OSA's Digital Library

Optics Express

Optics Express

  • Editor: C. Martijn de Sterke
  • Vol. 18, Iss. 14 — Jul. 5, 2010
  • pp: 14604–14615
« Show journal navigation

High performances III-Nitride Quantum Dot infrared photodetector operating at room temperature

A. Asgari and S. Razi  »View Author Affiliations


Optics Express, Vol. 18, Issue 14, pp. 14604-14615 (2010)
http://dx.doi.org/10.1364/OE.18.014604


View Full Text Article

Acrobat PDF (1032 KB)





Browse Journals / Lookup Meetings

Browse by Journal and Year


   


Lookup Conference Papers

Close Browse Journals / Lookup Meetings

Article Tools

Share
Citations

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 A l 0.2 G a 0.8 N QD (capping layer) embedded in A l 0.8 G a 0.2 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 × 108CmHz1/ 2/W is achieved at room temperature.

© 2010 OSA

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

1. B. F. Levine, “Quantum well infrared photodetectors,” J. Appl. Phys. 74(8), R1–R81 (1993). [CrossRef]

,2

2. A. Goldberg, S. Kennerly, J. Little, T. Shafer, C. Mears, H. Schaake, M. Winn, M. Taylor, and P. Uppal, “Comparison of HgCdTe and quantum-well infrared photodetector dual-band focal plane arrays,” Opt. Eng. 42(1), 30–46 (2003). [CrossRef]

]. 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 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

3. A. Rogalski, “Infrared Detectors”, NewYork: Gordon and Breach, 155–650 (2000).

]. Another serious drawback is the fact that, the n-type QWIPs cannot detect normal incidence radiation, due to the polarization selection rules [1

1. B. F. Levine, “Quantum well infrared photodetectors,” J. Appl. Phys. 74(8), R1–R81 (1993). [CrossRef]

]. 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

4. S. Y. Wang, S. D. Lin, H. W. Wu, and C. P. Lee, “Low dark current quantum-dot infrared photodetectors with an AlGaAs current blocking layer,” Appl. Phys. Lett. 78(8), 1023 (2001). [CrossRef]

7

7. S. Y. Wang, M. C. Lo, H. Y. Hsiao, H. S. Ling, and C. P. Lee, “Temperature dependent responsivity of quantum dot Infrared photodetectors,” Infra. Phys. Technol. 50, 166 (2007). [CrossRef]

]. 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

8. D. Pan, E. Towe, and S. Kennerly, “Normal-incidence intersubband (In, Ga)As/GaAs quantum dot infrared photodetectors,” Appl. Phys. Lett. 73(14), 1937 (1998). [CrossRef]

10

10. L. Jiang, S. S. Li, N. Yeh, J. Chyi, C. E. Ross, and K. S. Jones, “In0.6Ga0.4As/GaAs quantum-dot infrared photodetector with operating temperature up to 260 K,” Appl. Phys. Lett. 82(12), 1986 (2003). [CrossRef]

], (ii) reduced electron-phonon scattering, so long excited state lifetime, and high current gain [7

7. S. Y. Wang, M. C. Lo, H. Y. Hsiao, H. S. Ling, and C. P. Lee, “Temperature dependent responsivity of quantum dot Infrared photodetectors,” Infra. Phys. Technol. 50, 166 (2007). [CrossRef]

, 11

11. U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42(14), 8947–8951 (1990). [CrossRef]

, 12

12. Z. Ye, J. C. Campbell, Z. Chen, E.-T. Kim, and A. Madhukar, “Noise and photoconductive gain in InAs quantum-dot Infrared photodetectors,” Appl. Phys. Lett. 83(6), 1234 (2003). [CrossRef]

]. (iii) The QDIP technology is believed to be promising for high-temperature operations [13

13. S. Chakrabarti, A. D. Stiff-Roberts, P. Bhattacharya, S. Gunapala, S. Bandara, S. B. Rafol, and S. W. Kennerly, “High-temperature operation of InAs-GaAs quantum-dot infrared photodetectors with large responsivity and detectivity,” IEEE Photon. Technol. Lett. 16(5), 1361–1363 (2004). [CrossRef]

, 14

14. S. Tang, C. Chiang, P. Weng, Y. Gau, J. Luo, S. Yang, C. Shih, S. Lin, and S. Lee, “High-temperature operation normal incident 256/spl times/256 InAs-GaAs quantum-dot infrared photodetector focal plane array,” IEEE Photon. Technol. Lett. 18(8), 986–988 (2006). [CrossRef]

].

