phys. stat. sol. (a) 204, No. 5, 1480–1485 (2007) / DOI 10.1002/pssa.200674398

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

New transport phenomena probed by dielectric spectroscopy

of oxidized and non-oxidized porous silicon

B. Urbach, E. Axelrod, and A. Sa’ar*

Racah Institute of Physics and the Center for Nanoscience and Nanotechnology,

the Hebrew University of Jerusalem, Jerusalem 91904, Israel

Received 17 March 2006, revised 15 September 2006, accepted 15 November 2006

Published online 19 April 2007

PACS 73.63.Bd, 77.22.Gm, 78.30.Am, 78.30.Ly, 78.55.Mb, 81.07.Bc

Dielectric spectroscopy accompanied by infrared (IR) and photoluminescence (PL) spectroscopy have

been utilized to reveal the correlation between transport, optical and structural properties of oxidized

porous silicon (PS). Three relaxation processes at low-, mid- and high-temperatures were observed,

including dc-conductivity at high-temperatures. Both the low-T relaxation and the dc conductivity were

found to be thermally activated processes that invlove tunneling and hopping in between the nanocrystals

in oxidized PS. We have found that the dc-conductivity is limited by geometrical constrictions along the

transport channels, which are not effected by the oxidation process and are characterized by activation en-

ergis of about ~0.85 eV. The low-T relaxation process involves thermal activation followed by tunneling

in between neighbor nanocrystals, with somewhat lower activation energies.

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

1 Introduction

Porous silicon structures have attracted much attention over the recent years, mainly due to their po-

tential applications for developing photonic, optoelectronic and bio-photonic devices. However, freshly

made PS is known to be unstable and certain degree of stabilization via oxidation treatments is required.

Transport measurements, including dc and ac conductivity, have been reported for non-oxidized PS

[1, 2], but the effect of oxidation on transport and relaxation processes and the correlation between these

phenomena, the optical and the structural properties of oxidized PS, are less known. In this work we

present our investigation of transport and relaxation processes in oxidized and non-oxidized PS using

broadband dielectric spectroscopy [3]. Our experimental results show the presence of new transport

phenomena that have not been revealed in PS so far [4, 5]. The present work focus on those transport

processes that take place in between the nanocrystals (nc’s), particularly the low-T relaxation process and

the dc conductivity at high-T.

2 Experiment

The PS samples used for our experiments include thermally oxidized and non-oxidized PS samples

[3–5]. Non-oxidized PS (sample R) was prepared by standard anodization in the dark, while oxidized PS

samples were obtained after post dry thermal oxidation in oxygen ambient at 900 °C for different times

ranging from 0 to 150 seconds, followed by alloying (460 °C, 20 min) of a newly evaporated backside Al

contact. The samples were fabricated in the form of a metal (Al)–PS–semiconductor capacitor structure,

and were placed in a broadband dielectric spectrometer that measures both the real and the imaginary

* Corresponding author: e-mail: saar@vms.huji.ac.il

phys. stat. sol. (a) 204, No. 5 (2007) 1481

www.pss-a.com © 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim

Original

Paper

R 0 20 40 60 80 100 120 140 16002468

1040

80

120

812 cm-1

1065-1071 cm-1

1173-1188 cm-1

880 cm-1

Inte

grat

edA

bs.x

104

(cm

-2)

Oxidation Time (sec)

(a)

R 0 20 40 60 80 100 120 140 160

1.70

1.75

1.80

1.85

Oxidation Time (sec)

PLPe

akE

nerg

y(e

V) (b)

Fig. 1 (a) Integrated IR absorption and (b) PL peak energy vs. the time of oxidation. The notation R

stands for the reference, non-oxidized PS sample.

parts of the complex dielectric function over a wide range of frequencies and temperatures [3]. The real

and the imaginary parts of the complex dielectric function are related to the capacitance and the conduc-

tance of the PS capacitor respectively. PL spectra were measured using the 488 nm line of Ar+ ion laser

at room temperature. Infrared absorption spectra were measured using a Fourier transform infrared

(FTIR) spectrometer.

3 Results and data analysis

The IR absorption spectra revealed several absorption lines that are related to Si–O–Si bonds (at 812

and 1065–1190 cm–1) [6–8] and Si–OH bonds (at 880 cm–1) [9]. In Fig. 1a the integrated absorption of

these lines is presented vs. the oxidation time. The Si–O–Si bonds have been found to increase in inten-

sity only after 30 seconds of oxidation and to saturate after 60 seconds. On the other hand, the Si–OH

bonds decrease with oxidation time and disappear after 30 seconds of oxidation. Similar phenomenon of

no blue shift of the PL peak energy at the first 30 seconds of oxidation and a blue shift hereafter has been

observed in the PL experiment and is shown in Fig. 1b.

