Electrooptical Characterization of MWIR InAsSb Detectors

InAs1−xSbx material with an alloy composition of the absorber layer adjusted to achieve 200-K cutoff wavelengths in the 5-μm range has been grown. Compound-barrier (CB) detectors were fabricated and tested for optical response, and Jdark–Vd measurements were taken as a function of temperature. Based on absorption coefficient information in the literature and spectral response measurements of the midwave infrared (MWIR) nCBn detectors, an absorption coefficient formula α(Ε, x, T) is proposed. Since the presently suggested absorption coefficient is based on limited data, additional measurements of material and detectors with different x values and as a function of temperature should refine the absorption coefficient, providing more accurate parametrization. Material electronic structures were computed using a k·p formalism. From the band structure, dark-current density (Jdark) as a function of bias (Vd) and temperature (T) was calculated and matched to Jdark–Vd curves at fixed T and Jdark–T curves at constant Vd. There is a good match between simulation and data over a wide range of bias, but discrepancies that are not presently understood exist near zero bias.


INTRODUCTION
The AWARE Broadband program requires an innovative detector architecture and processing techniques to achieve pioneering performance of MWIR detectors at 200 K. One of the ambitious requirements is to obtain high (>80%) quantum efficiency (QE) over a broad, 0.5 lm to 5.0 lm spectral range while maintaining high D * (>1.0 9 10 11 cm ÖHz/W) in the 3.0 lm to 5.0 lm spectral range. A prime method to accomplish these goals is by reducing the dark diffusion current in the detector via reducing the volume fill ratio (VFR) of the detector while optimizing absorption through the design of photon-trap topological structures in the absorber layer upon which the radiation is incident. For the program, InAsSb was chosen as the absorber layer of the multilayer compoundbarrier detector architecture.
MWIR photodetector performance improvements were realized through the development of devices that rely upon bandgap engineering for the reduction of dark currents associated with depletionregion Shockley-Read-Hall (SRH) generation, surface current generation, and bulk diffusion. In particular, the nBn 1,2 device in the InAsSb/AlAsSb materials system is based on a simple design that utilizes a large conduction-band barrier to suppress the flow of majority carrier electrons, thus eliminating the electric field associated with a conventional p-n junction that results in high dark currents associated with depletion-region generationrecombination currents. Thus, a properly designed nBn structure facilitates diffusion-dominated detector performance determined by the bulk minority carrier (hole) lifetime.

DETECTOR ARCHITECTURE
Innovative nBn barrier detectors 1,2 were designed to suppress majority carrier currents while maintaining low electric fields. This nBn design was considered a remedy to the generation-recombination currents originating in the depletion region of p-n junction devices. AlAsSb alloy is used as a widebandgap barrier material, due to its having no significant valence-band offset with respect to InAsSb, which facilitates collection of minority carriers (holes) while providing a large barrier to majority carriers. However, the original InAsSb/AlAsSb barrier device design can have potential deficiencies associated with the choice of AlAsSb as the barrier material due to the alignment between the active layer and the barrier. Circumventing some of the difficulties inherent to the original nBn design, a compound-barrier (CB) detector architecture 3 was designed and implemented with the alloy composition of the InAsSb absorber layer adjusted to achieve a 200-K cutoff wavelength of 4.3 lm. 4,5 The novel detector structure, which is displayed in Fig. 1, utilizes pyramid-shaped absorbers. Each detector pixel has an array of multiple pyramidshaped absorbers. This detector structure provides the combination of reduced volume of absorber material, elimination of front-side reflection for incident light over a broad bandwidth, and enhanced photon trapping for high absorbance of incident light.
Infrared radiation is incident on the array of pyramids fabricated in the n-type InAsSb absorber, which also serves as the array common or substrate contact. The detector array is hybridized via indium bumps to a Si fanout chip. The chip, when inserted into an 84-pin leadless chip carrier (LCC), permits direct access to approximately 80 detectors. Detector areas ranged from 3.6 9 10 À5 cm 2 to 1.15 9 10 À3 cm 2 . The common contact to the absorber layer is a remote contact, and adjacent detectors were not biased during measurement of the reference detector.