In order to improve the performance of these detectors, different structures and materials have been investigated [4

4. S. Y. Wang, S. D. Lin, H. W. Wu, and C. P. Lee, “Low dark current quantum-dot infrared photodetectors with an AlGaAs current blocking layer,” Appl. Phys. Lett. 78(8), 1023 (2001). [CrossRef]

8

8. D. Pan, E. Towe, and S. Kennerly, “Normal-incidence intersubband (In, Ga)As/GaAs quantum dot infrared photodetectors,” Appl. Phys. Lett. 73(14), 1937 (1998). [CrossRef]

, 15

15. S. Y. Lin, Y. R. Tsai, and S. C. Lee, “High-performance InAs/GaAs quantum-dot infrared photodetectors with a single-sided Al0.3Ga0.7 blocking layer,” Appl. Phys. Lett. 78(18), 2784–2786 (2001). [CrossRef]

, 16

16. H. Lim, W. Zhang, S. Tsao, T. Sills, J. Szafraniec, K. Mi, B. Movaghar, and M. Razeghi, “‘’Quantum dot infrared photodetectors: Comparison of experiment and theory,” Phys. Rev. B 72(8), 085332 (2005). [CrossRef]

]. It has been shown that a current blocking layer can be effectively used to reduce the dark current. Lin et al. [15

15. S. Y. Lin, Y. R. Tsai, and S. C. Lee, “High-performance InAs/GaAs quantum-dot infrared photodetectors with a single-sided Al0.3Ga0.7 blocking layer,” Appl. Phys. Lett. 78(18), 2784–2786 (2001). [CrossRef]

] and Stiff et al. [9

9. A. Stiff, S. Krishna, P. Bhattacharya, and S. Kennerly, “High-detectivity, normal-incidence, mid-infrared (λ~4 μm)InAs/GaAs quantum-dot detector operating at 150 K,” Appl. Phys. Lett. 79(3), 421 (2001). [CrossRef]

, 17

17. A. D. Stiff, S. Krishna, P. Bhattacharya, and S. Kennerly, “Normal-incidence, high-temperature, mid-infrared, InAs-GaAs vertical quantum-dot infrared photodetector,” IEEE J. Quantum Electron. 37(11), 1412–1419 (2001). [CrossRef]

] have reported QDIPs with a single AlGaAs blocking layer on one side of the InAs/GaAs QD layers. Wang et al. [4

4. S. Y. Wang, S. D. Lin, H. W. Wu, and C. P. Lee, “Low dark current quantum-dot infrared photodetectors with an AlGaAs current blocking layer,” Appl. Phys. Lett. 78(8), 1023 (2001). [CrossRef]

] 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

18. T. Wang, J. Bai, and S. Sakai, “Influence of InGaN/GaN quantum-well structure on the performance of light-emitting diodes and laser diodes grown on sapphire substrates,” J. Cryst. Growth 224(1-2), 5–10 (2001). [CrossRef]

20

20. S. Shishech, A. Asgari, and R. Kheradmand, “The effect of temperature on the recombination rate of AlGaN/GaN light emitting diodes,” Opt. Quantum Electron. , under press (2010).

]. 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 Al0.2Ga0.8N QD embedded in Al0.8Ga0.2N layer is assumed. The proposed structure has been shown in Fig. 1
Fig. 1 The proposed cubic shaped GaN QD within a large Al0.2Ga0.8NQD.
.

Five layers with QD density of Nd=1024m3 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

21. L. W. Wang, A. J. Williamson, A. Zunger, H. Jiang, and J. Singh, “Comparison of the k⋅p and direct diagonalization approaches to the electronic structure of InAs/GaAs quantum dots,” Appl. Phys. Lett. 76(3), 339–342 (2000). [CrossRef]

24

24. M. Califano and P. Harrison, “Presentation and experimental validation of a single-band, constant-potential model for self-assembled InAs/GaAs quantum dots,” Phys. Rev. B 61(16), 10959–10965 (2000). [CrossRef]

]. 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

22. C. Y. Ngo, S. F. Yoon, W. J. Fan, and S. C. Chua, “Effects of size and shape on electronic states of quantum dots,” Phys. Rev. B 74(24), 245331 (2006). [CrossRef]

]:
H=221m*(x,y,z)+v(x,y,z).
(1)
In which m* is the electron effective mass and is given by:
m(x,y,z)={m*GaNinQDm*Al0.2Ga0.8Nincappinglayerm*Al0.8Ga0.2Ninbarrier,
(2)
and
V(x,y,z)={0insideGaNQDΔEcelse.
(3)
WhereΔEcis the conduction and valance bands discontinuity [25

25. O. Ambacher, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, W. J. Schaff, L. F. Eastman, R. Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck, “Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures,” J. Appl. Phys. 85(6), 3222 (1999). [CrossRef]

]:
ΔEc=0.7(x×6.13+(1x)×3.42x(1x)Eg0)eV,
(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:
H=221m*(x,y,z)+v(x,y,z)+eF.r
(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. 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

26. S. De Rinaldis, I. D’Amico, E. Biolatti, R. Rinaldi, R. Cingolani, and F. Rossi, “Intrinsic exciton-exciton coupling in GaN-based quantum dots: Application to solid-state quantum computing,” Phys. Rev. B 65(8), 081309 (2002). [CrossRef]

]:
Fd=Lbr(PtotbrPtotd)ε0(Ldεbr+Lbrεd).
(6)
Where εbr(d) is the relative dielectric constant of the barrier (dot), Ptotbr/d is the total polarization and Lbr/dis the width of the barrier and height of the dot.
Ptotbr/d=Ppiezobr/d+Pspbr/d.
(7)
The Piezoelectric polarization includes: one part induced by the lattice mismatch (ms), and the other caused by thermal strain (ts): Ppiezobr/d=Pmsbr/d+Ptsbr/d, where Pmsbr/d=2(e31e33c13c33)(aa0a) and Ptsd=3.2×104c/m2 [26

