Supporting Information:
Measuring Photoexcited Electron and Hole Dynamics in ZnTe and Modeling Excited State
Core-Valence Effects in Transient Extreme Ultraviolet Reflection Spectroscopy
Hanzhe Liu,
1,2,*
Jonathan M. Michelsen,
1,*
Jocelyn L. Mendes,
1
Isabel M. Klein,
1
Sage R. Bauers,
3
Jake M. Evans,
1
Andriy Zakutayev,
3
Scott K. Cushing
1,†
1
Division of Chemistry and Chemical Engineering, California Institute of Technology, Pasadena,
CA 91125, USA.
2
Department of Chemistry, Purdue University, West Lafayette, IN 47907, USA.
3
Materials Science Center, National Renewable Energy Laboratory, Golden, CO 80401, USA.
*
These authors contributed equally.
†
Corresponding author. Email:
scushing@caltech.edu
Supporting Information Overview
S1. Dopant characterization of intrinsic bulk ZnTe
S2. Growth and structural characterization of sputter-deposited ZnTe thin films
S3. Ground state optical sample characterization
S4. Experimental setup: Transient extreme ultraviolet reflection spectrometer
S4.1. Characterization of few-cycle white light pulse for XUV pulse generation
S4.2. Representative XUV probe spectrum
S5. Theoretical methods: Ground state and excited state core-level spectra
S5.1. Ground state calculation
S5.2. Excited state calculation
S6. Transient XUV spectra on ZnTe thin films and under different pump intensities
S7. Nanosecond transient XUV measurement
S1. Dopant characterization of intrinsic bulk ZnTe
To rule out the possibility of mid-gap defect states that could potentially lead to the
experimentally observed transient decrease in reflectivity within the gap, we perform X-ray
photoemission spectroscopy (XPS) and a 4-point probe measurement on intrinsic bulk ZnTe.
Figure S1 shows an XPS survey on bulk ZnTe. While carbon and oxygen on the surface
are observed, there is no evidence for hetero-atom dopants. Quantification furthers shows a
roughly 50:50 Zn:Te ratio. Figure S2 shows the 4-point probe measurements. The resistivity is
measured to be
. The dopant density is related to the resistivity via
휌
=
(
1.26
±
0.3
)
×
10
9
Ω
푐푚
푛
, where is carrier mobility and is estimated to be
. The dopant
휌
=
1
푒휇푛
휇
휇
≈
100
푐푚
2
푉
―
1
푠
―
1
density is estimated at
. The dopant density is too small to be responsible for the
5
×
10
7
푐푚
―
3
observed mid-gap transient spectral feature, whose amplitude is comparable to the transient
reflectivity change caused by high concentrations of photoexcited carriers at
.
10
20
푐푚
―
3
Figure S1. XPS measurements on intrinsic bulk ZnTe. Carbon and oxygen are observed on the
surface. No hetero-atom dopants are observed.
Figure S2. 4-point probe measurements of resistivity and dopant density on intrinsic bulk ZnTe.
S2. Growth and structural characterization of sputter-deposited ZnTe thin films
ZnTe thin films were prepared on a 50.8 mm x 50.8 mm Corning EXG glass substrate by
RF sputtering from a ZnTe target. A stainless-steel 130
μ
m thick shadow mask was placed over
the substrate to create two distinct regions: a large blanket film and smaller discrete patterns. The
substrate + mask assembly was clamped to an Inconel plate which was heated by a SiC serpentine
resistance heater. The plate was held at the setpoint of 300 °C for a minimum of 1 hour prior to
deposition. Chamber pressure at this temperature was 3 x 10
-7
Torr prior to flowing any process
gases. During the sputter process, 16 sccm of Ar was flowed through the system and the pumping
was throttled to achieve the desired growth process pressure of 2.7 mTorr. The plate was rotated
at approximately 30 revolutions per minute during the 2-hour growth. Samples were cooled under
Ar prior to being removed from the growth chamber.
The blanket region of the ZnTe film was characterized by X-ray diffraction (XRD) at 22
distinct points (Figure S3) to verify structural uniformity as a function of position. XRD patterns
were collected by a 2D solid state detector scanning in an
ω
-2
θ
geometry using Cu-
K
α
radiation.
Figure S4 shows the resulting XRD patterns for all 22 points as a false color plot. No appreciable
changes were observed in diffraction patterns between points. An intensity vs. 2
θ
line scan from
point 10 is also shown. Comparing the experimentally measured diffraction pattern against a
simulated pattern generated using a reference ZnTe crystallographic information file (Inorganic
Crystal Structure Database entry #77072), we find that the peak positions match and the ZnTe film
adopts the expected zincblende crystal structure. The high relative intensity of the (111) peak at
ca. 25° in the experimental data (versus the reference pattern) is attributed to crystallographic
texture.
Figure S5 shows film thickness measurements collected from three different regions using
a stylus profilometer. The regions were from the masked portions of the film and geometrically
equivalent to the positions of points 3, 9, and 17 (Figure S3). Raw profilometry data were notably
sloped and bowed. A first-order polynomial subtraction was carried out to flatten the profiles over
the region of interest (i.e., the masked ZnTe sample), but higher-order bowing was ignored. As
seen in Figure S3, the sampled points are ca. 400-450 nm thick. It is difficult to pinpoint whether
any discrepancies between the points are due to nonuniformity or experimental factors, such as
substrate topology, shadowing from the stainless-steel mask. 100 nm thick calibration samples
grown with nominally identical chamber conditions were measured by X-ray reflectometry (XRR),
and thicknesses over a similar area were uniform to ±2 nm with <1 nm RMS roughness.
Figure S3.
Spatial map of point locations on a 25.4 mm by 50.8 mm region of the glass substrate
used to verify uniformity of ZnTe thin films.
Figure S4.
X-ray diffraction from the ZnTe thin films. The false color map shows uniformity of
the XRD patterns from the 22 sampled points. A reference pattern (generated from Inorganic
Crystal Structure Database entry #77072) and line scan (collected from point 10) presented using
more typical intensity vs. 2-theta axes are also provided.
Figure S5:
Stylus profilometry collected from ZnTe thin films. Data were collected from a part of
the substrate with masked regions, with the points being symmetrically equivalent during growth
to those shown in Figure S3.
S3. Ground state optical sample characterization
The band gap of both bulk and thin film ZnTe was determined using UV-VIS
spectroscopy (Cary 5000) (Figure S6, S7). The PRISA software was used to calculate the
bandgap of the thin film sample while also mitigating thin-film interference effects
1
. Figures S6
and S7 present
(αhν)
1/r
vs energy plots where r = 1/2 for direct allowed transitions. The estimated
direct bandgap is found to be 2.19 eV and 2.18 eV for bulk and thin films, respectively.
Figure S6:
Tauc plot of the ZnTe bulk. The direct band gap is measured to be 2.19 eV.
Figure S7
: Tauc plot of ZnTe thin film. The direct band gap is measured to be 2.18 eV.
S4. Experimental setup: Transient extreme ultraviolet reflection spectrometer
The reported bulk ZnTe measurements are obtained using photoexcitation of a ~50 fs, 400
nm frequency doubled output of a BBO crystal with p-polarization, pumped with an 800 nm, 1
kHz regeneratively amplified Ti:Sapphire laser (Coherent Legend Elite Duo). The optical
excitation fluence is 1.74 mJ/cm
2
, resulting in an initial photoexcited carrier density of 5.41 × 10
20
cm
-3
. Transient reflection is measured by varying delay times between the excitation and probe
pulses using an optomechanical delay stage. The photoexcited carrier dynamics are probed with
an XUV pulse produced by high-harmonic generation in argon with an s-polarized few-cycle white
light pulse (<6 fs, 550 nm - 950 nm, Figure S8). The residual white light beam is removed with a
200 nm thick Al filter (Lebow). The generated XUV continuum is used to probe the Te N
4,5
absorption edges around 40 eV. A typical XUV spectrum is shown in Figure S9. An edge-pixel
referencing scheme was used to reduce noise due to intensity fluctuations based on signal-free
spectral regions.
2
The reflection measurement uses a 10-degree grazing incidence geometry (80
degrees from normal incidence).
The static sample reflectivity around the Te N
4,5
edge is shown in Figure S10. The
reflectivity decreases around the conduction band minimum (around 40 eV from Te 4d core states).
The static XUV reflectivity of ZnTe is found by dividing the measured static reflectivity spectrum
of ZnTe by the static reflectivity of a Si wafer, which does not have any absorption features in this
energy region.
