Charge carrier dynamics in amorphous semiconductors has been a topic of intense research that has been propelled by modern applications in thin-film solar cells, transistors and optical sensors. Charge transport in these materials differs fundamentally from that in crystalline semiconductors owing to the lack of long-range order and high defect density. Despite the existence of well-established experimental techniques such as photoconductivity time-of-flight and ultrafast optical measurements, 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). We observe an unexpected regime of fast diffusion immediately after photoexcitation, together with spontaneous electron–hole separation and charge trapping 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

Li, Heng

Liao, Bolin

Minnich, Austin J.

Najafi, Ebrahim

Zewail, Ahmed H.

Caltech Authors - Main

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	
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DOI: 10.1038/NNANO.2017.124
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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.  
 
 
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Supplementary Figure 2. SUEM Images Taken at a Higher Pump Fluence. The data 
is measured with a pump fluence of ~67 µJ/cm2 (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. 
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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/cm2) 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 expansion is similar. 
  
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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 and holes together through 
Coulombic interaction, here characterised 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 electrical 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 characterise the extent of the charge 
separation, and study how the parameters affect the ratio using the Monte Carlo 
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simulation. Shown in Supplementary Fig. 4 (a) is how the ratio at 40 ps after the 
photoexcitation is affected by the concentration of photocarriers and 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 charge 
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 1018 cm-3 and 1021 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).  
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 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 1018 cm-3 and 1021 cm-3 are shown in (c) and (d) 
respectively. The carrier concentration is controlled 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 electrons 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 
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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 (%)
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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 interpret 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 experiment the 
excited carrier concentration (~1018 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 scale 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 distribution with width σ , and in the 
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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 1.024σ . 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 significantly even if 
recombination played a role in our experiment. 
  
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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). 
 
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Photo-excited hot carrier dynamics in hydrogenated amorphous silicon imaged by 4D electron microscopy

https://authors.library.caltech.edu/73817/4/nnano.2017.124-s1.pdf

Photo-excited hot carrier dynamics in hydrogenated amorphous silicon imaged by 4D electron microscopy

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