1989 - performance limitations of gaasalgaas infrared superlattices.pdf

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Performance limitations of GaAs/AlGaAs infrared superlatticesM. A. Kinchand A. Yariv

Citation: Appl. Phys. Lett. 55, 2093 (1989); doi: 10.1063/1.102093View online: http://dx.doi.org/10.1063/1.102093

View Table of Contents: http://apl.aip.org/resource/1/APPLAB/v55/i20

Published by the American Institute of Physics.

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erformance limitationso Ga sl JGa s infrared superlatticesM. A. KinchTexas Instruments Incorporated, Dallas, Texas 75265A. YarivCalifornia Institute of Technology, Department ofApplied Physics, Pasadena, California 91125Received 17 May 1989; accepted for publicat ion 13 September 1989)

The performance of the GaAslAIGaAs superlattice as an infrared detecting material ismodeled as a function of temperature for two cutoff wavelengths, namely, 8.3 and 1O.0,um.The results are compared with HgCdTe, the present industry standard material for infraredsystems. The limiting performance of the GaAslAIGaAs materials system is found to beorders of magnitude below that of HgCdTe for any specific cutorr wavelength and operatingtemperature.

The concept of infrared OR) photodetection by intersubband absorption in superlattices first proposed by Smithet al. 1 has recently become the subject ofextensive investigation2 utilizing the GaAslAIGaAs system, and strong claimshave been made regarding the performance of this IR materials system relative to that of HgCdTe. It is the purpose ofthis letter to meaningfully compare the ultimate performance of these two materials systems with a view to theirpotential application in infrared systems. To this end a quantitative analysis is carried out of a )-c = 8.3 pm superlattice,and this is compared both to the published data and to aHgCdTe photoconductor operating at the same cutoifwavelength. These arguments are then extended to the more relevant range for IR systems, namely, Ac = 10-12 p,m.

The GaAslAIGaAs multiquantum well detector is amajority-carrier device, and as such the noise is determinedby the variance in the density of majority carriersl ,4 withinthe device, namely, (b.n 2 ) = n = n, + n p. where l l , is thedensity of thermally generated carriers and f l , the density ofphoton-generated carriers. The photon-generated carrierdensity consists of two components, due to signal (s) andbackground flux (CPR) and in the 8-12,um spectral region isdominated by the background optical flux component nBThe ultimate in IR system performance is achieved whennddJ > n as the noise is then dominated by the incident background flux, and background-limited performance (BUP)is achieved.

The thermally generated carrier density for the multiquantum well structure is obtained from a consideration ofthe density of states in the associated bandstructure of a s i n ~gle quantum welL The geometry of the structure consideredconsists of 50 GaAs quantum wells of width 40 A withAI,Ga1_xAs barriers (x = 0.31) of thickness 300 A andheight 250 mV. An envelope function approximationS calculation for this structure yields the energy-level diagramshown in Fig. 1. The first subband lies approximately 100m V above the GaAs conduction-bandedge, and the secondsubband lies approximately 3 mV above the continuum edgeof the barrier. The GaAs wells are doped at no = 2 X 10 18 toprovide the necessary IR absorption coefficient for the structure. The Fermi level is ca lculated, to a good approximation,assuming an infinite barrier , so that for the two-dimensionaldensity of states associated with the first subband E 1, wehave

(1)where d s the wen width and m the effective mass. Forno = 2X Wig cm - 3 , d = 40 A and m* = 0.067mo, we haveEF = 28.7 mY. Using the model of Fig. 1 we treat the continuum as a wide quantum well of width L equal to the meanwell spacing, and the two-dimensional density of states isthen assuming only one state, n = 1, is confined in the deepwen)

. m* { [(2m*(E - V)1I2]}P2D E) = 2 1 Int L 2IIil 1 i ~ (2)where Int (x) = largest integer


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Xe ulkr duo (4)

For the parameters of Fig. 1, IntlL V(2m*u/i j2n2) j = 0 for u < 3 mY, and = 1 for u> 6 mY. At u = 6mY, exp( - u/kT) e x p - 1) at 77 K. To first order wecan neglect the lnt( ) term in Eq. (4), obtaining

(5)noting that this will represent a slight underestimate of n IThis approximation is tantamount to assuming that all thermal carriers are generated by the first electron subband ofthe quantum well.

