of 22
1
Dynamics
of Photo
-
excited
Hot
Carriers
in
Hydrogenated
Amorphous Silicon
Imaged
by 4D Electron Microscopy
Bolin Liao
a
,b
, Ebrahim Najafi
a
, Heng Li
a
, Austin
J.
Minnich
b,c
*
and Ahmed
H.
Zewail
a
,b
a
Physical Biology Center for Ultrafast Science and Technology, Arthur Amos Noyes
Laboratory of Chemical Physics, California Institute of Technology,
Pasadena,
CA 91125
b
Kavli Nanoscience Institute,
California Institute of Technology,
Pasadena,
CA 91125
c
Div
ision of Engineering and Applied Science, California Institute of Technology,
Pasadena, CA 91125
The dynamics of charge carriers
in amorphous semiconductors fundamentally
differ
from those
in crystalline
semiconductors
1,2
due to t
he lack of long
-
range order
and the high
defect density. Despite
intensive
technology
-
driven
r
esearch interests
3,4
and the existence of well
-
established experimental techni
ques, such as
photoconductivity
time
-
of
-
flight
5
8
and ultrafast optical measurements
9
12
,
many
aspects of
the
dynamics of photo
-
excited charge carriers
in amorphous
semiconductors
remain poorly understood
. Here we demonstrate
direct
imaging
of
carrier dynamics
in space and time
after photo
-
excitation in hydrogenated
amorphous
silicon
(a
-
Si:H)
by
scanning ultrafast electron microscopy
(SUEM)
13,14
.
W
e observe
an unexpected regime of fast diffusion
immediately after
photoexcitation
along with
spontaneous electron
-
hole separation
15
and charge
trapping
1
induced by the atomic disorder
.
Our findings demonstrate
the rich
dynamics
of hot carrier transport in amorphous semiconductors that can be
revealed by direct imaging based on SUEM
.
*
To whom correspondence should be addressed.
Email: aminnich@caltech.edu
Deceased
2
C
harge carrier dynamics in amorphous semiconductors
has been a topic of
sustained research
, particularly propelled
by modern applications in thin film solar
cells
16
, transistors and
optical
sensors
4
. In amorphous semiconductors, the absence of
long
-
range order leads to the breakdown of familiar concepts in crystalline materials
related to the charge transport, such as Blo
ch states, reciprocal space
and the momentum
selection r
ule
1
.
Instead, even in a
fully coordinated and defect free
amorp
hous
semiconductor
, Anderson localization
17
gives rise to localized electronic states nea
r the
edges of the conduction and the valence bands
with a
density of state
decay
s
ex
ponentially
with energy
into the band gap
1
. These localized
band
-
tail
states
are
separated from extended states inside the bands at specific energies
,
called
“mobility
edges”
18
.
In addition, in real amorphous semicondu
ctors
the
high level of defects, such as
dangling bonds and
voids
, contribute to the formation of deep defect states within the
band gap
18
.
Both band
-
tai
l and deep defect states can trap charge carriers in amorphous
semiconductors, thus limit
ing
the carrier mobility and lifetime of these materials
19
.
Given
the paramount importance of these “trap states” in determining
the electrical properties of
amorphous semiconductors, a complete understanding of the interactions
between
carriers and trap states
has been
a central pursuit in the field
.
Amongst all amorphous semiconductors, hydrogenated amorphous silicon (a
-
Si:H) has
served as an archetypical example due to its elemental simplicity and
technological relevance
3,19,20
.
Atomic hydrogen
in a
-
Si:H passivate
s
the silicon dangling
bonds and largely reduce
s
the density of the in
-
gap deep defect states,
leading
to
significant
improvement in
electrical properties
19
.
Numerous studies have been
directed
towards
understand
ing
the
charge carrier dynamics in a
-
Si:H
.
Of particular interest
are
3
the dynamics of photo
-
excited carriers in a
-
Si:H, which directly
affect
the performance of
a
-
Si:H
-
based
thin film solar cells
16
and optoelectronic devices
4
. One widely used
techni
que is the photoc
onductivity time
-
of
-
flight
measurement in
the
nanosecond
5,6
to
picosecond regimes
7,8
.
