# Heteroepitaxy
Heteroepitaxy is the growth of a single-crystalline film on a substrate of a different material, with the film's crystallographic orientation dictated by the substrate. It differs from [homoepitaxy](https://www.edgepedia.org/homoepitaxy), where film and substrate are the same material and defect densities are far lower. Examples in the published literature range from GaN LEDs on sapphire to GaAs films on silicon.[1](https://www.mdpi.com/2073-4352/7/6/178) • [2](https://www.mdpi.com/2079-4991/12/5/741)
| Key fact | Value |
|---|---|
| Misfit measure | \( \varepsilon_{m}(\%) = (1 - d_{f}/d_{s}) \times 100 \), with \( d_{f} \) and \( d_{s} \) the in-plane lattice plane spacings of film and substrate [3](https://api.intechopen.com/chapter/pdf-download/64923.pdf) |
| Classical growth modes | Frank–van der Merwe, Volmer–Weber, and Stranski–Krastanov, classified in 1958 by Ernst Bauer [1](https://www.mdpi.com/2073-4352/7/6/178) |
| Planar-growth threshold | Mismatch below about 0.5% tends toward planar growth; larger mismatch drives islanding [4](https://www.intechopen.com/chapters/71034) |
| Defect benchmark | Heteroepitaxial GaN on sapphire or SiC carries \( 10^{8} \)–\( 10^{10} \) cm⁻² threading dislocations versus \( 10^{2} \)–\( 10^{4} \) cm⁻² for homoepitaxy [5](https://jnep.sumdu.edu.ua/download/numbers/2011/1,%20Part%201/articles/jnep_2011_V3_N1%28Part1%29_067-084.pdf) |
| Remote epitaxy | Single-crystal films grow through a monolayer graphene interlayer and can be exfoliated; demonstrated in 2017 [6](https://doi.org/10.1038/nature22053) |
| Industrial scale | The MOCVD-produced LED market was estimated at about $100 B in 2023, with a projected 11.35% CAGR to about $171 B in 2028 [7](https://innovation.us.nipponsanso.com/wp-content/uploads/2023/11/JVST-MOCVD-Review-Article-Dupuis.pdf) |
## How it works
The equilibrium growth mode follows from surface and interface energies. The criterion uses \( \Delta\sigma = \sigma + \sigma_{i} - \sigma_{s} \), the sum of overlayer surface energy and interface energy minus substrate surface energy: incomplete wetting (\( \Delta\sigma > 0 \)) gives three-dimensional Volmer–Weber islands; complete wetting with negligible misfit gives layer-by-layer Frank–van der Merwe growth; and complete wetting with non-zero misfit gives Stranski–Krastanov growth, a wetting layer followed by 3D islands.[8](https://pubs.rsc.org/en/content/articlehtml/2023/ce/d3ce00664f)
In the Stranski–Krastanov mode, strain energy accumulating in a pseudomorphic (film strained to copy substrate's crystal lattice) layer rises with thickness until the system switches from 2D to 3D morphology; Ge on Si(100), with 4.2% misfit, forms faceted pyramids this way.[9](https://www.epfl.ch/labs/lns/wp-content/uploads/2018/08/2001_Brune_EN.pdf)
Mismatch magnitude and sign both matter. Below roughly 0.5% mismatch growth tends to planar; strain relief then produces [misfit dislocation](https://www.edgepedia.org/misfit-dislocation) grids at the interface.[4](https://www.intechopen.com/chapters/71034) The critical-thickness concept has models that agree with experiment for misfits above 1%, while People–Bean overestimates below 1%.[10](https://hal.science/jpa-00229591/file/ajp-jphyscol198950C560.pdf) GaP grown on GaAs gave better morphology and crystalline quality than the reverse, indicating that negative misfit is more favorable; under the convention above, negative misfit corresponds to a film spacing larger than the substrate spacing, which leaves a coherent growing layer in compression.[1](https://www.mdpi.com/2073-4352/7/6/178) At high supersaturation, kinetics can override thermodynamics and produce 3D growth even where equilibrium predicts layer-by-layer growth.[9](https://www.epfl.ch/labs/lns/wp-content/uploads/2018/08/2001_Brune_EN.pdf)