Combining Eqs. (1) and (5) we have(6)

The background-generated carrier density is given by, foran incident angle of 45,

fl1'n = 11B,1\12t, (7)where 7 represents the effective lifetime of excess carriers, tthe device thickness, and 7 the device quantum efficiency.The measured2 flattening of responsivity with bias voltagefor Vh > 4 V indicates that 7is then ~ 7 d / 2 = t /2v, where 7 /is the transit time of a hot electron across the device structure, and v its limiting velocity, which for GaAs/AIGaAswill be ~ 107 cm/s. Thus, 7 ~ 8.5 X 10- 12 S. This hot-electron lifetime value is considerably larger than that found forabsorption in GaAs quantum wells between two boundstates,6 where 7-1-2X 10 13 S. This could possibly be attributed to both the unbound nature of the first excited subband, and to the larger AIGaAs barrier widths employed.The hot electron thus spends a large fraction of its lifetime inthe barrier region, where it cannot lose its excess energy. Itshould be pointed out that these observed values are somewhat lower than would be predicted by hot-electron theory,7.8 assuming energy loss simply by electron-phonon interactionso This is possibly due to the role played byelectron-electron scattering. Thc quantum efficiency is determined from the measured responsivity in the sweepoutmode, namely, Yjq/ 2y2hv), where a photoconductive gainof 1/2 and a 4S angle of incidence have been assumed. Themeasured value

2for unpolarized light is 0.42 A/W, giving17-17.5%0 Assuming two passes of IR radiation through

the superlattice at an angle of 45, this corresponds to anabsorption coefficient for unpolarized light, a - 750 em .. [,in reasonable agreement with measured values2 for this device at 8.3 fim.

From Eqs. (6) and (7) the BLIP condition is achievedwhen WPjJ7/tv2 > f i t or rearranging we have BLIP whenthe 45 incident background rate of carriers,Tj jJ/V2 > nJ /T, the thermal generation rate of carriers inthe detector. The thermal generation rate can be viewed asthe rate at which any departure from equilibrium in the device is accommodated. A calculation of the thermal genera-2094 Appi. Physo Lett., VoL 55, Noo 20. 13 November i 989

tion current, J, ( = n,tqh), in the 8.3 f 1m GaAs-AIGaAss ~ l p e r l a t t i c e as a function of temperature is shown in Figo 2,assuming T = 8.5 ps, t = L7 fl,m, d = 40 A L , , ~ 340 A andno = 2 X 1O S em - 3. The current is normalized by the effective material quantum efficiency ( = 0.175/\12) so as tofacilitate comparison with other materials systems. Plottedon the right-hand axis is the equivalent incident photon flux.This plot immedia tely gives the required minimum temperature of operation such that n t ~ ~ n 1 > B For example, at a typicalsystem background flux of 1016 photons/cm 2 s, the requiredtemperature of operation for the 8.3 pm GaAs-AIGaAs superlattice is < 69 K to achieve the BLIP condition.

Operation at 8.3 lm is not particularly meaningful forpracticallR systems, and a cutoff wavelength of 10.0 pm ismore relevant The preceding calculation is extended to consider this casc. The quantum well width is changed to 30 Aand the remaining parameters assumed the sameo This willyield an intersubband transition energy ~ O 1 2 4 eV. The calculated thermal generation rate (and hence current) for thiscase is also shown in Fig. 2 as a function of temperature.BLIP performance for 10 Lm wavelengths in a 10[6 cm 2 senvironment requires operating temperatures < 58 K.Similar arguments can be readily applied to HgCdTeoperating at the same cutoff wavelengths. HgCdTe devicesare dominated by minority-carrier statistics, so for n-typeHgCdTe the BLIP condition becomesp t /Tp < 7Jn wherep = nT/no, l1 i being the intrinsic carrier concentration. Ingood quality HgCdTe, the minority-carrier lifetime 7p is limited by Auger recombination 9 and is given by

(8)where 7 Ai is the intrinsic Auger lifetime. Thus, the thermalgeneration rate of minority carriers in good quality HgCdTeis given by

(9)TA.i has been measurcd9 for a variety of HgCdTe composi-

---,10 218.3 ilm GaAs- . - 1a 01m GaAs- - - 8.3 lim HgCdTe- - - - 10 101m HgCdTe .'

Iii

,;,;/

,; '

FIG, 2, Thermal generation current vs temperature fur GaAslAIGaAs IRs u p e r l a t t i c , ~ s and H gCdTc alloys at ) e = 8.3 and 10 1m. The assumed effective quantum efficiencies are 11 = 0.125 and 007 for GaAslA1GaAs andHgCdTc, respectivc\yo

M. A. Kinch and A Yariv 2094

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tions, is in reasonable agreement with theory, 10 and is givenapproximately by

r Ai = [ 8 . 3 X l O n E ~ / 2 / k T ) 3 J 2 1 exp(EglkT), 0 )where a value for the overlap integral /F)?2/ 2 = 0.25 hasbeen assumed to fit the experimental data.

