In heteroepitaxy, the substrate is more than a mechanical support. On r-plane sapphire — a substrate that intrinsically imposes anisotropic lattice mismatch — the geometry of the patterned template directly governs strain relaxation in the overgrown film. This study uses high-resolution X-ray diffraction (HRXRD) and reciprocal space mapping (RSM) to quantitatively compare the strain states of planar, stripe, and microrod-template samples.

Characterization: Why It's So Involved

Unlike c-plane GaN, (11–20) non-polar GaN lacks six-fold symmetry and exhibits anisotropic biaxial strain that leads to orthorhombic distortion. Accurately determining the lattice constants is therefore far from trivial.
RSM is performed on the asymmetric (11–22) reflection, which allows simultaneous extraction of in-plane and out-of-plane lattice parameters. The 430 μm-thick sapphire substrate — far thicker than any epilayer — serves as a reference. The qx and qz coordinates correspond to interplanar spacings along the in-plane [0001] direction and out-of-plane [11–20] direction, respectively.
 
 
[Figure 1 ] (11–22) reciprocal space maps for (a) the as-grown sample and (b) the microrod-array overgrown sample. The sapphire substrate peak is used as reference.
 
However, RSM data along [0001] alone are insufficient to characterize in-plane anisotropy. Data along the perpendicular m-direction are also required. Unfortunately, the r-plane sapphire lacks an XRD peak along this direction, so no sapphire reference is available.
Instead, the study adopts the method of Laskar et al.: measuring the interplanar spacing dhkl across multiple symmetric and asymmetric reflections — including (11–20), (2–1–10), (11–22), (10–12), (20–20), (21–30), and (21–32) — then accounting for the orthorhombic distortion and applying least-squares minimization to extract the true lattice constants.
The core relation is:
 
where a and c are lattice constants, δ is the deviation of the basal-plane angle γ, and h, k, l are Miller indices.

Strain Calculation and Elastic Constants

Once the lattice parameters are obtained, strains are computed along three directions: out-of-plane εxx along [11–20], in-plane εzz along [0001], and in-plane εyy along [1–100]. The growth-direction stress σxx is zero by convention; stresses σzz and σyy are derived from the elastic stiffness coefficients Cij.
 
Unstrained GaN reference parameters:

Parameter	Value
Lattice constant a₀	3.1893 Å
Lattice constant c₀	5.1851 Å
Lattice constant m₀	2.7620 Å
Elastic constant C₁₁	390 GPa
Elastic constant C₁₂	145 GPa
Elastic constant C₁₃	106 GPa
Elastic constant C₃₃	398 GPa

 

Strain Comparison Across Three Sapphire Templates

The complete strain data for all samples are summarized below ("+" denotes tensile strain, "–" denotes compressive strain):

Sample	as (Å)	cs (Å)	ms (Å)	γ (°)	ε11–20 (%)	ε0001 (%)	σzz (GPa)	σyy (GPa)
A (1100℃)	3.1926	5.1769	2.7579	119.87	+0.102	–0.158	–0.681	–0.605
B (1120℃)	3.1926	5.1769	2.7578	119.87	+0.103	–0.158	–0.681	–0.612
C (1140℃)	3.1928	5.1764	2.7575	119.86	+0.109	–0.169	–0.730	–0.660
D (stripe, 1100℃)	3.1944	5.1810	2.7571	119.83	+0.160	–0.080	–0.337	–0.547
As-grown	3.1935	5.1799	2.7540	119.79	+0.132	–0.101	–0.570	–1.049

1. Planar As-Grown Sapphire Sample

In-plane strains: ε₁₋₁₀₀ = –0.291%, ε₀₀₀₁ = –0.101%. The [1–100] compressive strain is nearly three times that along [0001], representing strong anisotropy. The compressive stress along the m-direction reaches –1.049 GPa.
Origin: the 16% vs. 1% lattice mismatch asymmetry between r-plane sapphire and a-plane GaN along the two directions.

2. One-Dimensional Stripe Template (Sample D)

In-plane strains: ε₁₋₁₀₀ = –0.178%, ε₀₀₀₁ = –0.080%. The [1–100] strain is roughly twice the [0001] strain; anisotropy remains pronounced.
Mechanism: growth initiates at the stripe sidewalls and expands freely along [0001] until coalescence, with voids forming beneath the stripes. However, [1–100] lateral growth is continuously obstructed by the parallel stripe geometry. Strain relaxes readily along [0001] but cannot relax effectively along [1–100].

3. Two-Dimensional Microrod Array (Samples A/B/C)

Taking Sample A (1100℃) as an example: ε₁₋₁₀₀ = –0.150%, ε₀₀₀₁ = –0.158%. The two in-plane compressive strains differ by less than 0.01 percentage points.
Because the microrod pattern is two-dimensional, GaN can laterally expand in all in-plane directions despite direction-dependent growth rates. Coalescence and void formation occur in every direction, enabling strain relaxation uniformly across the plane and producing a nearly isotropic in-plane strain distribution.