In
these measurements, the transient
signal re
sulted from the
photo
-
generated charge carriers inside an a
-
Si:H p
-
i
-
n junction device is recorded either
electrically or optically, and the drift mobility of the charge carriers can be estimated
using measured transit time, sample thickness
,
and applied e
lectrical collection field.
Alternatively, picosecond optical pump
-
probe measurements
9
11
have been used to
characterize
the recombination an
d trapping dynamics of charge carriers after photo
-
generation.
However, these
techniques are indirect
as they infer the
dynamics from
secondary effects such as photo
-
induced absorption
9
or photo
-
bleaching of
electroabsorption
7
,
complicating
the interpretation of results
and impeding efforts to
directly
trace the actual transport processes.
In this letter
we report direct
imaging
of th
e charge carrier dynamics in a
-
Si:H
after photo
-
excitation with scanning ultrafast electron microscopy (SUEM)
13,14,21,22
.
SUEM is a
pump
-
probe
microscopy
technique that combines the spatial resolution of
the
electron probe with
the temporal resolution of
the
ultrafast laser
23
. SUEM is uniquely
suited
for studying charge carrier
s’ spatiotemporal
dynamics
at
the
surfaces and
interfaces
of semiconductors
.
Previously
, SUEM
was
used to
image
the entire process of
charge carrier
generation, transport and recombination
at the
silicon
p
-
n junction,
providing new insights into the ballistic transport across the junction
22
.
In the
present
work, we observe striking evidence
of
an anomalously fast diffusion, compared to the
rate expected from
the bulk mobility, after photoexcitation, as well as
spontaneous
4
electron
-
hole separation
24
and
a transition from diffusion to trapping for both electrons
and holes.
The
se
observations are reproduced by numerical Monte Carlo simulations
incorporating scattering and trapping events
.
Our st
udy demonstrates the rich and
unexpected dynamics of hot carrier transport in amorphous semiconductors that can be
revealed by direct imaging based on SUEM.
Details of the operation and image interpretation of SUEM can be found in
Methods.
Figure 1
displays the
SUEM
images taken at different
time
delay
s between the
laser pump and the electron probe
, where the bright and the dark contrast indicate excess
electron and hole populations, respectively (see Methods)
.
For visual clarity, a low
-
pass
Gauss
ian
filter was used to remove high
-
spatial
-
frequency noise, while the raw images
were used for the quantitative analysis
elsewhere in the paper
.
In Fig. 1, we
observe a
bright contrast
just
after the arrival of the pump pulse, which after 20 ps transforms int
o
a
bright disk
due to
electron
-
hole
-
pair generation.
Between
20 ps
and
100 ps, the
bright
disk
expands rapidly, while its center
becomes
dark
.
After
100 ps, the size of the
resulting
ring stabilizes
, while
its center continues to get
progressively darker
,
peaking at
870 ps.
From
these images
we identify
two distinct regimes
. At times shorter
than
100 ps
the
ring
forms and quickly expands
,
while after
100 ps
the size of the ring stabilizes and the dark
contrast
at the center
becomes increasingly prominent.
To quantitatively
interpret
this
observation, we construct
a simple model to
describe the dynamics of electrons and holes after photo
-
excitation. As depicted in Fig.
2(a), we assume
the electron and hole densities evolve as
Gaussian distributions in space
following the Gaussian profile of the laser beam intensity
.
Given the higher
mobility
of
electrons
19
,
they
transport
out more rapidly than hole
s
, giving rise to a net charge
5
distribution
with excess holes in the center and excess electrons in the surrounding area.
Because exc
ess electrons
(
holes
)
produce bright
(
dark
)
contrasts in SUEM,
this net
charge distribution
lead
s
to the observed ring shape.
To comp
are the
model with our
observation, we extracted the spatial profiles along a stripe
-
shaped area in the SUEM
images, as marked by the yellow lines in Fig. 2(b), and plotted as blue solid lines in Fig.