## How it is done
**Molecular beam epitaxy (MBE)** runs in ultrahigh vacuum, about \( 10^{-8} \, \mathrm{Pa} \), and morphology is controlled through pressure, deposition rate, substrate temperature, and substrate structure; reducing pressure, raising temperature, and slowing deposition all promote layer-by-layer growth, which reflection high-energy electron diffraction (RHEED) intensity oscillations verify in real time.[4](https://www.intechopen.com/chapters/71034) Reactive-ion MBE of GaN used growth temperatures of 450–800 °C, \( N_{2} \)⁺/Ga flux ratios of 1–5, and \( N_{2} \)⁺ kinetic energies of 35–90 eV; the lowest defect densities came at \( T_{s} \geq 650 \) °C, flux ratio ≥ 3.5, and 35 eV.[11](https://pubs.aip.org/aip/jap/article/73/1/189/176807/Heteroepitaxial-wurtzite-and-zinc-blende-structure)
**MOCVD (MOVPE)** dominates III–V production; Harold M. Manasevit published a complete description of the MOCVD process in a January 1968 [Applied Physics Letters](https://www.edgepedia.org/applied-physics-letters) paper.[12](https://doi.org/10.1063/1.1651934) For GaN on sapphire, the low-temperature buffer route is standard: a GaN nucleation layer is deposited between 500 and 600 °C and annealed at 1080 °C before high-temperature growth.[13](https://www.cambridge.org/core/journals/materials-research-society-internet-journal-of-nitride-semiconductor-research/article/micro-epitaxial-lateral-overgrowth-of-gansapphire-by-metal-organic-vapour-phase-epitaxy/EBE2E4B85DED741E4A918700094C185F) **HVPE** operates near equilibrium at low supersaturation and is the only method giving fast (hundreds of μm/h) and thick (up to millimeters) growth of binaries such as GaN, GaP, and GaAs, whereas MBE and MOCVD operate far from equilibrium at high supersaturation, favoring 2D growth.[1](https://www.mdpi.com/2073-4352/7/6/178) **Pulsed laser deposition** delivers ablated species at about 16 eV, versus roughly 0.1 eV thermal energy in evaporation, lowering the thermal budget needed for epitaxy.[3](https://api.intechopen.com/chapter/pdf-download/64923.pdf) Across all routes, low-temperature growth initiation, two-step growth, and growth on vicinal substrates reduce defect densities; a suitable low-temperature buffer layer can lower film defect density by more than two orders of magnitude.[10](https://hal.science/jpa-00229591/file/ajp-jphyscol198950C560.pdf)
## Origin
The earliest known successful laboratory experiments on epitaxy grew sodium nitrate from aqueous solution on a calcite crystal. [10](https://hal.science/jpa-00229591/file/ajp-jphyscol198950C560.pdf) Single-crystal GaN can be grown on sapphire by hydride vapor phase epitaxy, and it has a direct bandgap of about 3.39 eV at room temperature.[14](https://iopscience.iop.org/article/10.1143/JJAP.45.9001/pdf)
A low-temperature-deposited thin AlN buffer layer on sapphire enabled atomically flat GaN growth [15](https://link.aps.org/doi/10.1103/RevModPhys.87.1133); the corresponding paper by H. Amano and colleagues appeared in Applied Physics Letters in 1986.[16](https://doi.org/10.1063/1.96549) In 1988, low-energy electron beam irradiation (LEEBI) enabled p-type GaN, and the first GaN p–n junction blue/UV LEDs followed in 1989.[15](https://link.aps.org/doi/10.1103/RevModPhys.87.1133) [Shuji Nakamura](https://www.edgepedia.org/shuji-nakamura), Yasuhiro Harada, and Masayuki Seno reported a low-temperature GaN buffer route in a 1991 Applied Physics Letters paper.[17](https://doi.org/10.1063/1.105239)
