EBSD Measurement of Strains in GaAs due to Oxidation of Buried AlGaAs Layers

We have characterized elastic strain fields associated with the wet-thermal oxidation of buried AlxGa1-xAs (x ~ 0.98) layers of thickness 80 nm, situated between GaAs layers of thickness 200 nm, on a GaAs substrate. The compressive strains accompanying oxidation can exceed 6% and may lead to interlayer delamination or fracture. Automated electron backscatter diffraction measurements were performed about individual oxide growth fronts on longitudinally cross-sectioned samples. We found that the elastic strain fields can be detected and mapped with a spatial resolution of better than 30 nm, using pattern sharpness quantification. Measured strain fields are elongated along the interfaces and extend approximately 1 μm around the growth front. We present efforts to quantify the spatial extent of these strain fields, as well as finite element simulations of the mechanics of oxide formation in this structure. Introduction We present the use of electron backscatter diffraction (EBSD) in a scanning electron microscope (SEM) for measuring elastically distorted regions of a multilayer compound semiconductor system, AlxGa1-xAs/GaAs, containing a buried aluminum oxide layer. Such systems are central to the functionality of vertical cavity surface-emitting lasers (VCSELs), which present an attractive alternative to the limitations faced by conventional edge-emitting lasers. One benefit of the VCSEL architecture is the combination of both electron and photon confinement, afforded by the presence of an optical aperture, typically made of an amorphous aluminum oxide [1]. This aperture, however, is a potential source for serious reliability problems. The aperture is formed by selective oxidation of the AlxGa1-xAs layer with the highest aluminum content [2]. Accompanying the conversion from AlxGa1-xAs to aluminum oxide is a severe volume contraction. Although the observed oxide is an amorphous structure, an upper bound estimate of this contraction can be given by considering the case of crystalline γ-Al2O3 as compared to AlAs, which is a good approximation to AlxGa1-xAs with high aluminum content. The zincblende AlAs structure, with 4 aluminum atoms per unit cell, shows a volume per aluminum atom of 0.0448 nm. The defective spinel γ-Al2O3 structure [3] contains 21 aluminum atoms per unit cell, resulting in a volume per aluminum atom of 0.0235 nm. The resulting spacings between aluminum atoms in these materials differ by 20%, with that in alumina being smaller. *Contribution of NIST. Not subject to copyright in the USA. Microelectronic Engineering, Volume 75, Issue 1, July 2004, Pages 96-102 Cross-sectional TEM observations [4] from structures containing a buried amorphous aluminum oxide layer have indicated a linear contraction of approximately 7% upon transforming an AlAs layer to oxide. The discrepancy is largely due to the difference between crystalline and amorphous alumina. In VCSEL fabrication, thermal cycles subsequent to aperture formation can result in oxide/semiconductor delamination. In this paper, we demonstrate the application of automated EBSD for measuring distorted regions associated with the formation of buried oxide layers for optical apertures. Experimental Multilayer structures of AlxGa1-xAs/GaAs (x ~ 0.98) were grown by molecular beam epitaxy onto (001) GaAs substrates. We refer subsequently to the AlxGa1-xAs as AlGaAs for simplicity. Aluminum-containing layers were approximately 80 nm thick and the GaAs layers 200 nm thick. Wet thermal oxidation at 460°C was performed for 5 minutes along edges associated with channels etched into the top surface of the structure. This caused formation of alternating layers of aluminum oxide laterally into the multilayer stack. Typical oxidation lengths were in the range of tens of micrometers. EBSD measurements were made on freshly-cleaved specimens in a Schottky-emitting SEM, operated at 15 kV. To minimize issues such as specimen/stage drift, all scans were completed in 5 minutes or less. All data presented here is in its “raw” form, i.e. we used no data “clean-up” algorithms sometimes available in commercial EBSD software. Details addressing EBSD spatial resolution are presented later. Results and Discussion Strain Determination by EBSD: Constant Elastic Strain We begin with the simple case of a load applied along one axis of a cubic crystal. Bragg’s law implies that the associated change in lattice spacing for that crystal direction will cause the scattering angle for the corresponding family of planes to vary inversely with the sense of the load, for constant electron energy. For example, a tensile load along a [100] direction would cause the (100) interplanar spacing to increase and the (100) Bragg angle to decrease. This would be detected in the EBSD pattern as a decrease in Kikuchi band width, as depicted schematically in figure 1. A multi-axial strain state would affect multiple Kikuchi bands in an analogous manner. Shear strains make analysis somewhat more complex, since both lattice spacings and lattice angles are expected to change. In that case, we expect changes in band widths as well as angles between bands. In principle a single diffraction pattern should contain information about many components of an elastic strain tensor. We note that research on extracting elastic strain states using the geometrically identical convergent-beam electron diffraction method [5] suggests that the process can be tedious. Using these ideas, we performed a calibration using GaAs (ao = 0.5653 nm) and GaP (ao = 0.5451 nm), which have a lattice parameter mismatch of 3.6%. Intensity profiles across (440) Kikuchi bands revealed a difference of 3.4%, which compares favorably. Uncertainties in strain determination by EBSD within a uniform elastic field arise from several factors, including detector resolution, Kikuchi line curvature, and energy Microelectronic Engineering, Volume 75, Issue 1, July 2004, Pages 96-102 coherency of the incident electron beam. All of these factors limit the method to an uncertainty of approximately 0.2% strain, for relative strain measurement. Strain Determination by EBSD: Elastic Strain Gradient The discussion of uniform strain effects on Kikuchi band width suggests that if the electron beam were sampling a volume of material containing a non-uniform strain, then one should expect a non-uniform distribution of Bragg angles and therefore Kikuchi band widths. The distribution in Bragg angles would be manifest as an increase in the width of the edge of a Kikuchi band, as shown in figure 2. Effectively, the pattern loses “sharpness,” sometimes referred to as image quality. Concurrent with a change in pattern sharpness is a decrease in overall pattern contrast, which is somewhat subtler effect. We refer to the dynamical electron diffraction discussion in reference [6] for quantitative details. For a constant number of electrons scattering out of a crystal in some unit of time, a perfect or uniformly strained crystal will exhibit a well-defined EBSD rocking curve (intensity profile across a Kikuchi band), with a distinct intensity maximum within the interior of the band, between the two Bragg scattering angles. The contrast across a Bragg angle for such a band depends upon the difference in backscattering efficiency between the most strongly excited Bloch wave on either side of the Bragg position and the inelastically scattered background signal. The set of Bloch waves in this case has the periodicity of the perfect or uniformly strained lattice. An elastic strain gradient across the sampling volume of the electron beam requires that what was initially a single set of periodic Bloch waves in the perfect crystal becomes a distribution of waves with amplitudes that depend upon position [7]. This requires that backscattering out of any one Bloch wave becomes much less efficient than that for the case of a perfect or uniformly strained crystal. The inelastically scattered background, on the other hand, should remain unaffected. This results in an overall decrease in contrast, of which we can take advantage. Manufacturers of electron backscatter diffraction systems have relied upon a Hough transformation approach to automate the pattern indexing process. This method has resulted in the definition of a parameter that can be termed a pattern sharpness or image quality (IQ) figure. For one such system, the IQ parameter is defined by: