Solid-State Electronics 80 (2013) 96–104

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Solid-State Electronics

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Modelling of MWIR HgCdTe complementary barrier HOT detector

Piotr Martyniuk ⇑, Antoni RogalskiInstitute of Applied Physics, Military University of Technology, 2 Kaliskiego St., 00-908 Warsaw, Poland

a r t i c l e i n f o a b s t r a c t

Article history:Received 9 July 2012Received in revised form 11 October 2012Accepted 26 October 2012Available online 21 December 2012

The review of this paper was arranged byProf. E. Calleja

Keywords:Complementary barrier infrared detectorsUnipolar barrier detectorsnBn detectorsHgCdTeType-II InAs/GaSb superlattices

0038-1101/$ - see front matter � 2012 Elsevier Ltd. Ahttp://dx.doi.org/10.1016/j.sse.2012.10.021

⇑ Corresponding author.E-mail address: pmartyniuk@wat.edu.pl (P. Marty

The paper reports on the photoelectrical performance of medium wavelength infrared (MWIR) HgCdTecomplementary barrier infrared detector (CBIRD) with n-type barriers. CBIRD nB1nB2 HgCdTe/B1,2-n typedetector is modelled with commercially available software APSYS by Crosslight Software Inc. The detailedanalysis of the detector’s performance such as dark current, photocurrent, responsivity, detectivity versusapplied bias, operating temperature, and structural parameters (cap, barriers and absorber doping; andabsorber and barriers compositions) are performed pointing out optimal working conditions. Both con-duction and valence bands’ alignment of the HgCdTe CBIRD structure are calculated stressing theirimportance on detectors performance. It is shown that higher operation temperature (HOT) conditionsachieved by commonly used thermoelectric (TE) coolers allows to obtain detectivities D⁄ � 2 � 1010 -cm Hz1/2/W at T = 200 K and reverse polarisation V = 400 mV, and differential resistance area productRA = 0.9 Xcm2 at T = 230 K for V = 50 mV, respectively.

Finally, CBIRD nB1nB2 HgCdTe/B1,2-n type state of the art is compared to unipolar barrier HgCdTe nBn/B-n type detector, InAs/GaSb/B-Al0.2Ga0.8Sb type-II superlattice (T2SL) nBn detectors, InAs/GaSb T2SLsPIN and the HOT HgCdTe bulk photodiodes’ performance operated at near-room temperature(T = 230 K). It was shown that the RA product of the MWIR CBIRD HgCdTe detector is either comparableor higher (depending on structural parameters) to the state of the art of HgCdTe HOT bulk photodiodesand both AIIIBV 6.1 Å family T2SLs nBn and PIN detectors.

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1. Introduction

Hitherto, the infrared radiation (IR) industry is conquered byHgCdTe bulk photodiodes [1–3] and GaAs/AlGaAs intersubbandquantum well infrared photodetectors (QWIP) [4,5]. The require-ment of the infrared detectors’ cryogenic cooling is a major imped-iment preventing from their extensive application that is whydetector’s cooling push boundaries to increase device operatingtemperature. It is known that the critical condition which mustbe fulfilled to construct the HOT IR detector is to achieve bothlow dark current and high values of the quantum efficiency. Amongthe mechanisms generating the dark current in detector’s structurethe following must be enumerated: band-to-band (BTB) tunnelling,trap assisted tunnelling (TAT), Schockley-Read-Hall (SRH) genera-tion-recombination (GR) process, Auger GR process, and leakagecurrents.

It was found that an incorporation of the type II superllatice(T2SLs) e.g. InAs/GaSb 6.1 Å AIIIBV family into detector architectureallows to reduce adverse BTB/TAT currents and GR Auger’s contri-bution to the total dark current. Therefore T2SLs could be consid-ered as an alternative to the bulk HgCdTe HOT detectors and

ll rights reserved.

niuk).

GaAs/AlGaAs IR material systems [6]. Unfavourable SHR GR andleakage dark current’s components could be limited by the prop-erly selected barriers incorporated into detectors structure. Thebarrier’s selection plays crucial role due to the lattice constantmatching of the detectors’ constituent layers, the barrier’s heightin both conduction and valance bands connected directly to theband alignment. It must be stressed that band alignment playingimportant role in design of the barrier IR structures is often fortu-itous and extremely difficult to control from technological perspec-tive [7].

The very first barrier structures were commonly known AIIBVI

and AIIIBV heterostructures invented to increase device’s perfor-mance by suppression of the diffusion currents from the detector’sactive region. The next stage in IR detector’s development was dou-ble layer heterojunction (DLHJ) allowing reducing both majorityand minority carriers diffusion currents in comparison to thehomojunction IR detectors. Another variation of the DLHJ was agraded gap structure incorporated between hole blocking layerand absorber to suppress tunnelling and GR currents [8].

