Modeling Ellipsometry for SrTiO3 MBE Epitaxial Films on 

Si(100)

by Daniel M. Potrepka

ARL-TR-5435 January 2011

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ARL-TR-5435 January 2011 

Modeling Ellipsometry for SrTiO3 MBE Epitaxial Films on 

Si(100) 

Daniel M. Potrepka

Sensors and Electron Devices Directorate, ARL

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Modeling Ellipsometry for SrTiO3 MBE Epitaxial Films on Si(100) 

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14. ABSTRACT 

SrTiO3 (STO) was deposited onto silicon using Molecular Beam Epitaxy (MBE). In order to characterize the sample, x-ray 

diffraction (XRD) measurements were made for the film, and the optical constants were obtained from ellipsometry 

measurements. STO XRD showed that the STO was textured with rocking curve full width at half maximum (FWHM) 0.65 +

0.07 degrees. Optical constants were obtained from fitting of the film’s ellipsometric parameters, Psi and Delta, and the 

thickness of the STO film was determined to be 23.6 nm. Preliminary deposition of PbZr0.52Ti0.48O3 (PZT) showed the presence 

of only the 100 orientation for PZT XRD peaks. 

15. SUBJECT TERMS

STO on Si, ellipsometry, x-ray diffraction, modeling, optical constants, thickness 

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iii

Contents

List of Figures iv

List of Tables iv

1. Introduction 1

2. Experiment 1

3. Results and Discussion 2

3.1 X-ray Diffraction .............................................................................................................2

3.2 Ellipsometry ....................................................................................................................5

3.3 Optical Constants ............................................................................................................6

3.4 Thickness of the STO ......................................................................................................8

3.5 PZT XRD Characterization .............................................................................................8

4. Conclusion 9

5. References 10

Distribution List 11 
iv

List of Figures

Figure 1. (a) XRD scan for MBE-grown STO on Si (100)—samples T0061, T0083, and 

T0084, and (b) same but at full intensity range to show height of Si (400) peak. .....................2

Figure 2. STO rocking curves for (a) 200 and (b) 400 x-ray peaks of STO. ..................................4

Figure 3. Ellipsometry parameters for STO on Si (100) sample T0083 at angles of incidence 

55, 60, 65, 70, and 75 degrees....................................................................................................5

Figure 4. Optical constants for 20 nm STO/Si deposited by MBE resemble those of a bulk 

STO sample (h = 4.13566733(10)×10−15 eV*s). ........................................................................7

Figure 5. Oriented PZT on STO/Si sample T0061. ........................................................................9

List of Tables

Table 1. X-ray diffraction peak positions for 200 and 400 STO peaks. .........................................3

Table 2. X-ray diffraction statistics for rocking curve scans of the 200 and 400 STO peaks. 

FWHM and XC are in degrees (2θ) ............................................................................................5
v

Acknowledgment

The author wishes to acknowledge Eric Readinger (Veeco Instruments Inc.) for preparation of 

the STO/Si sample, Luz Sanchez (ARL) for processing the PZT, and Ron Synowicki (J.A. 

Woollam Co., Inc.) for his many discussions about ellipsometer modeling. 
vi

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1

1. Introduction

SrTiO3/silicon (STO/Si) wafers with high crystalline quality and smooth surface morphology are 

highly desirable for developing novel devices such as next generation dynamic random access 

memory and oxide field effect devices. Very high quality STO/Si epitaxial wafers are being 

investigated to prepare for production using the Molecular Beam Epitaxy (MBE) platform (1). 

This focus on high quality STO on Si has, in turn, stimulated interest in STO/Si as a platform for 

templating PbZr0.52Ti0.48O3 (PZT) growth. It is desirable to improve PZT 100 orientation for 

device applications in order to maximize the d31 piezo response, thereby achieving maximum 

electrical response in the 100 direction in order to maximize stress orthogonal to the 100 

orientation. 

