Diffusion of Gold and Native Defects in Mercury Cadmium Telluride

Journal of Electronic Materials, Jun 2005 by Ciani, Anthony J, Ogut, Serdar, Batra, Inder P, Sivananthan, Siva

The diffusion of defects is of great importance in nanoscale device fabrication, making it essential to understand theoretically the microscopic mechanisms governing how native and dopant defects diffuse. To gain this insight, we have performed, for the first time, ab initio density functional calculations to determine the diffusion barriers for multiple pathways of Au impurities and native species in mercury cadmium telluride (MCT). We consider interstitial and vacancy-mediated diffusion mechanisms and calculate the corresponding activation energies using ab initio pseudopotential total energy calculations. Depending on the stoichiometry, the activation energies for Hg self-diffusion are calculated to range from 1.35 eV to 1.60 eV (interstitial mechanism) and from 1.60 eV to 1.85 eV (vacancy mechanism). These theoretical values suggest that Hg self-diffusion is predominantly interstitial mediated, and are in good agreement with existing experimental estimates, which suggest possible activation energies ranging from 1.05 eV to 1.75 eV. For Te self-diffusion via the interstitial mechanism, the calculated activation energy ranging from 2.35 eV to 2.60 eV is also in good agreement with the experimental estimates near 2.30 eV. For Au impurities, whether they are incorporated into the interstitial or Hg site, we find the interstitial mediated mechanism to be the dominant one. Our calculated barrier of 0.35 eV for Au interstitials is also in good agreement with the experimental estimate of 0.45 eV.

Key words: Mercury cadmium tellurium (MCT), gold, density functional theory, dopant, defect concentration, diffusion, activation energy, migration

INTRODUCTION

Mercury cadmium telluride, Hg^sub 1-x^Cd^sub x^Te (MCT), is the material of choice for high-performance infrared detectors. The performance (i.e., carrier lifetime, signal-to-noise ratio, and quantum efficiency) of MCT-based detectors is controlled significantly by the native and impurity defect densities and their diffusion. A theoretical understanding of the underlying energetics and mechanisms is, therefore, important toward improving detector performance and fabrication techniques. For example, a microscopic elucidation of the self-diffusion of the native species is crucial in searching for optimal annealing strategies for molecular beam epitaxy (MBE) grown devices. Gold can be used as a p-type dopant, and theoretical information about how Au diffuses may provide better control over its concentration profile during device fabrication.

There is no general consensus on the precise diffusion mechanisms for any of the native species or Au in MCT. This is partly due to the lack of a comprehensive theoretical study of self- and impurity-diffusion mechanisms. There have been several experimental papers published,1-9 particularly on the self-diffusion of Hg, which have been carefully reviewed by Shaw.1 These experiments show a broad range in the temperature and mercury partial pressure-dependent diffusion behavior of Hg, Te, and Au.

In this paper, we address self- and Au diffusion in MCT using a first-principles approach employing ultra-soft pseudopotential calculations in the framework of density functional theory. For the first time, we calculate ab initio migration barriers for self- and Au diffusion via the simplest of mechanisms mediated by interstitials and vacancies. We conclude that the predominant diffusion mechanism for Hg and Te self-diffusion and Au diffusion is interstitial mediated. We also find that, in Te-rich samples, the Hg self-diffusion via Hg vacancies is competitive with the interstitial mechanism. Our theoretical values for diffusion energies are in good agreement with experiment.

COMPUTATIONAL METHODS

The total-energy calculations were performed using the density functional package VASP.10,11 The wave functions were expressed in a plane wave basis set with an energy cutoff of 180 eV. The Brillouin zone integrations were performed using the Monkhorst- Pack scheme12 with a 2 × 2 × 2 k-point mesh. Ionic potentials were represented by ultra-soft pseudopotentials, and the local density approximation (LDA) was used for the exchange-correlation potential. The convergence with respect to the energy cutoff (~8 meV per atom) and number of k-points (~2 meV per atom) was tested. The calculations were performed at the theoretical LDA lattice constant of 6.46 A, which also coincides with the experimental value.

Truly ab initio computations in MCT are complicated because MCT has a compositional disorder on the metal sublattice, and there are no straightforward methods to handle this disorder. However, HgTe and CdTe both have similar bonding characteristics, and structural properties, which provide a means of simplifying the calculations. We make the assumption that a migrating defect in Hg^sub 1-x^Cd^sub x^Te for small χ values (x ≤ 0.20) will have a similar behavior to the same migrating defect in pure HgTe. To that end, the migration of a defect is represented by a 64 atom cubic supercell of HgTe plus the migrating defect. To calculate the migration barrier, the migration pathway is divided into multiple segments. The migrating defect is held fixed at each segment, while the rest of the lattice is allowed to relax, giving an energy profile whose maximum height with respect to the lowest energy configuration gives the migration barrier. In some cases, the gradient of the migration barrier was high enough to allow long-range relaxations that "dragged" the lattice before the force-based stopping criterion could be reached. Because of this, it was necessary to relax the minimum force criterion slightly, which could result in a 0.05 eV error in the migration barrier.