Currently, among the barrier IR detectors (BIRDs) the leadingposition is occupied by minority carrier devices called unipolarbarrier infrared detectors (UBIRD) proposed by Maimon and Wicks[9]. Among electron-blocking UBIRD detectors the most importantare these designed with AIIIBV compounds (GaSb, InAs1–zSbz-caplayers, InAs1–ySby-active region, AlSb1–xAsx–barrier), T2SLs nBn

P. Martyniuk, A. Rogalski / Solid-State Electronics 80 (2013) 96–104 97

InAs/GaSb with AlGaSb/T2SLs barriers and UBIRD nBn HgCdTedetectors, while among hole-blocking UBIRD devices should beconsidered a four layer architectures: InAs/GaInSb/InAs/AlGaInSboften called ‘‘W’’ structures and GaSb/InAs/GaSb/AlSb referencedas ‘‘M’’ structures [10–12]. The most sophisticated structures con-taining both electron and hole blocking barriers (AlSb/T2SLs barri-ers) were proposed by Ting et al. [13] (called either complementarybarrier infrared detectors – CBIRD) or PbIbN after Gautam et al.[14] showing possible advantages in suppressing dark currentsby blocking majority and minority carriers and circumventingtechnological problems with making ohmic contact to the wide-gap layers.

Potential interest in InAs/GaSb T2SLs results not only from un-ique inherited capabilities of the new artificial material with en-tirely different physical properties in comparison to theconstituent layers (InAs and GaSb), but also from the nearly zeroband offsets leading to the desirable UBIRD/CBIRD band align-ments difficult to attain in HgCdTe [15]. In addition, the 6.1 Å fam-ily’s capabilities to tune the position of the conduction and valanceband edges in independent way and near lattice matching is extre-mely helpful in designing of the unipolar and complementary bar-rier detectors. Although the abovementioned physical propertiesindicates potential T2SLs’ superiority over bulk materials (includ-ing HgCdTe ternary allys), the T2SLs’ quantum efficiency leaves alot of to be desired (g = 20–30% in MWIR range and g = 8–12% inLWIR range depending on nBn/pBp architecture) which stems fromlow level of wavefunction overlapping and technological problemsconnected with growth of uniform and thick enough SLs [16].What is more, short minority carrier lifetimes (sDIF, sGR < 10 ns intemperature range >200 K) also impedes the development of theT2SLs IR devices [17]. Similarly, theoretical simulations provedquantum dot infrared detectors (QDIPs) to be an alternative tothe HgCdTe, but technological problems related to the growth ofself-organized QDs led to the suspension of the research on thistype of the detector [18,19].

Even though, HgCdTe does not exhibit valance zero band offset,it is commonly known that bulk HgCdTe offers quantum efficiencyg = 50–70%, therefore recently research groups have attempted toapply UBIRD architecture to HgCdTe alloy (n type barrier) whichoffers technological advantages over p–n HgCdTe homojunction(simplifying the fabrication process) [20,21]. Moving forward, itis worth applying CBIRD architecture to HgCdTe alloy incorporat-ing n type barriers to reduce dark current in comparison to UBIRDnBn HgCdTe/B-n type detector. Taking this into consideration, thispaper presents the performance estimation of the MWIR CBIRDnB1nB2 HgCdTe/B1,2-n type detector with cut-off wavelength ofkc = 5.2 lm at temperature T = 200 K. The temperature and bias

Fig. 1. CBIRD detector with the nB1nB2/B1,2-n type design: (a) sch

voltage dependences of the dark current and RA product, respon-sivity, and detectivity of the CBIRD HgCdTe are analysed. Finally,near-room temperature MWIR CBIRD HgCdTe detector state ofthe art is compared to nBn/B-n type HgCdTe UBIRD, nBn InAs/GaSb/B-Al0.2Ga0.8Sb T2SLs, PIN InAs/GaSb T2SL and HOT HgCdTebulk photodiodes’ performance.

