrared radiation. The small signal component, I(z,t) and nqw(z,t) can be expressed as
nqw ( z , t ) nqw, eit and I ( z , t ) I e jL e L ( j 1) L w
1
B
jLw z
eit
(4)
I ' eit
in well material is used in the calculation.
where, nqw, and I are respectively the small signal components of electron sheet concentration and intensity of
The rate equation for the bound states electrons in the quantum well (QW) is given by
2
ACCEPTED MANUSCRIPT infrared radiation modulated with modulation frequency , L1 is the distance of the nearest well from the front of the emitter contact layer. is the absorption coefficient. The calculation of absorption coefficient for GaAs/AlGaAs bases QWIP has already been reported by the authors elsewhere [29].
je
qN d
1 cap
(9) s
E 2 I where s M I 0 d ln m Et I0 1 cap jm
Now, the ratio of tr /cap can be considered as (1-cap), which indicates probability of electron capture at the barrierwell interface i.e. cap define the effectiveness of the electrons transfer over the barrier which are not captured at the barrierwell interface. The second term in the right hand side of the equation indicates the electrons are emitted due to photoexcitation which is considered to be the dominating process of escape of carriers from the well.
and I m
1
(10)
qN d
where, s is the characteristics time of the quantum well filling due to the steady state injected current density from the emitter.
Since, the carrier generation does not occur in the continuum states and also no recombination take place within the states. Considering the above assumptions, the continuity equation for the continuum states over the barrier can be expressed as
Therefore, the additional injection of current density increases the carrier concentration near the emitter which can be found from the following formula
n( z , t )
Small signal analysis of n(z,t) in the continuum states can be calculated from Eq. (5) and is written as
t
e
n( z , t ) z
0
n( z , t )
(5)
at z 0
n ( z )
je / qe
i
(11)
where n(z, t) is the electron concentration in the continuum states, e is the drift velocity of an electron and J (z, t) is the electron current density and can be written as J ( z , t ) q e n ( z , t ) . The term n(z, t) can be expressed as
In the region 0 z L1 ; applying boundary conditions at z=0
n( z , t ) n0 n( z , t )
& z = L1, small signal current density at the barrier-well hetero-interface (je) can be written as
where n( z , t ) n e
i t
z
(6)
je1
where, n0 and n are the steady state and small signal components of electron concentration in the continuum state.
qN d I 0 1 cap
dje dEe
Ee
n ( z ) 0
q nqw,
1 cap s
e
i tr
(12)
(13)
The small signal component, nqw, in the above equation can be calculated from rate equation given in Eq. (3) at the barrierwell hetero-interface. The solution of the small signal analysis of Eq. (3) is obtained as
(7)
nqw,
Now, infinitesimal change of the electric field in the emitter results in an increase of the injected current density at the emitter and is given by [26, 31]
je
e
where tr = L1/e
At steady state condition, the value of I is zero and solution of Eq. (3) in the emitter contact layer gives steady state current density at z=0 i.e. j0 = j|z=0 which coincides with je and after detail calculation, it can be expressed as
j0
nqw,0 I ' i I 0
1
s
e
(14) i ttr
Current in the well-barrier interface has two parts, one is due to the carriers from previous barrier after surviving loss due to capture in the well {process 2 in Fig. 2}. Other part is due to photo-excitation in the well. This approach is applied below to calculate photocurrent in a well {process 3 in Fig. 2}. In the region; L1 ≤ z ≤ Lw, current density in the 1st QW is due to the injected current coming from the emitter after survival loss due to capture. This can be written as
(8)
where dje/dEe is the differential conductivity of the emitter barrier. Using Eq. (1), Eq. (2), Eq. (7) & Eq. (8) is solved considering Nd ~ nqw, after detail calculation,
jw11, cap je e
i ttr
(15)
Now, the photocurrent in the quantum well is due to the photo excitation may be calculate from Eq. (3) by considering cap=
3
ACCEPTED MANUSCRIPT where ћω is the incident photon energy. Using Eq. (19), Eq. (21) & Eq. (22), one may get final expression of responsivity and is obtained as
0 (since there is no loss in this case) and nqw t 0 . So, the photo-excitation current at the end of a well (well-barrier interface) is obtained as
jw12, q ( nqw, I 0 nqw,0 I ' )
R
(16)
1 e
R0 i tr
cap
1st
Applying boundary condition at z =L1+Lw for the quantum L well (i.e. j=1), then Iꞌ can be written as I ' I e
L M 1 i ( M 1) cap e e 2 ei 1 cap i s M jL i M j i ( M j ) cap e e i s 1 cap e j 2 i ( M 1) x e 1 tr
w
and put the value of I' in Eq. (16), one may obtain (17)
w
The calculated current (jc1,) at the collector of the 1st quantum well considering L1 and LB are of equal barrier width and it is given as
cap je e q jc1, je1 e e L ( nqw,0 I e nqw, I 0 ) i tr
i z
where, = L/e R0
i z
e
w
tr
w
jw12, q ( nqw, I 0 nqw,0 I e L )
I 0 s i s i ( M 1)
tr
q nqw ,0
(23)
tr
.
(18)
e
w
Now, the above current is appeared at the barrier-well interface of 2nd QW and the current for 2nd quantum well can be determined similarly as was calculated in the 1st QW providing boundary condition at z=L1+2Lw+LB and j=2 for the 2 L 2nd quantum well i.e. I ' I e . w
Continuing the above carrier transport process for the Mth QW, the final expression of the photocurrent density (jcM,) can be obtained as
jcM ,
q nqw,0 I
1 e cap
i tr
I 0 s i s
Fig. 3: Electric field spatial distributions in QWIP.
L M 1 i ( M 1) cap e e 2 ei 1 cap i s i z M e jL i M j i ( M j ) 1 e e e i cap cap s j 2 tr
w
tr
e
w
tr
III. RESULTS AND DISCUSSION
tr
To study the frequency dependent responsivity of the QWIP, we need to calculate the absorption coefficient which again requires determination of Eigen energy states and wave functions. Detail calculation of absorption coefficient has already been reported by the authors elsewhere [29]. It is observed in our previous study that peak absorption coefficient and corresponding operational wavelength of QWIP strongly depend on the doping concentration in active well layer. The calculation of doping dependent absorption coefficient is considered in this model to calculate responsivity in frequency domain using eqn. (23). In this calculation low field velocity of electron, which again depends on electric field, is considered. Position dependent electric field, as shown in Fig.3, inside the device is considered in this calculation. It is seen that the distribution of electric field is non uniform mainly for first 3 to 4 QWs and is uniform thereafter. Moreover, values of material parameters are very important to calculate R. Values of some important material parameters for GaAs and AlGaAs, used in this calculation, are summarized in Table I for quick reference. Device parameters
(19) where, nqw,0 can be calculated from the following relation given in [32]
nqw,0
Lw
(20)
The small signal component of the total current density can be determined from the following formula
J
A W
W
j
cM ,
dz
(21)
0
Now, small signal responsivity (R) can be obtained from the following expression
R
J A I
(22)
4
ACCEPTED MANUSCRIPT are chosen in accordance with the fabricated structure reported in literature [13]. Width of the well layer (Lw) is taken as 5.2nm and is doped with 5 x 1017 cm-3 Si donors. Width of the barrier layer (LB) is taken as 30nm and the incident optical power (Pinc) is assumed to be 1mW. The device is considered to be of mesa structure with an illumination area (A) of 200x200 µm2. The incident photon of infrared radiation (I0) is calculated from the relation [33], I0=Pinccos()/Aћω. The value of is taken as x10-15 cm2 and so, the calculated Et is 573kV/cm and jm is 1.3x106 A/cm2. The low field velocity of electron is calculated from e= µE /(1+( µE/ s)). Electron mobility (µ) is taken as 1000 cm2V-1s-1 and temperature dependent saturation velocity (s) is taken as 7.2x106 cms-1 at T=300K which are in accordance with some measured values reported in literature [32,34-36]. Saturation velocity, s at T=77K, is calculated using the relationship [35], s(T)= s(300K)/((1-AGaAs)+AGaAs(T/300K)) where, AGaAs is the coefficient at T=77K. Value of this coefficient is taken as 0.44 to calculate s(77K).
