Fundamental Physics of Infrared Detector Materials

Transcription

1 Journal Fundamental of ELECTRONIC Physics MATERIALS, of Infrared Vol. 29, No. Detector 6, 2000 Materials 809 Special Issue Paper Fundamental Physics of Infrared Detector Materials MICHAEL A. KINCH DRS Infrared Technologies, PO Box , Dallas, Texas, 75374; The fundamental parameters of IR photon detection are discussed relevant to the meaningful comparison of a wide range of proposed IR detecting materials systems. The thermal generation rate of the IR material is seen to be the key parameter that enables this comparison. The simple materials physics of 1) intrinsic direct bandgap semiconductors; 2) extrinsic semiconductors; 3) quantum well devices, including types I, II, and III superlattices; 4) Si Schottky barriers; and 5) high temperature superconductors, will be examined with regard to the potential performance of these materials as IR detectors, utilizing the thermal generation rate as a differentiator. The possibility of room temperature photon detection over the whole IR spectral range is discussed, and comparisons made with uncooled thermal detection. Key words: Infrared detector, photon detector, thermal detector, HgCdTe INTRODUCTION The choice of available infrared (IR) detectors for insertion into modern IR systems is both large and confusing. The objective of this IR detector tutorial is to generate a simple set of fundamental IR detector parameters that can be utilized to compare the different IR materials technologies, and hopefully minimize any confusion that might exist within the minds of today s IR materials and system scientists. IR detectors fall into two broad categories, namely photon and thermal. In the classical photon detector, photons are absorbed and generate free carriers, which are sensed by an electronic readout circuit. If the carriers are majority carriers then the sensing is photoconductive in nature. For minority carriers both photoconductive and photovoltaic modes of detection can be utilized. The following section contains a simple consideration of the IR materials parameters that are relevant to detector operating temperature and sensitivity, from a purely fundamental point of view. Excess current sources such as tunnel and thermal generation within the depletion region of diodes are ignored, together with 1/f noise issues. These phenomena are typically associated with defects in the bandgap, and are considered to be avoidable in a suitably fabricated detector, and only serve to confuse any attempt at a fundamental comparison of different (Received December 9, 1999; accepted January 5, 2000) materials technologies. In the case of photovoltaic detection this assumption is tantamount to considering only the diffusion limited operation of the diode. In these circumstances the key IR materials parameters are found to be 1) the thermal generation rate per unit volume of the detector material, and 2) the quantum efficiency for photon absorption, or the absorption coefficient of the IR material. These two parameters totally determine the maximum useful operating temperature of the IR material. They also determine, together with the IR detector internal quantum efficiency (i.e., the fraction of photon generated carriers that are detected in the external circuit), the ultimate sensitivity of the IR material. These criteria are used to assess the relative merits of the current generation of IR detector technologies, and serve to explain the dominance of HgCdTe in the present day IR marketplace. Third generation IR systems requirements will require focal plane operation at even higher sensitivities and operating temperatures, even into the realm of uncooled. The thermal generation rate parameter can be utilized to predict IR materials requirements to enable these third generation systems. There is also a section devoted to an assessment of the possibility of driving the operating temperature of the photon detector into the uncooled regime, utilizing the High Operating Temperature detector (HOT) concept first proposed by Elliott and Ashley. 1 The thermal detector, on the other hand, is a power 809