This work will characterize MBE-grown STO/Si through ellipsometric measurement of the STO 

and compare the results to those for similar measurements on bulk and thin film STO in the 

literature. In this work, ellipsometric measurements were made on STO/Si deposited after in situ 

Si procedures to clean the surface and remove native oxide, and pre-deposition of a template 

seed layer. The STO film is characterized by x-ray diffraction (XRD) measurements, and its 

thickness was obtained after modeling of the ellipsometric data. A PZT film deposited on the 

STO was subsequently characterized and found to be oriented in the 100 direction, ideal for PZT 

growth.

2. Experiment

Three 20 nm thick STO films, supplied by Veeco Inst. Inc., were deposited under similar 

conditions onto ozone-cleaned Si 100 using a Veeco GEN 10 Automated MBE system, with 

proprietary control of oxygen pressure (< 2.0 % deviation) and ramp rate (2). 

I made XRD measurements for all the films using a Rigaku Ultima III diffractometer, with a 

CuKα x-ray source (tube) in the Bragg Brentano (focusing) measurement mode. A θ-2θ scan 

was made at 20–110° using a 0.01° step width, and a 1 deg/min scan rate for 2θ. Rocking curves 

were then measured for the 200 and 400 peaks at 0.02° step width, and a 1 deg/min scan rate, 

varying θ over a range of 21–25° while holding 2θ fixed at the peak maximum measured in the 

θ-2θ scan. The full width at half maximum (FWHM) was then computed for each rocking curve. 

I obtained ellipsometric parameters Ψ and ∆ of the STO/Si using the Woollam M200F 

ellipsometer. For these measurements, the angle of incidence was varied over the range of 55–

75°, and the photon source provided measurements over the range of 200–1000 nm. The data 

was analyzed with WVase 32 software provided by the J.A. Woollam Co., Inc. in order to obtain 
2

optical constants and a model for STO/Si. This was used to compute the thickness of the STO 

films.

Four layers of PZT were deposited onto a PbTiO3 seed layer on the STO Sample #T0061 by 

MOSD spin-on method. Pyrolysis was done at 350 °C for 2 min (not strict ramp schedule), then 

an RTA anneal was done by ramping the temperature at 4 °C per minute to 700 oC and holding 

temperature for 60 s. The PZT was then characterized by XRD. For this, a scan at 20–110° was 

used with a 0.01° step-width and a scan rate of 1 deg/min in 2θ.

3. Results and Discussion

3.1 X-ray Diffraction

Figure 1a shows that the strained Si 200 peak occurs for Sample T0061, and that textured STO is 

indicated by the presence of the 100, 200, and 400 STO peaks. For reference, figure 1b shows 

the height of the Si 400 peak, which is cut off at the top of figure 1a. 

20 40 60 80 100 120

0

1x104

2x104

Intensity (cps)

2θ

T0061

T0083

 T0084

(400)

(200)

(100)

Strained

Si(200)

Si(400)

20 40 60 80 100

0

1x105

2x105

3x105

Intensity (cps)

2θ

Figure 1. (a) XRD scan for MBE-grown STO on Si (100)—samples T0061, T0083, and T0084, and 

(b) same but at full intensity range to show height of Si (400) peak.

The positions of the 200 and 400 STO peaks are given in table 1 in degrees (2θ). Variations in 

position can be attributed to slight misorientation of the Si crystal from sample to sample, 

relative to the normal in the x-ray holder. An external alumina standard was used to verify 

repeatability of wafer placement in the sample holder, with repeatability of the 012, 116, and 226 

Al2O3 peaks. Variations in position were verified to be ~ 0.02 < degrees over the course of 20 

placements of the standard into the sample holder over a 4-month time-span around the time of 

the measurement. These alumina standard measurements documented the stability of the 

alignment of the x-ray tube, sample, sample holder, and detector as well as negligible aging 

effects in the x-ray tube for the duration of the measurement period.
3

Table 1. X-ray diffraction peak positions for 200 and 400 STO peaks. 