26. S. De Rinaldis, I. D’Amico, E. Biolatti, R. Rinaldi, R. Cingolani, and F. Rossi, “Intrinsic exciton-exciton coupling in GaN-based quantum dots: Application to solid-state quantum computing,” Phys. Rev. B 65(8), 081309 (2002). [CrossRef]

]. e31 and e33 are the piezoelectric coefficients, c13 and c33 are elastic constants, and ‘a’ is the lattice constant of AlxGa1xN and is a=(0.077x+3.189)Ao. (All other material parameters can be found in [27

27. R. Cingolani, A. Botchkarev, H. Tang, H. Morkoç, G. Traetta, G. Coli, M. Lomascolo, A. Di Carlo, F. Della Sala, P. Lugli, H. M. G. Traetta, G. Coli, M. L. A. D. Carlo, F. D. Sala, and P. Lugli, “Spontaneous polarization and piezoelectric field in GaN/Al0.15Ga0.85N quantum wells: Impact on the optical spectra,” Phys. Rev. B 61(4), 2711–2715 (2000). [CrossRef]

]).

The spontaneous polarization for AlxGa1xN is Al molar fraction dependent and is given by: Psp=(0.052x0.029).

To solve the Schrödinger equation, assuming that the wave functions are expanded in terms of the normalized plane waves [22

22. C. Y. Ngo, S. F. Yoon, W. J. Fan, and S. C. Chua, “Effects of size and shape on electronic states of quantum dots,” Phys. Rev. B 74(24), 245331 (2006). [CrossRef]

]:
ψnx,ny,nz(x,y,z)=1LxLyLznx,ny,nzanx,ny,nzexpi(knx.x+kny.y+knz.z).
(8)
whereknx=kx+nxKx,kny=ky+nyKy, knz=kz+nzKz and Kx=2πLx, Ky=2πLy, Kz=2πLz. Lx,LyandLz are lengths of the unit cell along the x, y and z directions. nx,ny,nz are the number of plane waves along the x, y and z directions respectively.

As reported in [28

28. M. A. Cusack, P. R. Briddon, and M. Jaros, “Electronic structure of InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 54(4), R2300–R2303 (1996). [CrossRef]

], 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. nx,ny,   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
Fig. 2 Energy diagram for the proposed structure and the strongest transition ‘a’.
.

The transition matrix element, rif=<ψi|r|ψf> can be calculated using obtained wave functions. In this relation ψiandψfare the initial and final transition states, respectively. The oscillator strength, fif, of a given transition is one of the most important factors in the absorption coefficient α(ω)and is given by:
fif=2m2(EiEf)​    |rif|2,
(9)
where Ei and Ef are the initial and final transition state energy, respectively.

The absorption coefficient can be expressed as [16

16. H. Lim, W. Zhang, S. Tsao, T. Sills, J. Szafraniec, K. Mi, B. Movaghar, and M. Razeghi, “‘’Quantum dot infrared photodetectors: Comparison of experiment and theory,” Phys. Rev. B 72(8), 085332 (2005). [CrossRef]

]:
α=πNdnope2m*εε0c(ninf)fifΓ(ωωif)2+Γ2,
(10)
where Γ is the life time broadening which is considered 3×103eV . Nd is QD volume density, nop is refractive index, ε0 and ε are the permeability of free space and the medium, respectively. ni and nf are the occupation probabilities of the initial and final states. The occupation probability can be defined as:
ni=eEi/kBT(seEs/kBT+teEt/kBT+εcdερ(ε)f(ε)/Nd),
(11)
where Es is the quantum dot energy levels, ρ(ε) is the density of continuum states, kB is Boltzmann constant, and Et is the trap levels. For the low temperatures, ni1 and nf0 and the specific transition is high, but with increasing the temperature, the carriers redistributed and the transition decreases.

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

R/R0=ni(υeceEec(F)/kBTυ0+υeceEec(F)/kBT)F.
(14)

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 ni 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
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.
. We have not considered the temperature dependency of the life time 1/ν0(T) 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

4. S. Y. Wang, S. D. Lin, H. W. Wu, and C. P. Lee, “Low dark current quantum-dot infrared photodetectors with an AlGaAs current blocking layer,” Appl. Phys. Lett. 78(8), 1023 (2001). [CrossRef]

,5

5. X. Lu, J. Vaillancourt, and M. J. Meisner, “Temperature-dependent photoresponsivity and high-temperature (190 K) operation of a quantum dot infrared photodetector,” Appl. Phys. Lett. 91(5), 051115 (2007). [CrossRef]

,9

9. A. Stiff, S. Krishna, P. Bhattacharya, and S. Kennerly, “High-detectivity, normal-incidence, mid-infrared (λ~4 μm)InAs/GaAs quantum-dot detector operating at 150 K,” Appl. Phys. Lett. 79(3), 421 (2001). [CrossRef]

].

