In the format provided by the authors and unedited.
Supplementary Information
Photo-excited Hot Carrier Dynamics in Hydrogenated Amorphous Silicon Imaged
by 4D Electron Microscopy
Bolin Liao, Ebrahim Najafi, Heng Li, Austin J. Minnich
*
and Ahmed H. Zewail
†
*
To whom correspondence should be addressed. Email: aminnich@caltech.edu
†
Deceased
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
1
Supplementary Figure 1. Raman Characterization of the Sample.
The Raman
spectrum of the
sample shows the wide “optical peak” of the amorphous silicon thin film
at 475 cm
-1
(see Beeman et al.
1
) and the narrow peak of the crystalline silicon substrate at
520 cm
-1
.
150
200
250
300
350
400
450
500
550
600
Wavenumber (cm
-1
)
0.5
1
1.5
2
2.5
3
3.5
4
Counts (a.u.)
×
10
4
cSi substrate
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
2
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
Supplementary Figure 2. SUEM Images Taken at a Higher Pump Fluence.
The data
is measured with a pump fluence of ~67 μJ/cm
2
(repetition rate at 5 MHz). The feature is
significantly larger than that with the lower fluence as reported in the main text. This is
because
higher density of electrons and holes are excited above the detection threshold of
the SUEM.
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
3
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
Supplementary Figure 3.
Fast diffusion of electrons and holes at the higher pump
fluence.
The squared radii of the electron and hole distributions with the higher pump
fluence (67 μJ/cm
2
) are shown as a function of time delay. In comparison to the data at
the lower fluence reported in the main text, the time dependence here is closer to be
linear, than quadratic, whereas the average speed of expansio
n is similar.
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
4
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
Supplementary Note 1: More discussion of the Monte Carlo simulation
In this Note, we provide more discussions of the Monte Carlo simulation,
especially on the effect of various parameters in the simulation on the observed hot
carrier dynamics. Intuitively speaking, the spontaneous electron
-hole separation is
controlled by two opposing forces: one that tends to drive electrons and holes apart, in
this case the difference between the mobilities of electrons and holes and the initial high
temperature; the other one that tends to hold electrons an
d holes together through
Coulombic interaction, here characteris
ed by the dielectric relaxation time, which is
further controlled by the electrical conductivity. Another factor is the excited carrier
concentration, which effectively controls the strength of the Coulombic interaction,
because given the same spatial profiles of electrons and holes, higher carrier
concentration leads to stronger electric field. This was also discussed by Ritter et al.
2
in
their seminal study of a-Si:H. In other words, the electron-hole separation should always
happen in principle as long as the mobilities of electrons and holes are different; but the
extent of the separation is controlled by the initial velocities of electrons and holes (here
controlled by the temperature),
the electrical conductivity
and the photoexcited carrier
concentration. In the case presented here, the extent of separation is significant because
of 1) large differences in the mobilities of electrons and holes; 2) the initial high
temperature; 3) the low electr
ical conductivity and 4) the low concentration of photo
-
excited carriers.
To quantify the effect of each of these parameters, we use the ratio between the
average widths of electron and hole
distributions to characteris
e the extent of the charge
separation, and study how the parameters affect the ratio using the Monte Carlo
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
5
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
simulation.
Shown in Supplementary Fig. 4 (a) is how the ratio at 40 ps after the
photoexcitation is affected by the concentration of photocarriers a
nd by the elastic
scattering time of electrons and holes. All the other parameters are kept the same as
reported in the main text. It is clearly seen from the simulation that, as the carrier
concentration increases, the charge separation is suppressed, in
agreement with the
conclusion of Ritter et al.
2
. Also when the elastic scattering time is increased, the ch
arge
separation becomes less significant. This is consistent with the fact that a longer
scattering time corresponds to a higher electrical conductivity, and thus a shorter
dielectric relaxation time.
In Supplementary Fig. 4(b) we examine the effect of the
initial
temperature of electrons and holes. If this value is increased to 16000K, the charge
separation is significantly enhanced, due to a stronger driving force to separate electrons
and holes by diffusion. To illustrate the difference between charge
-separation and
ambipolar diffusion, the radial distribution functions of electrons and holes when the
carrier concentration is 10
18
cm
-3
and 10
21
cm
-3
are shown and compared in
Supplementary Fig. 4(c)(d). When the carrier concentration is high, the Coulombic
interaction is strong enough to bind electrons and holes together, and the electron and
hole distributions essentially overlap in space, as shown in Supplementary Fig. 4(d).
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
6
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
Supplementary Figure 4.
Effects of the transport parameters on spontaneous charge
separation.
