Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia

Daniel Franta; David Nečas; Ivan Ohlídal

doi:10.1364/AO.54.009108

Applied Optics
Vol. 54,
Issue 31,
pp. 9108-9119
(2015)
•https://doi.org/10.1364/AO.54.009108

Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia

Daniel Franta, David Nečas, and Ivan Ohlídal

Not Accessible

Your library or personal account may give you access

Get PDF
Email
Share
Get Citation
Copy Citation Text
Daniel Franta, David Nečas, and Ivan Ohlídal, "Universal dispersion model for characterization of optical thin films over a wide spectral range: application to hafnia," Appl. Opt. 54, 9108-9119 (2015)

Export Citation
- BibTex
- Endnote (RIS)
- HTML
- Plain Text
Citation alert
Save article

Abstract

A dispersion model capable of expressing the dielectric response of a broad class of optical materials in a wide spectral range from far IR to vacuum UV is described in detail. The application of this universal dispersion model to a specific material is demonstrated using the ellipsometric and spectrophotometric characterization of a hafnia film prepared by vacuum evaporation on silicon substrate. The characterization utilizes simultaneous processing of data from multiple techniques and instruments covering the wide spectral range and includes the characterization of roughness, nonuniformity, transition layer, and native oxide layer on the back of the substrate. It is shown how the combination of measurements in light reflected from both sides of the sample and transmitted light allows the separation of weak absorption in films and substrates. This approach is particularly useful in the IR region where the absorption structures in films and substrates often overlap and a prior measurement of the bare substrate may be otherwise necessary for precise separation. Individual phenomena that contribute to the dielectric response, i.e., interband electronic transitions, electronic excitations involving the localized states, and phonon absorption, are discussed in detail. A quantitative analysis of absorption on localized states, permitting the separation of transitions between localized states from transitions between localized and extended states, is utilized to obtain estimates of the density of localized states and film stoichiometry.

Full Article | PDF Article

Corrections

29 October 2015: Corrections were made to the funding section.

More Like This

Wide spectral range optical characterization of yttrium aluminum garnet (YAG) single crystal by the universal dispersion model

Daniel Franta and Mihai-George Mureșan
Opt. Mater. Express 11(12) 3930-3945 (2021)

Optical characterization of inhomogeneous thin films with randomly rough boundaries exhibiting wide intervals of spatial frequencies

Ivan Ohlídal, Jiří Vohánka, Vilma Buršíková, Jan Dvořák, Petr Klapetek, and Nupinder Jeet Kaur
Opt. Express 30(21) 39068-39085 (2022)

Optical properties of hafnia and coevaporated hafnia:magnesium fluoride thin films

Y. Tsou and F. C. Ho
Appl. Opt. 35(25) 5091-5094 (1996)

Previous Article Next Article

Cited By

You do not have subscription access to this journal. Cited by links are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Figures (12)

You do not have subscription access to this journal. Figure files are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Tables (4)

You do not have subscription access to this journal. Article tables are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Equations (37)

You do not have subscription access to this journal. Equations are available to subscribers only. You may subscribe either as an Optica member, or as an authorized user of your institution.

Contact your librarian or system administrator
or
Login to access Optica Member Subscription

Parameter	Value	Unit	Description
$d_{s}$	$0.4093 \pm 0.0002$	mm	Substrate thickness
$d_{f}$	$112.7 \pm 0.1$	nm	Film thickness (IR measurements)
$δ (d_{f})$	$- 2.6 \pm 0.1$	nm	Mean thickness difference (UVISEL)
$δ (d_{f})$	$- 1.1 \pm 0.1$	nm	Mean thickness difference (UVISEL2 VUV)
$δ (d_{f})$	$- 2.2 \pm 0.1$	nm	Mean thickness difference (VUVAS 2000)
$δ (d_{f})$	$- 1.7 \pm 0.1$	nm	Mean thickness difference (Lambda 1050)
$σ (d_{f})$	$1.23 \pm 0.05$	nm	rms value of thickness (UVISEL)
$σ (d_{f})$	$2.23 \pm 0.02$	nm	rms value of thickness (VUVAS 2000)
$σ (d_{f})$	$1.03 \pm 0.02$	nm	rms value of thickness (Lambda 1050)
$d_{o}$	$2.826 \pm 0.007$	nm	Thickness of back side native layer
$d_{t}$	$3.29 \pm 0.03$	nm	Thickness of transition layer
$σ$	$2.19 \pm 0.06$	nm	rms value of roughness (AFM: 0.56 nm)
$τ$	$6.3 \pm 0.3$	nm	Autocorrelation length (fixed from AFM)

