Hopping conduction in SiO2 films containing C, Si, and Ge clusters
Minoru Fujiia)
Division of Science of Materials, The Graduate School of Science and Technology, Kobe University,Rokkodai, Nada, Kobe 657, Japan

Yoku Inoue, Shinji Hayashi, and Keiichi Yamamoto
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University,
Rokkodai, Nada, Kobe 657, Japan~Received 1 December 1995; accepted for publication 22 April 1996!
Temperature dependence of electrical characteristics of SiO2 films doped with C, Si, and Ge werestudied. The conductivity s was found to vary with the temperature as lns }T 21/4 over a wide
temperature range, indicative of the conduction by the variable range hopping ~VRH! mechanism.
Since the previous optical studies for the same films indicate the existence of clusters in the films,
it is very likely that the VRH through localized states associated with clusters dominates theconduction process, irrespective of the kind of group IV elements. © 1996 American Institute ofPhysics. @S0003-6951~96!02626-5#

During the past few years, considerable attention has
been paid on the strong photoluminescence in the visible
region from nanostructures made of group IV elements, suchas porous Si,1 Si,2–4 and Ge5 nanocrystals prepared by various methods. Although optical properties of these nanostructures have been widely studied, their electrical transport
properties have not been investigated, except for those ofporous Si.6–11 The conduction mechanism of porous Si is
attracting much interest because of its possibility of realizing
efficient electroluminescent devices. However, porous Si is
not an appropriate sample for investigating transport properties of Si nanostructures, because its electrical properties depend highly on the chemical species adsorbed in pores.7,9,11
In fully understanding the transport properties of nanostructures of group IV elements and realizing various device applications, those of much simpler systems should be studied.
In our previous papers, we have studied SiO2 films
doped with C,12–14 Si,15,16 and Ge17–19 by photoluminescence, Raman and infrared ~IR! absorption spectroscopy, andhigh-resolution transmission electron microscopy ~HREM!.
Our data strongly suggested that these films are the systemsof C, Si, and Ge clusters smaller than about 2 nm dispersedin SiOx matrices. In particular, in HREM studies of Ge
doped SiO2 films, we could directly observe dark patches
less than 2 nm corresponding to Ge clusters.17,18 Although
direct observations of C and Si clusters by HREM were notsuccessful due to the background images of SiO2 matrices,
we could demonstrate clear evidences of the cluster formation by Raman spectroscopy.13–16
In this letter, we report results of electrical measurements made for these films. The purpose of this work is toextract common electrical properties of nanostructures ofgroup IV elements. We will show that these films generallyexhibit T 21/4 dependence of lns , where T and s are thetemperature and conductivity, respectively. This suggeststhat variable range hopping ~VRH! dominates the conduction
process, irrespective of the kind of group IV elements. The
hopping conduction is believed to be mediated by the locala!

Electronic mail: fujii@eedept.kobe-u.ac.jp

ized states associated with the clusters distributed in thefilms.
SiO2 films containing C, Si, and Ge clusters were prepared by a rf magnetron cosputtering method described indetail in our previous papers.12,15,19 Thin plates of C, Si, andGe of ;531530.5 mm3 in size were placed on a SiO2
target 10 cm in diameter and they were cosputtered in Ar gasof 2.7 Pa at a rf power of 200 W. The film thickness was set
to 200 nm for all the samples. The dopant concentration wascontrolled by varying the number of the thin plates. Hereafter, we distinguish the samples doped with C, Si, and Ge as
C~n!–SiO2, Si~n!–SiO2, and Ge~n!–SiO2 , respectively,
where n denotes the number of the thin plates. Although
exact values of the dopant concentration were not measured,
we roughly estimated the concentration by IR absorption
spectroscopy15 and x-ray photoelectron spectroscopy.19 The
dopant concentration in the samples studied in this work is
less than 35 vol %.
Prior to the cosputtering, an Al electrode 2 mm wide and
100 nm thick was deposited onto a glass substrate. After thesample deposition, upper Al electrode of the same size wasdeposited. The upper electrode was arranged to make theright angle with the lower electrode. The active device areais thus 232 mm2. The dc current–voltage (I – V) andcurrent-temperature (I – T) measurements were made between 100 and 300 K in a closed-cycle type He cryostat~Iwatani Cryomini! by an Advantest R8340 electrometer.
The I – T measurements were performed at the applied electric fields of 53104 to 23105 V/cm.
We first present experimental data obtained for Si–SiO2
films and compare them with those of C-SiO2 and Ge-SiO2films. In order to study conductivity mechanism, it is convenient to plot logarithm of the conductivity, lns , as a functionof T 2 a , and find proper value of a which straightens out
experimental curves. We first plotted lns as a function ofT 21 ~Arrhenius plot!. However, the Arrhenius plot cannot be
fitted by a single straight line. This means that carriers are
not simply activated to a mobility edge above which extended states exist. On the other hand, lns versus T 21/4
shown in Fig. 1 are well fitted by straight lines for threesamples having different Si concentration @Si~14!, Si~24!,