MATERIAL AND DETECTOR MODELING
Modeling InAs 1Àx Sb x -based device performance requires obtaining experimental and/or theoretical material parameters. InAs 1Àx Sb x is a ternary compound whose bandgap changes as a function of x and temperature T. Clear-cut experimental or theoretical information on InAs 1Àx Sb x (x, T) is sparse, therefore requiring the utilization of approximations that ''best'' fit the data or equations available, and then generalizing the model.
Bandgap E g (x, T) and Cutoff Wavelength k c The InAs 1Àx Sb x bandgap 4,5 E g (x, T) in eV is given by Eq. 1, and to a first approximation the cutoff wavelength is given by Eq. 2. The cutoff wavelength as a function of x at temperature T = 200 K is displayed in Fig. 2. The bandgap and cutoff wavelength at any other temperature can be calculated using Eqs. 1 and 2. E g ðx; TÞ ¼ 0:411 À 3:4 Â 10 À4 T 2 210 þ T À 0:867x þ 0:70x 2 þ 3:4 Â 10 À4 xTð1 À xÞ: (1) To a first approximation, the cutoff wavelength k c in microns is k c ðx; TÞ ¼ 1:2398 E g ðx; TÞ : Using these expressions, x % 0.21 gives k c = 5.25 lm at T = 200 K.
Absorption Coefficient a(k, x, T) Absorption coefficient information for InAs above the bandgap 6 at room temperature and separately    8 was modified so that a(E g ) does not drop to zero but gives a value at the energy gap a(E g ) = 800 cm À1 . Energies below the bandgap utilize the Urbach tail 9 expression. The constants in Eqs. 3a, b were picked to best replicate below-bandgap data in Ref. 6. Above the bandgap, the coefficients K and c in Eqs. 4a-c were picked to give values that attempted to match calculations made using the expression for InAs at T = 300 K found in Ref. 6. Shown in Fig. 3 is the absorption coefficient a(k, x = 0, T = 300 K), i.e., for InAs at T = 300 K. Use of Eqs. 3 and 4 permits one to calculate the absorption coefficient as a function of wavelength, x, and T, as shown in Fig. 4 for x = 0.19 and T = 200 K, i.e., for k % 5.05 lm at 200 K. The constants used in Eqs. 3 and 4 are not unique and will require refining as more absorption coefficient and spectral response data are acquired or become available. This section attempted to collate material properties from several sources, and an equation for the absorption coefficient was developed to best match the available data. The absorption coefficient in Eqs. 3 and 4 will be utilized to calculate the absorption coefficient versus wavelength for a MWIR InAs 0.81 Sb 0.19 -based detector at 200 K. Further investigation into the spectral response of InAs 1Àx Sb x detectors will test the utility of the following absorption coefficient expressions.

Band Structure
The material electronic structures were computed with a kAEp formalism. 10 The zone-center states are calculated in Fourier space using a 14-band basis. The need to rely on a 14-band basis rather than the more common 8-band basis arises because of the sensitivity of the optical and electronic properties to the electronic structure in the secondary regions of the band structure. Errors inherent in the 8-band model become significantly more pronounced as the states one is interested in become farther from the band edge. 10,11 Results of the InAs 1Àx Sb x electronic structure calculations for x = 0.19 at T = 200 K are displayed as a band structure plot in Fig. 5. Figures 6a, b and 7a, b show the conduction and valence bands through the nCBn detector at bias values V d = À0.2 V, À0.4 V, À1.4 V, and À3.0 V, respectively. The n-type InAs 1Àx Sb x absorber region, which may be a $5-lm-thick layer or a thin layer contoured with pyramids, is at the left of  Figs. 6a, g and 7a, b. In all references through this paper, the bias sign convention is for bias applied to the n + contact region. In other words, a bias listed as V d = À0.4 V implies a bias of À0.4 V applied to the n + contact layer while the n-type absorber layer is held at zero bias, or conversely that the n + contact layer is held at zero bias while a +0.4 V bias is applied to the n-type absorber layer. As can be seen from Fig. 6a, there is still a $100 meV valence-band barrier when V d = À0.2 V is applied to the n + contact layer. Therefore, it should be expected that the QE will be low at V d = À0.2 V. At V d = À0.4 V, the valence-band barrier is virtually nonexistent and the QE should be high. At V d = À1.4 V and À3.0 V, there is no valence-band barrier (Fig. 7a, b), resulting in photogenerated holes having unimpeded flow to the n + contact, which has the potential for high QE. However, the dark current can increase substantially at V d = À3.0 V from tunneling currents which result in a lowering of QE.