Results of dielectric spectroscopy for samples R and t90 (txx stands for the oxidation time of the

sample) are presented in Fig. 2, where three dimensional plots of the the imaginary part (ε″) of the com-

plex dielectric function, ( ) jε ω ε ε′ ″= - , versus frequency and temperature are shown. Following the

analysis described in Ref. [3], we define three temperature regimes where three distinct relaxation proc-

esses can be observed at low-, mid- and high-temperatures (see Fig. 2). For the rest of this work we will

focus our analysis on the low-T relaxation process and on the high-T dc-conductivity. Analysis of the

other relaxation processes at mid- and high-T are given elsewhere [4, 5].

Fig. 2 Three dimensional plots of the imaginary part of the complex dielectric function vs. frequency

and temperature, for samples (left) R and (right) t90.

1482 B. Urbach et al.: New transport phenomena probed by dielectric spectroscopy

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-a.com

2.0 2.2 2.4 2.6 2.8

10-14

10-13

10-12

10-11

10-10

10-9

10-8

10-7

Rt0t10t30t60t150

dc-C

ondu

ctiv

ity( Ω

-cm

)-1

1000/T (K-1

)

(a)

R 0 30 60 90 120 15010-5

10-4

10-3

10-2

10-1

100

101

102

0.4

0.6

0.8

1.0

σ 0(Ω

− cm

)-1

O xidation T im e (sec)

(b)

Ε dc

Fig. 3 (a) Arrhenius plot of the dc-conductivity vs. the inverse temperature for various PS samples. The solid lines

represent fitting to a simple thermally activated process; see text. (b) Experimental values of the dc-conductivity

prefactors (!) and the corresponding activation energies (−) versus the oxidation time.

dc conductivity has been observed for all PS samples at temperatures above 400 K. In order to distin-

guish between high temperature relaxation processes and the dc conductivity we have used the following

procedure [3]: The dc-conductivity contributes only to the imaginary part of the complex dielectric func-

tion, ε″(ω). Therefore, by applying the Kramers–Kronig relations [10] to the real part of the measured

dielectric function, ε ′(ω), and subtracting the result from the imaginary part of the measured dielectric

function, we have found the difference between these two quantities to behave as follows:

( ) ( )[ ] dc

0

,Hσ

ε ω ε ω

ωε

- =¢¢ ¢ (1)

where σdc is the dc-conductivity, H[ε ′(ω)] is the Hilbert transform of ε ′(ω). Arrhenius plot of the dc-

conductivity vs. the inverse temperature for various PS samples is shown in Fig. 3a. The solid lines in

this figure represent fitting to thermally activated process of the form, σdc = σ0 exp (–Edc/kT), where σ0 is

the dc-conductivity prefactor and Edc is the activation energy of the dc-conductivity.

Low-T process (170–340 K): this relaxation process has been observed for samples that were oxidized

up to 30 seconds. The process is characterized by a Cole–Cole (CC) relaxation function given by [11]:

( )

∆( ) ,

1 iα

ε

ε ω

ωτ

=

+

(2)

where ∆ε is the amplitude of the process, τ is the relaxation time and α is the CC stretching exponent that

is ranging in between 0 and 1. From Fig. 2 one can see that the low-T CC process is characterized by a

local maximum that is shifted to higher frequencies with the increasing temperature. This behaviour

demonstrates the strong dependence of the relaxation times on temperature. In Fig. 4a we plot the

CC relaxation times versus the inverse temperature for several PS samples. The relaxation times follow

Arrhenius behaviour of the form, 0 CCexp ( / )E kTτ τ= , with ECC being the activation energy of the Cole–

Cole process and τ0 is the relaxation time prefactor.

4 Discussion

Following the PL and the IR absorption measurements shown in Fig. 1, we can define two distinguish-

able oxidation regimes. In the first regime (up to 30 seconds of oxidation), the oxidation gives rise to a

replacement of silicon-hydrogen bonds by silicon-oxygen bonds in the amorphous host matrix of the PS

medium, while the silicon nc’s are not affected. In the second regime of oxidation times longer then

30 seconds, all hydrogen terminated bonds have already disappeared from the PS medium (see Fig. 1a)

phys. stat. sol. (a) 204, No. 5 (2007) 1483

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Original

Paper

3.0 3.3 3.6 3.9 4.2

10-5

10-4

10-3

10-2

240 270 300 3300.04

0.06

0.08

0.1τ

(sec

)

1000/T (K-1)

t0t10t20t30

(a)

∆ε

Temperature (K)

t10t20t30

(b)

Fig. 4 (a) Arrhenius plot of the low-temperature, Cole–Cole relaxation times, for various PS samples.

(b) Amplitude of the Cole–Cole relaxation process vs. temperature for various oxidized PS samples. The

solid line represents the exponential dependency of the amplitude on temperature.

and the silicon nc’s begin to oxidize; see the blue-shift of the PL peak energy during this stage of oxida-

tion (Fig. 1b).

