Optical properties of (001) GaN/AlN quantum wells

doi:10.1016/j.mejo.2005.06.014

Microelectronics Journal

Volume 37, Issue 1, January 2006, Pages 12-18

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Abstract

The absorption coefficient and the photoluminescence of (001) GaN/AlN quantum wells are calculated for several values of the well width, with and without the excitonic effect corrections, in the usual monoelectronic approach and as a many-body problem. The calculation was performed considering separate isolated bands for electrons, heavy and light holes. The monoelectronic approach to the optical properties was performed by assuming infinite well walls and finite well walls, respectively. The calculation including the excitonic effect as a many-body problem was performed within a recent approach designed for low-dimensional systems. The different wells studied here present many localized states and a complicated absorption spectrum. The monoelectronic approach in the infinite quantum well approximation reproduces quite well the spectrum of the wide wells due to the fact that the ground states of electrons and holes are well fixed by this model of quantum well.

Introduction

The nitride III–V semiconductors have wide gaps and are materials of great interest for device applications. In the last years they have gained importance because of their present and potential uses. They are intensively studied due to their potentialities in optoelectronics and as light emitting materials [1], [2], [3], [4], [5], [6], [7], [8], [9], specially in the realization of blue, green and yellow light-emitting diodes. These materials usually crystallize in the wurtzite structure, but it has been shown that they can be grown in the zinc-blende structure on different substrates [10], [11], [12], [13], [14], [15], [16], [17], [18], [19]. These systems could show enhanced electronic properties as compared to the wurtzite phase. The zinc-blende nitrides are expected to have higher mobility due to the decrease of the phonon number for the higher symmetry structure. The cubic films are also deemed to be better suited for n- and p-type doping, than the wurtzite nitrides.

Quantum wells are very important for the design of laser devices. There are many experimental and theoretical works on wurtzite quantum wells. This is not the case for the zinc-blende quantum wells. There are more studies on QW's based on GaN/AlGaN than those based in GaN/AlN. This is due to the fact that the growth of such systems is an experimental challenge due to the large lattice mismatch between both materials [20]. In [20], [21] the photoluminescence of wurtzite GaN/AlN QW is studied experimentally.

There are some uncertainties concerning the data of zinc blende GaN and AlN [22]. Because of these uncertainties it would be convenient to use a simple, but reliable model to study the electronic and optical properties of these systems. The envelope function approximation (EFA) has been very useful in the study of the electronic properties of heterostructures. The envelope of the heterostructure wavefunction is described regardless of atomic details. In spite of the very simplified description provided by the EFA, this approach has obtained great success, due mainly to a quite reasonable compromise between the simplicity of the method and the reliability of the results and it will be used here.

The absorption coefficient is one of the main optical properties to be considered when studying different systems of reduced dimensions. In the present work the absorption coefficient of a (001) GaN/AlN QW is calculated considering the usual treatment [23] in the monoelectronic approximation, including also the excitonic correction. On the other hand calculations considering the exciton as a many-body effect and starting by considering the envelope function approximation to describe the states of electrons and holes in the system, have also been performed. Several well thicknesses have been studied in order to see their effects on the optical properties. Additionally a magnitude proportional to the photoluminescence has been calculated.

The quantum mechanical treatment was done by describing the electron and hole states within the EFA. Independent parabolic bands for electrons, heavy and light holes were assumed and characterized by the parameters available in the literature. The monoelectronic approach to the optical properties was performed by using the two simplest approximations: the infinite barrier potential, forming an infinite quantum well (IQW) and the finite barrier well (FQW). The excitonic correction for the IQW has been included. The finite barrier well (FQW) was assumed for the many-body calculations to be compared with the monoelectronic approximation results.

The calculation including the excitonic effect was done by means of a many-body technique described in [24] which is specially designed for low dimension systems, including the multi-subband energy spectrum which they possess. As a starting point we shall keep the model as simple as possible not including in our calculations the strain due to lattice mismatch, although it would be easy to include it in the solution of the Schrödinger equation. The formal analysis used here to calculate the optical properties would not need any changes. In any case the picture coming out from our calculations would not be altered in an essential way.

In Section 2 we discuss the models and theoretical methods employed in the calculations, in particular the many-body technique here employed. The results are presented and discussed in Section 3. Conclusions are presented in Section 4.

Section snippets

Models for describing the absorption and the photoluminescence of a QW

The energy states of electrons and holes are described within the EFA model of parabolic independent bands and the parameters used, taken from [22], are given in Table 1. The effective masses of holes given in the table were calculated with the usual formulae given in [22]: $\frac{m_{o}}{m_{h h}^{*}} = γ_{1} - 2 γ_{2} \frac{m_{o}}{m_{ℓ h}^{*}} = γ_{1} + 2 γ_{2}$

The usual EFA calculation of the monoelectronic interband transition probability made in the time dependent perturbation approximation gives for the absorption coefficient the expression: $α (ω, T) = \frac{π e^{2} P^{2}}{3}$

Numerical results

The calculations of the absorption coefficient and of the photoluminescence of the (001) GaN/AlN QW in the zinc blende phase were made for various well widths. The first two very thin d=10 and 15 Å and the others with values d=30, 50, 100, 200 Å. No dielectric discontinuity was included in the calculations because it is known that this effect is not too big and can be neglected for these materials [27]. We use the value of the static dielectric constant shown in Table 2 for the whole structure.

Conclusions

The absorption coefficient and the photoluminescence intensity spectra of the GaN/AlN QW in the zinc blende phase have been calculated for wells of widths ranging from 10 to 200 Å. We have used different approximations such as the monoelectronic with and without excitonic effect and one including the exciton effect as a many body calculation. For narrow wells the monoelectronic calculations give results quite close to those obtained by including the exciton effect as a many-body effect. They

Acknowledgements

This work has been partially supported by the Ministerio de Ciencia y Tecnología (Spain) through Grant MAT2003-04278 and the Spanish-Cuban agreement CSIC-CYTMA.

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Optical properties of (001) GaN/AlN quantum wells

Abstract

Introduction

Section snippets

Models for describing the absorption and the photoluminescence of a QW

Numerical results

Conclusions

Acknowledgements

Microelectron. J.

J. Phys. D

J. Appl. Phys.

J. Vac. Sci. Technol. B

J. Appl. Phys.

Jpn. J. Appl. Phys.

Appl. Phys. Lett.

The Blue Laser Diode

MRS Bull.

J. Vac. Sci. Technol. A

Appl. Phys. Lett.

Phys. Stat. Sol. (b)