A Yariv

AM Itsuno

CH Grein

D. Benyahia

J Arriaga

J Piotrowski

J Wenus

J. Antoszewski

J. Rutkowski

KH Yoo

L. Faraone

M. Kopytko

ND Akhavan

P. Madejczyk

P. Martyniuk

R. Gu

T Ashley

VO Turin

W Scott

W. Gawron

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nBn HgCdTe infrared detector with HgTe(HgCdTe)/CdTe SLs barrierD. Benyahia1 • P. Martyniuk1 • M. Kopytko1 •J. Antoszewski2 • W. Gawron1 • P. Madejczyk1 •J. Rutkowski1 • R. Gu2 • L. Faraone2Received: 1 October 2015 /Accepted: 25 January 2016 / Published online: 29 February 2016 The Author(s) 2016. This article is published with open access at Springerlink.comAbstract Several strategies have been implemented to improve the performance ofinfrared single pixel detectors at higher operating temperature condition. The most efficientand effective in HgCdTe technology are: non-equilibrium architectures and currently anidea of the barrier detector to include unipolar and complementary structures. Valenceband offset between active layer and barrier impeding the minority carrier transport isconsidered to be the most important issue to overcome. Currently, implementation of theCd composition and doping graded interfaces has been proposed. In this paper we presentthe performance (dark current, detectivity, time response) of the nBn detector withHgTe(HgCdTe)/CdTe superlattice barrier. The superlattice barrier is believed to decreasevalence band offset between active and barrier layers. Theoretically estimated detectivityof mid-wave (cut-off wavelength, 4.8 lm) detector is *391012 cmHz1/2/W and timeresponse 150 ps for zero valence band offset, bias 2 V and temperature 155 K.Keywords HOT  HgCdTe  BIRD  nBn  SLs HgTe(HgCdTe)/CdTeThis article is part of the Topical Collection on Numerical Simulation of Optoelectronic Devices, NUSOD’15.Guest Edited by Julien Javaloyes, Weida Hu, Slawek Sujecki and Yuh-Renn Wu.& P. Martyniukpmartyniuk@wat.edu.pl; piotr.martyniuk@wat.edu.pl1 Institute of Applied Physics, Military University of Technology, 2 Kaliskiego Str., 00-908 Warsaw,Poland2 Microelectronics Research Group, The University of Western Australia, 35 Stirling Highway,Crawley 6009, Australia123Opt Quant Electron (2016) 48:215DOI 10.1007/s11082-016-0439-81 IntroductionCurrently, the infrared detector industry is dominated by mercury cadmium telluride(HgCdTe) detectors. A number of concepts to improve HgCdTe IR detectors’ performancehave been proposed, but significant improvement in reduction of the dark current has beenreached by suppression of Auger thermal generation by implementing non-equilibriumconditions (Piotrowski and Rogalski 2004). In practice, most of HgCdTe N?p(p)P? Augersuppressed photodiodes are based on complex, technologically difficult to grow graded gapand doping multi-layer structures (Ashley and Elliott 1985). A new strategy to achievehigher operating temperature (HOT) detectors includes the barrier structures (Maimon andWicks 2006). Itsuno et al. presented nBn HgCdTe bulk device being a prospect for cir-cumventing of the p-type doping problems in molecular beam epitaxy (MBE) technology(Itsuno et al. 2011). Valence band offset (VBO) between active layer and barrier blockingthe minority carrier transport is considered to be the most important issue to overcome.Currently, implementation of the Cd composition and doping graded interfaces has beenproposed (Akhavan et al. 2014, 2015). An alternate approach for reduction of the VBO isto use a HgTe(HgCdTe)/CdTe superlattice (SLs). HgTe(HgCdTe)/CdTe SLs have a type-III band alignment. Considered SLs is composed of alternating layers of HgTe(HgCdTe)and CdTe. The HgTe(HgCdTe) layers are the wells and the CdTe layers form the barriersfor both types of carriers: electrons and holes. Band engineering capability may beintroduced by incorporation of Hg into the barrier layers. The C1 and HH1 energy dif-ference of SLs is controlled by the thicknesses of the HgTe(HgCdTe) well layers allowingfitting to the absorber layer in terms of VBO. The transport properties of carriers inHgTe(HgCdTe)/CdTe SLs are completely different in comparison to HgCdTe alloys,meaning that the