# Observation of Quantum Confinement

Authors: Andreas Othonos; Demetra Tsokkou; Emmanouil Lioudakis
Journal: Research Letters in Physics
 (2008)

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## Abstract

We report on the observation of quantum confinement effects and the
influence of surface-related states due to the formation of nanograins on ultrashort
relaxation near the direct critical points of silicon nanofilms following UV-excitation.
Direct photoexcitation of the samples in the vicinity of theΓ critical points of the first
Brillouin zone has been achieved using femtosecond pulses in the spectra range of
290–400 nm. Transient absorption measurements show a substantial enhancement of
state filling with decreasing the film thickness down to 5 nm due to quantum confinement
in the z-direction. Furthermore, the state filling of surface-related states of nanograins
suggests that the critical points of these states follow the ellipsometry extracted energy-curve.


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## Body

## 1. Introduction

Polycrystalline
silicon is considered an important component of the silicon-based
integrated-circuit technology and is currently utilized in a wide range of
devices applications [1–3]. Driven
by the promising technological applications of the polycrystalline silicon
films, significant progress has been made in understanding the structural,
electrical, and optical properties of this material [4].
However, little effort has been focused on ultrathin nanoscale polycrystalline
films. At these thicknesses due to the large fraction of boundary-atoms and
quantum effects imposed from the vertical structural confinement, the energy
states of these nanofilms are modified [5–8]. A
study of the optical properties under steady-state conditions using spectroscopic
ellipsometry of such nanostructures have been recently published [9]. Based on the extracted information from that work, recently we have
reported on carrier dynamics and the effect of grain boundaries and quantum
confinement in these samples using visible ultrashort pulse excitation [10]. Although some interesting effects have been
revealed, there still a great deal of unexplored area in the field of carrier
dynamics especially when exciting in the UV part of the spectrum which is
energetically position near the Γ points (direct critical points) of the first Brillouin
zone.In this letter, we report
on the observation of quantum confinement effects and the influence of
relaxation dynamics near the Γ points of the first Brillouin zone due to the surface-related
states surrounding the nanograins using transient absorption measurements. The
samples investigated were nanocrystalline silicon films with thickness ranging
between 30 to 5 nm. In our studies, we use UV photoexcitation, energetically
located within the vicinity of the direct critical points of the first
Brillouin zone. A direct consequence of this excitation is an enhance dipole
matrix coupling as opposed to older studies where phonon-assisted excitation
generated the initial carriers within the band structure of this material. In this
work, we are able to time-resolve the relaxation paths within the complex
energy structure of the nanofilms.


## 2. Experimental

The source of excitation consists of
a self-mode-locked Ti:Sapphire oscillator-amplifier system generating 45 femtoseconds
pulses at 800 nm. An optical parametric amplifier provided wavelength tunable
pulses in the UV part of the spectrum in a typical noncollinear pump probe
setup where the differential reflected and transmission signals were measured
using lock in amplifiers. A small fraction of the fundamental pulse was used to
generate super continuum white light by focusing the beam on a sapphire plate
for nondegenerate measurements. The temporal variation in the absorption was
extracted using the transient reflection and transmission measurements [11, 12] in the
range of  290–400 nm. Measurements
reveal that approximately 68% of the incident energy is absorbed by the thin
films. There is a ±5% variation in the absorbed energy depending to the film
thickness. In view of this, the
incident fluences were adjusted to maintain a carrier density of approximately ~1×1019 carriers/cm3 for all the nanofilms. The samples under investigation were
as grown nanocrystalline silicon films fabricated on a quartz substrate using
LPCVD of silicon from silane at 610°C and 300 mTorr. High-resolution
transmission electron microscopy images exhibit high degree of crystallinity
for all samples, more structural detail on these samples are described
elsewhere [9, 10, 13]. Spectroscopic ellipsometry
measurements carried out on these samples [9] reveal
the energy positions of the direct critical points Γ1 (~3.5 eV) and
Γ2 (~4.2 eV) in the first Brillouin zone.