2(c). The
subtraction of the
Gaussian fits
for electron and ho
le populations, representing
the net charge density,
are plotted as orange solid lines
and show reasonable
agreement
s
with the experimental data.
The apparent charge imbalance between electrons and holes
, evidenced by the
formation of bright ring and dark
center regions
,
indicates
the absence of ambipolar
diffusion. In most crystalline semiconductors, photo
-
excited electron
-
hole pairs tend to
diffuse together with an intermediate diffusivity due to the Coulombic interaction
between them.
Instead,
here
we se
e spatial separation of electrons and holes after photo
-
excitation.
The charge separation and the emergence of spatial distribution of net charges
were predicted to happen in so
-
called “relaxation semiconductors”
15
, including most
wide
-
gap crystalline semiconductors and amorphous semiconductors. In these materials,
the resistivity is usually so high that the dielectric r
elaxation time
τ
d
=
ε
ε
0
(
)
σ
(here
ε
is the relative permittivity,
ε
0
is the
vacuum
permittivity and
σ
is the electrical
conductivity) can be significantly longer than the recombination tim
e of the photo
-
excited carriers. The dielectric relaxation time deter
mines the time scale over w
hich a net
charge distribution can be neutralized.
I
n
the
case
of a long dielectric relaxation time,
the
effect of the electric field resulting from charge separation is
effectively
weak and the
6
local charge neutrality cannot be mainta
ined. In particular, a case study of this
phenomenon in a
-
Si:H was conducted by Ritter et al.
24
.
From the fitted model we can
evaluate
the
transport properties of electrons and
holes. In Fig. 3(a) we plot the squared
1
e
radius of the Gaussian distributions
l
2
as a
function of time
t
.
In a normal (Gaussian) diffusion process,
l
2
=
4
D
t
, where
D
is the
diffusivity.
In Fig. 3a we give linear
fits
to the data b
elow
100 ps.
The
deviation of
experimental results from the linear fit suggests a “superdiffusive” behavior immediately
after the photo
-
excitation
.
For comparison, we also plot
quadratic fits
in Fig. 3a, which
agree
better
with the data.
However, we caution that the exact time dependen
ce here is
not conclusive
due to
the
limited signal
-
noise ratio
of the experiment
. We conducted
another measurement with a higher fluence (see Sup
plementary Information), and
observed the fast diffusion behavior as well
with
time dependence
closer to
linear
.
The
linear fits indicate diffusivity values on the order of 10
3
cm
2
/s for both electrons (
8
×
10
3
cm
2
/s) and holes (
3.8
×
10
3
cm
2
/s), several orders of magnitude higher than
those
extracted
from steady
-
state measurements
25
.
A similar effect has been
recently
observed
in crystalline silicon with SUEM
26
, explained by the fast initial expansion of hot electron
and
hole
densities
.
Particularly in a
-
Si:H, the
average
initial temperature of photo
-
excited
electrons and holes can
be estimated to be
E
ph
E
G
(
)
k
B
8000
K
, where
E
ph
=
2.4
e
V
is the energy of incident photons and
E
G
=
1.73
e
V
is the optical band gap of a
-
Si:H
19
.
Our observation in a
-
Si:H suggest
s that
this
process
is not sensitive to the long
-
range
disorder
and thus can occur
in amorphous materials
, an intriguing conclusion that is
worth further theoretical and experimental investigation
s
.
To the best of our knowledge,
this
fast diffusion
behavio
r was not observed in earlier picosecond photoconductivity
7
time
-
of
-
flight experiments on a
-
Si:H
7
, possibly
because
in these experiments
the photo
-
carriers diffuse equally to the positive and negative electrodes, generating no net
electrical effects. Although an electrical
collection field is usually used in these
experiments, this field is not effective in driving carrier transport in “relaxation
semiconductors” as discussed above
15
.
The observation of
this fast
diffusion
process
in
an
amorphous semiconductor
is surprising and
may have
important
implications with regard
to optoelectronic device applications, since the performance of amorp
hous
-
semiconductor
-
based
optoelectronic
and photovoltaic
devices
is largely limited by the
poor charge transfer ability of the amorphous semiconductors.