2. Simulation procedure

Theoretical modelling of the MWIR UBIRD nBn/B-n type HgCdTedetector was performed by Velicu et al. [21] and Martyniuk andRogalski [22]. For the comparison reasons, the similar structuralparameters for MWIR CBIRD nB1nB2 HgCdTe/B1,2-n type detectorwere used. In the same way, for modelling purposes three layerselectron barrier (EB–barrier I) was applied in order to mitigatethe kinks emerging in energy diagrams between detector’s constit-uent layers caused by compositional uniformity (see Fig. 1). Inter-diffusion was modelled by applying gauss tail doping(dx = 0.05 lm). The modelled structure consists of the 0.16 lmthick n-type HgCdTe cap layer doped to ND = 7 � 1014 cm–3. Afterthe cap layer, an n-type 0.15 lm thick HgCdTe barrier doped toND = 2 � 1015 cm–3 was incorporated. As mentioned, in our modelthe EB layer was divided on three sub-layers with compositiongrading fitted to the cap layer and absorber respectively (e.g.x = 0.33–0.6–0.275). The EB thickness was assumed to be thick en-ough to prevent electron tunnelling between the top contact layerand the absorbing layer, therefore the majority current is blockedby the barrier material under reverse applied bias. Next, n-typeHgCdTe absorber with a thickness of 5–10 lm doped toND = 1014 ? 5 � 1016 cm–3 and composition x = 0.275 for MWIRrange was used. Finally, 0.15–0.5 lm thick hole blocking (HB – bar-rier II) layer consisted of two n-type sub-layers fitted to the absor-ber were utilized (e.g. x = 0.275–0.6) and doped toND = 1014 ? 5 � 1017 cm–3. Similarly to EB, interdiffusion at absor-ber–barrier II (HB) interface was modelled by applying gauss taildoping.

Numerical calculations were performed utilizing commercialsoftware APSYS by Crosslight Software Inc. Specific equations andrelations used in device’s modelling are listed in Table 1 andAppendix. The 50% cut-off wavelength was calculated to bekc = 5.2 lm at T = 200 K. Detector’s area was assumed to be120 � 120 lm2.

The noise current was calculated using the expression includingJohnson–Nyquist noise, optical and electrical shot noises:

inðVÞ ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffið4kBT=RAþ 2qIDARK þ 2qIBÞ

q; ð1Þ

ematic of the heterostructure and (b) the device’s structure.

Table 1Parameters taken in modelling of MWIR CBIRD nB1nB2 HgCdTe/B1,2-n type detectors.

Cap Electron barrier (EB – barrier I) Absorber Hole barrier (HB – barrier II)

Donor concentration, ND (cm–3) 7 � 1014 2 � 1015 1014 ? 5 � 1016 1014 ? 5 � 1017

Doping concentration’s gauss tail, dx (lm) 0.05Composition, x (lm) 0.15 ? 0.5 0.33 ? 0.6 ? 0.275 0.275 (kc = 5.2 lm at T = 200 K) 0.275 ? 0.6Geometry, d (lm) 0.16 ? 1 0.15 2 ? 10 0.15 ? 0.5 lmDevice electrical area, A (lm2) 120 � 120Background temperature, TB, field of view, h 300 K, 20�(f# = 2.835)Overlap matrix F1F2 0.2Trap energy level, ETrap Eg/2Trap concentration, NTrap (cm–3) 1016

Minority carrier lifetime SHR, sn, sp (ls) 0.4, 1Target incident power density, U (W/m2) 50 � 104

98 P. Martyniuk, A. Rogalski / Solid-State Electronics 80 (2013) 96–104

where A is a detector’s area, RA is the dynamic resistance area prod-uct, IDARK and IB are the dark current density and background in-duced current, respectively, and kB is the Boltzmann constant.

The background wavelength dependent current was calculatedaccording to the expression:

IB ¼2pcq

k4 sin2 h2

� �Z kc

0ðexpðc=kBTBkÞ � 1Þ�1gðkÞdk; ð2Þ

where TB is a background temperature, h is the detector’s field ofview (h = 20�), and TB = 300 K was assumed.

The quantum efficiency is a function of the incident radiationwavelength and current responsivity, Ri, according to the relation:

gðkÞ ¼ 1:24Ri

k; ð3Þ

The detector’s detectivity is defined by expression:

D� ¼ Ri

inðVÞffiffiffiAp

: ð4Þ

Fig. 2 depicts calculated dark current versus reverse bias for se-lected operating temperatures which could be obtained using TEcooling. The electron barrier’s influence is clearly evident in I–Vcharacteristics, where ‘‘turn-on’’ voltage (the voltage required tominimize valance band barrier) was assumed to be V = 0.2 V. ForT = 200 K and V = 400 mV dark current reaches 0.1 A/cm2, whilefor T = 240 K dark current increases to 1 A/cm2. The inset comparessimulation results of the structure presented in Fig. 1 with darkcurrent obtained for UBIRD HgCdTe nBn/B-n-type (cap: x = 0.33,d = 0.16 lm, ND = 7 � 1014 cm–3; barrier: x = 0.33–0.6–0.275,