Figures 2a and 2b show the rocking curves for the 200 and 400 STO peaks. Using equation 1, a 

Pearson VII fit was performed on the rocking curve XRD statistics. The peak position (XC), peak 

area (A), and FWHM (w in equation 1) that were generated are given in table 2, along with the 

dimensionless parameter μ. 
4

(a)

(b)

Figure 2. STO rocking curves for (a) 200 and (b) 400 x-ray peaks of STO.

y = A 2√μe

�Γ�21⁄μ−1��

πe�Γ(μ−0.5)�W [1 + 4 21⁄μ−1

W2 (x − xc)2]

−μ (1)

0

2000

4000

6000

8000

10000

12000

14000

16000

18000

21 22 23 24 25

Intensity (cps)

Theta (deg)

Veeco STO(200) Rocking Curve

T0061

T0083

T0084

-100

0

100

200

300

400

500

600

700

800

50 51 52 53 54

Intensity (cps)

Theta (deg)

Veeco STO(400) Rocking Curve

T0061

T0083

T0084
5

Table 2. X-ray diffraction statistics for rocking curve scans of the 200 and 400 STO peaks. FWHM and XC are in 

degrees (2θ).

 

Sample FWHM(200) Xc(200) A(200) μ (200) FWHM(400) Xc(400) A(400) μ (400)

T0061 0.57699 23.20149 22624.22 1.38862 0.68344 52.1224 876.0439 28.79689

T0083 0.65229 23.26177 20668.58 169.26792 0.66636 52.24845 908.8244 170.3579

T0084 0.70936 23.3839 19524.41 7.97372 0.71006 52.29615 839.1938 6.13653

Sample #T0061 and T0083 exhibit slightly sharper rocking curve peaks than that of Sample 

#T0084 as shown by their smaller FWHM, 0.67-0.68° versus 0.71°.

3.2 Ellipsometry

The experimental optical parameters, Ψ and Δ, obtained by ellipsometry measurements are 

shown in figure 3. These are related to the reflectance coefficients, RP and RS, by 

tan(Ψ) ei∆ = RP

RS

 , (2)

which in turn are related to the optical constants through appropriate modeling to Fresnel’s 

equation (3–5).

200 400 600 800 1000

-100

-50

0

50

100

150

200

250

300

55 deg

60 deg

65 deg

70 deg

75 deg

∆ (deg)

λ (nm)

200 400 600 800 1000

0

10

20

30

40

Ψ (deg)

λ (nm)

Figure 3. Ellipsometry parameters for STO on Si (100) sample T0083 at angles 

of incidence 55, 60, 65, 70, and 75°.

Data analysis proceeds as follows (6): after a sample is measured, a model is constructed to 

describe the sample. The model is used to calculate the predicted response from Fresnel’s 

equations, which describe each material with thickness and optical constants. If these values are 

not known, an estimate is given in order to provide a preliminary calculation. The calculated 
6

values are compared to experimental data. Any unknown material properties can then be varied 

to improve the match between experiment and calculation. The number of unknown properties 

should not exceed the amount of information contained in the experimental data. For example, a 

single-wavelength ellipsometer produces two data points (Ψ, Δ), which allows a maximum of 

two material properties to be determined. Finding the best match between the model and the 

experiment is typically achieved through regression. An estimator, like the Mean Squared Error 

(MSE), is used to quantify the difference between curves. The unknown parameters are allowed 

to vary until the minimum MSE is reached. The best answer corresponds to the lowest MSE. 

3.3 Optical Constants

The optical constants for a material will vary for different wavelengths and must be described at 

all wavelengths probed with the ellipsometer (6). A table of optical constants can be used to 

predict the material’s response at each wavelength. However, it is not very convenient to adjust 

unknown optical constants on a wavelength-by-wavelength basis. It is more advantageous to use 

all wavelengths simultaneously. A dispersion relationship often solves this problem by 

describing the optical constant shape versus wavelength. The adjustable parameters of the 

dispersion relationship allow the overall optical constant shape to match the experimental results. 

Compared to fitting individual n, k values at every wavelength, this greatly reduces the number 

of unknown “free” parameters. For transparent materials, the index is often described using the 

Cauchy or Sellmeier relationship.

