Determination of thickness and optical constants of solgel derived polyvinylpyrrolidone/ZrO<sub>2</sub>films from transmission spectra using different dispersion models

Hongbao Jia; Jinghua Sun; Yao Xu; Dong Wu

doi:10.1364/AO.51.006937

Applied Optics
Vol. 51,
Issue 29,
pp. 6937-6944
(2012)
•https://doi.org/10.1364/AO.51.006937

Determination of thickness and optical constants of solgel derived polyvinylpyrrolidone/ ${ZrO}_{2}$ films from transmission spectra using different dispersion models

Hongbao Jia, Jinghua Sun, Yao Xu, and Dong Wu

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Hongbao Jia, Jinghua Sun, Yao Xu, and Dong Wu, "Determination of thickness and optical constants of solgel derived polyvinylpyrrolidone/ZrO₂films from transmission spectra using different dispersion models," Appl. Opt. 51, 6937-6944 (2012)

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- Instrumentation, Measurement, and Metrology
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About this Article
History
- Original Manuscript: June 6, 2012
- Revised Manuscript: September 2, 2012
- Manuscript Accepted: September 7, 2012
- Published: October 4, 2012

Abstract

Transmission measurements have been used to investigate the optical properties of polyvinylpyrrolidone $(PVP) / {ZrO}_{2}$ films synthesized by the solgel route. The optical constants of $PVP / {ZrO}_{2}$ films deposited on quartz substrates were determined by fitting transmission spectra in the wavelength range of 200–800 nm with the Tauc–Lorentz and Cody–Lorentz physical models. Combined with Urbach tail, both models give a good description of transmission data and reveal that refractive index of film slightly decreases with increasing PVP mass fraction. X-ray reflectivity (XRR) measurements were also performed on $PVP / {ZrO}_{2}$ films to complement the thicknesses. The value of film thickness, including interface information from transmission spectra, is consistent with that result obtained from XRR, indicating that fitting transmission spectrum is a high reliable optical characterization.

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Sample	ZP00	ZP05	ZP10	ZP15
XRR fit
$σ_{1}$ (nm)	$1.50 \pm 0.20$	$1.73 \pm 0.19$	$2.08 \pm 0.32$	$2.21 \pm 0.53$
$d_{XRR}$ (nm)	$110.1 \pm 0.3$	$127.0 \pm 0.4$	$156.6 \pm 1.2$	$218.5 \pm 1.3$
$σ_{2}$ (nm)	$1.67 \pm 0.27$	$2.09 \pm 0.30$	$3.12 \pm 0.50$	$3.95 \pm 0.42$
Transmission Spectra Fit
TL Model
$χ_{TL}^{2}$	4.667	2.105	2.214	5.619
$d_{1 - TL}$ (nm)	$0.57 \pm 0.20$	$0.87 \pm 0.15$	$1.10 \pm 0.20$	$1.40 \pm 0.17$
$d_{2 - TL}$ (nm)	$107.0 \pm 0.2$	$125.5 \pm 0.2$	$152.3 \pm 0.1$	$214.4 \pm 0.1$
$d_{3 - TL}$ (nm)	$0.85 \pm 0.40$	$1.21 \pm 0.20$	$1.48 \pm 0.20$	$1.90 \pm 0.15$
$d_{TL}$ (nm)	$108.4 \pm 0.8$	$127.6 \pm 0.6$	$154.9 \pm 0.5$	$217.7 \pm 0.4$
TLU Model
$χ_{TLU}^{2}$	0.556	0.813	1.290	1.825
$d_{1 - TLU}$ (nm)	$0.80 \pm 0.16$	$0.90 \pm 0.08$	$1.30 \pm 0.24$	$1.12 \pm 0.03$
$d_{2 - TLU}$ (nm)	$106.8 \pm 0.1$	$124.6 \pm 0.1$	$153.8 \pm 0.1$	$213.9 \pm 0.1$
$d_{3 - TLU}$ (nm)	$0.92 \pm 0.20$	$0.90 \pm 0.22$	$1.88 \pm 0.14$	$1.70 \pm 0.25$
$d_{TLU}$ (nm)	$108.5 \pm 0.5$	$126.4 \pm 0.4$	$157.0 \pm 0.4$	$216.3 \pm 0.4$
CLU Model
$χ_{CLU}^{2}$	0.507	0.318	0.414	1.778
$d_{1 - CLU}$ (nm)	$0.73 \pm 0.10$	$0.91 \pm 0.10$	$1.26 \pm 0.10$	$1.25 \pm 0.10$
$d_{2 - CLU}$ (nm)	$107.0 \pm 0.1$	$126.2 \pm 0.1$	$152.3 \pm 0.1$	$213.5 \pm 0.1$
$d_{3 - CLU}$ (nm)	$1.10 \pm 0.30$	$1.10 \pm 0.14$	$1.96 \pm 0.20$	$2.66 \pm 0.23$
$d_{CLU}$ (nm)	$108.8 \pm 0.5$	$127.5 \pm 0.4$	$155.5 \pm 0.4$	$217.4 \pm 0.4$