After the initial
fast expansion within
100 ps, there is a clear transition of the
dynamics of both el
ectrons and holes: the widths of their distributions stop increasing and
stabilize
at times
up to 2 ns
, as shown in Fig. 3(a)
.
We interpret this distinct behavior as
the trapping of hot carriers as they cool down to the band
-
tail localized states and
/or
deep
in
-
gap defect states, a well
-
known feature of amorphous semiconductors that limits the
drift mobility of charge carriers
1
.
In particular, the change of the intensities of the bright
ring
and
dark
center
, as shown in Fig. 3(b),
suggests
details of the trapping process. The
intensity
within the
ring, where hot
elect
rons reside, decreases monotonically,
indicative
of
the trapping of energetic electrons with a time scale of hundreds of picoseconds. The
fit
to the experimental data
shown in Fig. 3(b) is
cubic
-
polynomial
;
the data cannot be
fitted with an exponential function
satisfactorily
,
suggesting that the trapping process
cannot be described by a single time constant.
Si
multaneously
, the
contrast
of
the dark
center
reg
ion
f
irst
gets darker
till
900 ps, and then slowly
becomes less dark
.
This
behavior implies that the
hot
electrons
are trapped in a faster time scale than the
hot
8
holes,
resulting
in
an
initial increase in the
dark contrast
. Beyond
900 ps, the trapping of
hot
holes becomes appreciable and the dark contrast starts to
reduce
. The excitation and
trapping processes are s
ch
ematically shown in Fig. 3(c);
in
this
experiment the trapping
into the localized band
-
tail states and into the deep defect states
is
not
resolved
.
In an
ultrafast optical pump
-
probe measurement of a
-
Si:H, Vardeny et al.
9
observed
exponential decay of photo
-
induced absorption in a similar time scale, which they
interpreted as the trapping process of photo
-
excit
ed carriers, in agreement with our
observation;
however, they were unable to identify
the
separate
behavior
s
of electrons
and holes.
We note
that the carrier recombination
occurs over
a longer time scale (a few
nanoseconds) than
the time window of our expe
riment
at this carrier concentration for
which
Auger
recombination is
weak
11
, and so little recombination is observed over the
time delays measured here.
A
quantitative transport model of the hot carrier exp
ansion process in a
-
Si:H is
currently not accessible due to the lack of a
clear understanding of charge scattering
mechanisms and a
practical formalism of electronic transport in amorphous
semiconductors. In particular, the Boltzmann transport equation, wh
ich is the standard
tool used in crystalline materials, is known to be inapplicable in amorphous
semiconductors
2
. Instead, we att
empt to unify the observed fast
diffusion
and trapping
processes using a phenomenological Monte
Carlo simulation. See Methods for details of
the simulation. Briefly, we initiate the expansions of the hot electron and hole gase
s at a
starting temperature of 8
000 K.
The kinetic energies of electrons and holes are damped at
constant rates, representing
inelastic scattering events that cool down the electron/hole
gases
.
Simultaneously
, the travel directions of the particles are randomized at each time
9
step with a certain probability set by a characteristic lifetime associated with elastic
scattering events. The randomized travel directions also follow a probability distribution
that favors small
-
angle scatterings
,
typical of
point defect scattering
27
.
Whenever the
kinetic energy of a specific particle drops below
a certain threshold (“mobility edge”),
this particle is deemed “trapped” and fixed in space. In Fig. 3(a), the solid curves
represent the second moments
r
2
of the electron and hole distributions as a function of
time from the Monte
Carlo simulation. We also show in Fig. 4 the simulated SUEM
images at different time delays
(Fig. 4(a) to (c))
, in qualitative agreement with our
experimental results, as well as the time evolution of the radial distribution functions of
electrons and holes in the simulatio
n
(Fig. 4(d) and (e)), which clearly shows the
slowdown of the initial fast expansion process and the transition into
the
trapping
dy
namics.
In conclusion,
we have directly imaged the
dynamics of photo
-
excited
hot
carriers
in a
-
Si:H
at ultrafast timescales
by
SUEM.
