Empirical extension to the multioscillator model: the beta-distributed oscillator model

Steffen Wilbrandt; Olaf Stenzel

doi:10.1364/AO.56.009892

Applied Optics
Vol. 56,
Issue 36,
pp. 9892-9899
(2017)
•https://doi.org/10.1364/AO.56.009892

Empirical extension to the multioscillator model: the beta-distributed oscillator model

Steffen Wilbrandt and Olaf Stenzel

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Steffen Wilbrandt and Olaf Stenzel, "Empirical extension to the multioscillator model: the beta-distributed oscillator model," Appl. Opt. 56, 9892-9899 (2017)

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Abstract

An empirical extension to the multioscillator model has been deduced. In order to comply with inhomogeneous line broadening, we have developed a novel approach based on the application of the beta distribution of single oscillators called the (β_do) model. The new model has been successfully applied in the course of optical constants determination from photometric measurements of single dielectric, amorphous semiconductor, metal, and organic layers. Thereby, the number of required model parameters can be significantly reduced when compared with the multioscillator model, while the Kramers–Kronig consistency remains guaranteed.

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		Hafnia	Zirconia
Background [Eq. (5)]	$ν_{0} in {cm}^{- 1}$	87,857	74.826
Background [Eq. (5)]	$J in {cm}^{- 1}$	300,119	307,380
( $β_do$ ) set	$ν_{\min} in {cm}^{- 1}$	19,170	30,253
	$ν_{\max} in {cm}^{- 1}$	98,695	74,582
	$J_{β_do} in {cm}^{- 1}$	60,095	47,423
	$Γ_{β_do} in {cm}^{- 1}$	96.3	97.2
	$a$	35.9	13.7
	$b$	35.9	13.7

		$a$ -Ge	Cu
Drude model	$ν_{Drude} in {cm}^{- 1}$	511.5	69,368
Drude model	$Γ_{Drude} in {cm}^{- 1}$	5.15	307.6
Background [Eq. (5)]	$ν_{0} in {cm}^{- 1}$	63,703	38,777
Background [Eq. (5)]	$J in {cm}^{- 1}$	532,173	68,360
( $β_do$ ) set	$ν_{\min} in {cm}^{- 1}$	6329.7	17,711
	$ν_{\max} in {cm}^{- 1}$	36,176	41,413
	$J_{β_do} in {cm}^{- 1}$	388,443	127,101
	$Γ_{β_do} in {cm}^{- 1}$	376.1	530
	$a$	2.79	$1 + 2.1 e - 7$
	$b$	2.79	$1 + 2.1 e - 7$

Background [Eq. (5)]	$ν_{0} in {cm}^{- 1}$	42,754
	$J in {cm}^{- 1}$	93,302
( $β_do$ ) set	$ν_{\min} in {cm}^{- 1}$	12,907	1003.9
	$ν_{\max} in {cm}^{- 1}$	15,110	30,056
	$J_{β_do} in {cm}^{- 1}$	474.1	7189
	$Γ_{β_do} in {cm}^{- 1}$	2.75	369.3
	$a$	3.6	85.5
	$b$
Lorentzian oscillator	$ν_{0 j} in {cm}^{- 1}$	24,031
	$J_{j} in {cm}^{- 1}$	1245.8
	$Γ_{j} in {cm}^{- 1}$	1473

		Hafnia	Zirconia
Background [Eq. (5)]	$ν_{0} in {cm}^{- 1}$	87,857	74.826
Background [Eq. (5)]	$J in {cm}^{- 1}$	300,119	307,380
( $β_do$ ) set	$ν_{\min} in {cm}^{- 1}$	19,170	30,253
	$ν_{\max} in {cm}^{- 1}$	98,695	74,582
	$J_{β_do} in {cm}^{- 1}$	60,095	47,423
	$Γ_{β_do} in {cm}^{- 1}$	96.3	97.2
	$a$	35.9	13.7
	$b$	35.9	13.7

		$a$ -Ge	Cu
Drude model	$ν_{Drude} in {cm}^{- 1}$	511.5	69,368
Drude model	$Γ_{Drude} in {cm}^{- 1}$	5.15	307.6
Background [Eq. (5)]	$ν_{0} in {cm}^{- 1}$	63,703	38,777
Background [Eq. (5)]	$J in {cm}^{- 1}$	532,173	68,360
( $β_do$ ) set	$ν_{\min} in {cm}^{- 1}$	6329.7	17,711
	$ν_{\max} in {cm}^{- 1}$	36,176	41,413
	$J_{β_do} in {cm}^{- 1}$	388,443	127,101
	$Γ_{β_do} in {cm}^{- 1}$	376.1	530
	$a$	2.79	$1 + 2.1 e - 7$
	$b$	2.79	$1 + 2.1 e - 7$

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Equations (21)

Applied Optics