INTERDIFFUSION OF HgTe / CdTe HETERO - INTERFACES

In this paper we present results of a study of interdiffusion in HgTe/CdTe heterostructures. Our samples were grown by MBE at HRL Laboratories and had Cd x values ranging from 0.2 to 0.35. The samples were annealed at temperatures ranging from 250 °C to 425 °C in both Hg vapor and vacuum ambients. The samples annealed under vacuum were coated with a layer of CdTe prior to annealing. The data were simulated using Darken's equation, and results show strong agreement between the simulated and experimental profiles. Significantly more diffusion was observed for anneals under Hg-rich ambients than under vacuum. For Hg-rich anneals, the activation energy was 1.50 eV at temperatures less than 350 °C and 1.33 eV at higher temperatures. This is the first time that two activation energies for the interdiffusion coefficient have been reported. The mechanisms responsible for this behavior are discussed. 1.0 INTRODUCTION The fabrication of all HgCdTe-based infrared detectors involves the formation of one or more hetero-interfaces. With the increasing interest in developing detectors in the SWIR as well as the MWIR and LWIR bands, and the desire for multispectral sensitivity, the number and complexity of heterointerfaces is increasing. Because the performance of these detectors depends critically on the precise placement of the hetero-interfaces, any interdiffusion at these interfaces must be understood and controlled. Although much work has been done in this area, the mechanisms underlying the diffusion are still not fully understood [1-5]. Moreover, a comprehensive model of the interdiffusion that accounts for variations in temperature, Hg pressure, x value, and Fermi level has not been developed. Recent advances Approved for public release; distribution is unlimited. in process modeling codes now make it possible to build a numerical model of interdiffusion that accounts for the above dependencies [6, 7]. Interdiffusion is usually modeled using a form of Darken’s equation [8]: DMCT = DCd 1 − x ( )+ DHgx [ ]1 + ∂ lnγ Cd ∂ ln x     (1) Here DCd is the diffusion of Cd in HgTe, DHg the diffusion of Hg in CdTe, x the Cd fraction, and γ the activity coefficient. The second term in brackets is known as the thermodynamic factor. The thermodynamic factor accounts for the fact that the diffusivity depends nonlinearly on x. When γ equals zero, the interdiffusion coefficient is linear with x and the system is said to be ideal. γ is a measure of the chemical potential of the system. In binary alloys, it is a function of x value, temperature, and any other influences on the chemical potential, such as the position of the Fermi level. For pseudobinary alloys, such as HgCdTe, the anion-to-cation stoichiometry must also be accounted for. This usually takes the form of the partial pressure of the dominant vapor species (Hg in the case of HgCdTe). Modeling interdiffusion is therefore a matter of defining the activity coefficient as a function of the critical variables. For HgCdTe, these are x value, Hg pressure, temperature, and Fermi level. Although Darken’s equation is physically correct, it does not tell us anything about the atomiclevel mechanisms controlling the diffusion. If the atomic mechanisms are understood and accurately calibrated, then the activity coefficient as a function of the critical variables can be determined. Diffusion in semiconductors occurs via point defects. In the case of HgCdTe, the dominant defects for diffusion are cation vacancies and interstitials. These species may be electrically charged, but the location of the energy levels is not accurately known. Diffusion via charged point defects means that Fermi level effects are particularly important in HgTe/CdTe interdiffusion because of the strong dependence of the band gap on x value. The full set of coupled continuity equations can be written as [9]: ∂CHgcation ∂t = ∇ D V Ccation CV∇CHgcation − CHgcation ∇C V ( )       − gHg CHgcation ( j − k)n +kR HgCHg I CV + k KOHg CHgI CCdcation (l − k)n − kKO Cd CCd I CHgcation (2) ∂C V ∂t = ∇ D V∇CV ( )+ jq kT ∇ DVCV ∇Ψ ( ) +g HgCHgcation ( j − k)n − k RHg CHgI CV + gCd CCdcation ( j − l)n − k RCd CCd I CV (3) ∂CCd cation ∂t = − ∂CV ∂t + ∂CHgcation ∂t       (4) ∂CHgI ∂t = ∇ D HgI ∇CHgI ( )− kq kT ∇ D HgI CHgI ∇Ψ ( ) +g HgCHgcation ( j − k)n − k RHg CHgI CV − kKO Hg CHgI CCd cation (l − k)n + k KOCd CCd I CHgcation (5) ∂CCd I ∂t = ∇ DCd I ∇CCd I ( )− lq kT ∇ D CdI CCd I ∇Ψ ( ) +gCd CCdcation ( j − l)n − k RCd CCd I CV + kKO Hg CHgI CCd cation (l − k)n − k KOCd CCd I CHgcation (6) DHgI and DCdI are the diffusion coefficients for Hg and Cd interstitials. DV, the vacancy diffusion coefficient, is a combination of vacancies diffusing by exchanging with Hg atoms, DV , and those diffusing by exchanging with Cd atoms, DV , where DV = (1-xCd)DV Hg + xCdDV . CHgI , CCdI , and CV equil are the equilibrium Hg and Cd interstitial concentrations and equilibrium cation vacancy concentration. CHgcation, CCdcation, Ccation are the concentrations of Hg, Cd, and total cation sites. n is the concentration of free electrons and q is the charge of an electron. Ψ is an electric field created by either an externally applied potential, internal variations in the bandgap, or charged point defect concentrations. Elucidating the parameters for the atomic mechanisms requires a combination of careful experimental study and first principals, ab-initio modeling. Toward this end, we have conducted an experimental study of interdiffusion in undoped HgCdTe at Cd compositions between 0.2 and 0.35. The results of this study are presented below. Much work remains to be done before a comprehensive model is obtained that can simulate interdiffusion in HgCdTe as a function of all the critical variables. However, these data provide a good foundation on which to build such a model. 2.0 EXPERIMENTAL PROCEEDURE The samples used in the study were grown by MBE at HRL Laboratories on CdZnTe substrates. Two types of samples were grown: a single step in x value from 0.2 to 0.25 to 0.2, and three steps in x value – 0.2, 0.25, 0.2, 0.3, 0.2, 0.35, 0.2. The samples were annealed at temperatures ranging from 275°C to 425°C. The annealing times at each temperature were set by simulating the expected interdiffusion using a process modeling program developed at Stanford University [10]. The model was calibrated using diffusion data from the literature. Some of the samples were capped with a layer of CdTe prior to annealing. The capped samples were annealed in a vacuum ambient (to approximate a Te-rich boundary condition), and the uncapped samples were annealed in a Hg ambient. After annealing, the Cd profiles were measured by SIMS at Charles Evans and Associates. 3.0 RESULTS AND DISCUSSION Examination of the SIMS data (see Figures 1-5) shows that the variation in the interdiffusion coefficient is not ideal. We used Darken’s equation to extract accurate diffusion coefficients from the SIMS data. The simplest model for deviations from ideality is the regular solution model [11], which assumes that the mixing entropy is ideal and that all of the non-ideality is in the mixing enthalpy. In this model, equation 1 becomes DMCT = DCd 1 − x ( )+ DHgx [ ]1 − zΩ RT (x)(1 − x)     (7) where z is the coordination number (=12 for a pseudobinary zinc blende alloy), Ω is the mixing enthalpy, R is the gas constant, and T is the absolute temperature. For HgCdTe, Ω/RT has been experimentally and theoretically determined to be approximately zero [11]. The regular solution model is therefore not physically correct for the HgTe/CdTe system. Nevertheless, over a limited range in x value, it provides a simple, computationally efficient, and accurate model with which to extract the diffusion coefficients. Equation 7 was implemented in the ALAMODE process simulator [7]. The as grown SIMS profiles were read into the simulator, along with the annealing time and temperature. ALAMODE generated 2dimensional composition maps of the annealed structure, from which a1-dimensional composition vs. depth profiles were sliced. A value of 3.9 for Ω/RT was found to provide the most accurate fit to the experimental data. The variation in the diffusion coefficient with composition for the ideal and regular solution models is shown in Figure 7. Examples of simulations