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Determination of the composition and thickness of semi-polar and non-polar III-nitride films and quantum wells using X-ray scattering
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10.1063/1.3678631
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Affiliations:
1 Department Materials Science and Metallurgy, University of Cambridge, Pembroke St., Cambridge, CB2 3QZ, United Kingdom
a) Electronic mail:mev20@cam.ac.uk.
J. Appl. Phys. 111, 043502 (2012)
/content/aip/journal/jap/111/4/10.1063/1.3678631
http://aip.metastore.ingenta.com/content/aip/journal/jap/111/4/10.1063/1.3678631

## Figures

FIG. 1.

Illustration of the axes x 1, x 2, and x 3 for three orientations: polar c-plane, non-polar a-plane and semi-polar and definition of the reciprocal space vectors S x, S y, and S z (S = 2 sinθ/λ).

FIG. 2.

(Color online) X-ray reflectivity data for a 10-repeat non-polar GaN/AlGaN MQW structure (Sample A). From the bottom of the figure to the top, the data sets show the experimental data, then simulated data calculated from the best-fit model (t AlGaN = 109 Å, t GaN = 70 Å), then from a model with a higher well-to-barrier thickness ratio (t AlGaN = 106 Å, t GaN = 73 Å) and finally from a model with a lower well-to barrier thickness ratio (t AlGaN = 112 Å, t GaN = 67 Å). The calculated data are offset vertically for clarity.

FIG. 3.

(Color online) ω/2θ scans of the reflection for a 10-repeat non-polar GaN/AlGaN MQW structure (Sample A). From the bottom of the figure to the top, the data sets show the experimental data collected using an analyzer crystal, then simulated data calculated using the best-fit model (Al0.169Ga0.831N thickness 109 Å and GaN thickness 70 Å), then experimental data obtained using an open detector, then simulated data from a model with a higher Al content and a higher well-to-barrier thickness ratio (Al0.173Ga0.727N thickness 106 Å and GaN thickness 73 Å) and finally from a model with a lower Al content and a lower well-to-barrier thickness ratio (Al0.164 Ga0.836N thickness 112 Å and GaN thickness 67 Å). The calculated data are offset vertically for clarity.

FIG. 4.

(Color online) X-ray reflectivity data for a 10-repeat semi-polar InGaN/GaN MQW structure (Sample B). From the bottom of the figure to the top, the data sets show the experimental data, then simulated data calculated from the best-fit model (t InGaN = 33 Å, t GaN = 81 Å), then from a model with a higher well-to-barrier thickness ratio (t InGaN = 36 Å, t GaN = 78 Å) and finally from a model with a lower well-to-barrier thickness ratio (t InGaN = 30 Å, t GaN = 84 Å). The calculated data are offset vertically for clarity.

FIG. 5.

A wide-angle reciprocal space map showing the measurable reflections that can be accessed in (a) the plane containing the 112 reflection, in which theanddirections both lie in-plane (φ = 0) and (b) the plane containing the 112 and 006 reflections and the c-axis (φ = 90). The spot size is approximately indicative of the relative intensity expected for each reflection.

FIG. 6.

(Color online) Reciprocal space maps of the and reflections for a 10-repeat semi-polar InGaN/GaN MQW structure (Sample B), taken with the sample set at φ = 90.

FIG. 7.

(Color online) ω/2θ scans of the reflection taken from a 10-repeat semi-polar InGaN/GaN MQW structure (Sample B). From the bottom of the figure to the top, the data sets show the experimental data collected using an analyzer crystal, then simulated data calculated using the best-fit model (In0.12Ga0.82N thickness 33 Å and GaN thickness 81 Å), then experimental data obtained using an open detector with a slit in front of it, then simulated data from a model with a lower In content and a higher well-to-barrier thickness ratio (In0.11Ga0.89N thickness 36 Å and GaN thickness 78 Å) and finally from a model with a higher In content and a lower well-to-barrier thickness ratio (In0.13Ga0.87N thickness 30 Å and GaN thickness 84 Å). The calculated data are offset vertically for clarity.

FIG. 8.

(Color online) X-ray reflectivity data from a 10-repeat semi-polar GaN/AlGaN MQW structure (Sample C). From the bottom of the figure to the top, the data sets show the experimental data, then simulated data calculated from the best-fit model ((t AlGaN = 105 Å, t GaN = 69 Å), then from a model with a higher well-to-barrier thickness ratio (t AlGaN = 102 Å, t GaN = 72 Å) and finally from a model with a lower well-to barrier thickness ratio (t AlGaN 108 Å, t GaN 66 Å). The calculated data are offset vertically for clarity.

FIG. 9.

(Color online) Reciprocal space maps of the reflection for a 10-repeat semi-polar GaN/AlGaN MQW structure (Sample C) taken with the sample set at different in-plane rotational positions, (a) φ = - 90, (b) φ = 0 and (c) φ = 90.

FIG. 10.

(Color online) Reciprocal space maps of the , , , and 0006 reflections for a 10-repeat semi-polar GaN/AlGaN MQW structure (Sample C).

FIG. 11.

(Color online) ω/2θ scans of the reflection taken from a 10-repeat semi-polar GaN/AlGaN MQW structure (Sample C). From the bottom of the figure to the top, the data sets show the experimental data collected using an analyzer crystal, then simulated data calculated using the best-fit model (Al0.126Ga0.874N thickness 105 Å and GaN thickness 69 Å), then experimental data obtained using an open detector, then simulated data from a model with a lower Al content and a lower well-to-barrier thickness ratio (Al0.122Ga0.878N thickness 108 Å and GaN thickness 66 Å) and finally from a model with a higher Al content and a lower well-to-barrier thickness ratio (Al0.129Ga0.871N thickness 102 Å and GaN thickness 72 Å). The calculated data are offset vertically for clarity.

## Tables

Table I.

Summary of the transformed elastic constants appropriate for commonly used semi-polar and non-polar orientations.

Table II.

Lattice parameters used to calculate lengths in Table I.

Table III.

Example of GaN described in a normalized cubic base with conversion to the semi-polar () setting.

Table IV.

Summary of X-ray results.

/content/aip/journal/jap/111/4/10.1063/1.3678631
2012-02-16
2014-04-25

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