Fig. 2. IDARK versus voltage for CBIRD nB1nB2 HgCdTe/B1,2-n type and UBIRD nBnHgCdTe/B-n type detectors for selected operating temperatures. Inset: IDARK forCBIRD nB1nB2 HgCdTe/B1,2-n type and UBIRD nBn HgCdTe/B-n type detectors versustemperature for V = 400 mV.

d = 0.15 lm, ND = 2 � 1015 cm–3; absorber: x = 0.275, d = 10 lm,ND = 1014 cm–3). Within the operating temperature range between180 and 240 K, the dark current increases from 0.01 to 0.7 A/cm2

while corresponding values for UBIRD structure change from 0.2to 4 A/cm2 pointing out that dark current for CBIRD architecturedecreases more rapidly than for UBIRD counterpart for lower tem-peratures. The hole barrier incorporation allows dark currentreduction more than one order of magnitude depending on theoperating temperature. It is clearly seen that for CBIRD nB1nB2

HgCdTe/B1,2-n type, the dark current IDARK = 0.7 A/cm2 is reachedat T = 238 K, while the same value of the dark current for UBIRDnBn HgCdTe/B-n type requires extra cooling to T = 192 K. ForT = 200 K and the bias voltages within the range V < 0.1 V, IDARK

for both types of the detectors keeps the same value which corre-sponds to the EB II barrier formation with applied voltage. Addi-tionally, it is shown that for voltages V < 200 mV dark currentincreases sharply (hole concentration increases harshly) whileabove V > 200 mV a typical photoconductive effect related to theincrease of the current versus bias is observed (detector structureconsists of four main n doped layers).

Fig. 3 depicts D⁄ versus wavelength for selected voltages withinturn-on voltage range. The maximum D⁄ was estimated to be1.6 � 1010 cm Hz1/2/W for T = 200 K and V = 400 mV (fork = 4.9 lm). Likewise UBIRD nBn HgCdTe/B-n type detector, CBIRDnB1nB2 HgCdTe/B1,2-n type structure operates in minority carriermanner thus dark current is mainly due to the hole transport fromabsorber’s layer. n-type wide HgCdTe hole blocking layer’s incor-poration suppresses dark current, changes turn-on voltage (forUBIRD HgCdTe nBn/B-n detector the turn-on voltage was foundto be V = 400 mV) and increases detectivity.

Fig. 3. D⁄ versus wavelength (MWIR range) for CBIRD nB1nB2 HgCdTe/B1,2-n typedetector for selected operating voltages (kc = 5.2 lm at T = 200 K).

Fig. 5. The SRH GR rate for cap–barrier I interface of CBIRD nB1nB2 HgCdTe/B1,2 n-type detector for different compositions x at V = 50 mV and at T = 200 K.

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3. CBIRD nB1nB2 HgCdTe/B1,2-n type barrier’s band alignment

The calculated energy band diagrams for unbiased (V = 0 V) andbiased conditions (V = 0.4 V and V = 1 V) are shown in Fig. 4. CBIRDnB1nB2 HgCdTe/B1,2-n type detector is reversely biased, i.e. positivevoltage is applied to the hole barrier contact. Unlike 6.1 Å AIIIBV

family exhibiting ‘‘staggered’’ zero valance band offset, HgCdTedemonstrates ‘‘nested’’ heterojunction which leads to unintendedvalance band offset being difficult to control from technologicalperspective [electron affinity was modelled by Eq. (A.2)]. Compar-ison of the energy band alignment between unbiased and biasedstructures directly indicates that likewise UBIRD nBn HgCdTe/B-ntype detector, CBIRD nB1nB2 HgCdTe/B1,2-n type one requires aproper level of voltage being applied to the detector (turn-on volt-age is V = 0.2 V) to align the valance band (at the cap–barrier I, bar-rier I–absorber and absorber–barrier II interfaces) to reduce theimpediment of desirable minority carrier transport to cap layer.

As is mentioned above, the barrier incorporation into detectorstructure suppresses SHR rate. Magnitude of the SHR GR rate (rSHR)versus position for cap–barrier I (EB) interface for selected compo-sitions is presented in Fig. 5. Barrier’s composition increase withinthe range x = 0.33–0.6 (sub-layer’s composition is fitted to the caplayer and absorber e.g. x = 0.33–0.4–0.275) and T = 200 K reducesrSHR nearly six orders of magnitude fully confirming the legitimacyof wide gap layers’ incorporation into n type HgCdTe detector’sstructure. Ting et al. presented even 10 orders of magnitude sup-pression of the rSHR for AIIIBV UBIRD nBn structure (InAsSb/B–AlS-bAs) and three orders of magnitude for InAs/GaSB T2SLs UBIRDnBn structure at T = 80 K [23].

Fig. 6 presents cap–barrier I (EB), barrier I–absorber and absor-ber–barrier II (HB) barrier’s heights DEc, DEv versus applied voltage

Fig. 4. Calculated energy band structures for the CBIRD nB1nB2 HgCdTe/B1,2 n-type detect

respectively. As for as reverse biased CBIRD nB1nB2 HgCdTe/B1,2 n-type detector is concerned the most important is DEc emerging atcap–barrier I interface (desirable majority carrier blocking fromcap layer), DEv at barrier I–absorber interface (unfavourable photogenerated carriers impediment) and DEc, DEv at absorber–barrier IIinterface responsible for electron and hole blocking, respectively.The both mentioned DEc and DEv at cap–barrier I directly dependon the applied voltage pointing out that applied voltage is atrade-off between DEc and DEv (e.g. for barrier I–absorber interfaceDEv � 160–50 meV and cap–barrier I interface DEc � 350–275 meVfor V = 0–1 V, respectively), while DEc at absorber–barrier II

or at: equilibrium (V = 0 V) (a) and under reverse biases: V = 0.4 V (b) and V = 1 V (c).

Fig. 6. DEc and DEv for cap–barrier I (EB), barrier I–absorber, absorber–barrier II(HB) interfaces versus applied voltage at T = 200 K.

Fig. 7. DEc and DEv for absorber–barrier II (HB) interface versus barrier’s II doping(barrier II: x = 0.275–0.6) and composition (barrier II: ND = 1017 cm–3). V = 0 V,T = 200 K.

100 P. Martyniuk, A. Rogalski / Solid-State Electronics 80 (2013) 96–104

interface changes within range DEc � 20–70 meV and DEv keepsconstant value 450 mV. Above V > 0.2 V, the absorber–barrier IIinterface, DEc, saturates leading to the dark slight increase (turn-on voltage level V = 0.2 V – see Fig. 2), while turn-on voltage forphotocurrent is found to be V = 0.4 V (see Fig. 4), where DEv at bar-rier I–absorber plays crucial role blocking photogenerated carriers.

Both barrier’s doping and composition also influence DEc andDEv (see Fig. 7). Once barrier I (EB) composition increases bothDEc and DEv at cap–barrier I and barrier I–absorber raises reducingdark and photo currents. The barrier II doping increase reduces ab-sorber–barrier II (HB) DEc (within the range 325–65 mV) andslightly raises DEv (425–450 mV) for ND < 1017 cm–3 while forND > 1017 cm–3 opposite behaviour is observed. Increase of barrierII composition raises both DEc and DEv at absorber–barrier IIinterface.

Fig. 8. IDARK and IPHOTO for CBIRD nB1nB2 HgCdTe/B1,2 n-type versus hole barriercomposition for selected voltages. T = 200 K. HB doping ND = 1017 cm�3.

4. Optimization of the CBIRD nB1nB2 HgCdTe/B1,2-n type barriers

The choice of the both electron and hole barriers’ doping andcomposition plays crucial role in designing CBIRD nB1nB2

HgCdTe/B1,2 n-type structures. HB width was checked thoroughly(within the range d = 0.15–5 lm) not revealing strict influence onD⁄. The EB width was chosen to be thick enough (d = 0.15 lm) to

prevent electron tunnelling from cap layer to the absorber. HgCdTeexhibits the potential issues with uniformity of the thin layers dueto the interdiffusion at the interfaces. In our model both EB and HBbarrier layers were divided on three (electron barrier)/two (holebarrier) sub-layers with composition grading fitted to cap and ab-sorber layers to simulate this unfavourable phenomenon (addi-tionally gauss tail’s doping profile was used, dx = 0.05 lm).

Figs. 8 and 9 present IDARK, IPHOTO (for selected voltages) and D⁄

(for selected temperatures) versus HB composition. As it is shownin Fig. 7, both hole barrier (DEc and DEv) increase with HB compo-sition resulting in IDARK decreasing for x < 0.35, while for x > 0.35IDARK saturates. HB composition influences IPHOTO for0.35 > x > 0.53 which should be attributed to HB DEc increase(x > 0.53) and IDARK raise for x < 0.35. D⁄ versus HB composition re-flects the trend exhibited by IPHOTO dependence on HB x.

HB doping influence on detector’s performance is depicted inFigs. 10 and 11. For hole barrier’s doping below ND < 1016 cm–3,both dark and photocurrent decrease two orders of magnitude incomparison to values obtained for ND = 1017 cm–3 for all analyzedvoltages. This behaviour is directly connected with HB DEc de-crease versus HB doping. The results presented in Fig. 11 pointsout that the highest detectivity is reached only for highly dopedHB (ND > 1016 cm–3) for all simulated voltages. Increase of the HBdoping within the range 1014–5 � 1017 cm–3 raises D⁄ from 108 to1010 cm Hz1/2/W for V = 400 mV. Above ND > 1016 cm–3, increaseof HB doping saturates to D⁄ � 1.6 � 1010 cm Hz1/2/W.

Similar considerations were conducted for EB barrier’s composi-tion. Direct dependence of the EB DEc and DEv on composition andvoltage is responsible for the both dark and photocurrent charac-teristics. Both EB DEc and DEv raise with composition resulting inIDARK and IPHOTO decrease (see Fig. 12). Below x < 0.4 both currentskeep nearly constant value for simulated voltages. To attain thehighest detectivity, the optimal composition increases with ap-plied voltage (see Fig. 13). The simulated structure reaches D⁄ -� 1.6 � 1010 cm Hz/1/2/W for V = 400 mV and T = 200 K, being oneorder of magnitude higher than UBIRD nBn HgCdTe/B-n type singlebarrier structure, whereas detectivity was estimated to beD⁄ = 3.5 � 109 cm Hz1/2/W for the same EB parameters, workingconditions and structural parameters (absorber’s doping andwidth).

5. Optimization of the CBIRD nB1nB2 HgCdTe/B1,2-n typeabsorber

Doping of absorbers also plays critical role and must be opti-mized for assumed voltages and operating temperatures. Figs. 14

Fig. 9. D⁄ for CBIRD nB1nB2 HgCdTe/B1,2 n-type versus hole barrier composition forselected temperatures. V = 400 mV. k = 4.95 lm.

Fig. 10. IDARK and IPHOTO for the CBIRD nB1nB2 HgCdTe/B1,2 n-type detector versushole barrier doping concentration for selected voltages. T = 200 K.

Fig. 11. D⁄ for CBIRD nB1nB2 HgCdTe/B1,2 n-type structure versus barrier dopingconcentration for selected voltages. T = 200 K, k = 4.95 lm.

Fig. 12. IDARK and IPHOTO for CBIRD nB1nB2 HgCdTe/B1,2 n-type versus electronbarrier’s composition for selected voltages.

Fig. 13. D⁄ for CBIRD nB1nB2 HgCdTe/B1,2 n-type versus applied voltage for selectedelectron barrier’s composition. T = 200 K, k = 4.95 lm.

Fig. 14. IDARK and IPHOTO for the CBIRD nB1nB2 HgCdTe/B1,2 n-type detector versusvoltage for different absorbers doping. T = 200 K.

P. Martyniuk, A. Rogalski / Solid-State Electronics 80 (2013) 96–104 101

and 15 present IDARK and IPHOTO versus applied voltage (for selectedabsorber’s doping) and absorber’s doping, respectively. Once ab-sorber’s doping increases, the photocurrent exhibits decreasingtrend lowering responsivity Ri = 2.3–1.3 A/W and quantum effi-ciency g = 59–32% (within the range 1014 < ND < 5 � 1016 cm–3).In doping range 1014 < ND < 1015 cm–3 both dark current and

photocurrents keep nearly constant value for simulated voltages.Above ND > 1015 cm–3 photocurrent decreases sharply which couldbe attributed to Burstein–Moss effect (minority carrier densitydrops). Once absorber’s doping raises, the dark current increasessharply (mainly due to Auger 1 process), while the photocurrentdecreases (free minority carrier concentration decreases). Clearly

Fig. 15. IDARK and IPHOTO for the CBIRD nB1nB2 HgCdTe/B1,2 n-type detector versusabsorber’s doping for selected voltages. T = 200 K.

Fig. 16. D⁄ for CBIRD nB1nB2 HgCdTe/B1,2-n type structure versus applied voltagefor selected absorber’s doping concentrations. T = 200 K.

Fig. 17. D⁄ for CBIRD nB1nB2 HgCdTe/B1,2-n type structure versus absorber’s widthfor selected voltages. T = 200 K, k = 4.95 lm.

Fig. 18. Temperature dependence of the RA and RoA products for MWIR nB1nB2

HgCdTe/B1,2-n type detector, nBn HgCdTe/B-n type detector, nBn InAs/GaSb/B-Al0.2Ga0.8Sb T2SL detector, HgCdTe HOT bulk diodes and PIN InAs/GaSb T2SL diodesoperating at near-room temperature (T = 230 K).