Considering the most important factors dark current could be written as [30

30. M. Razeghi, H. Lim, S. Tsao, J. Szafraniec, W. Zhang, K. Mi, and B. Movaghar, “Transport and photodetection in self-assembled semiconductor quantum dots,” Nanotechnology 16(2), 219–229 (2005). [CrossRef] [PubMed]

]:
Idark=AeμFNd(1ne)Cbesυscgs0fs1+wscfs(1ne)Cbe×eEsc/kBTeςEsc3/2/eFaeςEsc1/2eeFa/kBT1eςEsc1/2eeFa/kBT.
(15)
In this relation fs is the Fermi function for the s'th energy state, A is the illuminated area of the device, (1ne) is the probability that the state is empty. wSC is the escape rates between the band and QD states, ς=a(2me*2)12, and gS is the density of excited states. Considering I0=AeμFNd(1ne)Cbeυecgs0, the logarithm of the normalized dark current (IdarkI0) versus applied bias for different temperature has been plotted in Fig. 6
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.
. 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

16. H. Lim, W. Zhang, S. Tsao, T. Sills, J. Szafraniec, K. Mi, B. Movaghar, and M. Razeghi, “‘’Quantum dot infrared photodetectors: Comparison of experiment and theory,” Phys. Rev. B 72(8), 085332 (2005). [CrossRef]

, 30

30. M. Razeghi, H. Lim, S. Tsao, J. Szafraniec, W. Zhang, K. Mi, and B. Movaghar, “Transport and photodetection in self-assembled semiconductor quantum dots,” Nanotechnology 16(2), 219–229 (2005). [CrossRef] [PubMed]

, 31

31. Z. Ye, J. C. Campbell, Z. Chen, E.-T. Kim, and A. Madhukar, “Normal-Incidence InAs Self-Assembled Quantum-Dot Infrared Photodetectors With a High Detectivity,” IEEE J. Quantum Electron. 38, 1534–1538 (2002).

]. 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.

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
D=responsivity×AnoiseΔf=RAΔfiN.
(16)
In this relation iN is the noise current and defines asiN=4eIdgΔf, Δf is the band width frequency and we considered it~1.

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

15. S. Y. Lin, Y. R. Tsai, and S. C. Lee, “High-performance InAs/GaAs quantum-dot infrared photodetectors with a single-sided Al0.3Ga0.7 blocking layer,” Appl. Phys. Lett. 78(18), 2784–2786 (2001). [CrossRef]

].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
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.
.

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

32. X. Lu, J. Vaillancourt, M. J. Meisner, and A. Stintz, “Long wave infrared InAs-InGaAs quantum-dot infrared photodetector with high operating temperature over 170 K,” J. Phys. D Appl. Phys. 40(19), 5878–5882 (2007). [CrossRef]

], Peak specific photodetectivity D* of 3.8×109 cmHz1/2/W and 1.3×108 cmHz1/2/W 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 cmHz1/2/W [33

33. P. Bhattacharya, X. H. Su, S. Chakrabarti, G. Ariyawansa, and A. G. U. Perera, “Characteristics of a tunneling quantum-dot infrared photodetector operating at room temperature,” Appl. Phys. Lett. 86(19), 191106 (2005). [CrossRef]

]Bhattacharya et all, reported the some deal high detectivity, about 8.6×106cmHz1/2/W, in 17μm wave length for 300k temperature [34

34. A. G. U. Perera, P. V. V. Jayaweera, G. Ariyawansa, S. G. Matsik, K. Tennakone, M. Buchanan, H. C. Liu, X. H. Su, and P. Bhattacharya, “Room temperature nano- and microstructure photon detectors,” Microelectron. J. 40(3), 507–511 (2009). [CrossRef]

] and in the other work they reported 6×109D*(CmHz1/2/W)1011 for temperatures100KT200K [18

18. T. Wang, J. Bai, and S. Sakai, “Influence of InGaN/GaN quantum-well structure on the performance of light-emitting diodes and laser diodes grown on sapphire substrates,” J. Cryst. Growth 224(1-2), 5–10 (2001). [CrossRef]

,22

22. C. Y. Ngo, S. F. Yoon, W. J. Fan, and S. C. Chua, “Effects of size and shape on electronic states of quantum dots,” Phys. Rev. B 74(24), 245331 (2006). [CrossRef]

]. 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

34. A. G. U. Perera, P. V. V. Jayaweera, G. Ariyawansa, S. G. Matsik, K. Tennakone, M. Buchanan, H. C. Liu, X. H. Su, and P. Bhattacharya, “Room temperature nano- and microstructure photon detectors,” Microelectron. J. 40(3), 507–511 (2009). [CrossRef]

,35

35. H. R. Saghai, N. Sadoogi, A. Rostami, and H. Baghban, “Ultra-high detectivity room temperature THZ-IR photodetector based on resonant tunneling spherical centered defect quantum dot (RT-SCDQD),” Opt. Commun. 282(17), 3499–3508 (2009). [CrossRef]

].

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, 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.

References and links

1.

B. F. Levine, “Quantum well infrared photodetectors,” J. Appl. Phys. 74(8), R1–R81 (1993). [CrossRef]

2.

