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 language | English (US) |
|---|---|
| Article number | 063519 |
| Journal | Journal of Applied Physics |
| Volume | 105 |
| Issue number | 6 |
| DOIs | |
| State | Published - Apr 9 2009 |
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- Physics and Astronomy(all)
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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 journal › Article
}
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.
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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 -