Analytical strain relaxation model for Si1-xGex /Si epitaxial layers

Research output: Contribution to journalArticle

10 Citations (Scopus)

Abstract

An approximate but accurate analytical solution is presented for the system of differential equations used by Houghton to model kinetically limited strain relaxation in Si1-xGex alloys layers growing on Si substrates [J. Appl. Phys. 70, 2136 (1991)]. This solution makes it much easier to compare the relaxation model with experimental data. The analytical results are used to refit the Houghton model parameter n0 (representing the initial heterogeneous density of dislocation sources) to published relaxation data, including post-1991 experimental work. The fits, which include experiments in which the growth temperature ranged from 450 to 750 °C, show considerable scattering in n0, but suggests that n0 increases as the growth temperature is lowered. Since this trend was not apparent in the original Houghton work, a detailed analysis is carried out for samples grown and annealed at temperatures below 450 °C. For this purpose, the Houghton model is extended to include the reduction in effective stress as the strain relaxation advances as well as the effect of dislocation pinning. The analysis confirms that n0 increases as the growth temperature is lowered. Possible physical reasons are discussed, and an empirical fit to the temperature dependence of n0 is used to generate revised predictions of apparent critical thicknesses.

Original languageEnglish (US)
Article number063519
JournalJournal of Applied Physics
Volume105
Issue number6
DOIs
StatePublished - Apr 9 2009

Fingerprint

temperature
differential equations
trends
temperature dependence
predictions
scattering

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Analytical strain relaxation model for Si1-xGex /Si epitaxial layers. / Menendez, Jose.

In: Journal of Applied Physics, Vol. 105, No. 6, 063519, 09.04.2009.

Research output: Contribution to journalArticle

@article{ce3c5b401837438a9cda52d886ed14d4,
title = "Analytical strain relaxation model for Si1-xGex /Si epitaxial layers",
abstract = "An approximate but accurate analytical solution is presented for the system of differential equations used by Houghton to model kinetically limited strain relaxation in Si1-xGex alloys layers growing on Si substrates [J. Appl. Phys. 70, 2136 (1991)]. This solution makes it much easier to compare the relaxation model with experimental data. The analytical results are used to refit the Houghton model parameter n0 (representing the initial heterogeneous density of dislocation sources) to published relaxation data, including post-1991 experimental work. The fits, which include experiments in which the growth temperature ranged from 450 to 750 °C, show considerable scattering in n0, but suggests that n0 increases as the growth temperature is lowered. Since this trend was not apparent in the original Houghton work, a detailed analysis is carried out for samples grown and annealed at temperatures below 450 °C. For this purpose, the Houghton model is extended to include the reduction in effective stress as the strain relaxation advances as well as the effect of dislocation pinning. The analysis confirms that n0 increases as the growth temperature is lowered. Possible physical reasons are discussed, and an empirical fit to the temperature dependence of n0 is used to generate revised predictions of apparent critical thicknesses.",
author = "Jose Menendez",
year = "2009",
month = "4",
day = "9",
doi = "10.1063/1.3093889",
language = "English (US)",
volume = "105",
journal = "Journal of Applied Physics",
issn = "0021-8979",
publisher = "American Institute of Physics Publising LLC",
number = "6",

}

TY - JOUR

T1 - Analytical strain relaxation model for Si1-xGex /Si epitaxial layers

AU - Menendez, Jose

PY - 2009/4/9

Y1 - 2009/4/9

N2 - An approximate but accurate analytical solution is presented for the system of differential equations used by Houghton to model kinetically limited strain relaxation in Si1-xGex alloys layers growing on Si substrates [J. Appl. Phys. 70, 2136 (1991)]. This solution makes it much easier to compare the relaxation model with experimental data. The analytical results are used to refit the Houghton model parameter n0 (representing the initial heterogeneous density of dislocation sources) to published relaxation data, including post-1991 experimental work. The fits, which include experiments in which the growth temperature ranged from 450 to 750 °C, show considerable scattering in n0, but suggests that n0 increases as the growth temperature is lowered. Since this trend was not apparent in the original Houghton work, a detailed analysis is carried out for samples grown and annealed at temperatures below 450 °C. For this purpose, the Houghton model is extended to include the reduction in effective stress as the strain relaxation advances as well as the effect of dislocation pinning. The analysis confirms that n0 increases as the growth temperature is lowered. Possible physical reasons are discussed, and an empirical fit to the temperature dependence of n0 is used to generate revised predictions of apparent critical thicknesses.

AB - An approximate but accurate analytical solution is presented for the system of differential equations used by Houghton to model kinetically limited strain relaxation in Si1-xGex alloys layers growing on Si substrates [J. Appl. Phys. 70, 2136 (1991)]. This solution makes it much easier to compare the relaxation model with experimental data. The analytical results are used to refit the Houghton model parameter n0 (representing the initial heterogeneous density of dislocation sources) to published relaxation data, including post-1991 experimental work. The fits, which include experiments in which the growth temperature ranged from 450 to 750 °C, show considerable scattering in n0, but suggests that n0 increases as the growth temperature is lowered. Since this trend was not apparent in the original Houghton work, a detailed analysis is carried out for samples grown and annealed at temperatures below 450 °C. For this purpose, the Houghton model is extended to include the reduction in effective stress as the strain relaxation advances as well as the effect of dislocation pinning. The analysis confirms that n0 increases as the growth temperature is lowered. Possible physical reasons are discussed, and an empirical fit to the temperature dependence of n0 is used to generate revised predictions of apparent critical thicknesses.

UR - http://www.scopus.com/inward/record.url?scp=63749119951&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=63749119951&partnerID=8YFLogxK

U2 - 10.1063/1.3093889

DO - 10.1063/1.3093889

M3 - Article

AN - SCOPUS:63749119951

VL - 105

JO - Journal of Applied Physics

JF - Journal of Applied Physics

SN - 0021-8979

IS - 6

M1 - 063519

ER -