A. Goldberg, S. Kennerly, J. Little, T. Shafer, C. Mears, H. Schaake, M. Winn, M. Taylor, and P. Uppal, “Comparison of HgCdTe and quantum-well infrared photodetector dual-band focal plane arrays,” Opt. Eng. 42(1), 30–46 (2003). [CrossRef]

3.

A. Rogalski, “Infrared Detectors”, NewYork: Gordon and Breach, 155–650 (2000).

4.

S. Y. Wang, S. D. Lin, H. W. Wu, and C. P. Lee, “Low dark current quantum-dot infrared photodetectors with an AlGaAs current blocking layer,” Appl. Phys. Lett. 78(8), 1023 (2001). [CrossRef]

5.

X. Lu, J. Vaillancourt, and M. J. Meisner, “Temperature-dependent photoresponsivity and high-temperature (190 K) operation of a quantum dot infrared photodetector,” Appl. Phys. Lett. 91(5), 051115 (2007). [CrossRef]

6.

J. Phillips, P. Bhattacharya, S. W. Kennerly, D. W. Beekman, and M. Dutta. “Self-assembled InAs-GaAs quantum-dot intersubband detectors,” IEEE J. Quantum Electron. 35(6), 936–943 (1999). [CrossRef]

7.

S. Y. Wang, M. C. Lo, H. Y. Hsiao, H. S. Ling, and C. P. Lee, “Temperature dependent responsivity of quantum dot Infrared photodetectors,” Infra. Phys. Technol. 50, 166 (2007). [CrossRef]

8.

D. Pan, E. Towe, and S. Kennerly, “Normal-incidence intersubband (In, Ga)As/GaAs quantum dot infrared photodetectors,” Appl. Phys. Lett. 73(14), 1937 (1998). [CrossRef]

9.

A. Stiff, S. Krishna, P. Bhattacharya, and S. Kennerly, “High-detectivity, normal-incidence, mid-infrared (λ~4 μm)InAs/GaAs quantum-dot detector operating at 150 K,” Appl. Phys. Lett. 79(3), 421 (2001). [CrossRef]

10.

L. Jiang, S. S. Li, N. Yeh, J. Chyi, C. E. Ross, and K. S. Jones, “In0.6Ga0.4As/GaAs quantum-dot infrared photodetector with operating temperature up to 260 K,” Appl. Phys. Lett. 82(12), 1986 (2003). [CrossRef]

11.

U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42(14), 8947–8951 (1990). [CrossRef]

12.

Z. Ye, J. C. Campbell, Z. Chen, E.-T. Kim, and A. Madhukar, “Noise and photoconductive gain in InAs quantum-dot Infrared photodetectors,” Appl. Phys. Lett. 83(6), 1234 (2003). [CrossRef]

13.

S. Chakrabarti, A. D. Stiff-Roberts, P. Bhattacharya, S. Gunapala, S. Bandara, S. B. Rafol, and S. W. Kennerly, “High-temperature operation of InAs-GaAs quantum-dot infrared photodetectors with large responsivity and detectivity,” IEEE Photon. Technol. Lett. 16(5), 1361–1363 (2004). [CrossRef]

14.

S. Tang, C. Chiang, P. Weng, Y. Gau, J. Luo, S. Yang, C. Shih, S. Lin, and S. Lee, “High-temperature operation normal incident 256/spl times/256 InAs-GaAs quantum-dot infrared photodetector focal plane array,” IEEE Photon. Technol. Lett. 18(8), 986–988 (2006). [CrossRef]

15.

S. Y. Lin, Y. R. Tsai, and S. C. Lee, “High-performance InAs/GaAs quantum-dot infrared photodetectors with a single-sided Al0.3Ga0.7 blocking layer,” Appl. Phys. Lett. 78(18), 2784–2786 (2001). [CrossRef]

16.

H. Lim, W. Zhang, S. Tsao, T. Sills, J. Szafraniec, K. Mi, B. Movaghar, and M. Razeghi, “‘’Quantum dot infrared photodetectors: Comparison of experiment and theory,” Phys. Rev. B 72(8), 085332 (2005). [CrossRef]

17.

A. D. Stiff, S. Krishna, P. Bhattacharya, and S. Kennerly, “Normal-incidence, high-temperature, mid-infrared, InAs-GaAs vertical quantum-dot infrared photodetector,” IEEE J. Quantum Electron. 37(11), 1412–1419 (2001). [CrossRef]

18.

T. Wang, J. Bai, and S. Sakai, “Influence of InGaN/GaN quantum-well structure on the performance of light-emitting diodes and laser diodes grown on sapphire substrates,” J. Cryst. Growth 224(1-2), 5–10 (2001). [CrossRef]

19.

L.-W. Ji, T.-H. Fang, and T.-H. Meen, “Effects of strain on the characteristics of InGaN-GaN multiple quantum dot blue light emitting diodes,” Phys. Lett. A 355(2), 118–121 (2006). [CrossRef]

20.

S. Shishech, A. Asgari, and R. Kheradmand, “The effect of temperature on the recombination rate of AlGaN/GaN light emitting diodes,” Opt. Quantum Electron. , under press (2010).