2 810 Kinch Fig. 1. IR photon detection. law detector, and the incoming IR photons are absorbed by a thermally isolated detector element, resulting in an increase in temperature of the element, which is sensed by a parameter such as resistivity, or dielectric constant. Optimum performance of a thermal detector occurs when the temperature dependence of the parameter in question is large enough that the limiting noise of the thermal detector is determined by thermal fluctuations with the surrounding heat sink. Ultimate performance is achieved when the limiting thermal conductance is due to radiative coupling of the detector to its surroundings. The case of the perfect thermal detector operating at room temperature and its performance limitations compared to the uncooled photon detector are discussed in a subsequent section. IR PHOTON DETECTOR The standard IR photon detector is illustrated in Fig. 1. The IR material of the detecting element, of thickness t, is at a temperature T. Incident on the detector is a flux of background photons, Φ B /cm 2 /s, and a signal flux, Φ s /cm 2 /s. These photons are absorbed with an efficiency η a. The ultimate in detector performance is attained when the density of photon generated carriers in the detector is > the density of thermal carriers. The noise of the photon detector is then dominated by fluctuations in the carriers generated by the incident background flux. This is designated as background limited performance (BLIP), or alternatively background limited photodetector. The condition for BLIP is η a Φ B τ/t > n th, where n th is the density of thermal carriers at temperature T, and τ is the carrier lifetime. These carriers can be either majority or minority in nature. Re-arranging we have for the BLIP requirement η a Φ B > n th t/τ; i.e., the photon generation rate per unit area needs to be greater than n th t/τ, the thermal generation rate per unit area. For η a ~ αt, where α is the material absorption coefficient, we have a requirement for BLIP of Φ B > n th /ατ. The normalized thermal generation rate is thus defined as G th = n th /ατ (1) and can be utilized to unambiguously predict the ultimate performance of any IR material, and to compare the relative performance of different IR materials, as a function of temperature. The only requirement is a knowledge of the dependence of n th, and τ, on temperature. Photon detectors can be divided into two broad classes, namely majority and minority carrier devices. Five examples of generic IR materials systems, from each of these classes, are considered here, and their relative potential performance assessed. These materials systems are: 1. Direct bandgap semiconductors minority carrier Binary alloys InSb Ternary alloys tunable bandgap HgCdTe Type II, III superlattices InAs/GaInSb 2. Extrinsic semiconductors majority carrier Si:Ga Ge:Hg 3. Type I superlattices majority carrier GaAs/AlGaAs QWIPs 4. Silicon Schottky barriers majority carrier PtSi IrSi 5. High temperature superconductors minority carrier. All of these materials systems have been serious players in the IR systems marketplace with the exception of the high temperature superconductor. The superconductor is modeled here to illustrate the predictive power of the analytical method provided by utilizing the normalized thermal generation rate parameter. Taking literature values for n th and τ enables a direct assessment of the potential performance of the superconductor as an IR detector, which was being given serious consideration in the late 1980s, with the discovery of the high temperature species. The model indicates that this material has nothing to offer in the way of performance, even if the appropriate superconducting energy gap could be achieved, and hence did not justify the expense of a serious materials effort to this end. Direct Bandgap Semiconductor The direct bandgap semiconductor is a minority carrier device and in thermal equilibrium n min = n i2 /n maj, where n i is the intrinsic carrier concentration, and n maj the majority carrier concentration. The ultimate limit on lifetime in a direct gap semiconductor, with its gap at k = 0, is given by band to band recombination, by either radiative or Auger processes. The standard literature treatment of radiative recombination by van Roosbroeck and Shockley, 2 used for many years, yields a value for the radiative lifetime of τ R = 1/(B(n+p)), where B = ε 1/2 (m o / (m e +m h ) 3/2 (1+m o /m e +m o /m h )(300/T) 3/2 E g2, ε is the high frequency dielectric constant, and m e and m h the electron and hole effective masses. This expression has been shown by Humphreys 3 to represent a gross underestimate of the radiative lifetime in infrared semiconductors, due to noiseless photon re-absorption effects. Envision an n-type semiconductor of thickness, t, in thermal equilibrium with its surroundings at temperature, T. The generation rate of minority carriers per unit volume within the semiconductor, due to radiative transitions, is n i2 / n maj τ r, where τ r is the radiative lifetime, and n i the

