Supplementary material to”Transient birefringence and dichroism in ZnO

studied withfs-time-resolved spectroscopic ellipsometry”

O. Herrfurth1, S. Richter2,3, M. Rebarz3, S. Espinoza3, J. Zuniga-Perez4,C. Deparis4, J. Leveillee5, A. Schleife6, M. Grundmann1, J. Andreasson3

and R. Schmidt-Grund7

1Felix Bloch Institute for Solid State Physics, Universitat Leipzig, Leipzig, Germany.2Linkopings universitet, Institutionen for fysik, kemi och biologi, Linkoping, Sweden.

3ELI Beamlines/Fyzikalnı ustav AV CR, v.v.i., Dolnı Brezany, Czech Republic.4CRHEA-CNRS, Universite Cote d’Azur, Valbonne, France.

5Oden institute for computational engineering and sciences, The University of Texas at Austin, Austin, USA.6Dep. of Materials Science and Engineering, University of Illinois at Urbana-Champaign, Urbana, USA.

7Institut fur Physik, Technische Universitat Ilmenau, Ilmenau, Germany.

February 19, 2021

1 Noise reduction and ellipsometric data generation

In this section, we provide exemplary plots for the reflectance-difference spectra after the data reduc-tion procedure (Fig.S1) and the chirp correction (Fig.S2).

Photon energy (eV)

Ref

lect

ance

diff

eren

ce

1.5 2 2.5 3 3.5-0.5

0

0.5t = -7 ps

rawfiltered

1.5 2 2.5 3 3.5-0.5

0

0.5t = -0.15 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 0.14 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 0.4 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 0.66 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 0.92 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 1.18 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 1.44 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 1.9 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 2.9 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 4.4 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 7 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 10 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 18 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 50 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 115 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 180 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 290 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 600 ps

1.5 2 2.5 3 3.5-0.5

0

0.5t = 1500 ps

Figure S1: Reflectance-difference spectra for different time delays ∆t ps and constant compensator azimuth-angle(-69◦). Raw data are depicted in blue, filtered data in red.

1

Figure S2: Differences of the experimental ellipsometric parameters N, C, S during the first picoseconds with respectto the steady state of the ZnO thin film oriented with the optic axis parallel to the plane of incidence in the toprows (perpendicular plane of incidence in the bottom rows) The chirp of the probe white-light is fitted with an evenpolynominal indicated by the black line. Chirp correction is facilitated by readjustment of the ”true” zero delay for eachphoton energy.

2 Transient dielectric function of ZnO

Figure S3: Imaginary part of the DF tensor components in linear time delay scale. The color code features thedifference to the steady-state spectra depicted by the solid line. The dashed lines correspond to the respective spectrafor ∆t = 0.4 ps, 2.5 ps and 5 ps.

The transient dielectric function (DF, Fig. S3 and S4) was obtained from a wavelength-by-wavelengthanalysis of the ellipsometric parameters such that no assumptions on the line shape of the DF are made.Zoomed-in views on the low-energy absorption are shown in Fig. S5. A tentative local maximum is seenaround 1.75 eV, which could be related to inter-valence-band transitions or defect-related transitions.

2.1 Urbach rule analysis

In Fig.S6, we show the exponential line-shape fits to the transient absorption coefficient just belowthe bandgap.

2

Figure S4: Imaginary part of the DF tensor components for higher time delay ∆t. Note the logarithmic time-delayscale. The color code features the difference to the steady-state spectra depicted by the solid line.

0.0

0.1

0.2

0.3

0.4

0.5

1.5 2.0 2.5 3.0 3.50.0

0.1

0.2

0.3

0.4

0.5

1.5 2.0 2.5 3.0 3.5

esc 2

(a)

epc 2

Photon energy (eV)

(b)

Excitation Relaxation

Time delay (ps) -7 -0.1 0 0.1 0.2 0.4 0.7 1

Photon energy (eV)

Time delay (ps) 1 1.5 3 5 8 12 20 500

Figure S5: Same data as in Fig. 1(a, b) of the main part of the manuscript for a better view of the low-energy absorption.The left column comprises time delays around ∆t = 0 (excitation) whereas the right column shows ∆t ≥ 1 ps (relaxation).The dashed grey lines show the results from first-principles calculations accounting for 1020 cm−3 excited charge carriersat elevated temperatures [S1] and the dotted black line corresponds to the reference spectra obtained with a commercialellipsometer.

2.2 First-principles calculations

The imaginary part of the DF tensor components of ZnO for different electron-hole pair densitycalculated from first principles is shown in Fig.S7.

References

[S1] Steffen Richter, Oliver Herrfurth, Shirly Espinoza, Mateusz Rebarz, Miroslav Kloz, Joshua Lev-eillee, Andre Schleife, Stefan Zollner, Marius Grundmann, Jakob Andreasson, and RudigerSchmidt-Grund. Ultrafast dynamics of hot charge carriers in an oxide semiconductor probedby femtosecond spectroscopic ellipsometry. New Journal of Physics, 2020. doi:10.1088/1367-2630/aba7f3.

3

2.8 3.0 3.2 3.4 3.6

1×105

1×106

1×107

2.8 3.0 3.2 3.4 3.6Photon energy (eV)

ordinary ray

a (

m-1)

Photon energy (eV)

extra-ordinary ray

Figure S6: Exponential fits to the absorption coefficient of the ordinary and extra-ordinary ray in the range of timedelays ∆t = −100 . . . 300 fs.

0.001 0.01 0.1 1 2 3 40

1

2

3

4

5

6

e 2

Energy (eV)

1020 cm-3

1019 cm-3

without e-h pairs

Figure S7: First-principles calculation of the imaginary Part of the DF tensor components for different electron-hole-pair densities. It constitutes an ideal bulk-ZnO DF in contrast to the thin film measured here. The energy of theabsorption edge is lower (no strain effect) and features a higher amplitude (ideal crystal structure).

4