1. The effect of oxygen vacancies and strain on the optical bandgap of strained SrTiO3-δ thin films
Nathan Steinle, Barry D. Koehne, Ryan Cottier, Daniel A. Currie, and Nikoleta Theodoropoulou*
Texas State University Physics Department
Funded by NSF Career Award DMR
Spring 2015 National APS Meeting
Session T14: Dopants and Defects in TiO2, SrTiO3, and Other Oxides

2. Strontium Titanate SrTiO3 (STO)
Bulk
STO is used as a substrate for other oxides
Indirect Eg = 3.25 eV, Direct Eg =3.75 eV, T=300 K
Lattice Constant: a=b=c=3.905 Å
Thin Films
Grown by various deposition methods
STO easily grown on other oxides.
Very difficult to deposit on Si epitaxially
1.7% compressive strain on Si
STO Unit Cell c
In this project we studied strontium titanate which has perovskite structure at 300 kelvin. This is the STO unit cell…..
In bulk…
It has perovskite structure, shown in this image here, with Ti in the middle and O on the faces where (a) is the…
STO thin films can be manufactured by various deposition methods, and it is easily grown on other oxides. It’s very difficult to deposit onto Si directly. But we accomplished this and there’s a 1.7% compressive strain in the film.
In growing our films we borrowed from already published recipes, like those by these groups here. a
D. Schlom et al, Annu. Rev. Mater. Res :589–626
M. P. Warusawithana et al. Science 324 (5925), (2009)

3. STO Films of High Epitaxial Quality
Dr. Cottier grew STO/Si using MBE
XRD spectra show strained STO by changes in lattice constant (c).
When sufficiently thin STO films are ferroelectric at T = 300K.
We are curious about how oxygen vacancies and strain effect the direct bandgap of the STO film. Dr. Cottier grew the films without an interfacial silicon dioxide layer using texas state’s very own 9 chamber multi-functional MBE facility, shown here.
Dr. Cottier performed XRD analysis on these films and found them to be of very high quality epitaxially; Also AFM measurements showed smooth film surfaces, so no need to consider surface roughness in my modeling of the film.
From the XRD spectra we see a change in the out of plane lattice constant (c) for different thicknesses meaning that there is strain in our lattice.
We also found our films to exhibit ferroelectric behavior, which is a well-documented characteristic of STO thin films when they’re strained.
M. P. Warusawithana et al. Science 324 (5925), (2009)
R. Wordenweber et al, JAP 102, (2007)

4. Controlling P(O2)  Controlling oxygen vacancies (VO)
Controlling the oxygen pressure the film is exposed to during growth allows us to control oxygen vacancies introduced into the lattice. We controlled oxygen deficiency to investigate the interplay of the oxygen vacancies with lattice strain.
The Ti atoms in the lattice are attracted to the oxygen vacancies, and this image displays this nicely. This is a well-known phenomenon as well.
Ti atoms are attracted to VO meaning lattice constant (a) gets smaller with more VO.
Gryaznov et al. J. Phys Chem. C. 117, (2013)

5. Two Sample Sets Set A: d VARIES: 4-29 nm, P(O2) CONSTANT: 4E-8 Torr
Strain changes with thickness
Set B: P(O2) VARIES: 0.5E-7 to 4E-7 Torr
d CONSTANT: 8-9 nm
Strain changes with P(O2)
Of the many samples Dr. Cottier grew I worked with two sets: Set A vary among thickness and have constant oxygen deficiency, and Set B vary among oxygen deficiency and have constant thickness.
From the XRD spectra we calculated the out of plane lattice constant for these sets and found that in Set A the strain depends on the thickness, and in Set B the strain depends on the oxygen deficiency in the lattice.
It’s worth noting that samples in Set A (with constant oxygen pressure) are not fully stoichiometric – they have oxygen vacancies, whereas other teams generally emphasize the diminishing of such oxygen vacancies.
The more oxygen vacancies there are the more the titanium atom displaces, meaning oxygen vacancies cause deformations which result in strain.

6. Ellipsometry Spectroscopic Ellipsometer
Extract thickness (d) and optical constants (n, k) from measurement via model analysis.
Both n and k depend on energy.
Model analysis: two Tauc-Lorentz oscillators fit the optical constant shape as a function of photon energy using all energies simultaneously.
Wavelength by Wavelength: fits individual values of optical constants at every energy
Calculate the Direct Bandgap
Use k to approx. Direct Bandgap of each sample
Sample: d = 9.6 nm, P(O2) = 4E-8
My objective was to measure the optical properties and calculate the direct bandgap of STO on Si using ellipsometry.
I used a VASE by Woollam.
From each measurement I extracted thickness and optical constants (n for reflection and k for absorption) for each sample. Both optical constants, n and k, depend on photon energy.
To extract them I tried many different models, and the best is two Tauc-Lorentz oscillators to fit the optical constants to the data, and to make sure I had a good model I used a WvlbyWvl extraction of the optical constants as well.
This graph shows the extracted optical constants for one sample; pretty normal optical constants for a material like this; we note that there’s very little absorption at low energies.
Once I had the optical constants I used the extinction coefficient to calculate the direct optical bandgap of each sample.
A beam of light with known polarization is shone on and reflected from the sample’s surface and a detector measures the output polarization. So the spectroscopic ellipsometer measures this change in polarization of light in terms of two parameters, psi and delta, that are modeled in order to determine the optical constants, ε1 and ε2. ε1 represents reflection, and ε2 represents absorption in the material. Both depend on energy/wavelength of light.
So, I modeled my measurements using two Tauc-Lorentz oscillators for the STO layer, which essentially treat atoms in a lattice as masses connected by springs and the oscillatory frequencies of the masses model those of the actual atoms as they interact with the light.
Used ε2 to find the Direct Bandgap of each sample
I used a Variable Angle Spectroscopic Ellipsometer (VASE) M-2000 by Woollam.

7. Calculating the direct bandgap:
Film’s absorption coefficient α:
Linear fit of α and E relationship: ratio of y-intercept to slope of fit is the approximate direct bandgap.
So to calculate the direct bandgap I used the relation between photon energy E and the film’s absorption coefficient α (which is proportional to k) and did a linear fit of that relation as a function of photon energy.
The ratio of B:A = Eg the desired bandgap.
This graph shows one of the linear fits.
Tompkins, Harland G. Irene, Eugene A., Handbook of Ellipsometry

8. Results I: Thickness dependence of Bandgap
Thickness changes  strain changes  bandgap?
Constant VO  Constant sheet carrier concentration (ns)
Hall measurements (T = 100K):
Quantum Confinement (bound state):
Thicker film  more relaxed lattice  smaller Eg
Thickness (nm) 5 8 20
ns (cm-2)
2.7E12
1.3E14
1.58E14
For Set A, this is the same graph as before and because we can see that the strain changes with thickness we wonder how this effects the bandgap?
So here’s the data: we see a dependence of bandgap on thickness that as the thickness decreases the bandgap increases. We see that the bandgap approaches the bulk value the thicker the film is (which makes sense). Why does bandgap change?
We conducted Hall measurements on the samples at T = 100K and found that, as expected, the sheet carrier concentration is constant – our measurement is noisy at low temperatures for very thin films (which explains the 5 nm sample’s deviation from this expectation).
One explanation is that the free carriers are in a quantum confinement where as the film gets thicker the in plane lattice constant increases, meaning the lattice relaxes, resulting in a smaller bandgap.
Other teams have documented similar findings in similar systems, but we are the first to show this in STO/Si.
K. G. Eyink et al. APS 105, (2014)
J Price, A. C. Diebold, JVSTB 24, 2156 (2006)