21.

L. W. Wang, A. J. Williamson, A. Zunger, H. Jiang, and J. Singh, “Comparison of the k⋅p and direct diagonalization approaches to the electronic structure of InAs/GaAs quantum dots,” Appl. Phys. Lett. 76(3), 339–342 (2000). [CrossRef]

22.

C. Y. Ngo, S. F. Yoon, W. J. Fan, and S. C. Chua, “Effects of size and shape on electronic states of quantum dots,” Phys. Rev. B 74(24), 245331 (2006). [CrossRef]

23.

M. Roy and P. A. Makasym, “Efficient method for calculating electronic states in self-assembled quantum dots,” Phys. Rev. B , 68235308 (2003).

24.

M. Califano and P. Harrison, “Presentation and experimental validation of a single-band, constant-potential model for self-assembled InAs/GaAs quantum dots,” Phys. Rev. B 61(16), 10959–10965 (2000). [CrossRef]

25.

O. Ambacher, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, W. J. Schaff, L. F. Eastman, R. Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck, “Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures,” J. Appl. Phys. 85(6), 3222 (1999). [CrossRef]

26.

S. De Rinaldis, I. D’Amico, E. Biolatti, R. Rinaldi, R. Cingolani, and F. Rossi, “Intrinsic exciton-exciton coupling in GaN-based quantum dots: Application to solid-state quantum computing,” Phys. Rev. B 65(8), 081309 (2002). [CrossRef]

27.

R. Cingolani, A. Botchkarev, H. Tang, H. Morkoç, G. Traetta, G. Coli, M. Lomascolo, A. Di Carlo, F. Della Sala, P. Lugli, H. M. G. Traetta, G. Coli, M. L. A. D. Carlo, F. D. Sala, and P. Lugli, “Spontaneous polarization and piezoelectric field in GaN/Al0.15Ga0.85N quantum wells: Impact on the optical spectra,” Phys. Rev. B 61(4), 2711–2715 (2000). [CrossRef]

28.

M. A. Cusack, P. R. Briddon, and M. Jaros, “Electronic structure of InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 54(4), R2300–R2303 (1996). [CrossRef]

29.

A. Asgari, M. Kalafi, and L. Faraone, “The effects of partially occupied sub-bands on two-dimensional electron mobility in AlxGa1-xN/GaN heterostructures,” J. Appl. Phys. 95(3), 1185 (2004). [CrossRef]

30.

M. Razeghi, H. Lim, S. Tsao, J. Szafraniec, W. Zhang, K. Mi, and B. Movaghar, “Transport and photodetection in self-assembled semiconductor quantum dots,” Nanotechnology 16(2), 219–229 (2005). [CrossRef] [PubMed]

31.

Z. Ye, J. C. Campbell, Z. Chen, E.-T. Kim, and A. Madhukar, “Normal-Incidence InAs Self-Assembled Quantum-Dot Infrared Photodetectors With a High Detectivity,” IEEE J. Quantum Electron. 38, 1534–1538 (2002).

32.

X. Lu, J. Vaillancourt, M. J. Meisner, and A. Stintz, “Long wave infrared InAs-InGaAs quantum-dot infrared photodetector with high operating temperature over 170 K,” J. Phys. D Appl. Phys. 40(19), 5878–5882 (2007). [CrossRef]

33.

P. Bhattacharya, X. H. Su, S. Chakrabarti, G. Ariyawansa, and A. G. U. Perera, “Characteristics of a tunneling quantum-dot infrared photodetector operating at room temperature,” Appl. Phys. Lett. 86(19), 191106 (2005). [CrossRef]

34.

A. G. U. Perera, P. V. V. Jayaweera, G. Ariyawansa, S. G. Matsik, K. Tennakone, M. Buchanan, H. C. Liu, X. H. Su, and P. Bhattacharya, “Room temperature nano- and microstructure photon detectors,” Microelectron. J. 40(3), 507–511 (2009). [CrossRef]

35.

H. R. Saghai, N. Sadoogi, A. Rostami, and H. Baghban, “Ultra-high detectivity room temperature THZ-IR photodetector based on resonant tunneling spherical centered defect quantum dot (RT-SCDQD),” Opt. Commun. 282(17), 3499–3508 (2009). [CrossRef]

OCIS Codes
(250.0040) Optoelectronics : Detectors

ToC Category:
Detectors

History
Original Manuscript: April 20, 2010
Revised Manuscript: May 27, 2010
Manuscript Accepted: June 15, 2010
Published: June 23, 2010

Citation
A. Asgari and S. Razi, "High performances III-Nitride Quantum Dot infrared photodetector operating at room temperature," Opt. Express 18, 14604-14615 (2010)
http://www.opticsinfobase.org/oe/abstract.cfm?URI=oe-18-14-14604