3 Fundamental Physics of Infrared Detector Materials 811 Fig. 2. Dark current density vs. temperature for MWIR and LWIR N-HgCdTe. intrinsic carrier concentration. This equals the number of photons absorbed per unit volume from the surrounding enclosure, namely 2ηΦ B /t, where η is the quantum efficiency of absorption, and Φ B is the total incident background flux density for wavelengths shorter than the semiconductor bandgap. Thus the radiative lifetime for the semiconductor in thermal equilibrium is τ r = n i2 t/2n maj ηφ B, which is considerably longer than the value given by van Roosbroeck and Shockley. For many realistic situations radiative recombination can be ignored. Auger limited band to band recombination is represented by a minority carrier lifetime, τ min = 2τ Αι [n i2 / n maj (n maj +n min )], where τ Ai is the Auger lifetime for intrinsic material. The associated generation rate G th = n min /ατ min = n maj /2ατ Ai. For n-hgcdte these quantities are well known; 4 α ~ 10 3 /cm, and τ Ai1 = [ /2 E g exp(qe g / kt)]/(kt/q) 3/2, where E g is in ev, and the relevant Auger1 mechanism involves two electrons and a heavy hole. The thermal generation rate is given by G th = n maj T 3/2 1/2 /[E g exp(qe g /kt)]/cm 2 /s (2) The resulting thermally generated dark current density, given by G th q, is shown in Fig. 2, for MWIR and LWIR n-hgcdte, with a doping concentration of cm 3. Included in Fig. 2 is the background flux current for F/2 optics for the two nominal cutoff wavelengths of 5 µm and 10 µm. It is apparent that BLIP performance can be achieved at temperatures < 120 K for the LWIR, and at < 180 K for MWIR, for detector thicknesses ~1/α ~ 10 µm. Similar arguments apply for p-type material except that the relevant Auger7 mechanism involves two holes and an electron, and is predicted 5,6 to be somewhat weaker with τ Ai7 > τ Ai1 by a factor of 6 to 20. Other examples of direct bandgap semiconductors are 1) the binary alloys such as InSb, and 2) the bandgap engineered tunable gap type II strained superlattices, such as InAs/GaInSb, 7 and type III superlattices, such as HgTe/CdTe. 8 Binary alloys have the limitation of a fixed bandgap and as such are much less versatile than the tunable bandgap ternary alloys. The superlattices are tunable, and theoretically can be superior to HgCdTe in some respects, such as a larger effective mass with less tunneling, and potentially reduced Auger recombination. 9 Published data 10 on type III superlattices based on the HgTe/CdTe system indicates problems with interdiffusion at device processing temperatures. Type II superlattices, however, show promise, although significant materials work remains to be done. It should be emphasized here that the above limitation on dark current, and hence on performance, is truly fundamental to the material in question, and is independent of the detection mode utilized, be it photoconductive, photovoltaic, or metal-insulator-semiconductor, or for that matter any other proposed mode of sensing carriers in a direct gap semiconductor. Extrinsic Semiconductors The extrinsic semiconductor is strictly a majority carrier device. The carrier concentration in an n-type extrinsic semiconductor with a partially compensated singly ionized donor level is given by n maj = [(N d N a )/ 2N a ]N c exp( E d /kt), where N d is the donor concentration, N a the compensating acceptor concentration, N c the conduction band density of states, and E d the binding energy of the donor relative to the conduction band. The majority carrier lifetime is determined by the density of empty (ionized) donor levels, and for low temperatures, such that n maj < N a < N d, is given by τ = [σv th N a ], where σ is the capture cross-section for electrons into the donor level, and v th is the carrier thermal velocity. Estimates exist in the literature for values of σ for both doped germanium 11 and silicon, 12 with an upper limit of cm 2, for Ge:Hg, with an ionization energy of ev. The absorption coefficient 13 is given by α = (10 15 N maj )/cm, with N maj in cm 3. Thus the normalized dark current for an extrinsic semiconductor, with equivalent parameters to high quality Ge, is G th q = qn maj /ατ = q T 3/2 exp( qe d /kt) A/cm 2 (3) where we have assumed an effective mass m* = 0.4 m o. E d is in ev. It should be pointed out that the published data 12 for Si indicate recombination coefficients (= σv th ) a factor of 30 larger than used here for Ge. QWIPS The classic example of the QWIP is the GaAs/ AlGaAs materials system, and one version of the architecture is shown in Fig. 3. IR absorption is achieved by transitions between energy levels induced in the majority carrier conduction band by dimensional quantization. In Fig. 3 only the conduction band profile is shown and the relevant transitions are between the two lowest bound states in the GaAs conduction band. The AlGaAs layers are thick and act as barrier layers that serve the dual purpose of providing geometrical confinement, and hence quan-