(a)
Table I Some material parameters of GaAs and Al0.26Ga0.74As used in calculation at T=77K: Material
Effective mass of electron, me
Band Gap (Eg, eV)
GaAs
0.067 [37]
1.5076 [37-39]
Al0.26Ga0.74As
0.0886 [40]
1.8329 [37-38]
Responsivity in frequency domain is plotted for different values of doping concentration (N) in the active layers for a fixed value of capture time, cap=5.5ps and is shown in Fig. 4(a). The responsivity calculated here is always based on the peak value of absorption coefficient and hence responsivity shall always mean peak responsivity throughout the discussion in this section. It is seen from figure that the responsivity increases with increasing doping concentration. This is mainly due to the enhanced absorption at high doping concentration. It is also observed from the figure that 3-dB bandwidth decreases with increasing doping concentration but insignificantly. For example, bandwidth is changed from 74.4 GHz to 73.6 GHz with the increase in doping from 1.2x1017 cm-3 to 1x1018cm-3. However, the bandwidth decreases with doping significantly for high value of capture time which can be seen from Fig. 4(b) where the responsivity is plotted as a function of doping for cap=11ps. In this case, the bandwidth decreases from 73 GHz for a doping of 3.2x1017 cm-3 to 70.8 GHz for doping concentration of 1x1018 cm-3. The reason behind such variation can be explained as follows. With increase in doping in the active layer, the characteristic time (s) for quantum well filling is increased. Now, s and cap have combined effect on the photocurrent as seen from Eq. (23). In case of low capture time for a fixed transit time, s has less significant role whereas, for high value of capture time, effect of s is more significant. Thus, effect of doping on
(b)
Fig. 4: (color online) Variation of responsivity as a function of frequency for different doping concentration of a 20 periods GaAs/ Al0.26Ga0.74As QWIP: (a) cap= 5.5ps and (b) cap= 11ps. bandwidth is significant for high value of capture time. For better understanding, the variation of 3dB bandwidth with doping concentration is presented in Fig. 5. It indicates the 3dB bandwidth decreases nonlinearly with doping concentration for high value of capture time. So, it is important to select the optimum doping concentration for enhanced bandwidth of the device. However, there is a tradeoff between the variations of bandwidth and responsivity with doping. So, the performance of the device is truly being judged if the responsivity-bandwidth product is studied with the variation of doping in the active layer. Doping dependent responsivity-bandwidth(R-BW) product for different values of capture time is shown in Fig. 6. It is seen from the figure that the product increases non-linearly with increase in doping concentration. It is due to the dominant effect of doping on the responsivity.
5
ACCEPTED MANUSCRIPT wells is also important to study. A variation of R-BW product as a function of number of quantum wells for different doping concentrations in the active layer is given in Fig. 8. From figure, it is observed that the R-BW product is almost invariable with M for low values of doping. But for the higher value of doping, the R-BW product decreases linearly with the M. So, the R-BW product is greatly affected by number of wells at high value of doping concentration. So, the choice of the doping concentration in the active layer and number of wells is important to obtain optimized performance of the device.
Fig. 5: (color online) Variation of 3dB Bandwidth as a function of doping concentration for different capture time of a 20 periods GaAs/ Al0.26Ga0.74As QWIP.
Fig. 7: (color online) Variation of 3dB bandwidth and responsivity as a function of doping concentration for different number of quantum wells of a GaAs/ Al0.26Ga0.74As QWIP.
Fig. 6: (color online) Variation of responsivity-bandwidth product as a function of doping concentration for different capture time of a 20 periods GaAs/ Al0.26Ga0.74As QWIP. Usually, large number of QW layers in infrared detectors is recommended to obtain significant photocurrent at low intensity of infrared radiation. So, it is important to observe the effect of doping on the 3dB bandwidth for large number of QWs. Fig. 7 shows the variation of 3dB bandwidth and responsivity as a function of number of QWs (M) for different values of doping concentration. From the figure, it is seen that the 3dB bandwidth changes from 119.4GHz to 115.4GHz for the change in doping concentration from 1.2x1017 cm-3 to 10x1017 cm-3 for M =12. But lesser effect is observed for higher values of M. It is also observed that variation of responsivity with M is nonlinear for all values of doping concentration. Variation of R-BW product with the number of
Fig. 8: (color online) Variation of responsivity-bandwidth product as a function of number of quantum wells for different doping concentration of a GaAs/ Al0.26Ga0.74As QWIP.
6
ACCEPTED MANUSCRIPT
Fig. 9: (color online) Variation of responsivity-bandwidth product for different capture time of a GaAs/ Al0.26Ga0.74As QWIP.
Fig. 10 (b): Variation of peak value of detectivity with doping concentration for different M of a 20 periods GaAs/Al0.26Ga0.74As QWIP. Though the bandwidth decreases with M, responsivity enhancement effect is dominating here. It is also observed that R-BW product decreases linearly with the number of QWs for high value of capture time whereas the variation is nonlinear for lesser number of QWs for low value of capture time. This is due to the combined effect of responsivity and 3dB bandwidth with the number of the QWs for different capture times. Finally, one of the most important performance parameter of infrared photodetector is the detectivity which is a measure of sensitivity also, is studied in this paper. The variation of frequency dependent peak detectivity for different doping concentrations (N) in the active layer is plotted in Fig. 10(a). It is observed that at lower values of doping, detectivity increases with doping but at higher values of doping it decreases. Variation of detectivity with doping concentration can be understood more clearly from Fig. 10(b), where the plot of detectivity at particular frequency (1 GHz) as a function of doping for three different values of M is shown. It is seen that the detectivity initially increases with increasing doping concentration mainly because of the enhancement of responsivity, but after a certain value of doping, it starts decreasing due to the dominating effect of dark current in this regime. Moreover, the increment and decrement of detectivity with doping is nonlinear.