## 3. Results and Discussion

Typical time-resolved absorption measurements for the
nanostructured films are shown in Figure1. It depicts the temporal behavior of
the induced absorption following optical excitation at 300 nm. Clearly evident
is the sharp drop of the induced absorption for the 5 nm film followed by a
long recovery toward equilibrium. The observed negative change for the 5 nm
sample is much larger than the observed negative changes for the 10 and 15 nm
samples.Figure 1
Degenerate time-resolved absorption
measurements of the nanofilms with ultrafast UV excitation pulses at 300 nm.
The inset shows a schematic representation of the carrier dynamics following
photoexcitation.Time-resolved measurements for films
with thickness larger than 10 nm appear to have complex behavior. They have
negative and positive changes depending on the probing wavelengths and film
thickness. For the thicker samples, there is a fast rise in the induced
absorption which recovers within 10 picoseconds to a negative value followed by
a much slower recovery toward equilibrium (~nanosecond). Similar effects occur
at other excitation wavelengths.In a simple semiconductor system following optical excitation, these
carriers will lose their kinetic energy through optical phonon emission [12] and will relax to the bottom (top) of the
conduction (valence) band. However, due to the complex nanostructure of these
films, the presents of surface states [14],
boundaries, and spatial confinement [15, 16] will
effect the relaxation of the photogenerated carriers. The observed complex behavior
in the above time-resolved measurements (Figure 1) is attributed to the
position of the various energy states, their density and distribution with
respect to the excitation energy (see inset in Figure 1). In a degenerate
pump-probe experiment where the probing and excitation beams have the same wavelength,
one expects to see negative change in absorption due to the occupation of the
excitation/probing states by the photogenerated carriers. This effect, however,
is usually noticeable under direct photoexcitation, seen mainly in direct gap
semiconductors. In an indirect gap semiconductor like silicon this effect is
highly unlikely due to the required phonon-assisted absorption. For this reason,
in our work we use UV excitation where the photon energy may generate carriers near
the vicinity of direct Γ points of the first Brillouin zone. We should point
out that in addition to the above described state filling, there are also
effects due to secondary excitations of the photogenerated carriers introduced by
the probing laser pulse. With the relaxation of these carriers to various
available energy states of the material, there is a possibility that the
probing pulse will re-excite them to higher energy states if these are available.
This mechanism will appear as a positive change in absorption (photoinduced
absorption—PA) with its
strength depending on the coupling efficiency (dipole matrix element) and the
number of carriers presents in the initial energy state (see the inset of Figure
1).The time-resolved measurements in the nanofilms
reveal a complex behavior with both negative (state filling) and positive (PA)
contributions present. The observed recovery of the state filling effect seen
in the thinner sample can be expressed as a three exponential decay. The first
two components are approximately 1 picosecond and 20 picoseconds. The third
component to the decay is much longer and approximately 1 nanosecond. The first
two components are a combination of redistribution of the initially
photoexcited carriers within the states below the excitation level and
secondary excitation resulting in “pulling” the signal above zero and
artificially changing the decay constant. The long decay component is, however,
a characteristic time for the energy states within the excitation region. The
strong state filling which is only observed for the 5 nm thickness sample it is
believed to be due to an enhanced coupling coefficient resulting from the
spatial confinement in this sample. For comparison purposes, in Figure2 we
show the temporal behavior of the 5 nm thick sample for all the excitation
wavelengths. It is obvious that state filling is the dominant effect for the
shorter wavelengths; however, with increasing probing wavelength, PA becomes
more important. This is clearly seen for wavelengths longer than 350 nm (3.5 eV, energy of the Γ1 of the Si nanofilms) and at the longest
excitation wavelength of 400 nm the only term apparent in the transient
measurements is a positive PA contribution.Figure 2
Time-resolved absorption measurements
of the 5 nm film with UV excitation pulses ranging between 290 to 400 nm.The fast PA behavior observed for the
shorter wavelengths for the ticker samples (Figure1) is attributed to the
broad energy distribution of the pulse and the existing of various energy