Appl. Phys. Lett. 68 (26), 24 June 1996
0003-6951/96/68(26)/3749/3/$10.00© 1996 American Institute of Physics
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FIG. 1. dc conductivity ~in logarithmic scale! as a function of T 21/4 for
Si–SiO2 samples having various Si concentrations at an electric field of53104 V/cm.

and Si~36!–SiO2 ]. The T 21/4 dependence of lns is commonly considered to be a signature of VRH of carriers between localized states near the Fermi level in three dimensions. 20,21
For thick enough films, the conductivity of VRH can be
expressed as20

s 5A exp~ 2B/T 1/4! ,~1!

withB52.06@ a 3 k B N ~ E F !# 21/4,~2!

where A is a constant, k B is the Boltzmann’s constant,
N(E F ) is the density of states at the Fermi energy, and a isthe decay length of the localized state. Assuming Eqs. ~1!
and ~2!, we can determine the values of B from the slope ofexperimental lns versus T 21/4 straight lines. Unfortunately,
from the values of B only, it is not possible to deduce a andN(E F ) separately. In Fig. 1, we can see that the values ofB decrease as the Si concentration increases.
We have performed the same measurements for
C–SiO2 and Ge-SiO2 films having various C and Ge concentration. The results obtained were very similar to those of
Si-SiO2 films. Figure 2 compares the lns versus T 21/4 plotsobtained for C~44!–SiO2 , Si~24!–SiO2 , and Ge~8!–SiO2 .
To facilitate the comparison, we selected samples with similar conductivity. We can see that not only the data for Si–
SiO2 sample but also those for C–SiO2 and Ge–SiO2
samples can be very well fitted with the straight lines. This
result indicates that the conduction mechanism is generally
VRH in the SiO2 films doped with group IV elements irrespective of the kind of group IV elements.
The VRH requires localized electronic states around theFermi level. We now consider the origin of the localizedstates and try to correlate the transport properties with physical structures. In our previous papers,12–19 we have studied
the structures of C–SiO2 , Si–SiO2 , and Ge–SiO2 films byphotoluminescence, Raman, and IR absorption spectroscopy

FIG. 2. dc conductivity ~in logarithmic scale! as a function of T 21/4 for
C~44!–SiO2 , Si~24!–SiO2 , Ge~8!–SiO2 films at an electric field of 53104
V/cm.

and HREM. Our data strongly suggest that these films are thesystems of C, Si, and Ge clusters much smaller than about 2
nm embedded in SiOx matrices. In particular, we have observed peculiar Raman spectra in Si–SiO2 systems,15,16
which were different from those of bulk crystalline Si, amorphous Si, and microcrystalline Si, but very similar to thedensity of state spectra of Si33 and Si45 clusters calculated byFeldman et al.22 This result offers a direct evidence of Si
clusters smaller than about 2 nm in Si–SiO2 films. Although
the size and size distribution of the clusters are not known,
introduction of various size of clusters randomly into SiOx
thin films may generate localized electronic states. If theseprevious results are taken into account, it is rather straightforward to attribute the presently observed lns versus
T 21/4 behavior to the VRH conduction through the localized
electronic states associated with the C, Si, and Ge clusters.
As the Si concentration increases, the slopes (B) oflns versus T 21/4 straight lines in Fig. 1 decrease. This indicates that N(E F ) and/or a increases with the Si concentration. Since the increases in the Si concentration lead to theincreases in the size and/or number of Si clusters, the decreases in B may be attributed to the increase in the sizeand/or number of Si clusters. The decreases in B with increasing dopant concentrations were also observed for
C–SiO2 and Ge–SiO2 samples.
In conclusion, we have studied conduction mechanismof SiO2 films doped with C, Si, and Ge clusters. The temperature dependence of the conductivity could be well fitted
by the lns versus T 21/4 relation. This indicates that the conduction mechanism is generally VRH irrespective of the kindof group IV elements. Since our optical data indicated theexistence of clusters in the films, the present VRH conduction is thought to be mediated by the localized electronicstates associated with the clusters.
This work was supported by grants from Hyogo Scienceand Technology Association, and Takayanagi’s Foundation
for Electronics Science and Technology.

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