SLs in-plane transport properties are noticeably different from those inthe growth direction. The transport in the growth direction is of greatest importance for thedevice presented in this paper. The numerical simulations predict that the effective massesof electrons and holes can be tuned over a considerable range by varying the CdTe barrierlayer widths. The effective mass of electrons is expected to exceed up to an order ofmagnitude the effective mass in alloys with the same bandgap reducing the tunnelingcurrents by several orders of magnitude in the SLs-based detectors (Grein et al. 2006). Inthis paper we present the simulation of the dark current characteristics of the nBn barrierdetector with HgTe(HgCdTe)/CdTe SLs barrier at T = 155 K for mid-wave infrared range(MWIR). The SLs barrier is believed to decrease VBO between active and barrier layers.Fig. 1 Simulated nBn HgCdTe MWIR structure with HgTe(HgCdTe)/CdTe SLs barrier215 Page 2 of 8 D. Benyahia et al.123Theoretically estimated detectivity of MWIR (cut-off wavelength, kc = 4.8 lm) detectoris *3 9 1012 cmHz1/2/W and time response 150 ps for VBO = 0, bias 2 V and tem-perature, T = 155 K.2 Simulation procedureThe device presented in this work were grown by MBE and fabricated in MicroelectronicsResearch Group, The University of Western Australia. The schematic of a typical nBndetector structure with HgTe(HgCdTe)/CdTe SLs barrier design intended to operate in theMWIR (absorber layer Cd composition, x = 0.3, T = 155 K, cut-off wavelength,kc = 4.8 lm) spectral region is shown in Fig. 1. The detector structure was grown on aCdZnTe substrate and CdTe undopped buffer layers (d = 0.8 mm). The first layer of thedevices was bulk absorber grown with a thickness of 4 lm and Cd composition 0.3, n-typedoped with I (n = 1014 cm-3). Next the non-intentionally doped (n.i.d) HgTe(HgCdTe)/CdTe SLs (CdTe barrier d = 9 nm and HgTe well d = 2.5 nm) barrier layer was grownwith a thickness of 50 nm. After the barrier layer a 0.3-lm thick bulk HgCdTe n-typecontact doped with I (n = 1017 cm-3) was grown. The device diameter is 500 lm.This heterostructure design was chosen to block the majority carriers (electrons) whilethe minority carriers can flow with no impedance due to an assumed lack of VBO betweenabsorber and barrier layer. The barrier was found to be thick enough to prevent electrontunnelling between the top contact layer and active layer up to bias 4 V.nBn HgCdTe with barrier HgTe(HgCdTe)/CdTe SLs detector was simulated with Apsysplatform by Crosslight Inc. (Apsys 2015). The bulk based model was used in modeling ofthe device’s transport properties. Theoretical modeling of the MWIR HgCdTe barrierdetectors has been performed by numerical solving of the Poisson’s equation and thecarrier current continuity equations by the Newton–Richardson method. Ohmic contactswere modeled as Dirichlet boundary conditions—electron and hole quasi-Fermi levels areequal and assumed to be at the voltage of biased electrode, i.e., Efn = Efp = V. The appliedmodel incorporates both HgCdTe bulk and barrier HgTe(HgCdTe)/CdTe electrical prop-erties to estimate device performance taking into consideration radiative (RAD), AugerTable 1 Parameters taken inmodeling of SLsHgTe(HgCdTe)/CdTe in 8 9 8kp (Yoo and Aggarwal 1989;Arriaga and Velasco 1992)Parameter HgTe(HgCdTe) CdTeEg (eV) (bandgap) -0.302; 0.22 1.6D (eV) (spin–orbit coupling) 1.00 0.91F (Kane parameter) 0.0 0.0c1 (Luttinger parameter) 4.3675 1.540c2 = c3 (Luttinger parameter) 1.034 0.015a (eV) (hydrostatic deformation potential) 3.5 xb (eV) (shear deformation potential) -1.5 xm* (c) (effective mass in the c band) 0.026 0.087C11 (Gpa) (elastic constant) 53.61 53.8C12 (Gpa) (elastic constant) 36.6 37.4C44 (Gpa) (elastic constant) 21.23 20.18a (A˚) (lattice constant) 6.462 6.482c (%) (strain) 0.3 xnBn HgCdTe infrared detector with HgTe(HgCdTe)/CdTe SLs… Page 3 of 8 215123(AUG), Shockley Read-Hall (SRH) generation recombination (GR) mechanisms. RAD andAUG parameters for SLs layer were assumed to correspond to the bulk HgCdTe materialwith the same energy band gap (Eg). The carrier mobility dependence on bias