9. Results II: Oxygen Pressure dependence of Bandgap
VO changes  strain changes  bandgap?
Varied VO  Varied sheet carrier concentration (ns)
Hall measurements (T = 100K):
Burstein-Moss Shift: As lattice relaxes, more Vo, more free electrons  lower conduction band filled causing Eg redshift.
P(O2) (Torr)
4E-7
2E-7
4E-8
ns (cm-2)
4.2E12
4.0E12
1.0E14
For Set B, this is the same graph as before and because we see that strain changes with oxygen pressure we wonder how this effects the bandgap?
We see a very similar dependence of bandgap on oxygen pressure. More O vacancies result in a larger bandgap.
As opposed to the thickness dependence however, here we did vary oxygen deficiency so we expect the sheet carrier concentration to also vary. This is what we find from hall measurements.
Why does this affect the bandgap? One explanation is that with increased oxygen deficiency the free carrier concentration increases which occupy lower transitional energies in the conduction band, effectively resulting in a larger bandgap: this is called the Burstein – Moss effect.
Other teams have documented this phenomenon in other systems but we report the finding in this system for the first time as well.
Its thin films so we’re never going to recover what we have in bulk.
R. Al-Hamadany, JAP 113, (2013)
M. Choi et al, JAP 116, (2014)

10. Conclusions
I used ellipsometry to determine the effect of VO and strain on the direct bandgap Eg of ferroelectric, high quality epitaxially grown STO/Si thin films.
As thickness changes, Ti atoms displace causing change in strain and thus change in Eg  Quantum Confinement?
As oxygen pressure changes, VO changes and sheet carrier concentration changes and thus change in Eg  Burstein – Moss Effect?
Need more data!!!!!!
In summary, I used………………..

11. http://www. tf. uni-kiel

12. Our films are ferroelectric!
Piezoresponse Force Microscopy (PFM)
Phase shift of ~180° (shown here and in the hysteresis) demonstrates the ferroelectric behavior of the films.
So we’re confident that our films are strained and ferroelectric.
High and low regions were ~180° apart, confirming an up/down polarization regime.
Point spectroscopy showed hysteresis in the piezoresponse as shown.
Our films are ferroelectric!

13. What about broadening? Constant Thickness ~ 10 nm
Constant P(O2) = 4E-8 Torr
[1] J. Price, A. C. Diebold, JVSTB 24, 2156 (2006)
[2] K. G. Eyink et al. APS 105, (2014)

14. What’s ellipsometry? Two ways to analyze measurement data:
Spectroscopic Ellipsometer
Measure  (Ψ, Δ) 
Determine (n, k) (analysis)
Calculate Direct Bandgap
Extract Optical constants,
n reflection and k absorption. Both n and k depend on energy.
Two ways to analyze measurement data:
Model analysis using two Tauc-Lorentz oscillators describes the optical constant shape as a function of wavelength using all wavelengths simultaneously.
Wavelength by Wavelength fits individual values of optical constants at every wavelength
Use k to find the Direct Bandgap of each sample
My objective was to measure the optical properties and direct bandgap of STO on Si using ellipsometry.
Measure the change in polarization of light in terms of Ψ (reflection amplitude) and Δ (phase shift difference)
TL oscillators are a physical model  causality
A beam of light with known polarization is shone on and reflected from the sample’s surface and a detector measures the output polarization. So the spectroscopic ellipsometer measures this change in polarization of light in terms of two parameters, psi and delta, that are modeled in order to determine the optical constants, ε1 and ε2. ε1 represents reflection, and ε2 represents absorption in the material. Both depend on energy/wavelength of light.
So, I modeled my measurements using two Tauc-Lorentz oscillators for the STO layer, which essentially treat atoms in a lattice as masses connected by springs and the oscillatory frequencies of the masses model those of the actual atoms as they interact with the light.
Used ε2 to find the Direct Bandgap of each sample
I used a Variable Angle Spectroscopic Ellipsometer (VASE) M-2000 by Woollam.