ARTICLE IN PRESS Microelectronics Journal 40 (2009) 104– 107
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AlxGa1xN/GaN multi-quantum-well ultraviolet detector based on p-i-n heterostructures A. Asgari a,b,, E. Ahmadi a, M. Kalaﬁ a a b
Photonics-Electronics Group, Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163, Iran School of Electrical, Electronic and Computer Engineering, The University of Western Australia, Crawley, WA 6009, Australia
a r t i c l e in f o
a b s t r a c t
Article history: Received 15 April 2008 Accepted 14 June 2008 Available online 9 August 2008
We report on characterization of a set of AlGaN/GaN multiple-quantum-well (MQW) photodetectors. The model structure used in the calculation is the p–i–n heterojunction with 20 AlGaN/GaN MQW structures in i-region. The MQW structures have 2 nm GaN quantum well width and 15 nm AlxGa1xN barrier width. The cutoff wavelength of the MQW photodetectors can be tuned by adjusting the well width and barrier height. Including the polarization ﬁeld effects, on increasing Al mole fraction, the transition energy decreases, the total noise increases, and the responsivity has a red shift, and so the detectivity decreases and has a red shift. & 2008 Elsevier Ltd. All rights reserved.
Keywords: Quantum well UV detectors AlGaN/GaN
1. Introduction Recent advantages in III-nitride semiconductor structures growth and processing have allowed ultraviolet (UV) photodetectors based on these compounds to be well established today . Their detection edges can be tuned in the 200–360 nm range by changing the Al mole content in the (Al, Ga)N ternary alloy . Hence, they are ideal candidates for UV detection in a number of applications including early missile plume detection, ﬂame sensing, UV astronomy, space to space communication and biological effects . To date, most of the work on III-nitride UV photodetectors, inclusive of all types, has relied on bulk-like epilayers. Although some results have been presented recently about multiple-quantum-well photodetectors (MQWPs), there is yet a big lack in this area [4–6]. The reason to study the MQW–UV detectors is their advantages such as new controlled gain mechanisms due to the different tunneling rate for electrons and holes, extra ﬂexibility to tune the detection edge by adjusting well width and Al mole fraction, use of polarization ﬁelds, and the possibility of easier emitter, ﬁlter and detector structures integration. In spite of these advantages, it will be shown that the MQW–UV detector’s detection wavelength, in contrast with III-nitride bulk-like epilayers detectors, does not include the strategic window (230–280 nm) of ozone layer absorption. In this paper, we are modeling AlGaN/GaN MQW–UV detectors based on p–i–n heterostructures which include QWs with different Al mole
Corresponding author at: Research Institute for Applied Physics, University of Tabriz, Tabriz 51665-163 Iran. Tel.: +98 411 3393007; fax: +98 411 3347050. E-mail address: [email protected]
0026-2692/$ - see front matter & 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.mejo.2008.06.087
fraction in the presence of external electric ﬁeld. The calculations have been done both with and without the polarization ﬁeld effects.
2. Calculation model The ﬁrst step in the study of MQW detectors is the calculation of the quantum wells’ subband energy and related wavefunctions of electron and hole that have been done in this article by transfer matrix method (TMM) . Knowing the subband energy of electrons and holes and their related wavefunctions, one can ﬁnd the absorption spectrum of the structures and absorption coefﬁcient following Elliot’s theory . It has been assumed that the absorption in the studied QW structures is due to: (i) a continuum of transition between free particle state, and (ii) excitonic transitions. We have considered only ﬁrst subbands transition and assumed that the heavy and light hole states are uncoupled. So, only the 1s exciton state is considered as it has much higher oscillator strength and is distinguishable at high temperatures. The absorption coefﬁcient for the structure can be written as 
að_o; FÞ ¼ M2cv ðFÞqex Lð_o; E1;1 cv ðFÞ EB Þ Z
0 0 M 2cv ðFÞNqcon KðE0 ; E1;1 cv ðFÞÞ Lð_o; E Þ dE
where _o is the photon energy, F is the electric ﬁeld, Mcv(F) is the electric ﬁeld-dependent electron–hole overlap integral, qex and qcon are the oscillator strengths of excitonic and band to band transitions, respectively. L is the Lorentzian function for homogenous broadening in continuum and exciton, E1;1 is the cv