using Equation 7 are shown in Figures 1-6. To obtain accurate diffusion coefficients, the raw SIMS data were normalized in both depth and concentration to the as-grown profiles. The simulations match the data quite closely over the composition range between 0.2 to 0.35. The close match with the data allows us to extract accurate diffusion coefficients from the SIMS profiles. Figure 8 shows a plot of DMCT (x = 0.2) vs. temperature. At temperatures less than 350°C, samples annealed under a Hg ambient exhibited significantly more diffusion than those under a vacuum ambient. A small dependence on Hg pressure was also observed at the higher temperatures. The increase of DMCT with Hg pressure implies that cation interstitials are the dominant defect in the interdiffusion process. The lowtemperature data are in close agreement with those of Tang for both Hg-rich and Te-rich ambients. The data in Figure 8 yield the following expressions for the interdiffusion coefficient: Hg rich, T <= 350 °C: DCd(HgTe) = 5.35e-1 * exp(-1.50/kT) (8) Hg rich, T > 350 °C: DCd(HgTe) =1.99e-2 * exp(-1.33/kT) (9) Te rich, T <= 400 °C: DCd(HgTe) = 6.40e2 * exp(-1.93/kT) (10) Te rich, T > 400 °C: DCd(HgTe) =1.99e-2 * exp(-1.33/kT) (11) The same expression is used for both the Te-rich and Hg-rich ambients at higher temperatures because the data are within the experimental error. The change in activation energy and pressure dependence between the high and low temperature regimes suggests a change in the diffusion mechanism. We believe that this is the first time that two activation energies for the interdiffusion coefficient have been reported. These activation energies will be valuable in understanding and modeling the atomic mechanisms underlying the diffusion. The strong negative deviation from ideality evidenced by the data implies that the equilibrium point defect concentrations and/or the hop activation energies are also strong functions of composition. The exact nature of these dependencies will need to be determined in order to calibrate the parameters in equations 2 6. Determination of the diffusion coefficients reported in this work, extracted under well-controlled experimental conditions, is the first step toward building a comprehensive model of interdiffusion in HgTe/CdTe hetero-structures. The work needs to be expanded to other compositions and into extrinsic doping effects. Parameters that cannot be obtained from experiments, such as point defect concentrations as a function of composition, pressure, and Fermi level, must be found through an accurate ab-initio study of the HgCdTe system. A comprehensive model, based on the defect chemistry of this system, will lead to higher-quality, higher-performance, and lower-cost HgCdTe infrared detectors. ACKNOWLEDGMENTSThis work was sponsored by the Navy Theater Wide Program (PMS 452), PEO (TAD), PMS 422,and BMDO as a subcontract to Santa Barbara Research Center. The authors acknowledge J.E. Jensen andR.D. Rajavel of HRL Laboratories for growing the MBE samples, and Arden Sher and Marcy Berding atSRI, and Mike Deal and Mike Chase at Stanford University for helpful discussions. REFERENCES[1] Leute, V., H. M. Schmidtke, W. Stratmann and W. Winking, Phys. Stat. Sol. A 67, 183 (1981).[2] Tang, M.-F. S., and D. A. Stevenson, Appl. Phys. Lett. 50, 1272 (1987).[3] Tang, M.-F. S., and D. A. Stevenson, J. Vac. Sci. and Technol. B 7, 544 (1989).[4] Zanio, K., J. Vac. Sci. Technol. A 4, 2106 (1986).[5] Zanio, K., and T. Massopust, J. Electron. Mater. 15, 103 (1986).[6] Law, M. L., http://www.tec.ufl.edu/~flooxs/ (1998).[7] Yergeau, D. W., E. C. Kan, M. J. Gander and R. W. Dutton, inSimulation of Semiconductor Devicesand Processes (Springer-Verlag, Wien, Austria, 1995), p. 66.[8] Tuck, B., Introduction to Diffusion in Semiconductors (Pereginus, Stevenage, 1974).[9] Holander-Gleixner, S., H. G. Robinson and C. R. Helms, to appear in J. Elect. Mat. (1998).[10] Robinson, H. G., to appear in J. Elect. Mat. (1998).[11] Chen, A.-B., and A. Sher, Semiconductor Alloys: Physics and Materials Engineering (Plenum, NewYork, 1995). 0.20.250.30.350.4 0 2 4 6 8 10 12 14 16SIMS As GrownSIMULATIONSIMS Annealed