OPTICAL DATA AND ANALYSIS
InAs 1Àx Sb x with a bandgap corresponding to a cutoff wavelength of 5.05 lm at 200 K was grown on a GaAs substrate. The measured devices had the carrier wafer removed, providing the opportunity to measure detectors with the incident radiation impinging directly on the pyramid array. Knowledge of the blackbody temperature, transmission of a narrow-band filter, window transmission, Dewar geometry, and distances of the blackbody from the detector were utilized to calculate the flux incident on the detector. The photocurrent density J photo as a function of bias V d was measured at blackbody temperature settings of 400 K and 450 K, the difference between the two providing the data for the calculation of the QE versus wavelength plot shown in Fig. 8. There is no multilayer antireflective (AR) coating since the pyramids perform this function. The QE attains its maximum value of 0.82 at À1.5 V bias. As the bias increases beyond À1.5 V, the QE starts to fall since the detector tends to be increasingly dominated by tunneling currents. It is presently unclear as to what energy barriers are present to result in the requirement for a À1.5 V bias to attain peak QE. Shown in Fig. 9 is a QE versus wavelength ''Data'' curve for the same detector as shown in Fig. 8. Measurements were taken using a Fourier-transform infrared (FTIR) spectrometer, and the QE is seen to be high across the entire 2.0 lm to 4.6 lm band. Measurements still need to be made in the visible wavelength region.
The bandgap from Eq. 1 and the absorption coefficient from Eqs. 3 and 4 were used to calculate the QE versus wavelength curve listed as ''Model'' in Since the detector has pyramids that minimize the reflectance and maximize absorption in the InAs 1Àx Sb x material, the reflectance in the model was set at 0.05 and the effective thickness of the absorber layer was set at 7 lm. The experimental QE falls toward zero much faster than the ''Model'' in the 5.4 lm to 5.8 lm range. One reason could be that the absorption coefficient in that range is higher than that obtained from Eq. 3. Another potential explanation is that the absorption of the pyramid photon-trap structures is higher than that modeled by a 7-lm-thick effective absorber. There are too many fitting parameters in the absorption coefficient equation to conclude that the absorption coefficient from Eqs. 3 and 4 is the absorption coefficient of InAs 1Àx Sb x . However, it serves as a starting point for determining the absorption coefficient, which can be adjusted based on additional measurements made by varying the temperature and x value of InAs 1Àx Sb x material.
ELECTRICAL MODELING, DATA, AND ANALYSIS

Modeling
Device transport was modeled employing a standard formalism (see, for example, Ref. 13). The principal equations are reproduced here to clarify which physical generation-recombination mechanisms are considered, how they are treated, and to introduce parameters that appear in Table I. Poisson's Eq. 5 and the two current continuity Eqs. 6 and 7 were solved self-consistently and with Fermi statistics under steady-state conditions to simulate device transport.
where D is the electrostatic displacement, and J n and J p are the electron and hole current densities, respectively.
the Auger rate by U Auger ¼ ðnp À n 2 i ÞðnC n þ pC p Þ; (11) and the band-to-band tunneling rate is where n and p are the electron and hole concentrations, n i is the intrinsic carrier concentration, s n0 and s p0 are the electron and hole SRH lifetimes, B is the radiative coefficient, C n and C p are the electron and hole Auger coefficients, and E is the electric field.