We
observe an unexpected regime of fast
diffusion immediately after photoexcitation,
likely due to the initial high temperature of
photoexcited carriers,
followed by trapping of both electrons and holes.
Our observations
are in good qualitative agreement with a transport model based on phenomenol
ogical
Monte Carlo simulations.
Furthermore
,
to the best of our knowledge, our
observation of
the spontaneous electron
-
hole separation is the first direct verification of the “relaxation
semiconductor” behavior predicted in the 1970s
15
.
This work demonstrates the power of
the SUEM
to provide new insights into hot carrier dynamics in diverse materials.
Methods
10
Sample Preparation
The sample studied is a
-
Si:H
(thickness ~100 nm) grown by PECVD on a
crystalline silicon substrate with a 1
-
μm
-
thick thermal oxide layer. The sample is further
characterized by Raman spectroscopy (
see
Supplementary Information).
Scanning Ultrafast Electron Microscopy
The detail
s
of S
UEM setup
have been
reported elsewhere
13,14
. Briefly,
infrared
laser pulses (1030 nm, 300 fs), generated by a Clark
-
MXR fiber laser system, are split to
generate green (515 nm) and UV (257 nm) pulses; the green is focused onto the sample
as both the photo
-
excitation and the clocking pulse, while the UV
pulse
is focused onto
the photocathode to generate ultrashort electron pulses.
The diameter of the pump is ~60
μm, and the fluence at 515 nm (photon energy 2.4 eV)
for data reported in the main text
is ~20 μJ/cm
2
with the pulse repetition rate at 25 MHz, corresp
onding to a peak carrier
concentration ~
3
×
10
18
c
m
3
28
.
The data for a fluence of ~67 μJ/cm
2
(repetition at 5
MHz) is reported in the Supplementary Information.
The electron pulses, which are accelerated at 30 kV, are delayed by a
delay stage
from
-
680 ps to 3.32 ns after the photo
-
excitation pulses and are
spatially rastered
over
the region of interest
to form an image
. The electron pulses incident on the sample
produces secondary electrons (SEs) from the top 1
-
10 nm of the sample, whic
h are
collected by a positively
biased Everhart
-
Thornley detector. To enhance the signal, the
background is removed by subtracting a reference image recorded prior to optical
excita
tion (at
-
680 ps), from the images recorded at different time delays. This results in
so
-
called “contrast images”, in which bright and dark contrasts are interpreted as
increased electron and hole concentrations, respectively. For a given material, the num
ber
11
of emitted SEs also depends on the surface topography, chemical composition, and local
fields. The removal of the background ensures that the observed contrast reflects only the
changes in local carrier density due
to the
optical excitation.
Monte Car
lo Simulation
10
6
electrons and holes
are included in the simulation, which are first randomly
assigned the positions and velocities from Gaussian distributions determined by the beam
radius and temperature, respectively. The effective masses used for electrons and holes
are
0.3
m
0
and
m
0
, respectively
19
. Subsequently the motion of each particle is tracked in
the simulation. The kinetic energy of each particle is damped at a constant
rate (28 ps for
electrons and
53
ps for holes).
The travel direction of each particle is also randomized at
each time step with a probability of
Δ
t
τ
e
l
a
s
t
i
c
, where
Δ
t
is the length of the time step
(100 fs in the simulation), and
τ
e
l
a
s
t
i
c
is a characteristic lifetime associated with elastic
scattering events (0.8 ps for electrons and 1 ps for holes). The scattering angle follows a
Gaussian distribution with a width of 45 degrees to favor small
-
angle scatterings.
Wh
en
the kinetic energy of a particle dr
ops below the mobility edge (0.1
eV for electrons and
0.25 eV for holes), the particle is “trapped” and fixed in space.
We emphasize here that
t
he parameters used here
are purely phenomenological and are chosen to
give
the best fits
to experimental results, as shown in Fig. 3(a).
