Defect Determination in Epitaxial a-plane GaN Layers

Mykhailo Barchuk,^a Václav Holý,^a Dominik Kriegner,^b Julian Strangl,^b Stephan Schwaiger,^c and Ferdinand Scholz^c

^a Charles University in Prague, Czech Republic.

^b Johannes Kepler University, Linz, Austria.

^c Ulm University, Germany.

E-mail: mikebarchuk@rambler.ru

Technological applications of optoelectronic devices based on (0001), i.e., c-oriented GaN are complicated by the piezoelectric effect along the [0001] direction. This phenomenon gives rise to a band bending, known as the quantum confined Stark effect [1].

Non-polar or semipolar GaN thin films overcome this problem. However, this type of material possesses a large number of defects, especially stacking faults (SF) so that a reliable method for the determination of the defect densities is of large importance.

We investigate non-polar a-plane oriented GaN epitaxial layers with the (11-20) surface orientation. In the layers of a-plane GaN, two types of basal plane stacking faults with the displacement vectors R = 1/6 and 1/3 are the most typical defects [2]. Another defect types (extrinsic basal stacking faults with R=1/2(0001), prismatic stacking faults with R=1/2) can also occur but their formation energy is significantly higher so that one can neglect their influence [3].

For the detection of SFs by x-ray diffraction, the visibility criterion can be applied. If g.R ¹ n (g is the diffraction vector, n is an integer), the diffuse x-ray scattering from the SFs has the form of [0001]-oriented streaks perpendicular to the fault planes; if g.R = n the defects are generally invisible by x-ray diffraction [4]. In the latter case, (for example in diffraction) a broadening of the diffraction maximum is observed caused by another defects such as dislocations, wafer curvature, and surface roughness.

We investigated a series of 4 samples grown by MOVPE technique [5] with various densities of stacking faults.

The x-ray diffraction (XRD) measurements were performed using a custom built rotating anode setup. A double bent parabolic multilayer mirror and a Ge(220) channel cut monochromator were used to produce a parallel beam of CuKα₁ radiation. The diffracted radiation was measured by a linear multichannel detector.

The reciprocal space maps of diffracted intensity were measured in a non-coplanar Bragg geometry. In order to reach the diffractions and , in which the visibility criterion is fulfilled, and using the scattering plane containing the [0001] streak direction, this scattering plane had to be tilted by 30 deg with respect to the surface normal. In this tilted plane, diffractions and are symmetric. In and diffractions we were able to observe the [0001]-streaks arising from the various types of SFs (Fig.1). For comparison, we measured also the reciprocal space maps in , where the visibility criterion is not fulfilled. In this diffraction, the SF-related streak does not appear indeed (Fig.1, the right panel).

Fig.1. Example of the reciprocal space maps of x-ray diffuse scattering measured in the symmetric non-coplanar (left) and diffractions (right) from the sample with the lowest stacking fault densities.

All the measured diffraction maxima are broader than expected from the estimated instrumental broadening. However, since we are interested in the shape of the peaks far from the sharp central peak, the resolution function does not influence our analysis.

Our model of simulation enables to calculate the profiles along the streaks in any diffraction. As input parameters we use the density of SFs, the coherence width of the primary beam and the shape factor of the coherence function in direct space. Using the Monte Carlo method we generate the positions of defects as a random Markov-like sequence. Then, we compute the displacement field caused by defects, and finally applying the kinematical approximation we obtain the intensity distribution along the [0001] direction in reciprocal space.

Comparison of the measured intensity distributions along the streaks with simulations supposing allows us to determine the prevailing displacement vector R of the SFs and their density. Depending on the sample growth mode the total densities vary between 10⁵– 10⁶ cm^-1.

This work has been supported by the Grant Agency of Charles University in Prague (projects SVV 263307 and 22310)

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