4 812 Kinch Fig. 3. The GaAs/AlGaAs bound to bound QWIP conduction band profile. Fig. 4. Dark current vs. temperature for LWIR and MWIR QWIPs. tization, and inhibiting any excess currents, such as tunneling, through the superlattice. The IR signal is detected as a photoconductive current, and the QWIP is a majority carrier device. The mode of operation is referred to as a bound to bound QWIP, and although not the most commonly used QWIP architecture it does serve to illustrate most simply the capabilities and limitations of this concept, as first pointed out by Kinch and Yariv. 14 The thermally generated majority carrier density for the QWIP is obtained from a consideration of the density of states in the associated bandstructure of a single quantum well. In thermal equilibrium the ground state is filled with n o electrons necessary for IR free carrier absorption. The Fermi level for these electrons is E F = (n o h 2 d)/(4πm*) where d is the well width, and h is Planck s constant. The carrier concentration in the second sub-band is determined by E F and the density of states in the second sub-band, and is given by n 2 = n o (kt/qe F )exp(qe F E 2 )/kt. The lifetime of carriers in the E 2 sub-band is determined by hot electron-phonon interactions, 15 modified by the time spent by the hot carrier in the barrier layers. Modeling of QWIP photoconductive gain, 16 which is a measure of carrier lifetime to carrier transit time, gives τ ~ 1 to s. The thickness of the simple QWIP is determined by the absorption coefficient for IR, which is complicated for the n-qwip by optical selection rules for these inter-band transitions, which allow transitions only for E-field polarization vectors normal to the detector surface. Various geometrical artifacts are used to circumvent this issue, including the use of grating couplers. In these circumstances the unpolarized absorption coefficient 17 for the active GaAs layer material is α ~ n o cm 1, and the maximum absorption quantum efficiency is 0.5, due to the unpolarized nature of the incident radiation. Typical values of n o are to cm 3. The thermal generation rate of the simple QWIP, with the thickness of the active GaAs layers equal to 1/α, assuming τ = s, is G th = (kt/qe F )exp[(qe F E 2 )/kt] which minimizes at E F = kt/q, giving G th = exp( qe g /kt)/cm 2 /s (4) where E g = E 2 E 1, and is in ev. The thermally generated dark current as a function of temperature for E g = ev and 0.25 ev are shown in Fig. 4, and compared to F/2 flux currents. A comparison of Figs. 2 and 4 indicates that the dark current in the QWIP is typically four to five orders of magnitude larger than HgCdTe with the same bandgap, operating at the same temperature. For tactical background fluxes HgCdTe can operate some fifty degrees higher in temperature whilst offering the same performance as the QWIP. BLIP performance for QWIPs can be achieved typically for T < 60 K in the LWIR, and for T < 115 K in the MWIR. This issue can be alleviated somewhat by the use of resonant structures, which enable IR absorption for significantly thinner QWIPs, at the expense of broad band spectral response, but the improvement is minimal. Silicon Schottky Barriers Silicon Schottky barriers are primarily majority carrier devices in which the IR absorption results in carrier transport over a metal/semiconductor-like barrier, as shown in Fig. 5. The IR absorption can be considered a three-stage process: 18 1) the incident radiation is absorbed by the carriers in the metal but only a small fraction of the resulting excited carriers will have sufficient energy to overcome the Schottky barrier; 2) the carriers must be transported to the barrier with sufficient energy to escape; 3) the carriers escape over the barrier and are detected in the external circuit. The first two stages constitute the absorption quantum yield in that they define the photon generated carrier concentration in the vicinity of the barrier relative to the thermally generated carrier concentration. The third stage represents an internal quantum yield, which is important in a calculation of device sensitivity, but is not important in defining the BLIP operating temperature of the material. The thermal carrier density at the barrier, obtained by a simple integration over the density of states, is n o = [(8πm 3/2 kt(2(e F +E g )) 1/2 h 3 ]exp( qe g /kt) = T exp( qe g /kt), where we have assumed that E F +E g ~8 ev. E g is the barrier height, again in ev. The lifetime of hot carriers in a metal is determined primarily by carrier-carrier scattering, with literature values 19 ~ /E g2 s, where E g is in ev. Resonant structures are the norm for Schottky de-