A point-by-point fit was made relating the optical constants to the optical parameters allowing 

the sample thickness to vary in order to generate the optical constants consistent with Fresnel’s 

equation. These are plotted versus the photon energy in figure 4 (h = 4.13566733(10)×10−15

eV∗s). The modeling for this analysis involved solving the Fresnel equationsfor an adjustable 

parameter optical model with:

• a Cauchy layer with Urbach absorption as the starting model to represent the STO (7) 

• the underlying Si wafer represented as a fixed model - a Si crystal 1 mm thick according to 

the model of (8). 
7

Figure 4. Optical constants for 20 nm STO/Si deposited by MBE resemble those 

of a bulk STO sample (h = 4.13566733(10)×10−15 eV*s).

Four Gaussian Oscillators were used in the oscillator model for STO. The oscillators can be 

described by a Gaussian lineshape in ε2 with a Kramers-Kronig consistent line shape for ε1 (9–

11)

εn_Gaussian = εn1 + iεn2, (3)

εn2 = Ane−�

E−En

σ �

2

− Ane−�

E+En

σ �

2

, (4)

σ = Brn

2�Ln(2)

, (5)

εn1 = 2

π P ∫ ξεn2(ξ)

ξ

2−E2 dξ ∞

0 , (6)

where the 1/2�ln (2) factor sets the broadening parameter, and Brn = FWHM.

Comparing our optical constants (figure 4) to those reported by others (4, 12–14) for single 

crystal STO, we find that our curves are the same except for minor local variations in magnitude. 

Our refractive index plot, n, versus energy exhibits local maxima with similar magnitudes at 

4.0 eV and 4.8 eV. Our extinction coefficient plot, k, versus energy exhibits the same absorption

onset at 3.71 eV, and turning points of approximately the same magnitude at 4.3 eV, 4.7 eV, and 

4.5 eV. Van Benthem obtained direct and indirect band gap energies using linear fits to the 

optical absorption coefficient (α = 4πk/λ) calculated from the ellipsometric extinction coefficient 

(4). These band-gap energies can vary depending on the range of absorption coefficients used in 

the linear fit (15). Comparing our data to that obtained by Zollner for both bulk and thin film 

STO (12), we found that unlike the films he studied, our data closely resembles that of his bulk 

STO plots as well as those of the van Benthem (4), Palik (13), and Trepakov (14) experimental 

groups, exhibiting similarly well-resolved structure at 3–5 eV.

0

0.5

1

1.5

2

2.5

3

3.5

0 2 4 6

Optical Constants

Energy (eV)

n

k 
8

3.4 Thickness of the STO

Thickness measurements are not independent of the optical constants (6). The film thickness 

affects the path length of light traveling through the film, but the index determines the light 

waves’ velocity and refracted angle. Thus, both contribute to the delay between surface 

reflection and light traveling through the film. Both n and k must be known or determined, along 

with the thickness, to get the correct results from an optical measurement. The film thickness is 

determined by interference between light reflecting from the surface and light traveling through 

the film. Depending on the relative phase of the rejoining light to the surface reflection, 

interference can be defined as constructive or destructive. The interference involves both 

amplitude and phase information. The phase information from Δ is very sensitive to films down 

to sub-monolayer thickness. Ellipsometry is typically used for films whose thicknesses range 

from sub-nanometers to a few microns. Thickness measurements also require that a portion of 

the light travel through the entire film and return to the surface, limiting absorbing materials to 

thin semi-opaque layers or spectral regions with little or no absorption. The MSE (16) can be 

expressed as

MSE(Ψ, ∆) = � 1

2N−M χ2, (7)

where N is the number of (Ψ, ∆) pairs, M is the number of variable parameters in the model, and 

χ = χ(σΨ , σ∆) is the chi square, with σΨ and σ∆ representing the standard deviations on the 

experimental Ψ and ∆ data points, respectively. A valid MSE is typically equal to 10 or less. 

Using our final model for STO on a 1 mm thick Si substrate, we computed the thickness and 

MSE of the STO on (at least) 1 mm Si, and found them to be 23.592 nm and 0.9492, respectively 

(Sample #T0083). 

The measured thickness is consistent with the predicted (~ 20 nm) thickness that is based on 

atom flux and growth time in the MBE, plus modeling of x-ray reflectivity measurements.