S4.1. Characterization of few-cycle white light pulse for XUV pulse generation
A dispersion scan (d-scan, Sphere Ultrafast Photonics)
3
was used to characterize the
broadband white light few-cycle pulse used for XUV pulse generation. In this method, a pair of
glass wedges with known dispersion are inserted in the beam path. The second harmonic spectra
of the white light generated with a BBO crystal are measured as a function of introduced dispersion
through wedge insertion. The electric field of the few-cycle pulse can be retrieved based on the
reconstruction algorithm of the d-scan trace.
Figure S8
. Characterization of few-cycle white light pulse with dispersion scan (d-scan). (a)
Measured second harmonic spectra as a function of wedge insertion. (b) Reconstructed d-scan
trace. (c) White light spectrum (red line), spectral phase (blue line) and polynomial fit of the
spectral phase (black line). (d) Retrieved white light pulse has an intensity profile with a temporal
FWHM of 4.9 fs.
S4.2. Representative XUV probe spectrum
The XUV probe pulse is produced through high-harmonic generation in an Ar gas cell.
Figure S9 shows a representative normalized XUV spectrum reflected from ZnTe with a 10 degree
incident angle (80 degrees from normal incidence).
Figure S9.
Representative reflected XUV spectrum from ZnTe with a 10 degree incident angle
relative to the sample surface (80 degrees from normal incidence). The energy range of the selected
spectrum is defined by the physical size and position of the detector to cover the Te N
4,5
edge.
S5. Theoretical methods: Ground state and excited state core-level spectra
To fully analyze the transient core-level spectra, state blocking, and the associated changes
in screening of the core-valence exciton must be considered, as well as any potential change in
spin-orbit coupling and angular momentum effects. These changes are calculated using an ab initio
combined theoretical approach based on density functional theory (DFT) and the Bethe-Salpeter
equation (BSE). The existing OCEAN code
4,5
(Obtaining Core-level Excitations using Ab-initio
calculations and the NIST BSE solver) is modified to accept excited state distributions to
determine how the ground state band structure relates to the observed XUV spectra and transient
changes. In this procedure, the band structure and the ground state wavefunction are first calculated
using DFT (Quantum Espresso)
6
. The BSE is solved to obtain core-valence exciton wavefunctions
including spin-orbit coupling and Coulomb screening of the core-valence exciton. The reflectivity
spectra are calculated from the complex dielectric function as calculated by OCEAN and converted
using the Fresnel equations.
S5.1. Ground state calculation
XUV reflection spectra were calculated with the OCEAN
4,5
code based on a converged
DFT calculation
6
. The DFT and BSE calculations are solved using a 20 × 20 × 20 k-point mesh.
We use 9 valence bands and 31 conduction bands in our calculation. The DFT calculation uses the
norm-conserving generalized gradient approximation (GGA), Perdew-Burke-Enzerhof (PBE)
pseudopotentials, a 300 Rydberg energy cut-off, and a converged lattice constant of 6.10 Å. The
OCEAN code uses the projector augmented wave method (PAW) to calculate core-level transition
matrix elements, which are then used in the BSE equation to calculate final states as modified by
the core hole. The OCEAN BSE calculation uses a screening mesh of 4 × 4 × 4, a dielectric
constant of 10.4, a 4.0 Bohr screening radius, and a 0.7 scaling factor for the slater G parameter.
A post-calculation broadening is used as a fitting method to achieve similar linewidth to that
observed in the experiment. The DFT calculation underestimates the band gap of ZnTe. After DFT
calculation, we add a band gap correction by scissor shifting conduction bands up by 1.02 eV to
achieve a correct band gap. In this theoretical framework, both the real and imaginary dielectric
function are directly calculated in the OCEAN code, allowing easy comparison between theory
and experiments done in transmission or reflection configurations.
Figure S10 shows the calculation of the ground state complex dielectric function (Figure
S10(a)), as well as the calculated reflectivity, overlaid with the experimentally measured static
sample reflection around the Te N
4,5
edge (Figure S10(b)). The measured ZnTe XUV reflection is
normalized to a Si wafer, which doesn’t exhibit any sharp spectral features around 40 eV. By
referencing to Si, the typical high-harmonic intensity profile is removed from the static reflection
spectrum. However, the absolute reflectivity of ZnTe and Si is difficult to obtain as variance of
sample surface roughness affects XUV reflectivity, such as Debye-Waller factors. For this reason,
a normalized reflectivity is shown in Figure S10(b).
