Strain dependence of second-harmonic generation in silicon

Clemens Schriever; Christian Bohley; Ralf B. Wehrspohn

doi:10.1364/OL.35.000273

Optics Letters
Vol. 35,
Issue 3,
pp. 273-275
(2010)
•https://doi.org/10.1364/OL.35.000273

Strain dependence of second-harmonic generation in silicon

Clemens Schriever, Christian Bohley, and Ralf B. Wehrspohn

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Clemens Schriever, Christian Bohley, and Ralf B. Wehrspohn, "Strain dependence of second-harmonic generation in silicon," Opt. Lett. 35, 273-275 (2010)

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Abstract

Strained silicon is a versatile new type of material, which has found application in microelectronics and integrated optics in the last years. Unlike ordinary silicon, it does not possess a centrosymmetric lattice structure. This allows for stimulation of nonlinear optical processes that involve second-order nonlinear susceptibility. Here, the dependence of the nonlinear susceptibility on the applied strain by means of reflected second-harmonic generation is investigated. This surface-sensitive technique is suitable for the investigation of bulk silicon strained by a layer of thermal oxide. The obtained relation between applied stress and susceptibility enhancement is compared to theoretical prediction based on an analytical model for the deformed silicon orbital. The knowledge of the stress-susceptibility dependence can be used to develop suitable photonic devices that benefit from second-order nonlinear processes in silicon.

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Azimuthal SHG Signal	SHG Frequency [eV]	Face	Oxide Thickness [nm]	Stress [GPa]	Susceptibility Enhancement	$χ_{enh}^{(2)} ∕ σ_{0}$ $[1 ∕ GPa]$	Ref.
$I_{p s} = {\| a_{p s} + c_{p s} \cos 3 ϕ \|}^{2} I_{0}^{2}$	2.33	(111)	61	$- 1.7$	$c_{p s}^{enh} (d_{11}) = 2.34$	$- 0.79$	[5]
$I_{s s} = {\| b_{s s} \sin 3 ϕ \|}^{2} I_{0}^{2}$	2.33	(111)	61	$- 1.7$	$b_{s s}^{enh} (d_{11}) = 2.5$	$- 0.88$	[5]

$I_{s p} = {\| a_{s p} \sin 4 ϕ \|}^{2} I_{0}^{2}$	3.26	(100)	58	—	$a_{s p}^{enh} (d_{11}) = 1.9$	—	[11]
$I_{s p} = {\| a_{s p} \sin 4 ϕ \|}^{2} I_{0}^{2}$	3.44	(100)	58	—	$a_{s p}^{enh} (d_{11}) = 3.7$	—	[11]

$I_{p p} = {\| a_{p p} + c_{p p} \cos 3 ϕ \|}^{2} I_{0}^{2}$	3.1	(111)	13	$- 0.69$	$a_{p p}^{enh} (d_{31}, d_{15}, d_{33}) = 2.55$	$- 2.21$	this work
$I_{p p} = {\| a_{p p} + c_{p p} \cos 3 ϕ \|}^{2} I_{0}^{2}$	3.1	(111)	13	$- 0.69$	$c_{p p}^{enh} (d_{11}) = 1.6$	$- 0.81$	this work

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