All results here are obtained at 40 ps after photoexcitation using Monte Carlo
simulation. (a) The effect of carrier concentration and the elastic scattering time, while all
other parameters are kept the same as reported in the main text
. (b) The effect of carrier
concentration and the initial temperature. The radial distribution functions of electrons
and holes at carrier concentrations of 10
18
cm
-3
and 10
21
cm
-3
are shown in (c) and (d)
respectively. The carrier concentration is control
led by varying how many electrons and
holes are “represented” by one particle in the Monte Carlo simulation.
We further examine the sensitivity of the parameters used in the Monte Carlo
simulation. We do this by calculating the change of the spatial variance
of the
electron/hole distribution after photoexcitation due to a variation of a certain parameter
within ±50% of its optimal value. The results are shown in Supplementary Fig. 5, where
the variance of the spatial distribution of electrons is calculated at 40 ps after
photoexcitation when changing the initial temperature, elastic scattering time and
inelastic scattering time of electron
s by ±50%, and at 120 ps after photoexcitation when
changing the position of the mobility edge of electrons by ±50%. It is seen from the plot
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
7
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
that the initial temperature is the most sensitive parameter that controls the early
dynamics of electrons, and the position of the mobility edge mainly affects the trapping
dynamics at longer delay times. Because we use the same set of parameters to fit
experimental data at multiple delay times, the actual parametric sensitivity is better than
that shown here in Supplementary Fig. 5, calculated only at a single delay time.
Supplementary Figure 5. The sensitivity of parameters used in the Monte Carlo
simulation.
For temperature, elastic scattering time and inelastic scattering time, the
variance of the spatial distribution of electrons is calculated at 40 ps after
photoexcitation; for the position of mobility edge, the variance of the spatial distribution
of electrons is calculated at 120 ps after photoexcitation.
-50
-40
-30
-20
-10
0
10
20
30
40
50
Variation of the Parameter (%)
-15
-10
-5
0
5
10
15
Variation of the Distribution Variance (%)
Temperature
Elastic Scattering Time
Inelastic Scattering Time
Position of Mobility Edge (at 120 ps)
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
8
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
Supplementary Note 2: More discussion of the fast diffusion
There is a possibility that the observed initial fast diffusion is an artifact due to spatially
-
non-uniform recombination,
which
will reduce the electron concentration in the inner part
of the disc but not in the outer part where there are no holes to recombine with. This will
shift the peak electron concentration and give an artificially high diffusion rate.
In the
main text we in
terpret the decay of the image intensity shown in Fig. 3b as the charge
trapping process into deep in-gap defect states, instead of recombination, for two reasons:
1) we observed a slightly faster decay of the intensity of the ring region than the center
region. If this decay were due to charge recombination, then the intensity of the center
region should decay much faster than the ring region, due to more overlap of electrons
and holes in the center region as pointed out by the reviewer. 2) in our experime
nt the
excited carrier concentration (~10
18
cm
-3
) is relatively low, and based on previous
extensive optical studies of aSi:H (for example, ref. 11
in the main text
and the references
therein), in this regime carrier trapping is a much faster process than
recombination.
Since our measurement cannot directly distinguish the trapping and the recombination
processes, we also estimate here how the measured diffusivity would be impacted if the
decay shown in Fig. 3b were indeed due to recombination. The time sca
le of the decay
shown in Fig. 3b is ~1 ns, much longer than the time scale of the fast diffusion (~100 ps).
Therefore, the decay of the image intensity in the first 100ps is roughly
1
−
exp
−
0.1
(
)
≈
9.5%
. If this decay were caused by recombination, then the center region
would decay faster than the outer region, effectively broadening the charge distribution,
and leading to an overestimated diffusivity, which is the concern of the reviewer. To give
a simple estimation, we consider a Gaussian distributi
on with width
σ
, and in the
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
9
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
extreme case, we assume the 9.5% decay only happens within the central region of
−
σ
,
σ
[
]
. Then the effective width (variance) of the new distribution can be calculated to
be
1.024
σ
. Because the diffusivity is proportional to the square of the effective width, it
is overestimated by ~5% in this case. So this estimation indicates that the extracted
diffusivity from our measurement would not be affected signifi
cantly even if
recombination played a role in our experiment.
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
10
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24
References
1.
Beeman, D., Tsu, R. & Thorpe, M. Structural information from the Raman
spectrum of amorphous silicon.
Phys. Rev. B
32,
874–878 (1985).
2.
Ritter, D., Zeldov, E. & Weiser, K. Ambipolar transport in amorphous
semiconductors in the lifetime and relaxation
-time regimes investigated by the
steady-state photocarrier grating technique.
Phys. Rev. B
38,
8296–8304 (1988).
©
2017 Macmillan Publishers Limited, part of Springer Nature. All rights reserved.
NATURE NANOTECHNOLOGY
|
www.nature.com/naturenanotechnology
11
SUPPLEMENTARY INFORMATION
DOI: 10.1038/NNANO.2017.1
24