## Variants
**Buffer engineering** is the workhorse variant. Multi-step buffer technology reduced GaN-on-sapphire defect density by at least an order of magnitude.[18](https://www.sciencedirect.com/science/article/abs/pii/S0022024898012275) For very large misfits, domain matching epitaxy matches integral multiples of lattice planes, handling cases such as TiN on Si at about 22.5% misfit.[3](https://api.intechopen.com/chapter/pdf-download/64923.pdf)
**Epitaxial lateral overgrowth (ELO)** and PENDEO epitaxy redirect dislocation propagation laterally: a dielectric mask or suspended seed blocks threading dislocations from propagating into the laterally growing layer.[1](https://www.mdpi.com/2073-4352/7/6/178) ELO-derived methods brought GaN threading dislocation densities to the order of \( 10^{7} \) cm⁻², and laser diodes with lifetimes beyond 10,000 h were made from such material.[14](https://iopscience.iop.org/article/10.1143/JJAP.45.9001/pdf)
**Van der Waals epitaxy**, introduced by Atsushi Koma, Kazumasa Sunouchi, and Takao Miyajima in a 1984 Microelectronic Engineering paper, achieves epitaxy on dangling-bond-free layered surfaces across large mismatches.[19](https://doi.org/10.1016/0167-9317%2884%2990057-1) **Remote epitaxy**, reported by Yunjo Kim and colleagues in Nature in 2017, grows single-crystal films through a monolayer graphene interlayer: adatoms register with the underlying substrate through a gap of up to nine ångströms, and GaAs(001), InP, and GaP films were demonstrated and exfoliated.[6](https://doi.org/10.1038/nature22053) The mechanism depends on polarity: covalently bonded Si shows an \( r^{-6} \) potential decay versus \( r^{-2} \) for partially ionic GaN, which is why remote homoepitaxy succeeds on GaN but not Si [20](https://pmc.ncbi.nlm.nih.gov/articles/PMC10457265/); Wei Kong and colleagues established the polarity dependence in a 2018 [Nature Materials](https://www.edgepedia.org/nature-materials) paper.[21](https://doi.org/10.1038/s41563-018-0176-4) The family divides into remote epitaxy (the substrate lattice governs), vdW epitaxy (the 2D material governs), and quasi-vdW epitaxy (a doped 2D material's potential fluctuation governs).[20](https://pmc.ncbi.nlm.nih.gov/articles/PMC10457265/) Direct vdW epitaxy of single-crystalline films on epitaxial graphene was reported by [Jeehwan Kim](https://www.edgepedia.org/jeehwan-kim) and colleagues in 2014.[22](https://doi.org/10.1038/ncomms5836)
## Applications
GaN-on-sapphire is the flagship: the low-temperature buffer route plus p-type activation produced the first GaN p–n junction blue/UV LEDs in 1989 [14](https://iopscience.iop.org/article/10.1143/JJAP.45.9001/pdf), and the MOCVD-produced LED market reached an estimated $100 B in 2023.[7](https://innovation.us.nipponsanso.com/wp-content/uploads/2023/11/JVST-MOCVD-Review-Article-Dupuis.pdf) GaAs on Si(100), with 4.1% mismatch, targets III–V integration on silicon platforms.[2](https://www.mdpi.com/2079-4991/12/5/741) Stranski–Krastanov growth is exploited for self-assembled quantum dot arrays, such as Ge on Si(100).[9](https://www.epfl.ch/labs/lns/wp-content/uploads/2018/08/2001_Brune_EN.pdf) Remote epitaxy adds exfoliable devices: GaN microrod LEDs on graphene-coated sapphire were reported by Junseok Jeong and colleagues in 2020 [23](https://doi.org/10.1126/sciadv.aaz5180), halide perovskite carrier lifetimes were enhanced via remote epitaxy by Jie Jiang and colleagues [24](https://doi.org/10.1038/s41467-019-12056-1), and complex-oxide membranes were integrated by remote epitaxy and 2D layer transfer by Hyun S. Kum and colleagues.[25](https://doi.org/10.1038/s41586-020-1939-z)