Sort:  Author  |  Year  |  Journal  |  Reset  

References

  1. B. F. Levine, “Quantum well infrared photodetectors,” J. Appl. Phys. 74(8), R1–R81 (1993). [CrossRef]
  2. A. Goldberg, S. Kennerly, J. Little, T. Shafer, C. Mears, H. Schaake, M. Winn, M. Taylor, and P. Uppal, “Comparison of HgCdTe and quantum-well infrared photodetector dual-band focal plane arrays,” Opt. Eng. 42(1), 30–46 (2003). [CrossRef]
  3. A. Rogalski, “Infrared Detectors”, NewYork: Gordon and Breach, 155–650 (2000).
  4. S. Y. Wang, S. D. Lin, H. W. Wu, and C. P. Lee, “Low dark current quantum-dot infrared photodetectors with an AlGaAs current blocking layer,” Appl. Phys. Lett. 78(8), 1023 (2001). [CrossRef]
  5. X. Lu, J. Vaillancourt, and M. J. Meisner, “Temperature-dependent photoresponsivity and high-temperature (190 K) operation of a quantum dot infrared photodetector,” Appl. Phys. Lett. 91(5), 051115 (2007). [CrossRef]
  6. J. Phillips, P. Bhattacharya, S. W. Kennerly, D. W. Beekman, and M. Dutta. “Self-assembled InAs-GaAs quantum-dot intersubband detectors,” IEEE J. Quantum Electron. 35(6), 936–943 (1999). [CrossRef]
  7. S. Y. Wang, M. C. Lo, H. Y. Hsiao, H. S. Ling, and C. P. Lee, “Temperature dependent responsivity of quantum dot Infrared photodetectors,” Infra. Phys. Technol. 50, 166 (2007). [CrossRef]
  8. D. Pan, E. Towe, and S. Kennerly, “Normal-incidence intersubband (In, Ga)As/GaAs quantum dot infrared photodetectors,” Appl. Phys. Lett. 73(14), 1937 (1998). [CrossRef]
  9. A. Stiff, S. Krishna, P. Bhattacharya, and S. Kennerly, “High-detectivity, normal-incidence, mid-infrared (λ~4 μm)InAs/GaAs quantum-dot detector operating at 150 K,” Appl. Phys. Lett. 79(3), 421 (2001). [CrossRef]
  10. L. Jiang, S. S. Li, N. Yeh, J. Chyi, C. E. Ross, and K. S. Jones, “In0.6Ga0.4As/GaAs quantum-dot infrared photodetector with operating temperature up to 260 K,” Appl. Phys. Lett. 82(12), 1986 (2003). [CrossRef]
  11. U. Bockelmann and G. Bastard, “Phonon scattering and energy relaxation in two-, one-, and zero-dimensional electron gases,” Phys. Rev. B 42(14), 8947–8951 (1990). [CrossRef]
  12. Z. Ye, J. C. Campbell, Z. Chen, E.-T. Kim, and A. Madhukar, “Noise and photoconductive gain in InAs quantum-dot Infrared photodetectors,” Appl. Phys. Lett. 83(6), 1234 (2003). [CrossRef]
  13. S. Chakrabarti, A. D. Stiff-Roberts, P. Bhattacharya, S. Gunapala, S. Bandara, S. B. Rafol, and S. W. Kennerly, “High-temperature operation of InAs-GaAs quantum-dot infrared photodetectors with large responsivity and detectivity,” IEEE Photon. Technol. Lett. 16(5), 1361–1363 (2004). [CrossRef]
  14. S. Tang, C. Chiang, P. Weng, Y. Gau, J. Luo, S. Yang, C. Shih, S. Lin, and S. Lee, “High-temperature operation normal incident 256/spl times/256 InAs-GaAs quantum-dot infrared photodetector focal plane array,” IEEE Photon. Technol. Lett. 18(8), 986–988 (2006). [CrossRef]
  15. S. Y. Lin, Y. R. Tsai, and S. C. Lee, “High-performance InAs/GaAs quantum-dot infrared photodetectors with a single-sided Al0.3Ga0.7 blocking layer,” Appl. Phys. Lett. 78(18), 2784–2786 (2001). [CrossRef]
  16. H. Lim, W. Zhang, S. Tsao, T. Sills, J. Szafraniec, K. Mi, B. Movaghar, and M. Razeghi, “‘’Quantum dot infrared photodetectors: Comparison of experiment and theory,” Phys. Rev. B 72(8), 085332 (2005). [CrossRef]
  17. A. D. Stiff, S. Krishna, P. Bhattacharya, and S. Kennerly, “Normal-incidence, high-temperature, mid-infrared, InAs-GaAs vertical quantum-dot infrared photodetector,” IEEE J. Quantum Electron. 37(11), 1412–1419 (2001). [CrossRef]
  18. T. Wang, J. Bai, and S. Sakai, “Influence of InGaN/GaN quantum-well structure on the performance of light-emitting diodes and laser diodes grown on sapphire substrates,” J. Cryst. Growth 224(1-2), 5–10 (2001). [CrossRef]
  19. L.-W. Ji, T.-H. Fang, and T.-H. Meen, “Effects of strain on the characteristics of InGaN-GaN multiple quantum dot blue light emitting diodes,” Phys. Lett. A 355(2), 118–121 (2006). [CrossRef]
  20. S. Shishech, A. Asgari, and R. Kheradmand, “The effect of temperature on the recombination rate of AlGaN/GaN light emitting diodes,” Opt. Quantum Electron. , under press (2010).