5 Fundamental Physics of Infrared Detector Materials 813 Fig. 5. Silicon Schottky barrier band structure. Fig. 6. Dark current temperature dependence of various LWIR materials. vices in the IR. The optimum thickness 18 of the IR absorbing layer in a PtSi structure is found to be 10 A to 20 A, yielding an absorption efficiency of 0.3. The thermal generation rate for the silicon Schottky barrier, assuming a thickness of 15 A is thus given by G th = n o t/τ = TE g exp( qe g /kt)/cm 2 /s (5) High Temperature Superconductor The advent of high temperature superconductivity resulted in proposals for detecting IR radiation by excitation across the superconducting energy gap, in much the same way as direct gap semiconductors. Here we consider the performance of hypothetical high temperature superconductors of energy gap E g, utilizing well-documented theory and experimental findings associated with conventional superconductors. The density of quasiparticles in a superconductor 20 is given by n t = 4N o [π kt/2] 1/2 exp( /kt), where N o is the single spin density of states at the Fermi level at T=0. E g = 2. The effective quasiparticle lifetime is dominated by electron-phonon interactions, 21 and is given by τ eff = τ + (n t /4N ωt )τ ph, where τ is the inherent lifetime associated with phonon emission, N ωt the equilibrium 1 density of phonons with energy hω/2π > 2, and τ ph the net transition probability for phonon loss by processes other than pair excitation. The second term in τ eff represents a lifetime enhancement effect associated with excess phonons generated by recombining quasiparticles. The smallest value occurs when they simply leave the device, and is given by t/2s, where s is the velocity of sound. In actuality acoustic mismatch results in a phonon loss inefficiency such that τ ph = βt/2s, where β > 1. The analysis by Rothwarth and Taylor indicates that for low temperature superconductors the second term in τ eff dominates. An application of this analysis to high temperature superconductors yields a similar conclusion. Thus τ eff = [βn t t/8n ωt s]. The device thickness will be ~ the absorption thickness, in the range 200 A to 1000 A. Thus the thermal generation rate of quasiparticles for the high temperature superconductor is G th = 8sN ωt /β = [ TEg2 /βs 2 ]exp( qe g /kt)/cm 2 /s (6) Technology Comparison of BLIP Operating Temperature The thermal generation rates for the various materials technologies expressed in Eqs. 2 through 6 are summarized in Fig. 6 for the LWIR spectral band with a chosen bandgap of ev. Some of the cases, such as the extrinsic semiconductor and the high temperature superconductor, are hypothetical, in that material has not been identified with the required band structure, but is included for comparison purposes. From a comparison of the above dark currents with the F/2 background flux current it is readily apparent that the highest BLIP operating temperature by far is achieved with the direct bandgap semiconductor, as typified by the tunable bandgap alloy, HgCdTe. Although not discussed here similar arguments can be made in favor of their bandgap engineered equivalents, namely type II and type III superlattices. IR Detector Sensitivity The sensitivity of an IR detector can be expressed in a variety of ways. However, the limiting factor in all of these is the fluctuation in the relevant carrier concentration, as this determines the minimum observable signal of the detector. This fluctuation is best envisioned by assuming that the detector current is integrated on a capacitive node, giving a variance N 1/2 = g[(i d +I Φ )τ/q] 1/2, where g is the gain, I d the dark current, I Φ the background flux current, and τ the integration time. The minimum observable signal, or noise equivalent flux is given by g ΦητA = N 1/2, where in this case η represents the overall quantum efficiency of the detector, including the internal quantum efficiency. Thus the noise equivalent flux is given by Φ = g(1 +I d /I Φ )Φ B /N 1/2 (7) The sensitivity can be expressed as a temperature difference by considering that Φ = T[dΦ B /dt]. Substituting above, we have for noise equivalent temperature difference NE T = g(1+i d /I Φ )Φ B /(dφ B /dt)/n 1/2 (8)