The minority-carrier generation current given by Eqs.(9) and (J 0) is shown in Fig. 2 as a function of temperaturefor both 8.3 and 10pm cutoff wavelengths. A quantum efficiency of 0.7 has been assumed to normalize the thermalcurrent axis. I t is readily apparent from Fig, 2 that the thermal generation rate at any specific temperature and cutoffwavelength is approximately five orders of magnitudesmaller than for the corresponding GaAs-AIGaAs superlattice, This translates into a cooling requirement of an additional 50 K for GaAs-AIGaAs to achieve the same performance as HgCdTe. The dominant factor favoring HgCdTein this comparison is the excess carrier lifetime, which for n-HgCdTe is > 10 6 S at 80 K, compared to 8.5 X 10 [2 Sfor the IR supcrlattice.

I t should be pointed out that the GaAslAIGaAs superlattices considered above are not theoretically optimizedstructures. Some benefit can be gained by trading off devicethickness and doping concentration, such that a high overallquantum efficiency is maintained but with a subsequent decrease in E p , and hence n . Some enhancement of carrierlifetime can be achieved by widening the barrier layers, butthere are limits. For the quantum wen geometries consideredtheInt [L 2m*u/1l2U 2 ) i l2} term in Eq, (4) will no longer benegligible for values of L > 500 A. Thus, any increase in Iwould be offset by an increase in I l l essentially due to thermally generated carriers in the AIGaAs barrier region. I t isalso not apparent that the photoconductive gain of this device must necessarily be limited to the value 1/2, The choiceof GaAs contacts2 generates Schottky barriers at the inputand output of the superlattice. It would seem that ajudiciouschoice of heavily doped AlxGa l ~ x s of the appropriate xcomposition could generate ohmic contacts to the superlattice device. Hence photoconductive gain greater than unitycould be achieved, provided the dielectric relaxation time

2095 Appl. Phys. Lett, Vol. 55, No. 20, 13 November 1989

( = Po, where p is the resistivity and," the dielectric constant) were fast enough for the operating conditions.

The thermal generation rate parameter can be used todirectly estimate D ' if so desired. For a photoconductivedetector, with radiation incident at an angle e to the normal,the specific peak detectivity is given byD* = 1/( 1 cos Olllt01l2/2hv, where J represents the absorbing quantum efficiency, which for the GaAs-AIGaAscases treated here was 17.5%. At 80 K the two supedatticesconsidered here would exhibit maximum valuesof D (8.3,um) = L85XlO lO cmHz l I 2 W- , andD (lO.O11m = 6.1 X [09 em Hz l /2 W ~ " compared toHgCdTe, with D I (8.3 ,um) = 1.75 X 1013 cm H Z l /2 ~ [andD (1O.Oll;m)=3.0XlO12cmHz1J2W I.

In summary, it is shown that the limiting performancef GaAs-AIGaAs IR superlattices is considerably below

that which can be achieved with HgCdTe devices at anyspecific temperature and cutoff wavelength, P e r f o r m a n c ~requirements of present day fR systems (operating in typical10 pm flux environment of l ~ 3 ) X 10 16 photons/cmz s]would necessitate operation of GaAs-AIGaAs supcrlatticesat temperatures below 60 K.One of the authors A.Y.) acknowledges the MaterialResearch Council of the Defense Advanced Projects Agencyand the Office of Naval Research for support of this work.The authors acknowledge fruitful discussions with Dr. T. C.McGill and Dr. H. Ehrenreich.

'J. S Smith, L. C. Chiu, S Margalit, A. Yariv, and A. Y. Cho, J. Vac. Sci.Techno . B 1.376 (1983).2B F. I ~ c v i n e . C. G. Bethea, G. Hasnain, J. Wulker, and R. J Malik, Appl.Phys. Lett, 53, 2196 (1988).'K. M. van Vliet, Proc. IRE 46,1004 (1958).4D Long, Infrared Phys. 7,169 (1967).'G. Bastard, Phys. Rev. B 25, 7584 (19821.( B. F. Levine, K. K. Choi, C. G. Bethea, J, Walker. and R. J. Malik, AppJ.Phys, Lett. 50, 1092 (1987).IR, Strattoll, Proc. R. Soc. London A 246, 406 (1957)."E. K. Ridley, 1 Phys. C 15. 5899 (1982), .OM A. Kinch, M. J Brau, and A. Simmons. J App . Phys, 44, 1649(1973) .

,op. E. Petersen, 1. App . Phys.41, 3465 (1970).

M. A. Kinch and A. Yariv 2095

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