states near the excitation region (see inset in Figure 1). Following short pulse
excitation, the carriers in the higher part of the energy distribution move to
nearby energy states that provide efficient secondary excitations due to
coupling with higher lying energy states. With energy relaxation of these
carriers into other states, the contribution of secondary excitations to the
induced absorption becomes negligible. At this point, state filling due to the
rest of the photoexcited carriers becomes evident which persist for
approximately 1 nanosecond. Since no measurable photoluminescence has been
detected from these samples, the carriers appear to recombine nonradiative with
time constant of the order of 1 nanosecond.Looking at the data over the entire
wavelength excitation range, it is interesting to point out that state filling
is initially important for the nanofilms where the excitation is below the Γ1 point (see Figure 3). This state filling is due to occupation of the surface
states energetically located below the Γ1 point as shown in the
inset of Figure 3. With reduction of the film thickness, the surface states
move energetically higher making state filing apparent at smaller wavelengths. Here,
we should note that the surface state filling effect is much smaller in
magnitude than the state filling observed for the 5 nm sample.Figure 3
Degenerate time-resolved absorption measurements
of the nanofilms where the apparent
state filling is due to occupation of surface states located below the Γ1 point. The inset shows the critical
points for the nanofilms obtained using ellipsometry measurements [9].It is important
to point out that the enhance state filling due the confinement in combination
with the strong free carrier absorption observed at longer wavelengths is a
property that may have direct application to optoelectronics for optical switching
where a tunable laser above or below the Γ points will result in a positive or
negative change in absorption. This is particularly useful since this property
is observed in silicon which is the basis for our semiconductor industry.Finally, to
further investigate the relaxation dynamics for the thinner sample where
quantum confinement effects become important, we have performed nondegenerated
time-resolved measurements over the excitation range of 290–400 nm.
Measurements reveal similar photoinduced absorption behavior over the entire
excitation range. Typical time resolved measurements with pump at 300 nm and
probe with different white light wavelengths are shown in Figure4. The smaller
probing wavelengths have a positive contribution with multiexponential recovery
toward equilibrium, whereas the longer probing wavelengths have a recovery
which is much faster (~1 picosecond) and it is single exponential.Figure 4
Time-resolved absorption measurements
of the 5 nm film with 300 nm excitation pulses and probing with white light
ranging between 450 to 850 nm.The analysis for the nondegenerated measurements is more
complex than that for the degenerate case; however, one may draw some general
conclusions. The fast relaxation seen for the long wavelength probing is
attributed to the relaxation of the carriers from populated states which couple
to nearby higher energy states. These occupied states have a relatively fast
relaxation as seen from the data in Figure4 (see 850 nm). With increasing
probing energy (shorter probing wavelength), the carriers available for
coupling to higher states are distributed over a number of energy states each
with a different relaxation rate. This makes the recover appear
multiexponential. A satisfactory fit to the short wavelength data shown in Figure
4 has been achieved using a three exponential function. The time-resolved data
for the 450 nm probing wavelength gave time constants of 3.2 picoseconds 17.5 picoseconds
and 183 picoseconds with approximately equal coefficients. The fact that one
observes longer recovery is attributed to the lower lying energy states where
energy relaxation is slower.


## 4. Conclusions

In conclusions, we have utilized ultrafast UV laser pulses to
investigate the photogenerated carrier dynamics near the vicinity of Γ points
of the Brillouin zone of a set of nanofilms. We have observed state filling
(negative change) and photoinduced absorption (free carrier absorption—positive change) as competing effects in the
transient absorption of these nanofilms. State filling becomes enhance in
ultrashort timescales for the smaller thickness samples where quantum
confinement begins to play an important role. Furthermore, we have observed
that the photogenerated carriers remain within the excitation states for a relatively
long period of time. This was confirmed through state filling and free carrier
absorption changes.



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*Source: 837503-2008-04-22.xml*