Fig. 10 (a): Variation of peak value of detectivity with frequency for a 20 periods GaAs/Al0.26Ga0.74As QWIP with GaAs well doped with 1.2x1017 cm-3, 3.2x1017 cm-3, 5x1017 cm-3 and 8x1017 cm-3 Si donors.
Now, another aspect is effect of capture time on the performance of QWIP. Because, the value of capture time may vary due to the fabrication defects and there are discrepancies in its values reported by the several authors [21, 31]. Effect of capture time on the responsivity-bandwidth product is also studied in this paper. Fig. 9 shows the variation of responsivity-bandwidth (R-BW) product as a function of M for different capture times. With increase in capture time, RBW product increases for a particular value of M. This is mainly due to the enhancement of responsivity with doping.
IV.
CONCLUSION
Effect of active layer doping concentration on the performance of GaAs/AlGaAs QWIP is studied theoretically. Doping concentration has insignificant role on the 3dBbandwidth for high capture rate but has significant role for low values of capture rate. At low carrier capture rate, bandwidth decreases nonlinearly with increasing doping in the active well
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ACCEPTED MANUSCRIPT [12] J. Moon, S. S. Li, J. H. Lee, “A high performance quantum well infrared photodetector using superlattice-coupled quantum wells for long wavelength infrared detection”, Infrared Phys. & Tech., vol 44, pp. 229234, 2003. [13] F. D. P. Alves, J. Amorim, M. Byloos, H. C. Liu, A. Bezinger, M. Buchanan, N. Hanson, and G. Karunasiri, “Three band Quantum well infrared photodetector using interband and intersubband transitions”, J. Appl. Phys., vol. 103, p. 114515, 2008. [14] L. J. Kozlowski, G. M. Williams, G. J. Sullivan, C. W. Farley, R. J. Andersson, J. K. Chen, D. T. Cheung, W. E Tennant and R. E. DeWames, “LWIR 128*128 GaAs/AlGaAs multiple quantum well hybrid focal plane array, “ IEEE Trans Electron Devices, vol. 38, pp. 1124-1130, 1991. [15] B.F. Levine, C.G. Bethea, G. Hasnain, V.O. Shen, E. Pelve, R.R. Abbott, S.J. Hsieh, “High sensitivity low dark current 10 μm GaAs quantum well infrared photodetector”, Appl. Phys. Lett., vol 56, p. 851, 1990. [16] C. G. Bethea, B. F. Levine, V. O. Shen, R. R. Abbott and S. J. Hseih, “10µm GaAs/AlGaAs multiquantum well scanned array infrared imaging camera,” IEEE Trans. Electron Devices, vol. 38, pp. 11181123, 1991. [17] A. Rajira, H. Akabli, A. Almaggousi, A. Abounadi, “The non parabolicity and the enhancement of the intersubband absorption in GaAs/GaAlAs quantum wells”, Superlattices and Microstructures, vol. 84, pp. 192–197, 2015. [18] V. Guériaux, A. Nedelcu and P. Bois, “Double barrier strained quantum well infrared photodetectors for the 3-5µm atmospheric window”, J. Appl. Phys., vol. 105, p. 114515, 2009. [19] F. Szmulowicz, M.O. Manasreh, D.W. Fischer, F. Madarasz, K.R. Evans, E. Stutz, T. Vaughan, “The temperature dependence of intersubband absorption in a barrier-doped GaAs/Al0.3Ga0.7As quantum well structure”, Superlattices and Microstructures, vol. 8, pp. 63-67, 1990. [20] M. K. Das and N. R. Das, “On optimum designs of a RCE Si/SiGe/Si MQW photodetector for long wavelengh applications”, Opt. Quant. Electron, vol. 41, pp. 539-549, 2009. [21] E. Rosencher, B. Vinter, F. Luc, L. Thibaudeau, P. Bois and J. Nagle, “Emission and capture of electrons in multiquantum-well structures”, IEEE Trans. Quan. Elec. vol. 30, p. 2875, 1994. [22] K.M.S.V. Bandara, B. F. Levine, R. E. Leibenguth and M. T. Asom, “Optical and transport properties of single quantum well infrared photodetectors”, J. Appl. Phys., vol. 74, no. 3, p. 1826, 1993. [23] B. F. Levine, A. Zussmann, S. D. Gunapala, M. T. Asom, J. M. Kuo,and W. S. Hobson, “Photoexcited escape probability, optical gain, and noise in quantum well infrared photodetectors,” J. Appl. Phys., vol. 72, pp. 4429-4443, 1992. [24] M. Ershov, C. Hamaguchi and V. Ryzhii, “Device physics and modelling of multiple quantum well infrared photodetectors”, Jpn. J. Appl. Phys., vol. 35, pp.1395-1400, 1996. [25] P. D. Grant, R. Dudek, M. Buchanan, L. Wolfson and H. C. Liu, “An ultra fast quantum well infrared photodetector”, Infrared Phys. & Tech. vol 47, pp. 144-152, 2005. [26] M. Ershov, S. Satou and Y. Ikebe, “Analytical model of transient photoresponse of quantum well infrared photodetectors”, J. Appl. Phys., vol. 86, pp. 6442-6450, 1999. [27] Neena Imam, Elias N. Glytsis, Thomas K. Gaylord, Kwong-Kit Choi, Peter G. Newman, and Lisa Detter-Hoskin, “Quantum-Well Infrared Photodetector Structure Synthesis: Methodology and Experimental Verification” J. Quan. Elec., vol. 39, p. 468, 2003. [28] A. Zussman, B.F. Levine, J.M. Kuo, J. de Jong, “Extended long‐wavelength λ=11–15‐μm GaAs/AlxGa1−xAs quantum‐well infrared photodetectors”, J. Appl Phys., vol 70, p. 5101, 1991. [29] M. A. Billaha and Mukul K Das, “Influence of Doping on the Performance of GaAs/AlGaAs QWIP for Long Wavelength Applications”, Opto-electronics Review, Degruter, vol. 24, Issue. 1, pp. 25-33, 2016.