ARTICLE IN PRESS A. Asgari et al. / Microelectronics Journal 40 (2009) 104–107
where l is the wavelength, h is the Planck’s constant, c is the light velocity, e is the electron charge, and G is the photoelectric gain, which has been assumed to be 1 in the p–i–n MQWs structures . The quantum efﬁciency Z as the total spectral response in p–i–n structure is the sum of spectral response in the p, n, and i- space charge region (SCR), Z ¼ Zp+Zn+ZSCR. The spectral response of p and n region can be calculated by solving the carrier transport equations, which is done in the room temperature within the minority carrier and depletion approximation. Also, the assumption of low injection, uniform doping, and abrupt charges in composition at heterojunction are justiﬁed for those structures and enable an analytical solution of transport equation . The spectral response of the SCR, which includes the Nw quantum well with Lw thickness, depends on absorbed incident photon ﬂux and can be expressed as  xp ab ð_oÞ
ZSCR ð_oÞ ¼ ½1 Rð_oÞe
b1 eab ð_oÞðWNW LW ÞNW aQW ð_oÞLW cZesc
where W is the total SCR, which includes the p and n region’s depletion layers, xp the thickness of no depleted p region, R(_o) is the surface reﬂectivity of structure, ab(_o) is the host material absorption coefﬁcient, NW is the number of quantum wells, LW is the quantum well width, and aQW(_o) is the MQW absorption coefﬁcient, which includes the internal electric ﬁeld (Eq. (1)). The Zesc is the electron escape probability from the well, which has been assumed to be 1 at room temperature for our modeled structures . Although the responsivity is one of the important parameters to characterize the detectors, it cannot be considered as ﬁgure of merit for a detector, because it increases with increasing of dark current. For this reason, the especial detectivity as ﬁgure of merit has been calculated. To calculate the especial detectivity one has to know the noise of the detectors. The most dominant noise in p–i–n UV detectors is the dark current and it is the combination of the radiative and non-radiative recombination currents. The non-radiative current can be calculated as Shockley–Read–Hall recombination and the radiative current can be obtained from the balance equation [13,14]. The non-radiative current is dispensable for biases of 1 V and higher. So, in our model samples because of strong piezoelectric effects inside the MQW structures, the non-radiative current will be neglected. To calculate the radiative current, we have used the balance theory assuming a constant quasi-Fermi level separation and equal to the applied voltage .
3. Results and discussion The model samples used in the calculation is the p–i–n heterojunction with 20 AlGaN/GaN MQW structures in the i-region and with an active area of 0.23 mm2. The MQW structures have 2 nm GaN quantum well width and 15 nm AlxGa1xN barrier width. Also the doping densities in p and n layers are 2 1018 cm3. The AlGaN (GaN) material parameters which have been used in the calculation are shown in Table 1. To obtain the detector characteristics, initially, the subband energies and related wavefunction have been calculated. The ﬁrst
Characterization of AlxGa1xN
Band gap (barrier) Band gap (well) ? m? e,B, me,w m? hh m? lh mJe mJhh mJlh Band offset ratio Permittivity Refractive index
Transition energy for E1-hh1 (eV)
Table 1 The AlxGa1xN characterization parameters
Transition energy for Ee1-LH1 (eV)
separation between the n ¼ 1 valance and conduction subband, N is the joint density, EB is the exciton binding energy [8,9]. Knowing the possibility of constructing UV detectors with AlGaN/GaN MQW by calculating electron–hole subband energy and related absorption coefﬁcient, we have calculated the detector characteristic parameters. One of the important parameters in detectors is the current responsivity, which is given by
(3.504+2.7156x) (eV) 3.504 (eV) (0.13+0.14x) m0 (1.52+1.16x) m0 (0.168+0.092x) m0 (0.16+0.12x) m0 (1.45+0.51x) m0 (1.45+0.51x) m0 70% 9.6 3.098
          
4.4 4.2 4 3.8 3.6 3.4 100 we 80 ll w 60 ide (An 40 20 ge str om )
0.6 0.4 ) ction a r f x (Al
5 4.5 4 3.5 3 100 80 ll w 60 ide (An 40 ge str om 20 )
0.8 0.2 0
0.6 0.4 tion) l frac x (A
Fig. 1. The transition energies of n ¼ 1 (a—heavy hole, b—light hole) for AlGaN/GaN/AlGaN quantum well as function of Al mole fraction and well width.