  21. L. W. Wang, A. J. Williamson, A. Zunger, H. Jiang, and J. Singh, “Comparison of the k⋅p and direct diagonalization approaches to the electronic structure of InAs/GaAs quantum dots,” Appl. Phys. Lett. 76(3), 339–342 (2000). [CrossRef]
  22. C. Y. Ngo, S. F. Yoon, W. J. Fan, and S. C. Chua, “Effects of size and shape on electronic states of quantum dots,” Phys. Rev. B 74(24), 245331 (2006). [CrossRef]
  23. M. Roy and P. A. Makasym, “Efficient method for calculating electronic states in self-assembled quantum dots,” Phys. Rev. B , 68235308 (2003).
  24. M. Califano and P. Harrison, “Presentation and experimental validation of a single-band, constant-potential model for self-assembled InAs/GaAs quantum dots,” Phys. Rev. B 61(16), 10959–10965 (2000). [CrossRef]
  25. O. Ambacher, J. Smart, J. R. Shealy, N. G. Weimann, K. Chu, M. Murphy, W. J. Schaff, L. F. Eastman, R. Dimitrov, L. Wittmer, M. Stutzmann, W. Rieger, and J. Hilsenbeck, “Two-dimensional electron gases induced by spontaneous and piezoelectric polarization charges in N- and Ga-face AlGaN/GaN heterostructures,” J. Appl. Phys. 85(6), 3222 (1999). [CrossRef]
  26. S. De Rinaldis, I. D’Amico, E. Biolatti, R. Rinaldi, R. Cingolani, and F. Rossi, “Intrinsic exciton-exciton coupling in GaN-based quantum dots: Application to solid-state quantum computing,” Phys. Rev. B 65(8), 081309 (2002). [CrossRef]
  27. R. Cingolani, A. Botchkarev, H. Tang, H. Morkoç, G. Traetta, G. Coli, M. Lomascolo, A. Di Carlo, F. Della Sala, P. Lugli, H. M. G. Traetta, G. Coli, M. L. A. D. Carlo, F. D. Sala, and P. Lugli, “Spontaneous polarization and piezoelectric field in GaN/Al0.15Ga0.85N quantum wells: Impact on the optical spectra,” Phys. Rev. B 61(4), 2711–2715 (2000). [CrossRef]
  28. M. A. Cusack, P. R. Briddon, and M. Jaros, “Electronic structure of InAs/GaAs self-assembled quantum dots,” Phys. Rev. B 54(4), R2300–R2303 (1996). [CrossRef]
  29. A. Asgari, M. Kalafi, and L. Faraone, “The effects of partially occupied sub-bands on two-dimensional electron mobility in AlxGa1-xN/GaN heterostructures,” J. Appl. Phys. 95(3), 1185 (2004). [CrossRef]
  30. M. Razeghi, H. Lim, S. Tsao, J. Szafraniec, W. Zhang, K. Mi, and B. Movaghar, “Transport and photodetection in self-assembled semiconductor quantum dots,” Nanotechnology 16(2), 219–229 (2005). [CrossRef] [PubMed]
  31. Z. Ye, J. C. Campbell, Z. Chen, E.-T. Kim, and A. Madhukar, “Normal-Incidence InAs Self-Assembled Quantum-Dot Infrared Photodetectors With a High Detectivity,” IEEE J. Quantum Electron. 38, 1534–1538 (2002).
  32. X. Lu, J. Vaillancourt, M. J. Meisner, and A. Stintz, “Long wave infrared InAs-InGaAs quantum-dot infrared photodetector with high operating temperature over 170 K,” J. Phys. D Appl. Phys. 40(19), 5878–5882 (2007). [CrossRef]
  33. P. Bhattacharya, X. H. Su, S. Chakrabarti, G. Ariyawansa, and A. G. U. Perera, “Characteristics of a tunneling quantum-dot infrared photodetector operating at room temperature,” Appl. Phys. Lett. 86(19), 191106 (2005). [CrossRef]
  34. A. G. U. Perera, P. V. V. Jayaweera, G. Ariyawansa, S. G. Matsik, K. Tennakone, M. Buchanan, H. C. Liu, X. H. Su, and P. Bhattacharya, “Room temperature nano- and microstructure photon detectors,” Microelectron. J. 40(3), 507–511 (2009). [CrossRef]
  35. H. R. Saghai, N. Sadoogi, A. Rostami, and H. Baghban, “Ultra-high detectivity room temperature THZ-IR photodetector based on resonant tunneling spherical centered defect quantum dot (RT-SCDQD),” Opt. Commun. 282(17), 3499–3508 (2009). [CrossRef]

Cited By

Alert me when this paper is cited

OSA is able to provide readers links to articles that cite this paper by participating in CrossRef's Cited-By Linking service. CrossRef includes content from more than 3000 publishers and societies. In addition to listing OSA journal articles that cite this paper, citing articles from other participating publishers will also be listed.


« Previous Article  |  Next Article »

OSA is a member of CrossRef.

CrossCheck Deposited