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seen are turn-on voltages for both dark and photocurrents. Thebarriers’ parameters were assumed to be as follows: EB x = 0.33–0.6–0.275, d = 0.15 lm, ND = 2 � 1015 cm�3; HB x = 0.275–0.6,d = 0.4 lm, ND = 1017 cm�3.

Since CBIRD nB1nB2 HgCdTe/B1,2 n-type detector is a minoritycarrier device, absorber’s doping decreases concentration of thefree holes lowering IDARK. Further absorber’s doping increase con-tributes to the IDARK current raise due to EB DEc lowering and Auger1 effect. The lowest value of IDARK = 0.5 A/cm2 for V = 400 mV couldbe obtained for ND = 5 � 1015 cm–3 for V = 100 mV but for this ab-sorber doping IPHOTO assumes the lowest value which indicates thatoptimal working conditions appears for ND < 1015 cm–3.

Fig. 16 presents D⁄ versus voltage for selected absorber’s dop-ing. Presented results indicate that the maximum value of the D⁄

= 1.6 � 1010 cmHz1/2/W for given structure could be obtained forabsorbers doping ND = 1014 cm–3 and V = 400 mV while at dopinglevel above 1014 cm–3, detectivity decreases rapidly due to darkcurrent increase and lowering of the photocurrent. Once absorber’sdoping increases, the optimal voltage to be applied to the structureto attain the highest detectivity decreases. Absorber width influ-ences the IR absorption what is shown in Fig. 17. For voltageV = 400 mV the optimal thickness is estimated to be d = 5 lmwhich allows reaching detectivity D⁄ = 2 � 1010 cm Hz1/2/W. Oncebias decreases optimal thickness decreases and for V = 300 mVequals d = 4 lm.

6. Comparison of the InAs/GaSb T2SLs and HgCdTe technologies

The very last figure (Fig. 18) shows the RoA and RA products ver-sus temperature for MWIR CBIRD nB1nB2 HgCdTe/B1,2-n typedetector, UBIRD nBn HgCdTe/B-n type (kc = 5.2 lm) detector,InAs/GaSb/B–AlGaSb T2SL nBn (kc = 5.4 lm) detector, InAs/GaSbPIN photodiode (kc = 6.2 lm), and finally HOT HgCdTe bulk photo-diodes (kc = 5.4 lm) fabricated at the joint laboratory run by Insti-tute of Applied Physics, Military University of Technology/VigoSystem SA. Theoretical estimation for the MWIR UBIRD nBnHgCdTe/B-n type was conducted by Martyniuk and Rogalski inRef. [22], whereas the performance of T2SLs nBn InAs/GaSb/B-Al-GaSb detector’s performance was presented in Ref. [24] where ananalytical approach was used to model the detectors’s perfor-mance. PIN T2SLs photodiodes were analysed by Wrobel et al.[25]. It is clearly seen that the performance of CBIRD nB1nB2

HgCdTe/B1,2-n type structure has reached a comparable leveldetermined by the state of the art of HgCdTe bulk photodiodesand put itself in superior position with reference to UBIRD nBnHgCdTe/B-n type, T2SLs nBn, and PIN detectors. The particular sig-nificance of the incorporation of the extra barrier for minority car-riers in CBIRD structures versus single barrier (majority carriers’blocking) in UBIRD detectors is clearly evident by RA product in-crease from 0.1 to 0.5 Xcm2 for T = 230 K (for the same absorber’s

P. Martyniuk, A. Rogalski / Solid-State Electronics 80 (2013) 96–104 103

doping ND = 1014 cm–3 and thickness d = 10 lm) resulting in raisingof detectivity e.g. from 3.5 � 109 to 1.6 � 1010 cm Hz1/2/W forV = 400 mV and T = 200 K. Once absorber’ thickness is reduced tothe optimal size to attain the highest detectivity, the RA product in-creases to 0.9 Xcm2 for T = 230 K and detectivity reaches 2 � 1010 -cm Hz1/2/W at V = 400 mV and T = 200 K. In fact, the RA products ofMWIR 5.2 lm CBIRD nB1nB2 HgCdTe/B1,2-n type is slightly higherin comparison to bulk HgCdTe photodiodes, but it was calculatedfor V = 50 mV reverse bias.

7. Conclusions

In the paper we theoretically estimated the performance of theCBIRD nB1nB2 HgCdTe/B1,2-n type detector versus operating condi-tions and structural parameters. The unfavourable compositionaluniformity and interdiffusion at the interfaces were modelled byproper barrier grading matched to the cap and absorber’s compo-sition respectively. The maximum RA product of the detector with5.2 lm cut-off wavelength is higher than 0.9 Xcm2 at 230 K whilemaximum detectivity was estimated to be 2 � 1010 cm Hz1/2/W atT = 200 K assuming an absorber thickness d = 5 lm andV = 400 mV. Inherited barriers in both conduction and valancebands were analysed in detail pointing the optimal operating con-ditions as for as bias and doping are concerned. Turn-on voltageabove which dark current increases slowly was estimated to beV = 0.2 V for dark current and 0.4 V for photocurrent respectively.