6 814 Kinch Fig. 7. D* temperature dependence for various LWIR materials technologies. where (dφ B /dt)/φ B = C, is the scene contrast. For unlimited available well capacity N 1/2 varies as g, and the above parameters Φ, and NE T are independent of the gain, g. However for a limited maximum well capacity N, both F and NE T will vary as g. The above parameters contain specific system and detector quantities such as area and bandwidth, where bandwidth is defined as f = 1/2τ. These quantities can be eliminated by normalization, resulting in the detector parameter known as detectivity, D*, which is defined as [signal/flux]a 1/2 /[Noise/ f 1/2 ]. Thus D* = [η/2/(g th +Φ B )] 1/2 /hν (9) where hν is the photon energy. The background flux, Φ B, can be assumed negligible, in which case the D* expression in Eq. 9 depends entirely on the properties of the IR material, and can be used to predict the maximum available D* at any operating temperature. The normalized thermal generation rate G th is thus a critical factor in determining the potential D* of the detector material, as well as the BLIP operating temperature, provided that η, the overall quantum efficiency of the detector, is utilized. Equations 2 through 6 yield a direct estimate of D* as a function of temperature for the various materials technologies, and is shown in Fig. 7. The only detector technology with an issue of internal quantum efficiency is the silicon Schottky barrier device. The overall quantum efficiency is estimated 18 to be ~ The current generation of IR FPAs reflects the data shown in Figs. 6 and 7. HgCdTe dominates the scanning tactical market. Staring systems utilize HgCdTe (LWIR and MWIR) and InSb (MWIR) operating at 77 K. Niche markets exist for extrinsic silicon in the VLWIR strategic FPA business because HgCdTe has not yet realized its potential at low temperatures and reduced backgrounds. QWIPs may be of use in tactical systems operating at 60 K, where cooling is not an issue, but they have not yet been deployed. FUTURE IR SYSTEMS REQUIREMENTS The dominance of the tunable direct bandgap semiconductor in the IR marketplace will be exacerbated by the requirements of next generation IR Fig. 8. Dark current vs. temperature for MWIR QWIPs, InSb, and HgCdTe. Fig. 9. HOT MWIR detector concept with dark current sources. systems, namely: Higher temperatures of operation ultimately uncooled Larger areas Faster frame rates shorter integration times Multi-spectral Of particular importance with regard to system cost, portability, and flexibility is the requirement of higher operating temperatures, driving eventually to uncooled, for all IR cutoff wavelengths. An example of the benefit derived from the tunable bandgap alloy is shown in Fig. 8, which compares the dark current as a function of temperature for MWIR QWIPs, InSb, and four different HgCdTe architectures. The three HgCdTe high density vertically integrated photodiode (HDVIP) architectures are n + /n - /p homojunctions, whereas the HgCdTe double layer heterojunction (DLHJ) is p + /n. Measurements at DRS 22 give lifetime values for extrinsic and vacancy doped p-hgcdte: τ ext = [p 1 +p]/(pn a ) τ vac = n 1 /(pn vac ) (10)

7 Fundamental Physics of Infrared Detector Materials 815 Fig. 10. Lifetime models vs. doping concentration for MWIR HgCdTe at 77 K. where for the extrinsic case N a is the extrinsic doping concentration, p the hole concentration, p 1 = N v exp(q(e r E g )/kt), N v is the density of states in the valence band, and E r represents the S-R center energy relative to the conduction band. Experimentally 22 E r is found to lie approximately at the intrinsic level for arsenic, copper, and gold, giving p 1 = n i. For the vacancy doped case N vac is the density of metal vacancies, n 1 = N c exp(qe r /kt), where E r is approximately 30 mv from the conduction band for x = 0.22 to 0.3. The three HDVIP architectures in Fig. 8 are associated with purely vacancy doped material, purely extrinsically doped material, and a standard mixture of extrinsic and vacancy doping ( cm 3 Cu, cm 3 vacancies). The dark current for the DLHJ is consistent with Eq. 2, using a donor concentration of cm 3. The QWIPs and HgCdTe are modeled with a constant bandgap of 0.25 ev at all