Next, let us discuss the transport mechanism that is responsible to the dc-conductivity. From Fig. 3(a)

one can see that the activation energies of all oxidized PS samples, including the reference PS (sample

R), are essentially the same (~0.85 eV). On the other hand, the dc-conductivity prefactor of the reference

PS sample substantially differs from those of the oxidized samples. These results are presented in

Fig. 3(b). We conclude that the transport mechanism associated with the non-oxidized sample differs

from that responsible to the dc-conductivity of the oxidized samples. Such a dual transport picture has

been proposed in Refs. [1, 2]. Following the pea-pod model of Ref. [12], we assign the first transport

channel, which takes place in the non-oxidized PS sample, to extended states transport in the conductive,

host amorphous tissue of the PS medium. However, for oxidized PS samples we find a second transport

channel that persists well into the second stage of oxidation. Hence, this transport channel is attributed to

inter-crystallites hopping, in agreement with the proposed model of Ref. [12].

The results shown in Fig. 3(b) also indicate that Edc is neither depends on the specific transport chan-

nel nor on the level of oxidation [13]. A possible explanation to activation energies that are independent

on the transport channel is the presence of geometrical constrictions along both transport paths of the PS

medium. These constrictions can be viewed as potential barriers that require from the carriers additional

thermal activation energy for passing through the constrictions. A similar model of surface/geometrical

constrictions along the conduction paths has been proposed by Lehmann et al. [14] for explaining the

high resistance of meso-PS.

Turning to the low-temperature CC relaxation process, we find that even though hydrogen bonds are

replaced by oxygen bonds during the first oxidation stage, the process amplitude (∆ε) does not change

0.2 0.3 0.4 0.5 0.6 0.710-14

10-13

10-12

10-11

10-10

Ecc

(eV)

τ 0 (sec

)

V0ECC

V0-ECC

Fig. 5 Experimental values of the CC relaxation time

prefactors as a function of the corresponding activation

energies for samples R, t0, t10, t20, and t30. The solid

line represents the best fit to the model discussed in the

text. Inset: a schematic description of the model.

1484 B. Urbach et al.: New transport phenomena probed by dielectric spectroscopy

© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim www.pss-a.com

during this stage (see Fig. 4b). This indicates that this relaxation process takes place in between the sili-

con nc’s rather then in the host amorphous tissue. For a given temperature of measurement, the relaxa-

tion times decrease with oxidation (Fig. 4a). For longer oxidation times (samples t60–t150) the relaxa-

tion time becomes shorter, so that the CC process goes out from the range of our measurements. For this

reason the CC process could be observed only during the first 30 seconds of oxidation in our experi-

ments.

From Fig. 4(a) we can extract the relaxation time prefactors, τ0, and the activation energies, ECC. These

are shown in Fig. 5, were τ0 is plotted versus ECC. The CC activation energies vary in the 0.2–0.7 eV

range that is lower compared to the activation energy for dc-conduction (0.85 eV; see Fig. 3b). Hence,

we deduced that the CC process involves thermal activation of carriers to energy levels below the

mobility edge, where they need to tunnel through an additional energy barrier into the neighbour

nanocrystal. Such a simple model of thermally activated sequential tunnelling in between neighbouring

nc’s is presented at the inset to Fig. 5. In this model, carriers are thermally excited into localized excited

states located at (average) energy, ECC, above the Fermi edge. Assuming a simple rectangular barrier

with a potential energy, V0, then, the additional barrier energy that the carriers should tunnel through is

~(V0 – ECC). Hence, the tunnelling time in between the nc’s can be estimated as follows:

0 CC2 ( )/CCCC

0

1 2 /( ) ~ e ,

2

L m V EE mT E

dτ

- -

= (3)

where T is the tunnelling probability, m is the effective mass of the holes, and d and L are the average

sizes of the nc’s and the tunnel barriers, respectively. From this simple model of sequential tunnelling we

find that, ln τ0 ≅ K(V0 – ECC)1/2, where K is a constant that depends on the geometry of the system.

The solid line in Fig. 5 represents a fitting of the experimental data to the above model of thermally acti-

vated sequential tunnelling in between the silicon nc’s. From the fitting we find the average barrier en-

ergy to be, V0 ≅ 0.7 eV, lower then the dc-conduction activation energy. This result is consistent with our

model for the dc conductivity as the distance walked by the carriers before the electric field changes his

polarity during the CC ac-conduction process is expected to be fairly short, of the order of the distance

between the nc’s. On the other hand, dc-conduction involves transport along the entire thickness of the

sample where the presence of narrow constrictions along the conduction path becomes the limiting fac-

tor.

5 Conclusion

In conclusion, the relation between the activation of the low-T, CC relaxation process and the dc-

conductivity in oxidized PS has been investigated and explained. We have found that the activation of

the dc-conductivity is dominated by geometrical constrictions along transport path while the low-T CC

process is related to thermally activated sequential tunnelling in between neighbour nc’s.

Acknowledgement This work was supported by a grant # 422/04 of the Israel Science Foundation (ISF).

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Original

Paper

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