layer. Maximum bandwidth of 72.7GHz is obtained for QWIP with 20 periods, doping concentration of 5x1017 cm-3 and cap=11ps. For the detection of low intensity infrared radiation, higher doping gives better result unlike for high speed operation. Number of QWs has also an important role on the performance of the device. With increasing number of QWs, responsivity increases but, R-BW product decreases. So, to obtain high responsivity and hence, detectivity, larger well can be used whereas for high speed operation, less QW periods is suggested. Number of active well layers and doping in the active layer has contrary effects on the responsivitybandwidth (R-BW) product. Therefore, choice of doping concentration and number of wells is important to obtain optimized performance of the device. A maximum value of RBW product is obtained as 5.35 A-GHz/W for 20 periods of QW at doping concentration of 5x1017 cm-3. Moreover, concerning the detectivity of the device, choice of doping concentration is very important. ACKNOWLEDGEMENTS This work is partly supported by the Centre of Excellence in Renewable Energy, project under FAST, MHRD, Govt. of India (Sanction Letter No. F. No. 5-6/2013-TS-VII). REFERENCES [1]
S. D. Gunapala, S. V. Bandara, J. K. Liu, E. M. Luong, N. Stetson, C. A. Shott, J. J. Bock, S. B. Rafol, J. M. Mumolo, and M. J. McKelvey, “Long-Wavelength 256 x256 GaAs/AlGaAs Quantum Well Infrared Photodetector (QWIP) Palm-Size Camera”, IEEE Trans. Electron Devices, vol. 47, no. 2, pp. 326-332, 2000. [2] R. Szweda, “QWIPs–Multi-spectral mine clearance and medical,” III-Vs Rev., vol. 18, p. 44, 2005. [3] E. R. Brown, K. A. McIntosh, F. W. Smith, and M. J. Manfra, “Coherent detection with a GaAs/AlGaAs multiple quantum-well structure,” Appl. Phys. Lett. vol. 62, pp. 1513–1515, 1993. [4] H. C. Liu, J. Li, E. R. Brown, K. A. McIntosh, K. B. Nichols, and M. J. Manfra, “Quantum well intersubband heterodyne infrared detection upto 82 GHz,” Appl. Phys. Lett., vol. 67, pp. 1594–1596, 1995. [5] B.F. Levine, C.G. Bethea, G. Hasnain, V.O. Shen, E. Pelve, R.R. Abbott, S.J. Hsieh, “High sensitivity low dark current 10 μm GaAs quantum well infrared photodetector”, Appl. Phys. Lett., vol 56, p. 851, 1990. [6] A. Rogalski, “Comparison of the performance of quantum well and conventional bulk infrared photodetectors”, Infrared Phys. Technol., vol. 38, pp. 295-310, 1997. [7] V. Ryzhii et al. “High-Frequency Response of Intersubband Infrared Photodetectors with a Multiple Quantum Well Structure”, Jap. J. Appl. Phys., vol. 36, p. 2596, 1997. [8] E. R. Brown, K. A. McIntosh, K. B. Nichols, F. W. Smith, and M. J. Manfra, in Quantum Well Intersubband Transition Physics and Devices, edited by H. C. Liu, B. F. Levine, and J. F. Andersson ~Kluwer, Dordrecht, Netherlands, pp. 207–220, 1994. [9] S. Ehret, H. Schneider, C. Schönbein, G. Bihlmann and J. Fleissner, “Analysis of the transport mechanism in GaAs/AlGaAsquantum-well infrared photodetection structures using time resolved photocurrent measurements,” Appl. Phys. Lett., vol. 69, pp. 931-933, 1996. [10] H. C. Liu, J. Li, M. Buchanan, and Z. R. Wasilewski, “High-frequency quantum-well infrared photodetectors measured by microwaverectification technique”, IEEE J. Quantum Electron. vol. 32, pp. 10241028, 1996. [11] A Rogalski, “HgCdTe infrared detector material: history, status and outlook,” Rep. Prog. Phys., vol. 68, pp. 2267–2336, 2005.
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ACCEPTED MANUSCRIPT [30] V. Ryzhii , “Characteristics of quantum well infrared photodetectors”, J. Appl. Phys., vol. 81, pp. 6442-6448, 1997. [31] H. Schneider and H. C. Liu, “Quantum Well Infrared Photodetectors Physics and Applications”, Springer-Verlag, New York, 2007. [32] L. Thibaudeau, P. Bois and J. Y. Duboz, “A self-consistent model for quantum well infrared photodetectors,” J. Appl Phys. vol 79, p. 446, 1996. [33] M. Henini and M. Razeghi, “Handbook of Infrared Detection Technologies”, 1st Edition, Elsevier Science, 2002. [34] K.M.S.V. Bandara, B. F. Levine, R. E. Leibenguth and M. T. Asom, “Optical and transport properties of single quantum well infrared photodetectors”, J. Appl. Phys., vol. 74, no. 3, p. 1826, 1993. [35] R. Quay, C. Moglestue, V. Palankovski and S. Selberherr, “A temperature dependent model for the saturation velocity in semiconductor materials”, Material Sci. in Semicon. Proc., vol. 3, pp. 149-155, 2000. [36] B. F. Levine, C. G. Bethea, K. K. Choi, J. Walker and R. J. Malik, “Bound-to-extended absorption GaAs superlattice transport infrared detectors,” J. Appl. Phys., vol. 64, p. 1591, 1988. [37] I. Vurguftman, J. R Meyer and L. R. Ram-Mohan “Band parameters for III-V compound semiconductors and their alloys”, J. Appl. Phys., vol. 89, p. 5815-5875, 2001. [38] D. E. Aspnes, “GaAs lower conduction-band minima: Ordering and properties”, Phys. Rev. B, vo. 14,p. 5331-5343, 1976. [39] M Levinshtein, S Rumyantsev and M Shur, “Handbook series on semiconductor parameters volume 1”, World Scientific Publishing, 1996. [40] S. Adachi, in Properties of Aluminium Gallium Arsenide, edited by S. Adachi (INSPEC, London,) , p. 58, 1993.
9
Aref Billaha, Mukul K. Das, S. Kumar PII:
S0749-6036(16)31328-3
DOI:
10.1016/j.spmi.2017.02.018
Reference:
YSPMI 4830
To appear in:
Superlattices and Microstructures
Received Date:
18 November 2016
Revised Date:
10 February 2017
Accepted Date:
12 February 2017
Please cite this article as: Aref Billaha, Mukul K. Das, S. Kumar, Doping Dependent Frequency Response of MQW Infrared Photodetector, Superlattices and Microstructures (2017), doi: 10.1016/j. spmi.2017.02.018
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ACCEPTED MANUSCRIPT
Doping, MQW, Transit time, Bandwidth, Responsivity
ACCEPTED MANUSCRIPT
Doping Dependent Frequency Response of MQW Infrared Photodetector 1,2,3
Md. Aref Billaha1, Mukul K. Das2, Senior Member, IEEE and S. Kumar3 Dept. of Electronics Engineering, Indian Institute of Technology (ISM) Dhanbad, India. [email protected], [email protected]
Abstract— This work is to study the effect of doping concentration in the active layer on the performance of multiple quantum well (MQW) infrared photodetector based on inter subband transitions. A theoretical model for the photocurrent and hence, responsivity of the detector in frequency domain is developed considering the effect of doping dependent absorption and carrier capture at the hetero-interfaces. Transit time and capture time limited bandwidth of the detector is computed from the frequency dependent photocurrent. Results show that, besides the usual effect of capture time, doping concentration in the active layer has an important effect on the bandwidth and responsivity of the device particularly for high value of capture time. KeywordsResponsivity.
Doping,
I.