3.5 PZT XRD Characterization

The θ-2θ XRD plot of the PZT deposited on the STO (figure 5) confirms the desired 100 

orientation with the presence of strong 100 (I = 2x105 cps), 200 (I = 1x105 cps), and 400 PZT 

peaks near 21.6, 45, and 99 deg, respectively. The small 110 and 310 PZT peaks suggest the 

presence of a relatively small randomly-oriented PZT component. 
9

20 40 60 80 100

0

1x103

2x103 Intensity (cps)

2θ (degrees)

PZT&STO (100)

PZT(110) Strained Si(200)

PZT&STO (200)

Si(400) PZT(310)

PZT(400) STO(400)

Figure 5. Oriented PZT on STO/Si sample T0061.

4. Conclusion

STO/Si was successfully modeled to obtain optical constants n and k consistent with values 

reported for single crystal STO in the literature, and superior compared to n and k reported in the 

literature for non-MBE films prepared on various substrates.

After generalized oscillator modeling, the thickness and MSE of the STO were computed and 

found to be 23.592 nm and 0.9492, respectively. The thickness is consistent with x-ray 

reflectivity measurements and predictions based on atom flux and growth time in the MBE. The 

PZT deposited on the STO is oriented in the 100 direction. A rocking curve analysis would 

enhance this study through quantitative characterization of the level of texture and orientation for 

further optimization of PZT/STO/Si film processes.
10

5. References

1. Gu, X.; Lubyshev, D.; Batzel, J.; Fastenau, J. M.; Liu, W. K.; Pelzel, R.; Magana, J. F.; Ma, 

Q.; Rao, V. R. Growth, Characterization, and Uniformity Analysis of 200 mm Wafer-scale 

SrTiO3/Si. J. Vac. Sci. Tech. B 2010, 28 (3), DOI: 10.1116/1.3292509, 2010.

2. Veeco film preparation – private communication from Eric Readinger, 2010. 

3. Guide to using WVASE32®. J.A. Woollam Co. Inc., pp. 40–51, 2008. 

4. van Benthem, K.; Elsässer, C.; French, R. H. Bulk Electronic Structure of SrTiO3: 

Experiment and Theory. J. Appl. Phys. 2001, 90 (12), 6156. 

5. Toussaint, U. V.; Schwarz-Selinger, T.; Hopf, Christian. AIP Conference Proceedings 872,

272–279 (2006). 

6. Ellipsometry Tutorial, http://www.jawoollam.com/ (accessed 2010). 

7. Guide to using WVASE32®. J.A. Woollam Co. Inc., p. 250 2008. 

8. Herzinger, C. M.; Johs, B.; McGahan, W. A.; Woollam, J. A.; Paulson, W. Ellipsometric 

Determination of Optical Constants for Silicon and Thermally Grown Silicon Dioxide via a 

Multi-sample, Multi-wavelength, Multi-angle Investigation. J. Appl. Phys. 1998, 83 (6), 

3323. 

9. Guide to using WVASE32®. J. A. Woollam Co. Inc., p. 275. 2008. 

10. De Sousa Meneses, D.; Malki, M.; Echegut, P. J. Non-Cryst. Solids 2006, 351 (2), 769: 

Section 3. 

11. Peiponen, K.-E.; Vartiainen, E. M. Phys. Rev. B 1991, 44 (15), 8301. 

12. Zollner, S.; Demkov, A. A.; Liu, R.; Fejes, P. L.; Gregory, R. B.; Curless, J. A.; Yu, Z.; 

Ramdani, J.; Droopad, R.; Tiwald, T. E.; Hilfiker, J. N.; Woollam, J. A. Optical Properties 

of Bulk and Thin-film SrTiO3 on Si and Pt. J. Vac. Sci. Technol. B 2000, 18 (4), 2242. 

13. Handbook of Optical Constants of Solids II, edited by E. D. Palik (Academic, San Diego, 

CA, 1991).

14. Trepakov, V.; Dejneka, A.; Markovin, P.; Lynnyk, A.; Jastrabik, L. 2009, 11, 083024. 

15. Matteis, L. F. Phys. Rev. B 1972, 6, 4718. 

16. Guide to using WVASE32®. J.A. Woollam Co. Inc., p. 54, 2008. 
11

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