Data and Analysis
The dark-current density J dark was measured as a function of bias V d for a number detectors as a function of temperature between 140 K and 220 K. To minimize operator intervention, a semiconductor parameter analyzer in conjunction with a switching matrix was used to acquire current as a function of bias for multiple detectors in sequence at each temperature. Figure 10 plots J dark versus V d for one of the detectors, #39. A switching matrix is used to acquire data for a multitude of detectors sequentially, reducing time and tedium for the involved experimenter. However, the switching matrix introduces noise that is evident in the J dark ÀV d curve at 140 K. The dark-current density J dark at V d = À1.5 V is plotted versus 1000/T in Fig. 11 to extract the activation energy at the bias at which QE attained its maximum value. From Fig. 11, the activation energy E a = 275.9 meV is extracted, which is close to the bandgap E g (x = 0.19, T = 0 K) = 269.8 meV, suggesting that the dominant dark current at V d = À1.5 V is a diffusion current. Figure 12a compares device transport simulations with experimental J dark versus temperature at V d = À1.5 V. There is good agreement at the higher temperatures, with some deviation as the temperature is decreased, the experimental values of J dark being lower than the simulated values. Figure 12b is a plot of the simulated and experimental J dark -V d at T = 200 K. The fit is good at large bias values, however the experimental values deviate from the simulation at reverse-bias values less than $0.5 V. Lower experimental J dark as compared with simulation in the $0.2 V to 0.5 V reverse-bias range is probably caused by the same barrier that limits the QE from not attaining a maximum value until the bias is À1.5 V. Table I specifies the input parameters employed to compute the dark-current density J dark -V d curve at 200 K. The properties (including the conduction electron and heavy hole effective masses m c and m hh , respectively, relative to the free electron mass m 0 ) were obtained from the cited sources. The last four columns are fitted parameters to reproduce the J dark -V d for detector #39. Zero values specify quantities that are not expected to affect results. Figures 13a, b, and 14a, b are plots of dark-current density J dark versus 1000/T that are used to extract the activation energy at À0.2 V, À0.4 V, À1.4 V, and À3.0 V, respectively. The activation energy E a (V d = À0.2 V) = 331.9 meV is close to the bandgap energy and valence-band barrier of 356 meV (Fig. 6a). However, at V d = À0.4 V, there is virtually no valence-band barrier (Fig. 6b), so the reason for the activation energy E a (V d = À0.4 V) = 342.7 meV is not well understood (Fig. 13b). As expected from the dominance of diffusion current at V d = À1.4 V, E a (V d = À1.4 V) = 278.9 meV is close to the bandgap energy, E g (x = 0.19, T = 0 K) = 269.8 meV. At V d = À3.0 V, the dark-current density has minimal temperature dependence, a characteristic of tunneling currents, a consequence of the conduction-and valence-band lineup seen in Fig. 7b.

CONCLUSIONS
InAs 1Àx Sb x nCBn detectors with cutoff wavelengths in the 5-lm range at 200 K were fabricated and characterized for optical properties and electrical performance as a function of temperature. Absorption coefficient information from the literature and spectral response measurements of the MWIR nCBn detectors were combined to propose an absorption coefficient a(E, x, T) model. Additional measurements of material and detectors with different x values and as a function of temperature are needed to provide a more accurate value of the absorption coefficient. Band structures were computed using a kAEp formalism, and from the band structure, the dark-current density as a function of bias and temperature was simulated and compared with J dark -V d curves at fixed T and J dark -T curves at constant V d . There is a good match between simulation and data over a wide range of bias, but between À0.4 V and zero bias, simulations and experiment diverge. Activation energy for the dark current was extracted at various biases using the  J dark -V d measurements with temperature as a parameter. The dark-current activation energy E a at V d = À0.2 V seems to be a function of the bandgap plus a valence-band barrier. At V d = À0.4 V, the high E a is not yet understood. E a is approximately equal to the bandgap in the À1.4 V to À1.5 V range, where the dominant dark current is a diffusion current and the QE is high. Tunneling dominates the dark current at V d = À3.0 V as expected from the band profile and confirmed by the low activation energy value.