MQW,
Transit
time,
have not yet been explored in detail by researchers. Position dependent intensity of infrared radiation is another important aspect needs to be considered for accurate analysis of the performance of the device. Effect of doping concentration on the absorption of inter sub-band transition in AlGaAs/GaAs QWIP has already been studied and reported by the authors elsewhere [29]. In this paper, physics based theoretical model for frequency response of MQW infrared photodetector is developed considering the effect of doping on absorption coefficient, effective band offsets, carrier capture etc. Variation of the performance parameters like responsivity, bandwidth and responsivity-bandwidth product with doping are studied. Rest of the paper is organized as follows. In section II, the detail calculation of the photocurrent and hence, responsivity in frequency domain is described. Simulation results are discussed in section III and finally, in section IV, the conclusion of the study is given.
Bandwidth,
INTRODUCTION
Infrared photodetector has attracted a lot of interest among researchers due to their wide-ranging and rapidly expanding applications such as medical science, military (e.g., navigation, night vision, weapons detection), environment monitoring and free space optical communication [1-2]. Such applications require detector having high sensitivity to the infrared incidence [3-4], low dark current [5-6] and high speed of operation [7]. Quantum well infrared photodetector (QWIP) using inter-subband photo-excitation meets such requirement over conventional detector and it has already been demonstrated by researchers [8-10]. HgCdTe has proved its capability to be used for infrared detector [11]. But, HgCdTe based detector is not preferred, for long wavelength infrared region (LWIR) detection in particular, because of difficulty in controlling material composition of HgCdTe. Moreover, HgCdTe devices are very much sensitive to the defects and surface leakage [11]. Recently, GaAs-based multiple quantum well (MQW) infrared photodetector (IP) is one of the most promising infrared detector because of its wide applications specially in infrared imaging at LWIR [12-15]. It has some other advantages also, like easy wavelength adjustment, high thermal stability etc. [16-19]. Carrier dynamics e.g., capture and escape of carriers into and from the quantum well play important roles for the high frequency performance of such devices. Theoretical and experimental studies on the performance of III-V based AlGaAs/GaAs IP considering those aspects have already been done by researchers in recent times [20-28]. To the best of authors knowledge, some of the important aspects like doping concentration dependent Eigen energy states and hence, wavelength of operation, doping dependent density of states and, hence, absorption coefficient
II.
DEVICE STRUCTURE AND EQUATION OF THE MODEL
Schematic structure of GaAs/AlxGa1-xAs MQW infra-red photodetector, considered in our analysis, is shown in Fig.1. It is formed by alternate layer of GaAs well and AlxGa1-xAs barrier on semi-insulating GaAs substrate. GaAs layer is considered to be the active layer and is doped with Si donors. Barrier layer of AlxGa1-xAs is considered to be the un-doped. Width of the GaAs top and bottom contact layers are considered as 0.7µm and 0.5µm respectively and are doped with 2 x 1018 cm-3 Si donors. On incidence of light on the device, carriers are generated and these photogenerated carriers, after transport through several hetero-interfaces, are collected by the contacts. Now, the normal incidence is not capable to cause inter sub-band transitions in quantum well structure as per the selection rule. So, the light is assumed to be incident on the detector at an angle () of 45° with the growth axis (z) as shown in Fig.1. Moreover, it is important to mention here that width of the well and barrier layers, doping in the well and mole fraction of Al (x) are chosen in such a way that there exist only one bound state and one quasi-bound state in the well. Under this condition, the highest energy state is almost aligned with top of the barrier. To determine the high frequency response of the device, it is important to consider the aspects of carrier transport including its capture and escape at each of the heterointerfaces. Fig. 2 illustrates the mechanism of carrier transport within the device. In our model, we have assumed that at
1
ACCEPTED MANUSCRIPT steady state, the carriers (only electrons here) are injected from emitter to the first quantum well by tunneling due to high electric field. Out of these injected carriers, some are captured into the bound state and rest of them is transported into the next barrier. Now, photo excitation of electrons is only process of escape of electrons from bound state to quasi-bound state. Capture and escape of carriers occur at each hetero-interface and capture probability entirely depends on the capture lifetime of electrons which is assumed to be same for all wells. But, photo-excitation and hence, escape is position dependent. Intensity of the incident infrared radiation is considered to be decayed exponentially with z. Although the electrons are generated in all wells at the same time due to the incident radiation, photo-generated electrons from different wells arrive at contact layers in different times depending on the position of the well where they are generated. Continuity of the drift current across the multiple quantum wells in the steady state condition is provided by the electron injection from the emitter contact layer which has already mentioned in the beginning of this section. It may be mentioned here that the escape of the carrier due to thermionic emission is negligible since the device is considered to be operating at low temperature.
i-AlxGa1-xAs
N+-GaAs (Collector)
AlxGa1-xAs
N-GaAs M
z direction 2 LB
Lw
1 45°
L1
N+-GaAs (Emitter)
z=0
Substrate
hν Fig. 1: Schematic layer structure of a GaAs/AlxGa1-xAs MQW infrared photodetector. 1,2….M shows the number of QWs. Widths of the well and the barrier layer are respectively denoted as Lw and LB .
Considering the above facts theoretical model for frequency response of the device is developed as follows. Injected electron current density (je) from emitter to the first QW depends on the applied bias and doping concentration in the emitter layer and is given as [30]
je jm e
Et Ee
(1)
where, jm is the maximum emitter current density which is generally dependent on the doping concentration. This can be estimated from the equation governed by jm~qN3d,eF where q is the charge of an electron, N3d,e is the doping concentration of the emitter, F is the electron Fermi velocity, Et is the characteristic tunneling electric field for the emitter barrier, Ee is the electric field in the emitter barrier with z 0 0 and
z W
Fig. 2: Schematic diagram of the conduction band where carrier transport processes are illustrated.
nqw t
applied bias voltage). Ee can be expressed as [30]
nqw
Nd
tr j nqw I q cap
(3)
where, cap is the capture lifetime of electrons, tr is the transit time of electrons, is the photo-excitation cross section, j is the current density, I is the intensity of the incident photon infrared radiation. The term I and nqw are expressed as
V , (here, is the electrostatic potential and V is the
Ee E MEd 1
(2)
nqw ( z , t ) nqw,0 nqw ( z , t ) and I ( z , t ) I 0 I ( z , t )
where, E is the average electric field, E=V/W, where W is the total length of the MQW photodetector i.e. W=(M+1)L (here, L is the length of one quantum well period i.e. L=LB+Lw and M is the number of quantum wells), Nd is the doping sheet concentration which can be calculated from the relationship Nd=NLW (here, N is the doping concentration in the active layer), nqw is the electron sheet concentration in the QW, and Ed 2 qN d æ , where æ is dielectric constant. Value of æ
where, nqw,0 is the steady state electron sheet concentration, I0 is the steady state value of intensity of infrared radiation. The small signal component, I(z,t) and nqw(z,t) can be expressed as
nqw ( z , t ) nqw, eit and I ( z , t ) I e jL e L ( j 1) L w
1
B
jLw z
eit
(4)
I ' eit
in well material is used in the calculation.