was cal-culated in accordance with Canali (Beta) model (Turin 2005), while low field carriermobility was assumed according to the paper by Scott (Scott 1972). The SLs was treated asan artificial material where C1 and HH1 effective masses were calculated using advanced8 9 8 kp model in equilibrium condition incorporated in Apsys numerical platform.Affinity of HgTe(HgCdTe)/CdTe barrier was assumed 3.8 eV, while for HgCdTe absorberand contact layer 4.03 eV to reach zero VBO between barrier and absorber layer. Thesimulation parameters used for SLs HgTe(HgCdTe)/CdTe in 8 9 8 kp were presented inTable 1.The calculated dispersion curves in growth direction for C1 and HH1 are presented inFig. 2. The VBO between HgTe(HgCdTe) and CdTe was assumed 350 meV. TheHgTe(HgCdTe)/CdTe SLs band gap energy was estimated at the level 548 meV. In growthdirection effective masses were extracted from dispersion curves and assumed in the bulkbased model, i.e. me = 0.082 m0 and mhh = 1.15 m0 respectively.Simple nBn structure requires that the valence bands of the three constituent layers lineup closely to allow minority carrier transport between the absorber and contact layers.Band diagrams of the simulated structure for electron affinity calculated according therelation c = 4.23 - 0.813[Eg(x, T) - 0.083] and electron affinity corresponding toVBO = 0 are shown in Fig. 3a, b respectively. The band energy discontinuity of bothbarrier and absorber layers seems to be the most decisive parameter influencing perfor-mance of barrier structure. The barrier in conduction band (DEc) is higher compared tobarrier in valence band (DEc[DEv) [see Fig. 3]. At 400 mV, DEv is *44 meV andDEc * 238 meV for electron affinity calculated with no correction (A = 0) while DEv is0 meV and DEc * 282 meV with extra component A (-50 meV) corresponding toVBO = 0. Dark and photocurrent are effectively blocked for DEv; DEc[ 3kBT & 39 meV (T = 155 K, kB—Boltzmann constant).Measured and calculated dark current (IDARK) and dynamic resistance (RD) versusvoltage are shown in Fig. 4. The calculations were performed assuming no intrabandquantum tunneling transport mechanism through barrier (blue sold line) and with quantumtunnelling through barrier (pink dashed line). For a rectangular barrier, the tunnelingFig. 2 Typical dispersionrelation for C1 and HH1 ingrowth direction forHgTe(HgCdTe)/CdTe SLs atT = 155 K, VBO = 350 meV215 Page 4 of 8 D. Benyahia et al.123Fig. 3 Calculated energy band structures for nBn HgCdTe/B-SLs HgTe(HgCdTe)/CdTe for V = 0.4 V,T = 150 K: A = 0 meV (a); A = -50 meV (b)Fig. 4 IDARK and RD versusvoltage for nBn detector with SLsHgTe(HgCdTe)/CdTe barrier atT = 155 K. (Color figure online)Fig. 5 Calculated dark and photocurrent versus barrier affinity for selected voltages 0.4–4 V (a);photocurrent versus voltage for selected affinity (b) for nBn HgCdTe/B-SLs HgTe(HgCdTe)/CdTe,T = 155 KnBn HgCdTe infrared detector with HgTe(HgCdTe)/CdTe SLs… Page 5 of 8 215123transparency was calculated with relation given by Yariv (1982). Oscillations in IDARKcharacteristics in vicinity of 1 and 2 V are believed to be related to the dependence ofenergy barrier in conduction band (DEc) versus voltage. For unbiased condition energybarrier in conduction band, DEc & 300 meV. It is shown that intraband quantum tunnelingtransport plays a decisive role for voltage[4 V.Dark current and photocurrent (calculated for k = 4 lm, power, P = 100 W/m2) ver-sus barrier electron affinity with extra correction A for selected voltages (0.4–4 V) arepresented in Fig. 5a. Dark current increases sharply by three orders of magnitude withinanalyzed voltages which should be attributed to the lowering of the barrier in conductionband (DEc) versus voltage. For A\ 0 meV photocurrent stay constant (*10-5 A) and forA[ 0 increases sharply due to the fact that energy barrier in conduction band decreasesallowing unimpeded flow of the photogenerated carriers. The saturation range within A,15–30 meV range is caused by the joint ratio of the DEc and DEv blocking and allowingunimpeded flow of the optically generated carriers. Detailed analysis of the photocurrentversus