## Limitations and alternatives
The dominant defect is the threading dislocation. Heteroepitaxial GaN on sapphire and SiC carries \( 10^{8} \)–\( 10^{10} \) cm⁻².[5](https://jnep.sumdu.edu.ua/download/numbers/2011/1,%20Part%201/articles/jnep_2011_V3_N1%28Part1%29_067-084.pdf) For GaAs on Si, interface dislocation densities near \( 10^{9} \)–\( 10^{11} \) cm⁻² are typical, and state-of-the-art films reach \( 10^{6} \)–\( 10^{7} \) cm⁻², still three orders of magnitude above homoepitaxial GaAs.[10](https://hal.science/jpa-00229591/file/ajp-jphyscol198950C560.pdf)
**Polar-on-nonpolar growth** produces anti-phase boundaries, which arise from the polarity difference between polar III–V surfaces and non-polar Si and can propagate through the whole epilayer.[2](https://www.mdpi.com/2079-4991/12/5/741) **Thermal mismatch** causes a separate failure: post-growth cooling of films thicker than the critical thickness introduces biaxial thermoelastic stress relieved by microcracks along cleavage planes [10](https://hal.science/jpa-00229591/file/ajp-jphyscol198950C560.pdf); GaAs's thermal expansion coefficient (\( 6.6 \times 10^{-6} \) K⁻¹) exceeds silicon's (\( 2.3 \times 10^{-6} \) K⁻¹).[2](https://www.mdpi.com/2079-4991/12/5/741)
Melt growth of GaN is prevented by its high vapor pressure, but bulk GaN crystals and free-standing substrates can be produced by methods such as ammonothermal growth or HVPE, enabling homoepitaxy on GaN substrates.[26](https://pubs.aip.org/aip/jap/article/128/5/050902/595963/Growth-of-bulk-GaN-crystals) • [1](https://www.mdpi.com/2073-4352/7/6/178) Where defects must be removed rather than prevented, selective epitaxial growth with aspect ratio trapping or ELO blocks dislocations at dielectric masks.[2](https://www.mdpi.com/2079-4991/12/5/741)
## References
1. [Heteroepitaxy, an Amazing Contribution of Crystal Growth to the World of Optics and Electronics (Crystals, 2017)](https://www.mdpi.com/2073-4352/7/6/178)
2. [Review of Highly Mismatched III-V Heteroepitaxy Growth on (001) Silicon (Nanomaterials, 2022)](https://www.mdpi.com/2079-4991/12/5/741)
3. [Epitaxial Growth of Thin Films (Rasic & Narayan, IntechOpen)](https://api.intechopen.com/chapter/pdf-download/64923.pdf)
4. [Growth Kinetics of Thin Film Epitaxy (IntechOpen chapter)](https://www.intechopen.com/chapters/71034)
5. [jnep 2011 V3 N1(Part1) 067 084 (jnep.sumdu.edu.ua)](https://jnep.sumdu.edu.ua/download/numbers/2011/1,%20Part%201/articles/jnep_2011_V3_N1%28Part1%29_067-084.pdf)
6. [Yunjo Kim and colleagues (2017). Remote epitaxy through graphene enables two-dimensional material-based layer transfer. Nature.](https://doi.org/10.1038/nature22053)
7. [III–V semiconductor devices grown by MOCVD (Dupuis review, JVST, 2023)](https://innovation.us.nipponsanso.com/wp-content/uploads/2023/11/JVST-MOCVD-Review-Article-Dupuis.pdf)
8. [Heteroepitaxial growth modes revisited (CrystEngComm, 2023)](https://pubs.rsc.org/en/content/articlehtml/2023/ce/d3ce00664f)
9. [Epitaxial film growth chapter (Brune, The Chemical Physics of Solid Surfaces)](https://www.epfl.ch/labs/lns/wp-content/uploads/2018/08/2001_Brune_EN.pdf)