where, nqw, and I are respectively the small signal components of electron sheet concentration and intensity of
The rate equation for the bound states electrons in the quantum well (QW) is given by
2
ACCEPTED MANUSCRIPT infrared radiation modulated with modulation frequency , L1 is the distance of the nearest well from the front of the emitter contact layer. is the absorption coefficient. The calculation of absorption coefficient for GaAs/AlGaAs bases QWIP has already been reported by the authors elsewhere [29].
je
qN d
1 cap
(9) s
E 2 I where s M I 0 d ln m Et I0 1 cap jm
Now, the ratio of tr /cap can be considered as (1-cap), which indicates probability of electron capture at the barrierwell interface i.e. cap define the effectiveness of the electrons transfer over the barrier which are not captured at the barrierwell interface. The second term in the right hand side of the equation indicates the electrons are emitted due to photoexcitation which is considered to be the dominating process of escape of carriers from the well.
and I m
1
(10)
qN d
where, s is the characteristics time of the quantum well filling due to the steady state injected current density from the emitter.
Since, the carrier generation does not occur in the continuum states and also no recombination take place within the states. Considering the above assumptions, the continuity equation for the continuum states over the barrier can be expressed as
Therefore, the additional injection of current density increases the carrier concentration near the emitter which can be found from the following formula
n( z , t )
Small signal analysis of n(z,t) in the continuum states can be calculated from Eq. (5) and is written as
t
e
n( z , t ) z
0
n( z , t )
(5)
at z 0
n ( z )
je / qe
i
(11)
where n(z, t) is the electron concentration in the continuum states, e is the drift velocity of an electron and J (z, t) is the electron current density and can be written as J ( z , t ) q e n ( z , t ) . The term n(z, t) can be expressed as
In the region 0 z L1 ; applying boundary conditions at z=0
n( z , t ) n0 n( z , t )
& z = L1, small signal current density at the barrier-well hetero-interface (je) can be written as
where n( z , t ) n e
i t
z
(6)
je1
where, n0 and n are the steady state and small signal components of electron concentration in the continuum state.
qN d I 0 1 cap
dje dEe
Ee
n ( z ) 0
q nqw,
1 cap s
e
i tr
(12)
(13)
The small signal component, nqw, in the above equation can be calculated from rate equation given in Eq. (3) at the barrierwell hetero-interface. The solution of the small signal analysis of Eq. (3) is obtained as
(7)
nqw,
Now, infinitesimal change of the electric field in the emitter results in an increase of the injected current density at the emitter and is given by [26, 31]
je
e
where tr = L1/e
At steady state condition, the value of I is zero and solution of Eq. (3) in the emitter contact layer gives steady state current density at z=0 i.e. j0 = j|z=0 which coincides with je and after detail calculation, it can be expressed as
j0
nqw,0 I ' i I 0
1
s
e
(14) i ttr
Current in the well-barrier interface has two parts, one is due to the carriers from previous barrier after surviving loss due to capture in the well {process 2 in Fig. 2}. Other part is due to photo-excitation in the well. This approach is applied below to calculate photocurrent in a well {process 3 in Fig. 2}. In the region; L1 ≤ z ≤ Lw, current density in the 1st QW is due to the injected current coming from the emitter after survival loss due to capture. This can be written as
(8)
where dje/dEe is the differential conductivity of the emitter barrier. Using Eq. (1), Eq. (2), Eq. (7) & Eq. (8) is solved considering Nd ~ nqw, after detail calculation,
jw11, cap je e
i ttr
(15)
Now, the photocurrent in the quantum well is due to the photo excitation may be calculate from Eq. (3) by considering cap=
3
ACCEPTED MANUSCRIPT where ћω is the incident photon energy. Using Eq. (19), Eq. (21) & Eq. (22), one may get final expression of responsivity and is obtained as
0 (since there is no loss in this case) and nqw t 0 . So, the photo-excitation current at the end of a well (well-barrier interface) is obtained as
jw12, q ( nqw, I 0 nqw,0 I ' )
R
(16)
1 e
R0 i tr
cap
1st
Applying boundary condition at z =L1+Lw for the quantum L well (i.e. j=1), then Iꞌ can be written as I ' I e
L M 1 i ( M 1) cap e e 2 ei 1 cap i s M jL i M j i ( M j ) cap e e i s 1 cap e j 2 i ( M 1) x e 1 tr
w
and put the value of I' in Eq. (16), one may obtain (17)
w
The calculated current (jc1,) at the collector of the 1st quantum well considering L1 and LB are of equal barrier width and it is given as
cap je e q jc1, je1 e e L ( nqw,0 I e nqw, I 0 ) i tr
i z
where, = L/e R0
i z
e
w
tr
w
jw12, q ( nqw, I 0 nqw,0 I e L )
I 0 s i s i ( M 1)
tr
q nqw ,0
(23)
tr
.
(18)
e
w
Now, the above current is appeared at the barrier-well interface of 2nd QW and the current for 2nd quantum well can be determined similarly as was calculated in the 1st QW providing boundary condition at z=L1+2Lw+LB and j=2 for the 2 L 2nd quantum well i.e. I ' I e . w
Continuing the above carrier transport process for the Mth QW, the final expression of the photocurrent density (jcM,) can be obtained as
jcM ,
q nqw,0 I
1 e cap
i tr
I 0 s i s
Fig. 3: Electric field spatial distributions in QWIP.
L M 1 i ( M 1) cap e e 2 ei 1 cap i s i z M e jL i M j i ( M j ) 1 e e e i cap cap s j 2 tr
w
tr
e
w
tr
III. RESULTS AND DISCUSSION
tr
To study the frequency dependent responsivity of the QWIP, we need to calculate the absorption coefficient which again requires determination of Eigen energy states and wave functions. Detail calculation of absorption coefficient has already been reported by the authors elsewhere [29]. It is observed in our previous study that peak absorption coefficient and corresponding operational wavelength of QWIP strongly depend on the doping concentration in active well layer. The calculation of doping dependent absorption coefficient is considered in this model to calculate responsivity in frequency domain using eqn. (23). In this calculation low field velocity of electron, which again depends on electric field, is considered. Position dependent electric field, as shown in Fig.3, inside the device is considered in this calculation. It is seen that the distribution of electric field is non uniform mainly for first 3 to 4 QWs and is uniform thereafter. Moreover, values of material parameters are very important to calculate R. Values of some important material parameters for GaAs and AlGaAs, used in this calculation, are summarized in Table I for quick reference. Device parameters
(19) where, nqw,0 can be calculated from the following relation given in [32]
nqw,0
Lw
(20)
The small signal component of the total current density can be determined from the following formula
J
A W
W
j
cM ,
dz
(21)
0
Now, small signal responsivity (R) can be obtained from the following expression
R
J A I
(22)
4
ACCEPTED MANUSCRIPT are chosen in accordance with the fabricated structure reported in literature [13]. Width of the well layer (Lw) is taken as 5.2nm and is doped with 5 x 1017 cm-3 Si donors. Width of the barrier layer (LB) is taken as 30nm and the incident optical power (Pinc) is assumed to be 1mW. The device is considered to be of mesa structure with an illumination area (A) of 200x200 µm2. The incident photon of infrared radiation (I0) is calculated from the relation [33], I0=Pinccos()/Aћω. The value of is taken as x10-15 cm2 and so, the calculated Et is 573kV/cm and jm is 1.3x106 A/cm2. The low field velocity of electron is calculated from e= µE /(1+( µE/ s)). Electron mobility (µ) is taken as 1000 cm2V-1s-1 and temperature dependent saturation velocity (s) is taken as 7.2x106 cms-1 at T=300K which are in accordance with some measured values reported in literature [32,34-36]. Saturation velocity, s at T=77K, is calculated using the relationship [35], s(T)= s(300K)/((1-AGaAs)+AGaAs(T/300K)) where, AGaAs is the coefficient at T=77K. Value of this coefficient is taken as 0.44 to calculate s(77K).
(a)
Table I Some material parameters of GaAs and Al0.26Ga0.74As used in calculation at T=77K: Material
Effective mass of electron, me
Band Gap (Eg, eV)
GaAs
0.067 [37]
1.5076 [37-39]
Al0.26Ga0.74As
0.0886 [40]
1.8329 [37-38]
Responsivity in frequency domain is plotted for different values of doping concentration (N) in the active layers for a fixed value of capture time, cap=5.5ps and is shown in Fig. 4(a). The responsivity calculated here is always based on the peak value of absorption coefficient and hence responsivity shall always mean peak responsivity throughout the discussion in this section. It is seen from figure that the responsivity increases with increasing doping concentration. This is mainly due to the enhanced absorption at high doping concentration. It is also observed from the figure that 3-dB bandwidth decreases with increasing doping concentration but insignificantly. For example, bandwidth is changed from 74.4 GHz to 73.6 GHz with the increase in doping from 1.2x1017 cm-3 to 1x1018cm-3. However, the bandwidth decreases with doping significantly for high value of capture time which can be seen from Fig. 4(b) where the responsivity is plotted as a function of doping for cap=11ps. In this case, the bandwidth decreases from 73 GHz for a doping of 3.2x1017 cm-3 to 70.8 GHz for doping concentration of 1x1018 cm-3. The reason behind such variation can be explained as follows. With increase in doping in the active layer, the characteristic time (s) for quantum well filling is increased. Now, s and cap have combined effect on the photocurrent as seen from Eq. (23). In case of low capture time for a fixed transit time, s has less significant role whereas, for high value of capture time, effect of s is more significant. Thus, effect of doping on
(b)
Fig. 4: (color online) Variation of responsivity as a function of frequency for different doping concentration of a 20 periods GaAs/ Al0.26Ga0.74As QWIP: (a) cap= 5.5ps and (b) cap= 11ps. bandwidth is significant for high value of capture time. For better understanding, the variation of 3dB bandwidth with doping concentration is presented in Fig. 5. It indicates the 3dB bandwidth decreases nonlinearly with doping concentration for high value of capture time. So, it is important to select the optimum doping concentration for enhanced bandwidth of the device. However, there is a tradeoff between the variations of bandwidth and responsivity with doping. So, the performance of the device is truly being judged if the responsivity-bandwidth product is studied with the variation of doping in the active layer. Doping dependent responsivity-bandwidth(R-BW) product for different values of capture time is shown in Fig. 6. It is seen from the figure that the product increases non-linearly with increase in doping concentration. It is due to the dominant effect of doping on the responsivity.
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ACCEPTED MANUSCRIPT wells is also important to study. A variation of R-BW product as a function of number of quantum wells for different doping concentrations in the active layer is given in Fig. 8. From figure, it is observed that the R-BW product is almost invariable with M for low values of doping. But for the higher value of doping, the R-BW product decreases linearly with the M. So, the R-BW product is greatly affected by number of wells at high value of doping concentration. So, the choice of the doping concentration in the active layer and number of wells is important to obtain optimized performance of the device.
Fig. 5: (color online) Variation of 3dB Bandwidth as a function of doping concentration for different capture time of a 20 periods GaAs/ Al0.26Ga0.74As QWIP.
Fig. 7: (color online) Variation of 3dB bandwidth and responsivity as a function of doping concentration for different number of quantum wells of a GaAs/ Al0.26Ga0.74As QWIP.
Fig. 6: (color online) Variation of responsivity-bandwidth product as a function of doping concentration for different capture time of a 20 periods GaAs/ Al0.26Ga0.74As QWIP. Usually, large number of QW layers in infrared detectors is recommended to obtain significant photocurrent at low intensity of infrared radiation. So, it is important to observe the effect of doping on the 3dB bandwidth for large number of QWs. Fig. 7 shows the variation of 3dB bandwidth and responsivity as a function of number of QWs (M) for different values of doping concentration. From the figure, it is seen that the 3dB bandwidth changes from 119.4GHz to 115.4GHz for the change in doping concentration from 1.2x1017 cm-3 to 10x1017 cm-3 for M =12. But lesser effect is observed for higher values of M. It is also observed that variation of responsivity with M is nonlinear for all values of doping concentration. Variation of R-BW product with the number of
Fig. 8: (color online) Variation of responsivity-bandwidth product as a function of number of quantum wells for different doping concentration of a GaAs/ Al0.26Ga0.74As QWIP.
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Fig. 9: (color online) Variation of responsivity-bandwidth product for different capture time of a GaAs/ Al0.26Ga0.74As QWIP.
Fig. 10 (b): Variation of peak value of detectivity with doping concentration for different M of a 20 periods GaAs/Al0.26Ga0.74As QWIP. Though the bandwidth decreases with M, responsivity enhancement effect is dominating here. It is also observed that R-BW product decreases linearly with the number of QWs for high value of capture time whereas the variation is nonlinear for lesser number of QWs for low value of capture time. This is due to the combined effect of responsivity and 3dB bandwidth with the number of the QWs for different capture times. Finally, one of the most important performance parameter of infrared photodetector is the detectivity which is a measure of sensitivity also, is studied in this paper. The variation of frequency dependent peak detectivity for different doping concentrations (N) in the active layer is plotted in Fig. 10(a). It is observed that at lower values of doping, detectivity increases with doping but at higher values of doping it decreases. Variation of detectivity with doping concentration can be understood more clearly from Fig. 10(b), where the plot of detectivity at particular frequency (1 GHz) as a function of doping for three different values of M is shown. It is seen that the detectivity initially increases with increasing doping concentration mainly because of the enhancement of responsivity, but after a certain value of doping, it starts decreasing due to the dominating effect of dark current in this regime. Moreover, the increment and decrement of detectivity with doping is nonlinear.