subband energy of electron and holes (heavy and light) for AlGaN/GaN/AlGaN quantum well has been calculated as a function of Al mole fraction and well width. Knowing the ﬁrst subbands energy it is easy to calculate the transition energy of the structures. As one can see from Fig. 1, which shows the transition energy of electron from heavy and light hole to the electron ﬁrst subband, the transition energy does not include the strategic
ARTICLE IN PRESS A. Asgari et al. / Microelectronics Journal 40 (2009) 104–107
polarization effects, the cutoff wavelength has blue shifts with Al mole fraction increasing. This behavior is related to transition energy increasing with Al mole fraction. The red shift in the responsivity of the structures is related to the strong polarization ﬁeld which increases with Al mole fraction. It should be mentioned that the polarization ﬁeld has approximately a linear behavior with Al mole fraction, so the red shift in cutoff wavelength of the responsivity by the Al mole fraction is approximately linear. As previously mentioned, the responsivity cannot be considered as ﬁgure of merit for a detector, because it increases with increase of dark current. For this reason, the especial detectivity has been calculated. Fig. 5 shows the detectivity of the p–i–n MQWP including and excluding polarization ﬁeld effects. As shown in this ﬁgure, in the case of excluded polarization ﬁeld, the detectivity cutoff wavelength has a red shift with increasing Al mole fraction and also there are only small changes in detectivity. On the other hand, in the case of polarization ﬁeld effects included, the detectivity cutoff wavelength has blue shift with increasing Al mole fraction. It is because of the transition
Transition Wavelength (nm)
window (230–280 nm) of ozone layer absorption, although all transitions are in the UV wavelengths. On the other hand, to model a photodetector, one has to know the effects of applied electric ﬁeld on it, so it is needed to know the effects of electric ﬁeld on electron and hole subband energies and wavefunctions. Our calculation results show that on increasing the applied electric ﬁeld the electron and hole energy decreases, where the decreasing ratio for holes is higher than that for electrons, so the energy gap between electron and hole (both electron–light hole and electron–heavy hole) decreases as shown in Fig. 2 for a sample with x ¼ 0.68 and Lw ¼ 2 nm. The electric ﬁeld not only changes the subband energy but also can affect the wavefunctions. The wavefunction and subband energy variation with electric ﬁeld may change the absorption coefﬁcient, which is a very important parameter in the modeling of detector characteristics. One of the important changes in absorption coefﬁcient is the absorption coefﬁcient peak shift to higher wavelength with increasing applied electric ﬁeld. On the other hand, the presence of strong spontaneous and straininduced (piezoelectric) polarization ﬁelds due to lattice mismatch between AlGaN/GaN is an important characteristic of the AlGaN/GaN material system. These polarization ﬁelds have been attributed to the reduced symmetry of wurtzite crystal structure and polar bonding nature of GaN and its alloy [18–21]. It is well known that the polarization ﬁeld is about 108 V/m and it is more than p–i–n diode built-in electric ﬁeld. So, to model correctly an electronic device from GaN-based heterostructure, one has to take into account the spontaneous and piezoelectric polarization effects. The effects of the polarization on the ﬁrst electron and heavy hole subband energy in AlGaN/GaN MQW with different Al mole fractions has been shown in Fig. 3. As evident from this ﬁgure, with increasing Al mole fraction the polarization ﬁeld increases and it can reduce the electron and hole subband energy. Therefore, the transition energy between electron and hole decreases with increasing Al mole fraction. Knowing the effects of polarization on subband energies and wavefunctions, the responsivity has been calculated for the p–i–n MQWP with 20 quantum wells including and excluding polarization ﬁeld effect. The quantum well width is 2 nm and the the barrier thickness is 15 nm. The Al mole fraction is varied from x ¼ 0.3 to x ¼ 0.6. Fig. 4 shows typical responsivity of AlGaN/GaN p–i–n MQWP with different Al contents. Excluding the
Transition Energy (eV)
Al mole fraction Fig. 3. The effects of polarization on transition energy as function of Al mole fraction in the single AlGaN/GaN/AlGaN quantum well with 2 nm well width and 15 nm barrier width. The solid line and dashed line are related to the case without polarization effects and with polarization effects, respectively. The energy has been calculated from the middle of the wells.
Eg (e-LH) Eg (e-HH)
0 50 100 Electric Field (V/μm)
Fig. 2. (a) First electron subband energy, (b) ﬁrst heavy hole and light hole subbands energies, and (c) energy gap between electron and hole ﬁrst subbands (transition energy) as function of applied electric ﬁeld for Al0.68Ga0.32N/GaN/Al0.68Ga0.32N quantum well.
ARTICLE IN PRESS A. Asgari et al. / Microelectronics Journal 40 (2009) 104–107
From this theoretical study on AlGaN/GaN p–i–n MQWP characterized parameter, it can be concluded that (1) the MQWP detectivity does not include the strategic window of ozone layer, (2) in AlGaN/GaN QW with increasing applied electric ﬁeld, the transition energy decreases and so the responsivity has a red shift with increasing applied electric ﬁeld, and (3) with including the polarization ﬁelds effects, by increasing Al mole fraction, the transition energy decreases, the total noise increases, and the responsivity has a red shift, and so the detectivity decreases and has a red shift.
x = 0.3 x = 0.4 x = 0.5
x = 0.6
Without Polarization 0.00 250
λ (nm) Fig. 4. The responsivity of p–i–n MQWP with 20 quantum wells with 2 nm width and barrier with 15 nm width and x ¼ 0.3, 0.4, 0.5, and 0.6.
4.5 with Polarization Detectivity (x109 cmHz1/2 W -1)
4.0 3.5 3.0 2.5
2.0 1.5 1.0 0.5 0.0 250
X = 0.3 X = 0.4 X = 0.5 X = 0.6 280
310 340 Wavelength (nm)
Fig. 5. The detectivity of p–i–n MQWP with 20 quantum wells with 2 nm width and barrier with 15 nm width and x ¼ 0.3, 0.4, 0.5, and 0.6.
energy decreasing with Al content increasing. Also, the detectivity peak decreases with increasing Al mole fraction, because the total noise increases with Al molar fraction.
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