The headline result: On a substrate that intrinsically imposes anisotropic mismatch — r-plane sapphire — a two-dimensional patterned template effectively equalizes the strain between orthogonal directions. For device engineers, this means performance is no longer strongly orientation-dependent, dramatically simplifying device layout and process integration for AlGaN/GaN heterostructures and LEDs.

 

Strain Evolution with Overgrowth Time and Temperature

 
[Figure 2] (a) Out-of-plane strain vs. overgrowth time for Samples A, B, and C; (b) in-plane strain vs. overgrowth time. Inset: cross-sectional SEM of the fully coalesced sample; red circles mark the two types of voids (inter-microrod voids and voids above the SiO₂ mask). Scale bar: 2 μm.
 
Samples were grown at three temperatures: 1100℃ (A), 1120℃ (B), and 1140℃ (C), with overgrowth times ranging from 1000 s to 8000 s.

1. Effect of Growth Time

1. 0–5000 s: As growth proceeds from sidewall-driven expansion toward near-full coalescence, strain progressively accumulates and the magnitude increases.

1. Beyond 5000 s: Once the surface is fully coalesced, two classes of enclosed voids form — between adjacent microrods and above each SiO₂ mask. These voids provide additional strain relaxation, and the strain magnitude actually decreases.

2. Effect of Growth Temperature

Strain along all directions increases with growth temperature, consistent with the expected increase in thermal strain. Comparing the three samples:

1. Sample A (1100℃): ε₀₀₀₁ = –0.158%, ε₁₋₁₀₀ = –0.150%;

1. Sample B (1120℃): ε₀₀₀₁ = –0.158%, ε₁₋₁₀₀ = –0.152%;

1. Sample C (1140℃): ε₀₀₀₁ = –0.169%, ε₁₋₁₀₀ = –0.164%.

A 40℃ temperature increase raises the in-plane compressive strain by roughly 10%, and the out-of-plane tensile strain rises from +0.102% to +0.109%. Growth temperature is therefore a critical process knob for tuning strain in non-polar GaN overgrown on sapphire.
 

Engineering Implications for Sapphire-Based Non-Polar GaN

1. Limits of one-dimensional stripes: Stripes reduce dislocation density and improve crystal quality, but cannot solve the core strain-anisotropy problem — strain relaxes freely along [0001] while remaining locked along [1–100].

2. Breakthrough of two-dimensional microrods: The chessboard microrod array on r-plane sapphire simultaneously reduces dislocation density from 10¹¹/cm² to 6×10⁸/cm² and achieves nearly isotropic in-plane strain.

3. Process trade-offs: Too short a growth time leaves the film incompletely coalesced and rough; beyond ~5000 s, stress relaxation improves but internal voids are retained. Excessive void density may compromise device reliability. Temperature must be optimized jointly for crystal quality and thermal strain.

4. The double-edged nature of voids: Voids are beneficial for strain relaxation (strain decreases after 5000 s) but are a potential reliability risk. Future process optimization must balance adequate relaxation against low void density.

Closing thoughts: r-plane sapphire is a critical low-cost platform for non-polar GaN. The substrate is not merely a mechanical support — the patterning geometry on its surface simultaneously governs defect propagation pathways and strain relaxation behavior. The two-dimensional microrod template offers a viable route to high-performance non-polar nitride power devices and long-wavelength LEDs on sapphire. For sapphire substrate suppliers, delivering ultra-flat, low-defect r-plane material at controlled patterning cost will be a key competitive edge in non-polar GaN manufacturing.

About JXT

JXT specializes in the R&D, production, and global sales of semiconductor substrate wafers. For the sapphire epitaxy scenarios discussed in this series, we offer a full range of sapphire substrates covering every crystallographic orientation required for GaN epitaxy:

Product	Orientation / Spec	Typical Applications
C-plane sapphire	(0001) C-plane	Mainstream blue LEDs, conventional GaN power devices, Micro-LED epitaxy substrates
R-plane sapphire	(1–102) R-plane	Non-polar (11–20) a-plane GaN epitaxy — the substrate featured in this article series
A-plane sapphire	(11–20) A-plane	Semipolar/non-polar GaN research, specialty-wavelength LEDs and high-frequency devices
M-plane sapphire	(1–100) M-plane	Semipolar (11–22) GaN epitaxy for green/amber LEDs
PSS patterned sapphire	Patterned Sapphire Substrate	Higher light extraction efficiency and reduced dislocation density for mainstream LED production
NPSS nano-patterned sapphire	Nano-PSS	High-brightness Micro-LED and Mini-LED epitaxy substrates with nano-scale periodicity

 
Whether you require standard C-plane PSS for LED mass production or R-plane, A-plane, or M-plane sapphire for non-polar/semipolar GaN research and development, JXT supplies substrates from 2-inch to 6-inch diameters, with customization of orientation, polish specification, and thickness. Contact us for samples and technical support.