Sample	ZP00	ZP05	ZP10	ZP15
$E_{g - TL}$ (eV)	$5.20 \pm 0.02$	$5.53 \pm 0.01$	$5.34 \pm 0.01$	$5.31 \pm 0.01$
$E_{g - TLU}$ (eV)	$5.45 \pm 0.01$	$5.51 \pm 0.01$	$5.42 \pm 0.01$	$5.37 \pm 0.02$
$E_{g - CLU}$ (eV)	$5.47 \pm 0.01$	$5.57 \pm 0.01$	$5.45 \pm 0.01$	$5.49 \pm 0.01$
$E_{g}$ (eV)	$5.88 \pm 0.04$	$5.90 \pm 0.04$	$5.87 \pm 0.04$	$5.85 \pm 0.04$

Sample	ZP00	ZP05	ZP10	ZP15
XRR fit
$σ_{1}$ (nm)	$1.50 \pm 0.20$	$1.73 \pm 0.19$	$2.08 \pm 0.32$	$2.21 \pm 0.53$
$d_{XRR}$ (nm)	$110.1 \pm 0.3$	$127.0 \pm 0.4$	$156.6 \pm 1.2$	$218.5 \pm 1.3$
$σ_{2}$ (nm)	$1.67 \pm 0.27$	$2.09 \pm 0.30$	$3.12 \pm 0.50$	$3.95 \pm 0.42$
Transmission Spectra Fit
TL Model
$χ_{TL}^{2}$	4.667	2.105	2.214	5.619
$d_{1 - TL}$ (nm)	$0.57 \pm 0.20$	$0.87 \pm 0.15$	$1.10 \pm 0.20$	$1.40 \pm 0.17$
$d_{2 - TL}$ (nm)	$107.0 \pm 0.2$	$125.5 \pm 0.2$	$152.3 \pm 0.1$	$214.4 \pm 0.1$
$d_{3 - TL}$ (nm)	$0.85 \pm 0.40$	$1.21 \pm 0.20$	$1.48 \pm 0.20$	$1.90 \pm 0.15$
$d_{TL}$ (nm)	$108.4 \pm 0.8$	$127.6 \pm 0.6$	$154.9 \pm 0.5$	$217.7 \pm 0.4$
TLU Model
$χ_{TLU}^{2}$	0.556	0.813	1.290	1.825
$d_{1 - TLU}$ (nm)	$0.80 \pm 0.16$	$0.90 \pm 0.08$	$1.30 \pm 0.24$	$1.12 \pm 0.03$
$d_{2 - TLU}$ (nm)	$106.8 \pm 0.1$	$124.6 \pm 0.1$	$153.8 \pm 0.1$	$213.9 \pm 0.1$
$d_{3 - TLU}$ (nm)	$0.92 \pm 0.20$	$0.90 \pm 0.22$	$1.88 \pm 0.14$	$1.70 \pm 0.25$
$d_{TLU}$ (nm)	$108.5 \pm 0.5$	$126.4 \pm 0.4$	$157.0 \pm 0.4$	$216.3 \pm 0.4$
CLU Model
$χ_{CLU}^{2}$	0.507	0.318	0.414	1.778
$d_{1 - CLU}$ (nm)	$0.73 \pm 0.10$	$0.91 \pm 0.10$	$1.26 \pm 0.10$	$1.25 \pm 0.10$
$d_{2 - CLU}$ (nm)	$107.0 \pm 0.1$	$126.2 \pm 0.1$	$152.3 \pm 0.1$	$213.5 \pm 0.1$
$d_{3 - CLU}$ (nm)	$1.10 \pm 0.30$	$1.10 \pm 0.14$	$1.96 \pm 0.20$	$2.66 \pm 0.23$
$d_{CLU}$ (nm)	$108.8 \pm 0.5$	$127.5 \pm 0.4$	$155.5 \pm 0.4$	$217.4 \pm 0.4$

Sample	ZP00	ZP05	ZP10	ZP15
$E_{g - TL}$ (eV)	$5.20 \pm 0.02$	$5.53 \pm 0.01$	$5.34 \pm 0.01$	$5.31 \pm 0.01$
$E_{g - TLU}$ (eV)	$5.45 \pm 0.01$	$5.51 \pm 0.01$	$5.42 \pm 0.01$	$5.37 \pm 0.02$
$E_{g - CLU}$ (eV)	$5.47 \pm 0.01$	$5.57 \pm 0.01$	$5.45 \pm 0.01$	$5.49 \pm 0.01$
$E_{g}$ (eV)	$5.88 \pm 0.04$	$5.90 \pm 0.04$	$5.87 \pm 0.04$	$5.85 \pm 0.04$

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Applied Optics