Pressure Dependence of Intersubband Transitions in HgTe/Hg^sub 0.3^Cd^sub 0.7^Te Superlattices

Journal of Electronic Materials, Jun 2005 by Becker, C R, Latussek, V, Landwehr, G, Bini, R, Ulivi, L

The optical absorption coefficient of HgTe/Hg^sub 0.3^Cd^sub 0.7^Te superlattices (SLs) and its pressure dependence has been investigated at hydrostatic pressures up to 30 kbar at room temperature. The corresponding intersubband transition energies result from a comparison of experimental and theoretical absorption coefficients. The latter is based on the band structure, which is calculated using Kane's four-band (8 × 8 k * p) model together with the envelope function approximation. The experimental linear pressure coefficients of the H1-E1 and H1-L1 intersubband transitions are in good agreement with the theoretical values, e.g., 7.15 ± 0.3 meV/kbar and 6.2 ± 0.3 meV/kbar compared to 7.4 and 6.4 meV/kbar, respectively. This is in stark contrast to the pressure dependence of ≤1 meV/kbar of the photoluminescence (PL) peaks of a similar SL reported in the literature. Consequently, we conclude that the reported PL peaks are not due to intersubband transitions and that the k * p model correctly reproduces the electronic band structure and its pressure dependence of HgTe/Hg^sub 1-x^Cd^sub x^Te SLs.

Key words: HgTe/HgCdTe, superlattices (SLs), hydrostatic pressure

INTRODUCTION

The HgTe/Hg^sub 1-x^Cd^sub x^Te superlattice (SL) is of fundamental interest as well as potential use as a material for infrared opto-electronic devices.1 The initial interest in these SLs was fueled by the possibility of a more accurate production of the desired cutoff wavelength, and the potential of a lower leak current. However, these advantages are partially offset by the more complex production of these SLs. Because leak current is much larger in optoelectronic devices in the far infrared, these SLs have recently been employed in very long wavelength photovoltaic detectors.2,3

Intersubband transitions in these SLs have been investigated by means of optical absorption4-6 and magnetoabsorption7 experiments in conjunction with theoretical calculations. These intersubband transitions, and in particular the lowest energy gap, have been linked to photoluminescence (PL) peaks in a number of investigations.8 However, Cheong et al.9 have observed that the hydrostatic pressure dependence of the PL peaks is much less than that predicted by k * p calculations based on the envelope function approximation. Their most prominent peak, which has been assigned to recombination across the SL band gap, has a pressure coefficient of ≤1 meV/ kbar. Other PL peaks, whose origins are not well established, occur at higher energies and their pressure coefficients are in the range of 0-2 meV/kbar. Their calculations employing the envelope function approximation (EFA) with a range of reasonable SL parameters predict a pressure coefficient of at least ~6.5 meV/kbar for the band gap. This value is obviously not comparable with the pressure coefficient of the main PL peak, i.e., ≤1 meV/kbar. The authors suggest that either Kane's four-band (8 × 8 k * p) model in the EFA is not applicable for this system or, alternatively, that the PL peaks are defect related and not due to the corresponding intersubband transitions.

In contrast, the pressure dependences of the PL peak energies in the GaAs/Al^sub 0.3^As^sub 0.7^As system have been successfully predicted by theory. For example, the valence band offset10 and the ΓX band mixing11 of this system have been determined by high-pressure experiments.

EXPERIMENTAL AND THEORETICAL DETAILS

The SLs employed in this investigation were grown on Cd^sub 0.96^Zn^sub 0.04^Te(001) substrates in a RIBER 2300 molecular beam epitaxial system at the University of Wurzburg, as has been described in detail elsewhere.5,6 The thicknesses of the HgTe and Hg^sub 0.3^Cd^sub 0.7^Te layers were chosen such that the corresponding intersubband transitions were >300 meV in order to allow high-pressure transmission measurements in a diamond anvil cell. The measurements were carried out at the European Laboratory for Non-Linear Spectroscopy (Florence, Italy) using a Fourier transform spectrometer, Bruker HR-120 (Ettlingen, Germany), and additional components, which have been described elsewhere.12 The infrared radiation was focused onto the sample such that all light would have to pass through the sample.

The samples were thinned to a thickness of ~25 µm and then cleaved such that a nearly square sample with dimensions of -120 × 120 µm^sup 2^ resulted. The sample together with a small ruby crystal was then loaded into a membrane diamond anvil cell from the BETSA company (Chevry-Cossigny, France). Hydrostatic pressure on the sample was generated by means of Ar through a membrane. Type lia diamonds were employed, which allow transmission measurements to be carried out above 2400 cm^sup -1^ (300 meV).

A large number of band structure calculations for the HgTe/Hg^sub 1-x^Cd^sub x^Te SL have been published during the last decade.4,13,15 Ram-Moham et al.14 employed the envelope function method and developed a transfer matrix procedure to calculate the SL states. He accounted for the full 8 × 8 Kane Hamiltonian including all second-order terms representing the far-band contributions, but did not apply his results to a calculation of the optical constants. On the other hand, Johnson et al.4 applied a slightly different version of the envelope function method, and deduced optical constants from his SL energies and eigenfunctions. However, in his approach, he used a simplified band model, which omits all the second-order far-band contributions, with the exception of a finite heavy hole mass. In order to overcome these shortcomings, we have combined the essential aspects of both approaches. This enables us to calculate the optical constants based on a realistic band structure model, which includes all second-order higher band contributions. This is a sound basis for a realistic comparison between theory and experiment. The model and the employed parameters are described in detail elsewhere.5