voltage for selected corrections A is shown in Fig. 5b.The noise current was simulated using the following expression that includes both thethermal Johnson–Nyquist noise and electrical shot noise contributions:in Vð Þ ¼ﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃﬃð4kBT=Rþ 2qIDARKÞp; ð1Þwhere R is the dynamic resistance area product, IDARK is the dark current, and kB is theBoltzmann constant. Detectivity (D*) limited by thermal Johnson–Nyquist noise andelectrical shot noise could be expressed by relation (where, Ri current responsivity and A isthe area of the detector):D ¼ RiinðVÞﬃﬃﬃAp: ð2ÞCalculated detectivity versus barrier affinity with extra correction A for selected volt-ages (0.4–4 V) is presented in Fig. 6a. For regular HgCdTe barrier (A = 0) detectivity is*1012 cmHz1/2/W while for VBO = 0 (A = -50 meV), D* reaches *491012 cmHz1/2/W. Increasing the DEv and reducing DEc assuming constant Eg allows to reach even*291013 cmHz1/2/W.Fig. 6 Calculated detectivity versus barrier affinity for selected voltages 0.4–4 V (a); and versus voltagefor selected affinities (b) for nBn HgCdTe/B-SLs HgTe(HgCdTe)/CdTe, T = 155 K215 Page 6 of 8 D. Benyahia et al.123Time response (s) characteristics versus affinity and voltage is presented in Fig. 7a, b.Time response strictly depends on minority carrier lifetime and drift time. For extra cor-rection A\ 0 meV, s keeps constant reaching *150 ps at 2 V corresponding to unim-peded hole transport to the contact. Once hole are blocked time response increases (A[ 0)up to 1200 ps.3 ConclusionnBn detectors based on bulk HgCdTe naturally present a potential barrier in the valenceband, which significantly reduces the performance. SLs HgTe(HgCdTe)/CdTe barriergives an opportunity to reduce VBO in nBn structures leading to unimpeded transport ofthe photogenerated carriers to the contacts. Theoretically estimated detectivity of MWIR(4.8 lm) detector is*391012 cmHz1/2/W and time response 150 ps for zero valence bandoffset, bias 2 V and T = 155 K.Acknowledgments This paper has been done under financial support of the Polish National ScienceCentre as the Research Projects: No. 2013/08/A/ST5/00773 and 2013/08/M/ST7/00913.Open Access This article is distributed under the terms of the Creative Commons Attribution 4.0 Inter-national License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution,and reproduction in any medium, provided you give appropriate credit to the original author(s) and thesource, provide a link to the Creative Commons license, and indicate if changes were made.ReferencesAkhavan, N.D., Umana-Membreno, G.A., Jolley, G., Antoszewski, J., Faraone, L.: A method of removingthe valence band discontinuity in HgCdTe-based nBn detectors. Appl. Phys. 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SPIE 6127, 61270W (2006)Itsuno, A.M., Phillips, J.D., Velicu, S.: Design and modeling of HgCdTe nBn detectors. J. Electron. Mater.40(8), 1624–1629 (2011)Maimon, S., Wicks, G.: nBn detector, an infrared detector with reduced dark current and higher operatingtemperature. Appl. Phys. Lett. 89, 151109 (2006)Piotrowski, J., Rogalski, A.: Uncooled long wavelength infrared photon detectors. Infrared Phys. Technol.46, 115–131 (2004)Scott, W.: Electron mobility in Hg1-xCdxTe. J. Appl. Phys. 43, 1055–1062 (1972)Turin, V.O.: A modified transferred-electron high-field mobility model for GaN devices simulation. Solid-State Electron. 49, 1678–1682 (2005)Wenus, J., Rutkowski, J., Rogalski, A.: Two-dimensional analysis of double-layer heterojunction HgCdTePhotodiodes. IEEE Trans. Electron Dev. 48(7), 1326–1332 (2001)Yariv, A.: An Introduction to Theory and Applications of Quantum Mechanics. Wiley, New York (1982)Yoo, K.H., Aggarwal, R.L.: HgTe/CdTe superlattice band calculation with a transfer matrix method. JVSTA 7, 415–419 (1989)215 Page 8 of 8 D. Benyahia et al.123

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nBn HgCdTe infrared detector with HgTe(HgCdTe)/CdTe SLs barrier

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nBn HgCdTe infrared detector with HgTe(HgCdTe)/CdTe SLs barrier

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