10. [Heteroepitaxy of semiconductors (J. Phys. Colloques, 1989)](https://hal.science/jpa-00229591/file/ajp-jphyscol198950C560.pdf)
11. [Heteroepitaxial wurtzite and zinc-blende structure GaN grown by reactive-ion MBE (J. Appl. Phys. 73, 189, 1993)](https://pubs.aip.org/aip/jap/article/73/1/189/176807/Heteroepitaxial-wurtzite-and-zinc-blende-structure)
12. [Harold M. Manasevit (1968). SINGLE-CRYSTAL GALLIUM ARSENIDE ON INSULATING SUBSTRATES. Applied Physics Letters.](https://doi.org/10.1063/1.1651934)
13. [Micro epitaxial lateral overgrowth of GaN/sapphire by MOVPE (MRS Internet J. Nitride Semicond. Res.)](https://www.cambridge.org/core/journals/materials-research-society-internet-journal-of-nitride-semiconductor-research/article/micro-epitaxial-lateral-overgrowth-of-gansapphire-by-metal-organic-vapour-phase-epitaxy/EBE2E4B85DED741E4A918700094C185F)
14. [Breakthroughs in Improving Crystal Quality of GaN and Invention of the p–n Junction Blue LED (Akasaki, Jpn. J. Appl. Phys. 2006)](https://iopscience.iop.org/article/10.1143/JJAP.45.9001/pdf)
15. [Nobel Lecture: Growth of GaN on sapphire via low-temperature deposited buffer layer (Amano, Rev. Mod. Phys. 2015)](https://link.aps.org/doi/10.1103/RevModPhys.87.1133)
16. [H. Amano and colleagues (1986). Metalorganic vapor phase epitaxial growth of a high quality GaN film using an AlN buffer layer. Applied Physics Letters.](https://doi.org/10.1063/1.96549)
17. [Shuji Nakamura, Yasuhiro Harada, Masayuki Seno (1991). Novel metalorganic chemical vapor deposition system for GaN growth. Applied Physics Letters.](https://doi.org/10.1063/1.105239)
18. [Renaissance and progress in crystal growth of nitride semiconductors (J. Crystal Growth, 1999)](https://www.sciencedirect.com/science/article/abs/pii/S0022024898012275)
19. [Fabrication and characterization of heterostructures with subnanometer thickness (Microelectronic Engineering, 1984)](https://doi.org/10.1016/0167-9317%2884%2990057-1)
20. [Lattice modulation strategies for 2D material assisted epitaxial growth (peer-reviewed review, PMC)](https://pmc.ncbi.nlm.nih.gov/articles/PMC10457265/)
21. [Wei Kong and colleagues (2018). Polarity governs atomic interaction through two-dimensional materials. Nature Materials.](https://doi.org/10.1038/s41563-018-0176-4)
22. [Jeehwan Kim and colleagues (2014). Principle of direct van der Waals epitaxy of single-crystalline films on epitaxial graphene. Nature Communications.](https://doi.org/10.1038/ncomms5836)
23. [Junseok Jeong and colleagues (2020). Remote heteroepitaxy of GaN microrod heterostructures for deformable light-emitting diodes and wafer recycle. Science Advances.](https://doi.org/10.1126/sciadv.aaz5180)
24. [Jie Jiang and colleagues (2019). Carrier lifetime enhancement in halide perovskite via remote epitaxy. Nature Communications.](https://doi.org/10.1038/s41467-019-12056-1)
25. [Hyun S. Kum and colleagues (2020). Heterogeneous integration of single-crystalline complex-oxide membranes. Nature.](https://doi.org/10.1038/s41586-020-1939-z)
26. [Growth of bulk GaN crystals (pubs.aip.org)](https://pubs.aip.org/aip/jap/article/128/5/050902/595963/Growth-of-bulk-GaN-crystals)
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*Topic: Encyclopedia › Physical world and mathematics › Physics › Matter and radiation physics › Condensed matter physics › Crystal and structural condensed matter*
*Initially written Sep 29, 2026 · Reviewed: Sep 30, 2026 · Edited: Sep 30, 2026 · Last review: Sep 30, 2026*
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