temperatures, as they are tunable. The advantage of HgCdTe is clear. BLIP operation at F/2 is possible at 110 K for QWIPs, 115 K for InSb, and at 170 K for HgCdTe. It is interesting to pose the question as to whether even higher operating temperatures can be achieved. The answer may well lie in the high operating temperature (HOT) photon detector concept, first proposed by Elliott and Ashley, 1 and depicted in Fig. 9 for an n + /π/p + architecture, where π designates an intrinsic region containing a p-type background dopant. The intrinsic IR absorbing volume is connected to both a minority carrier contact and a majority carrier contact. The geometry of the active volume is small relative to a minority carrier diffusion length. It is operated in strong non-equilibrium by reverse biasing the minority carrier contact to completely extract all of the intrinsically generated minority carriers. Charge neutrality in the active volume is destroyed, creating an electric field to sweep out the intrinsically generated majority carriers until the majority carrier concentration equals the background acceptor concentration. The active volume thus consists of a depletion region, with a width determined by the doping concentration and applied bias, and a field free region with a majority carrier concentration determined by background doping. Dark current from the active volume has two components. Generation by Auger mechanisms, which occur in the field free volume, due solely to the presence of majority carriers. Generation from S-R centers, which occurs throughout the whole volume. The Auger generation rate for n-type material is given by Eq. 2. For p-type material the intrinsic Auger lifetime is predicted 5,6 to be larger by a factor of 6 to 20. The S-R generation rate for the extrinsically doped active π volume is n i /τ ext, where τ ext is given by Eq. 10. The dependence of Auger1 (n-type), Auger7 (p-type), and extrinsic S-R lifetimes on doping concentration is shown in Fig. 10 for MWIR HgCdTe at 77 K. A value Fig. 11. S-R and Auger7 dark current vs. temperature for MWIR and LWIR HgCdTe with N a = cm 3.

8 816 Kinch Fig. 12. IR thermal detector. Fig. 13. Theoretical NEDT limit vs. integration time for LWIR and MWIR thermal detectors. of τ Ai7 = 20τ Ai1 has been assumed, in keeping with experimental values. The associated dark current for a state of the art HOT π-type active volume, with an arsenic doping concentration of cm 3, is shown in Fig. 11, for both LWIR and MWIR HgCdTe. It is apparent that BLIP operation can be achieved at close to room temperature for this doping concentration in both spectral bands. An improvement in state of the art material to doping concentrations <10 14 cm 3 would be beneficial in two respects. Firstly, the above dark currents would be reduced in a linear manner. Secondly, the depletion region would occupy a significantly larger portion of the active volume. The associated reduction in the majority carrier volume would tend to eliminate Auger generation altogether 23. The possible end result would be a HOT photon detector capable of BLIP performance at room temperature in all regions of the IR. THERMAL DETECTOR The principle of the thermal detector is illustrated in Fig. 12. The detector element, of heat capacity C th, is thermally coupled to a heat sink by a conductance G. In most of the modern versions of the thermal detector the element is micro-machined onto the surface of a silicon readout integrated circuit (ROIC) and the resulting pedestal is connected to the ROIC by thin metal buss leads. The pedestal can be fashioned from any one of a number of temperature sensitive materials that are process compatible with silicon ROIC processing. Current examples are vanadium oxide, α-silicon, thin film ferroelectrics, and a host of others. The exact nature of the detector element will be ignored here. We will assume that the temperature sensitivity of the element is sufficiently large that all noise sources other than temperature fluctuations of the detector element can be ignored. The power fluctuation of the element is then given by W n = [4kT 2 G f] 1/2, where f is the noise bandwidth. Thus the detectivity of the detector, which again is defined as [signal/flux power][a 1/2 /(noise/ f 1/2 )], is given by D* = [η 2 A/(4kT 2 G)] 1/2 (11) If G is radiatively limited then D* = cmhz 1/2 /W, and is independent of area. This value of D* is impressive, but provides only a Fig. 14. Theoretical NEDT comparison of uncooled thermal and HgCdTe uncooled photon detectors for LWIR and MWIR.

