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Dielectric relaxation and transition of nanosolid Si
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纳米硅介电驰豫,孙长庆,,Dielectric impedance measurements of nanosolid silicon within the frequency range of 50 Hz ~ 1.0 MHz and temperature range of 298 ~ 798 K revealed three semicircles in the Cole-Col
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Dielectric relaxation and transition of nanosolid Si
L. K. Pan, H. T. Huang and Chang Q Sun
*
School of Electrical and Electronic Engineering, Nanyang Technological University,
Singapore 639798
Dielectric impedance measurements of nanosolid silicon within the frequency range
of 50 Hz ~ 1.0 MHz and temperature range of 298 ~ 798 Κ revealed three semicircles
in the Cole-Cole plot when the temperature is raised to 773 Κ, which are suggested to
correspond to the contribution from grain interior, grain boundary, and electrode/film
interface, respectively. The conductivity enhancement by heating follows an
Arrhenius law with an activation energy transition from 0.07 to 0.79 eV at ~565 K,
which originates from band tail hopping occurring around Fermi edge. At the critical
temperature, a high degree of dispersion in the real and imaginary parts of the
permittivity also occurs at low frequencies. This dispersion behavior is interpreted as
the combination of electron-lattice polarization associated to the band tail hopping
and the crystal field weakening due to thermal expansion.
PACS: 82.60 Qr, 81.07 Bc, 61.46. +w
E-mail: ecqsun@ntu.edu.sg;
URL: http://www.ntu.edu.sg/home/ecqsun/rtf/JAP-LK-01.pdf
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1. INTRODUTION
The low-dimensional semiconductor structures are of high interest due to the significant
technological implications in optics and nanoelectronics. The wide interest in nanosolid or porous
silicon (PS) resulted primarily from the proposal,
i
in 1990, that efficient visible light emission
from high porosity structures. Large and varied bodies of studies have been published on the
optical properties of the PS.
ii, ,iii iv
However, few reports are available from the literature regarding
their dielectric performance upon being heated, or characterization of this material using
impedance analyzer when fields are frequency-dependent.
Impedance measurement is a flexible tool for simultaneous dielectric characterization of
materials. The technique has been widely employed to characterize the dielectric behavior of
ceramic materials.
v
Impedance measurement with respect to frequency allow us to inspect the
detailed physical processes inside the materials through their electrical analogs.
vi
In conjunction
with structural characterization, impedance analysis yields a complete physical picture of various
phenomena occurring in the specimen under different conditions. The most important advantage
of the impedance measurements is that they can distinguish individual contributions to electrical
conduction or to polarization arising from different sources like bulk, grain boundaries,
intergranular contact regions, and electrode-sample interface regions where defects are generated.
This work presents our findings in the impedance characterization of the complex dielectrics,
so-called Cole-Cole plot, as a function of the temperature with discussion of possible mechanisms.
2. EXPERIMENT
The PS samples were prepared on p-type (100) Si wafer with the resistivity of
1 - 25 cm at room temperature. Electrolyses have been performed by an galvanostat
and in a HF : C
2
H
5
OH : H
2
O solution, where the weight ratios were 1 : 5 : 4 while the
electrolyte was stirred during the process; the silicon substrates were used as anodes
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and the n-type (111) Si with a resistivity of 0.005 - 0.02 cm was used as cathode to
obtain a more homogeneous electric field in the electrolyte leading to samples with
very uniform surfaces.
vii
A current density of 80 mA/cm
2
was applied for 10 min.
After anodization, the PS samples were dried by pentane. The PS layers formed
exhibit a red photoluminescence with peak energy at about 2.0 eV under Xe lamp
(λ=458 nm) excitation
and corresponding particle size is about 1.8 nm obtained by
matching the measured PL shift with the predicted PL profile
viii
that matches
numerous sets of PL data of PS reported in the literature.
The dielectric measurements were performed in the frequency range of 50 Hz
to 1.0 MHz and in several stages from room temperature to 573 K in 50 K steps and
above 573 K in 25 K steps with an applied potential of 100 mV, using a FLUKE
PM-6303 RCL (resistance-capacitance-inductance) meter with the four-wire probe.
The temperature was held for 0.5 hour prior to each measurement. All the
measurements were carried out in atmospheric ambient. Fig. 1 (a) shows the
schematic diagram of this dielectric measurement. Due to the much higher
conductivity of Si substrate compared with PS,
ix, ,x xi
effects of conducting current
through the Si substrates on the measured resistance were estimated to be less than
0.1% and thus the effect of Si substrates could be ignored.
x,xii
Silver paste was used
for an ohmic contact. The samples were then dried at 353 K for 1h to make the
experimental data reproducible.
RESULTS AND DISCUSSION
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The impedance relaxation can be ideally illustrated with Debye’s expression,
where the material is represented by a parallel circuit with a pure resistor R and a
capacitor C. When the Cole-Cole plot is considered, the impedance response
commonly shows semicircular forms.
xiii
Fig. 2 illustrates the impedance response of
the PS sample from room temperature to 798 K. For temperature below 673 K,
complex impedance plots show only one depressed single semicircular arc indicating
that only one primary mechanism, the bulk grain behavior, exists for the polarization
within the PS film at temperature below 673 K. The second intercept on the real axis
made by the semicircle corresponds to the resistance offered by bulk grain. As
observed, with the temperature increase the intercept of the semicircles shift towards
lower Z′ values indicating reduction of the bulk grain resistance.
When the temperature is increased to 673 K or above, the grain boundary effect becomes
more significant with the presence of another overlapped semicircle. The two semicircles at high
and low frequencies may be assigned to charge transport within the grain interior and grain
boundary effects, respectively. In general, the grain boundary effect on electrical conductivity may
originate from a grain boundary potential barrier or from space charge layers that are depleted in
majority charge carriers and localized along the grain boundaries. It is found that low frequency
semicircular response is dominant with the elevation of temperature compared with the high
frequency one, which means that the dominating dielectric relaxation mechanism has changed
from bulk grain behavior to grain boundary behavior.
The impedance spectra of the PS exhibits three semicircles when temperature
reaches about 773 K, of which the formation of the tertiary semicircle in the low
frequency region. When the temperature is further elevated, this effect is more evident.
We attribute this semicircle to electrode/film interface effect. In general, the
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