The second moments of the distributions
of electrons and holes
r
2
are calculated using the following formula
r
2
=
r
2
f
r
(
)
d
2
r
f
r
(
)
d
2
r
=
r
2
φ
r
(
)
dr
0
+
φ
r
(
)
dr
0
+
,
(
1
)
12
where
r
is the position vector,
f
r
(
)
is the number of electrons per unit area, and
φ
r
(
)
=
2
π
r
f
r
(
)
Δ
r
is the radial distribution function,
which
count
s
number of particles
within a differential ring region (a “bin”) with width
Δ
r
and radius
r
.
The radial
distribution functions for
electrons and holes are plotted in Fig. 4(
d) and Fig. 4(e),
respectively, and they intuitively show the slowdown of the initial fast diffusion and the
transition into the trapping regime.
Acknowledgements
We thank Yangying Zhu for providing the sample
, and
Xuewen Fu for helpful
discussions.
This work is supported by the National Science Foundation (DMR
-
0964886)
and the Air Force Office of Scientific Research (FA9550
-
11
-
1
-
0055) in the Gordon and
Betty Moore Center for Physical Biology at the California Insti
tute of Technology. B. L.
is grateful to the financial support from the
KNI
Prize Postdoctoral Fellowship in
Nanoscience at the
Kavli Nanoscience Institute of California Institute of Technology
.
Author Contributions
B. L., E. N. and H. L. did the experiment and
analyzed
the results. B. L. wrote the
paper.
A.
J. M. proofread,
commented on the manuscript
and advised on the modeling
work
. A.
H.
Z
.
supervised the research.
Competing Financial Interests
The authors declar
e no competing financial interests.
13
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Figures and Captions
Figure 1
SUEM images at different delay times after the photo
-
excitation.
Images
shown here are “difference images” with
an image at
-
730ps as the refe
rence. Each image
represents
an average of 60 to 120 images at the same delay time. Raw images are
filtered with a low
-
pass Gaussian filter to suppress high
-
spatial
-
frequency noise and
enhance the visual contrast.
16
Figure 2
Analysis of the image intensity along a center
-
cut line.
(a) An illustration of
the model used to interpret the experimental observation. The blue and orange lines are
the spatial distributions of hole and electron concentration, respectively. The purple l
ine
is the difference of the hole and electron distributions, namely the net charge distribution.
(b) The yellow markers
indicate
the region within which the line
-
cuts are selected and
averaged. (c) The averaged intensity distribution within the strip regi
on shown in (b): the
blue lines are the experimental data, while the orange line is the least
-
square fit with the
model in (a).
17
Figure 3
Quantitative analysis of carrier diffusion and trapping processes.
(a) The
squared
1
/
e
radius
l
2
of the spatial distributions of electrons and holes versus the delay
time. The dashed
/
dot
-
dashed
lines are linear
/quadratic
fits to the experimental data before
100 ps.
The solid lines (labeled “M
C”) are results of the Monte Carlo simulation for the
entire dynamic process.
(b) The average intensities of the bright ring region and the dark
central region versus the
time
delay after 100 ps
. The dashed lines are cubi
c
-
polynomial
fits to guide the eye.
The error bars represent the standard deviation of the intensity
distribution within corresponding areas.
(c) An illustration of the typical density of states
and the excitation and trapping processes (green
arrows) in a
-
Si:H. The dark dashed lines
mar
k the mobility edges separating the localized band
-
tail states and extended states in
both conduction and valance bands. The blue circles with “+” and “
-
” signs represent
holes and electrons, respectively.
18
Figure 4
Monte Carlo simulation of the carrier dynamics.
The simulated SUEM
images at the time delays of (a) 40 ps, (b) 67 ps and (c) 93 ps. The intensity of the image
represents net distributions of electrons (above 0.5 on the color bar) and holes (below 0.5
on t
he color bar). (d) and (e) are the radial distribution functions of electrons and holes at
different time delays. The radial distribution functions are defined in Methods, and count
the number of particles within differential rings (“bins”) with a width of
200 nm and a
radius corresponding to the horizontal axes.
The radial distribution functions intuitively
show the slowdown of the initial fast diffusion and the transition into trapping.