9 Fundamental Physics of Infrared Detector Materials 817 limited insight into the suitability of the thermal detector for specific IR systems. Signal and spectral bandwidth requirements are important, and to this end it is meaningful to consider the available noise equivalent temperature difference, NE T. The limiting temperature fluctuation of the thermal detector element is given by T n = [4kT 2 R th f] 1/2. Correlated double sampling 24 of this bandwidth limited temperature fluctuation, with an integration time τ int, gives T n = [2kT 2 (1 exp( τ int /R th C th ))/C th ] 1/2, where we have assumed f = 1/4R th C th. Equating this to a signal temperature change given by T s = (dp/dt) T(1 exp( τ int /R th C th ))R th, gives NE T = [2kT 2 /C th / (1 exp( τ int /R th C th ))] 1/2 /(dp/dt)/r th, (12) where dp/dt is the differential change in radiated power per scene temperature change in the spectral region of interest. Image smearing considerations require τ int ~ 2R th C th, where the maximum value of R th is given by radiative coupling. For a required system integration time the only independent variable is the heat capacity, C th, but for micro-machined resonant detector structures there is a finite limit on thickness and volumetric specific heat. The available NE T for the perfect thermal detector, as a function of integration time, is shown in Fig. 13, for both LWIR and MWIR spectral bands. The assumed detector thickness, t, is 3000 A, typical of today s FPAs, with F/1 optics, a 1 mil pixel size, and a volumetric specific heat of 2J/cm 3 /K. The upper limit of R th, due to radiative coupling, is K/W for this pixel size. It is apparent that for long integration times in the LWIR excellent performance is achieved, with NE T values < 10 mk for frame rates of 30 Hz. However, for snapshot systems with τ int < 2 ms the available NE T is > 100 mk even at LWIR. For the MWIR band the thermal detector has obvious performance limitations at any frame rate. For slower optics the situation is exacerbated, varying as (F/#) 2. Thinner detector elements improve the NE T as t 1/2. In view of the obvious limitations associated with the thermal detector, with regard to meeting next generation systems requirements, it is of interest to compare the performance of uncooled thermal and photon detectors in the MWIR and LWIR. A comparison of the NE T of uncooled thermal and photon detectors operating at 290K, for the MWIR and LWIR bands, is shown in Fig. 14, again for F/1 optics and a 1 mil pixel size. For the purposes of the comparison the HOT detector is assumed to be Auger7 limited, with a p-type doping concentration of cm 3. The NE T for the photon detector is calculated using Eq. 8 and the dark current values in Fig. 11, assuming a gain of unity. It is also assumed that the detector node capacity can store the integrated charge due to detector dark current. The ultimate performance of the uncooled HgCdTe photon detector is obviously far superior to the thermal detector at all frame rates and spectral bands. An R&D investment in HgCdTe material, and for that matter, any other tunable bandgap alloy (or its bandgap engineered equivalent, such as InAs/GaInSb), could be well worth-while, with regard to the development of an uncooled photon detector technology covering the complete IR spectrum. CONCLUSIONS It is apparent from the foregoing discussions that the tunable bandgap semiconductor is by far the most efficient detector of IR radiation. The current material of choice is HgCdTe, which dominates present day systems. Next generation systems are driving toward higher operating temperatures and faster frame rates, which will only serve to reinforce the HgCdTe position. 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