As shown in Figure S10, the OCEAN calculation reproduces Te edges. However, it
underestimates the pre-edge absorption. In OCEAN, the calculation assumes perfect crystals,
where there is no pre-edge absorption. For actual samples used in experiments, many effects can
contribute to the pre-edge absorption, including but not limited to an imperfect crystal lattice,
surface states, an imperfect bonding environment, and surface-modified lattice configurations. We
note that the discrepancy between the calculated and measured ground state reflection plays a
much lesser role in the excited states interpretation. The reason is that for the excited states
calculation, we compare the changes in transient reflectivity, defined as
.
∆푂퐷
=
―
log
10
(
퐼
푝푢푚푝
표푛
퐼
푝푢푚푝
표푓푓
)
Under this definition, systematic error such as underestimated pre-edge absorption largely cancels
during the normalization between pump on and pump off spectra.
Figure S10
.
(a)
Calculated ground state complex dielectric constant.
(b)
Calculated ground state
reflectivity, overlaid with experiment. Experimentally measured refection is normalized to a Si
wafer to remove the high harmonic profile in the spectra.
S5.2. Excited state calculation
To capture the photoexcited electrons and holes, we modify the OCEAN package, which allows
us to selectively forbid or allow XUV transitions to the conduction or valence bands at different
momentum k-points. In this experiment, we aim to understand carrier thermalization from the
initial photoexcited states to the band gap minimum at the
Γ
point. To simulate this charge transfer
process, we discretize the states between the initial photoexcited states and the final states across
the direct band gap at the
Γ
point into a combination of 9 different electron configurations in the
conduction bands and 9 different hole configurations in the valence band. The discretization is
based on the energy difference between conduction and valence bands. As a result, each discretized
electron and hole configuration consist of multiple k-points in momentum space. The calculated
excited states spectra of the total 81 combined electron and hole configurations is shown in Figure
S11. The calculation is performed on a 20 × 20 × 20 mesh in k-space. Under this condition, both
electron and hole thermalization can be seen, with electron and hole energy resolution at ~60 meV
(calculated carrier energy difference between neighboring hole configurations). Better resolution
can be further achieved by increasing the k-space sampling rate or interpolating the spectra
between adjacent carrier distributions.
The momentum-resolved differential XUV transition probability amplitudes in Fig. 2(b)
are calculated by solving the core-valence wavefunctions using the OCEAN generalized minimal
residual method (GMRES) solver instead of the Haydock method used for calculations of spectra
7
.
When comparing theory with experiment, it is worth noting that in the excited states
calculation, we do not input the actual carrier density (in units of 10
20
/cm
3
) in our calculation.
Rather, we fully allow or forbid XUV transition to certain states in the conduction or valence
bands. For this reason, we do not simulate carrier density evolution as a function of time, which is
encoded in spectral intensity and is related to recombination and diffusion. It is the simulated peak
position, or peak energy (related to the hot carrier energy), rather than peak amplitude (associated
with carrier density) that we use to compare between experiment and theory.
A tentative reconstruction of the transient data is shown in Figure 2(c) of the manuscript,
where we fit the calculated excited state spectra to the measured transient spectra at each pump-
probe time delay. The reconstruction is performed for the first 800 fs after photoexcitation, before
phonon modulation dominates the spectra while the carrier relaxation largely finishes. Initial hot
electron and hole thermalization is observed in the theoretical reconstructed transient XUV spectra.
While an overall thermalized trend can be reconstructed, in the current example it is difficult to
assign the measured transient reflectivity at each pump-probe delay to a unique carrier
configuration. The resolution is limited by k-space sampling rate, small excess kinetic energy of
carriers from photoexcitation, and spectral fluctuations from the experiment. This method will
work best when the hot carriers have large excess kinetic energy compared to the band gap and
when the band structure is highly dispersive. In principle, this approach allows the theory to
reproduce state filling effects, carrier energy and momentum distributions, and relaxation
pathways, which could be of importance in various solar-driven semiconductor processes such as
multi-exciton generation.