Parameter	Value	Unit	Description
$N_{vc}$	$421 \pm 32$	${eV}^{2}$	Transition strength
$E_{g}$	$5.311 \pm 0.004$	eV	Bandgap energy
$A_{0}$	$0 \pm 2$		Amplitude of nonexcitonic term (fixed)
$A_{ex 1}$	1		Amplitude of 1st exciton (fixed)
$E_{ex 1}$	$6.98 \pm 0.01$	eV	Energy of 1st exciton
$B_{ex 1}$	$0.86 \pm 0.01$	eV	Broadening of 1st exciton
$A_{ex 2}$	$4 \pm 2$		Amplitude of 2nd exciton
$E_{ex 2}$	$11 \pm 1$	eV	Energy of 2nd exciton
$B_{ex 2}$	$4 \pm 1$	eV	Broadening of 2nd exciton
$E_{h}$	$20 \pm 3$	eV	Maximum energy of transitions (fixed)
$N_{vx}$	$1637 \pm 314$	${eV}^{2}$	Transition strength
$E_{x}$	$12 \pm 2$	eV	Minimum energy of $ξ^{*}$ band (fixed)

Parameter	Value	Unit	Description
$N_{ut}$	$7 \pm 2$	${eV}^{2}$	Transition strength
$E_{u}$	$0.65 \pm 0.02$	eV	Characteristic (Urbach) energy
$N_{loc}$	$0.067 \pm 0.003$	${eV}^{2}$	Transition strength
$E_{loc}$	$4.547 \pm 0.004$	eV	Mean energy of transitions
$B_{loc}$	$0.212 \pm 0.005$	eV	Energy broadening

Phonon	$ν_{ph}$ $({cm}^{- 1})$	$β_{ph}$ $({cm}^{- 1})$	$N_{ph}$ $({eV}^{2})$
1	$302 \pm 1$	$103 \pm 1$	$0.0047 \pm 0.0003$
2	$322 \pm 1$	$369 \pm 2$	$0.0220 \pm 0.0001$
3	$366 \pm 5$	$129 \pm 4$	$0.0039 \pm 0.0004$
4	$750 \pm 1$	$144 \pm 2$	$0.00089 \pm 0.00002$

Parameter	Value	Unit	Description
$d_{s}$	$0.4093 \pm 0.0002$	mm	Substrate thickness
$d_{f}$	$112.7 \pm 0.1$	nm	Film thickness (IR measurements)
$δ (d_{f})$	$- 2.6 \pm 0.1$	nm	Mean thickness difference (UVISEL)
$δ (d_{f})$	$- 1.1 \pm 0.1$	nm	Mean thickness difference (UVISEL2 VUV)
$δ (d_{f})$	$- 2.2 \pm 0.1$	nm	Mean thickness difference (VUVAS 2000)
$δ (d_{f})$	$- 1.7 \pm 0.1$	nm	Mean thickness difference (Lambda 1050)
$σ (d_{f})$	$1.23 \pm 0.05$	nm	rms value of thickness (UVISEL)
$σ (d_{f})$	$2.23 \pm 0.02$	nm	rms value of thickness (VUVAS 2000)
$σ (d_{f})$	$1.03 \pm 0.02$	nm	rms value of thickness (Lambda 1050)
$d_{o}$	$2.826 \pm 0.007$	nm	Thickness of back side native layer
$d_{t}$	$3.29 \pm 0.03$	nm	Thickness of transition layer
$σ$	$2.19 \pm 0.06$	nm	rms value of roughness (AFM: 0.56 nm)
$τ$	$6.3 \pm 0.3$	nm	Autocorrelation length (fixed from AFM)

Abstract

Corrections

Cited By

Figures (12)

Tables (4)

Equations (37)

Applied Optics