Fig. 10 (a): Variation of peak value of detectivity with frequency for a 20 periods GaAs/Al0.26Ga0.74As QWIP with GaAs well doped with 1.2x1017 cm-3, 3.2x1017 cm-3, 5x1017 cm-3 and 8x1017 cm-3 Si donors.
Now, another aspect is effect of capture time on the performance of QWIP. Because, the value of capture time may vary due to the fabrication defects and there are discrepancies in its values reported by the several authors [21, 31]. Effect of capture time on the responsivity-bandwidth product is also studied in this paper. Fig. 9 shows the variation of responsivity-bandwidth (R-BW) product as a function of M for different capture times. With increase in capture time, RBW product increases for a particular value of M. This is mainly due to the enhancement of responsivity with doping.
IV.
CONCLUSION
Effect of active layer doping concentration on the performance of GaAs/AlGaAs QWIP is studied theoretically. Doping concentration has insignificant role on the 3dBbandwidth for high capture rate but has significant role for low values of capture rate. At low carrier capture rate, bandwidth decreases nonlinearly with increasing doping in the active well
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ACCEPTED MANUSCRIPT [12] J. Moon, S. S. Li, J. H. Lee, “A high performance quantum well infrared photodetector using superlattice-coupled quantum wells for long wavelength infrared detection”, Infrared Phys. & Tech., vol 44, pp. 229234, 2003. [13] F. D. P. Alves, J. Amorim, M. Byloos, H. C. Liu, A. Bezinger, M. Buchanan, N. Hanson, and G. Karunasiri, “Three band Quantum well infrared photodetector using interband and intersubband transitions”, J. Appl. Phys., vol. 103, p. 114515, 2008. [14] L. J. Kozlowski, G. M. Williams, G. J. Sullivan, C. W. Farley, R. J. Andersson, J. K. Chen, D. T. Cheung, W. E Tennant and R. E. DeWames, “LWIR 128*128 GaAs/AlGaAs multiple quantum well hybrid focal plane array, “ IEEE Trans Electron Devices, vol. 38, pp. 1124-1130, 1991. [15] B.F. Levine, C.G. Bethea, G. Hasnain, V.O. Shen, E. Pelve, R.R. Abbott, S.J. Hsieh, “High sensitivity low dark current 10 μm GaAs quantum well infrared photodetector”, Appl. Phys. Lett., vol 56, p. 851, 1990. [16] C. G. Bethea, B. F. Levine, V. O. Shen, R. R. Abbott and S. J. Hseih, “10µm GaAs/AlGaAs multiquantum well scanned array infrared imaging camera,” IEEE Trans. Electron Devices, vol. 38, pp. 11181123, 1991. [17] A. Rajira, H. Akabli, A. Almaggousi, A. Abounadi, “The non parabolicity and the enhancement of the intersubband absorption in GaAs/GaAlAs quantum wells”, Superlattices and Microstructures, vol. 84, pp. 192–197, 2015. [18] V. Guériaux, A. Nedelcu and P. Bois, “Double barrier strained quantum well infrared photodetectors for the 3-5µm atmospheric window”, J. Appl. Phys., vol. 105, p. 114515, 2009. [19] F. Szmulowicz, M.O. Manasreh, D.W. Fischer, F. Madarasz, K.R. Evans, E. Stutz, T. Vaughan, “The temperature dependence of intersubband absorption in a barrier-doped GaAs/Al0.3Ga0.7As quantum well structure”, Superlattices and Microstructures, vol. 8, pp. 63-67, 1990. [20] M. K. Das and N. R. Das, “On optimum designs of a RCE Si/SiGe/Si MQW photodetector for long wavelengh applications”, Opt. Quant. Electron, vol. 41, pp. 539-549, 2009. [21] E. Rosencher, B. Vinter, F. Luc, L. Thibaudeau, P. Bois and J. Nagle, “Emission and capture of electrons in multiquantum-well structures”, IEEE Trans. Quan. Elec. vol. 30, p. 2875, 1994. [22] K.M.S.V. Bandara, B. F. Levine, R. E. Leibenguth and M. T. Asom, “Optical and transport properties of single quantum well infrared photodetectors”, J. Appl. Phys., vol. 74, no. 3, p. 1826, 1993. [23] B. F. Levine, A. Zussmann, S. D. Gunapala, M. T. Asom, J. M. Kuo,and W. S. Hobson, “Photoexcited escape probability, optical gain, and noise in quantum well infrared photodetectors,” J. Appl. Phys., vol. 72, pp. 4429-4443, 1992. [24] M. Ershov, C. Hamaguchi and V. Ryzhii, “Device physics and modelling of multiple quantum well infrared photodetectors”, Jpn. J. Appl. Phys., vol. 35, pp.1395-1400, 1996. [25] P. D. Grant, R. Dudek, M. Buchanan, L. Wolfson and H. C. Liu, “An ultra fast quantum well infrared photodetector”, Infrared Phys. & Tech. vol 47, pp. 144-152, 2005. [26] M. Ershov, S. Satou and Y. Ikebe, “Analytical model of transient photoresponse of quantum well infrared photodetectors”, J. Appl. Phys., vol. 86, pp. 6442-6450, 1999. [27] Neena Imam, Elias N. Glytsis, Thomas K. Gaylord, Kwong-Kit Choi, Peter G. Newman, and Lisa Detter-Hoskin, “Quantum-Well Infrared Photodetector Structure Synthesis: Methodology and Experimental Verification” J. Quan. Elec., vol. 39, p. 468, 2003. [28] A. Zussman, B.F. Levine, J.M. Kuo, J. de Jong, “Extended long‐wavelength λ=11–15‐μm GaAs/AlxGa1−xAs quantum‐well infrared photodetectors”, J. Appl Phys., vol 70, p. 5101, 1991. [29] M. A. Billaha and Mukul K Das, “Influence of Doping on the Performance of GaAs/AlGaAs QWIP for Long Wavelength Applications”, Opto-electronics Review, Degruter, vol. 24, Issue. 1, pp. 25-33, 2016.
layer. Maximum bandwidth of 72.7GHz is obtained for QWIP with 20 periods, doping concentration of 5x1017 cm-3 and cap=11ps. For the detection of low intensity infrared radiation, higher doping gives better result unlike for high speed operation. Number of QWs has also an important role on the performance of the device. With increasing number of QWs, responsivity increases but, R-BW product decreases. So, to obtain high responsivity and hence, detectivity, larger well can be used whereas for high speed operation, less QW periods is suggested. Number of active well layers and doping in the active layer has contrary effects on the responsivitybandwidth (R-BW) product. Therefore, choice of doping concentration and number of wells is important to obtain optimized performance of the device. A maximum value of RBW product is obtained as 5.35 A-GHz/W for 20 periods of QW at doping concentration of 5x1017 cm-3. Moreover, concerning the detectivity of the device, choice of doping concentration is very important. ACKNOWLEDGEMENTS This work is partly supported by the Centre of Excellence in Renewable Energy, project under FAST, MHRD, Govt. of India (Sanction Letter No. F. No. 5-6/2013-TS-VII). REFERENCES [1]
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