Figure S11
. Calculated excited state XUV differential spectra under different carrier
configurations. States between the initial photoexcitation and the final states at the
Γ
point are
discretized into 9 electron energy configurations and 9 holes energy configurations, with a
combined total 81 unique electron-hole energy configurations. In this plot, 81 configurations are
plotted and sorted by increasing electron and hole energy. For example, the carrier configuration
indices (y axis) 1 to 9 corresponds to having holes fixed at the lowest energy states (around the
Γ
point), while sweeping 9 electron configurations from low energies to high energies. Similarly, the
carrier configuration indexes 10 to 18 plot the same 9 electron configurations, but under a different
hole configuration with a higher hole energy. Clear electron and hole thermalization can be seen
in this plot.
S6. Transient XUV spectra on ZnTe thin films and under different pump intensities
The many-body nature of the mid-gap transient spectral feature reported in Figure 1 is
further confirmed by performing a transient XUV reflection measurement on high quality ZnTe
thin films (sample characterization in Supplementary Information section S2). The transient XUV
reflection spectra are shown in Figure S12. In Figure S12(a), a similar mid-gap transient spectral
signature is observed, as compared to the bulk ZnTe measurement reported in the main text. This
measurement rules out the possibility of the mid-gap response being dependent on the method of
sample growth, and strongly suggests that it is an intrinsic response of ZnTe, regardless of sample
growth methods. We further conclude that the mid-gap response depends on the photoexcited
carrier density. Figure S12(b) shows the transient XUV reflection measured at a higher excitation
density of 1.59 mJ/cm
2
. Under higher carrier density, the mid-gap dynamics are more pronounced,
where both the redshift and the lifetime are increased. This is consistent with the assignment of
many-body driven band gap renormalization, where higher carrier densities will increase energy
shifts as well as increase the lifetime as it takes longer for more carriers to reach equilibrium.
In addition to enhanced band gap dynamics, at higher excitation intensity we also observe
strong spectral intensity oscillations (Figure S12(b)). Fourier transformation between 40.2 eV and
41.4 eV reveals oscillation peaked at 2.79 THz (Figure S13). This frequency is associated with
acoustic phonon branches with wave vectors between
Γ-K
and
Γ-L
regions.
Figure S12.
Transient XUV spectra of ZnTe thin film. (a) Similar transient XUV signature
compared to bulk measurements in Figure 1 are reproduced on the thin film sample with an
excitation density of 1.06 mJ/cm
2
, suggesting the mid-gap feature is intrinsic to ZnTe and does not
depend on the sample growth method. (b) At a higher excitation intensity of 1.59 mJ/cm
2
, both the
spectral redshift and the lifetime of the band gap dynamics are increased. This observation is
consistent with the assignment of the many-body induced band gap renormalization picture to the
measured in-gap dynamics. Spectral intensity oscillations potentially due to acoustic phonons are
also observed.
Figure S13
. Frequency spectrum of intensity oscillations between 40.2 eV and 41.4 eV of the data
shown in Figure S12(b) reveals an oscillation frequency of 2.79 THz. This frequency is associated
with acoustic phonon branches with wave vectors between
Γ-K
and
Γ-L
regions.
S7. Nanosecond transient XUV measurement
As a complementary measurement to the fast femtosecond-to-picosecond carrier relaxation
dynamics presented in the manuscript, here we report the measurement of transient XUV spectra
up to 1 ns (Figure S14). The scanned time points are sampled on a logarithmic scale, and the pump-
probe temporal overlap has an offset of 2 ps, as shown in Figure S14. The spectral intensity of the
electronic Te 4d
5/2
to conduction band transition around 40 eV only exists for the first ~ 10 ps and
is quickly replaced with the overlapped Te 4d
3/2
to valence band transition (hole signature). For
this reason, we use the intensity of 4d
3/2
to conduction band transition to track the hot carrier
lifetime. Unlike the electron and hole diffusion rates of 2.21 ± 1.12 ps and 3.91 ± 3.58 ps reported
in the manuscript, we do not observe any significant signal decay at longer timescales up to 1 ns.
This suggests that the signal intensity drop reported in Figure 3 is likely due to surface carrier
diffusion, while the intrinsic carrier lifetime is significantly longer than 1 ns.
Figure S14
. Transient XUV reflection measurement to 1 ns. No significant carrier recombination
is observed, suggesting that the intrinsic carrier lifetime is longer than 1 ns.
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