Although, it is unfeasible to attain wanted band alignment invalance band, the theoretically predicted CBIRD nB1nB2 HgCdTe/B1,2-n type structure demonstrate performance which underlinesignificance and full legitimacy of the barriers’ incorporation tothe detector’s architectures. Similarly to UBIRD HgCdTe/B-n type,the analysed structure allows circumventing requirements for p-type doping reducing number of the processing steps. Barrier’sdoping and composition should be perceived as the most impor-tant parameters in CBIRD nB1nB2 HgCdTe/B1,2-n structure optimi-zation. The proper doping and composition choice leads to eitherbuilding up or lowering the barriers in both conduction and va-lance bands. It was shown that the raise of the operating temper-ature by nearly 50 K could be reached by additionalincorporation of the minority carrier barrier into UBIRD structure.The extra barrier leads to suppressing of the dark current by nearlyone order of magnitude.

As mentioned in introduction, T2SL InAs/GaSb 6.1 Å compoundfamily is the only one infrared material system theoretically pre-dicted to achieve higher performance than HgCdTe bulk photodi-odes. However, so far the HOT HgCdTe photodiode performancehas not been overcome by T2SL PIN and UBIRD nBn structures be-cause of the low quantum efficiency and presence of the SRHrecombination characterized by a relatively short carrier lifetime.Mentioned limitations could be circumvented by simplified CBIRDnB1nB2 HgCdTe/B1,2-n type structures and UBIRD nBn HgCdTe/B-ntype detectors. Finally, unlike T2SLs InAs/GaSb/B–AlGaSb nBndetector, CBIRD nB1nB2 HgCdTe/B1,2-n type and UBIRD nBnHgCdTe/B-n type detector do not require highly doped layerswhich should be perceived as a technological advantage.

Acknowledgement

This paper has been done under financial support of the PolishNational Science Centre, Project: DEC-2011/01/B/ST5/06283.

Appendix A

The CBIRD nB1nB2 HgCdTe/B1,2-n type detector was simulatedusing the following material parameters [1,26]:

Band-gap energy:

Egðx; TÞ ¼ �0:302þ 1:93x� 0:81x2 þ 0:832x3 þ 5035

� 10�4Tð1� 2xÞ: ðA:1Þ

Electron affinity:

c ¼ 4023� 0:813½Egðx; TÞ � 0:083�: ðA:2Þ

Carriers’ effective masses:

m�e ¼ 8:035� 10�2Egðx; TÞm0; ðA:3Þ

m�h ¼ 0:55m0: ðA:4Þ

Dielectric constant:

e ¼ 20:5� 15:5xþ 5:7x2: ðA:5Þ

The radiative recombination rate:

B ¼ 5:9052� 1018n�2i eT3=2

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ x

ð81:9þ TÞ

sexp � Eg

kBT

� �ðE2

g

þ 3kBTEg þ 3:75k2BT2Þ: ðA:6Þ

The Auger recombination coefficients Cn and Cp:

Cn ¼ 5� 10�12jF1F2jEg

kBT

� �3

exp 1þ 2m�gm�h

� �Eg

kBTðm�g=m�hÞ

!" #�1=2

n�2i 3:8� 10�18e2 1

m�g

!1þ 2

m�gm�h

� � ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi1þ

m�gm�h

s" #�1

; ðA:7Þ

Cp ¼ 0:1Cn: ðA:8Þ

The absorption coefficient:for: k > kc

a ¼ a0ag

a0

� �n

; ðA:9Þ

n ¼ 1:24=kc � e0

eg � e0; ðA:10Þ

for: k 6 kc

a ¼ ag expffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiB½1:24=kc � eg �

q� �; ðA:11Þ

Eg ¼ �0:295þ 1:87x� 0:28x2 þ ð6� 14xþ 3x2Þ � 10�4T

þ 0:35x4; ðA:12Þ

ag ¼ �65þ 1:883T þ ð8694� 10:314TÞx; ðA:13Þ

a0 ¼ expð�18:5þ 45:68xÞ; ðA:14Þ

e0 ¼ �0:355þ 1:77x; ðA:15Þ

B ¼ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi½�1þ 0:083T þ ð21� 0:13TÞx�

p: ðA:16Þ

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