Current transport properties of SiO2 films containing Ge nanocrystals
Minoru Fujiia)
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai,
Nada, Kobe 657, Japan

Osamu Mamezaki
Division of Electrical and Electronics Engineering, The Graduate School of Science and Technology,
Kobe University, Rokkodai, Nada, Kobe 657, Japan

Shinji Hayashi and Keiichi Yamamoto
Department of Electrical and Electronics Engineering, Faculty of Engineering, Kobe University, Rokkodai,
Nada, Kobe 657, Japan~Received 9 September 1997; accepted for publication 20 October 1997!
The electrical transport properties of SiO2 films (>3 m m in thickness! containing Ge nanocrystals
have been studied. We found that the films exhibit T 21/2 dependence of ln( s ) under relatively low
electric fields independent of the volume fraction of Ge in the films, where T and s are thetemperature and the conductivity, respectively. The observed electrical properties could be well
explained by the theory developed by Šimánek @Solid State Commun. 40, 1021 ~1981!# which
considers the tunneling of thermally activated carriers between neighboring nanocrystals. © 1998
American Institute of Physics. @S0021-8979~98!05303-1#

I. INTRODUCTION

Since the discovery of the highly efficient photoluminescence from porous-Si,1 nanostructures of Si2–6 and Ge7–15
prepared by various methods have been the subject of intensive optical studies. Ge nanostructures have been preparedby implantation of Ge into SiO2 films,7 cosputtering of Ge
and SiO2 and subsequent thermal annealing,8–12 H2 reduction of Six Ge12x O2 alloys,13,14 and oxidation of Six Ge12x
alloys.15 Although the preparation methods are different, all
the films prepared have almost the same structure, i.e., Ge
nanocrystals dispersed in SiO2 matrices. These films are often reported to exhibit strong visible photoluminescence atroom temperature7,10–15 and are expected to open up new
possibilities for fabricating visible light emitting devices
based on the Ge nanocrystals, although the mechanism of thevisible photoluminescence has not been determined conclusively.
In order to realize various device applications including
electroluminescent devices based on the Ge nanocrystals, detailed knowledge about the conduction properties of the systems consisting of Ge nanocrystals embedded in SiO2 matrices is indispensable. However, despite the intensive opticalstudies, electrical properties of these systems have not beenstudied in detail.
In this work, we have studied electrical transport properties of the SiO2 films containing Ge nanocrystals preparedby the cosputtering method. The SiO2 films containing Ge
nanocrystals may be modeled as three-dimensional resistance networks in which any site ~Ge nanocrystal! is connected by a finite tunneling resistance onto its neighbors. If
such films are very thin and only a few Ge nanocrystals arecontained in a vertical direction, we can expect to observe
the single-electron tunneling ~SET! effects such as the Coulomb blockade and the Coulomb staircases due to the largea!

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

J. Appl. Phys. 83 (3), 1 February 1998

charging energies of the nanocrystals, and the resonant tunneling effects via quantized energy levels of the Ge nanocrystals. In the case of Ge nanocrystals a few nanometers indiameter, these effects are expected to be observable even atroom temperature. On the other hand, if the films are very
thick and a large number of Ge nanocrystals are contained in
the vertical direction, the SET and resonant tunneling effects
will be smeared out and cannot be observed explicitly, although these effects will implicitly affect the conduction
properties of such films.
In this article, we report conduction properties of thick
SiO2 films (>3 m m in thickness! containing Ge nanocrystals. We have also studied the conduction properties of extremely thin films about 10 nm in thickness and observed theSET effects and the resonant tunneling effects. The results
for the thin films will be published elsewhere. In this article,
we first show the results of the high-resolution transmission
electron microscopic ~HRTEM! observations and demonstrate the formation of Ge nanocrystals in SiO2 matrices. We
will then show the results of electrical measurements. We
will demonstrate that the present samples exhibit T 21/2 dependence of ln( s ) at relatively low electric fields independent of the volume fraction of Ge nanocrystals in the films,
where T and s are the temperature and the conductivity,
respectively.
II. EXPERIMENT

SiO2 films containing Ge nanocrystals were prepared bya rf cosputtering method. Details of the preparation procedures are found in our previous articles.8,9 Small pieces ofGe chips ~5315 mm2 ) were placed on a SiO2 sputteringtarget 10 cm in diameter and they were cosputtered in Ar gasof 2.7 Pa. The purity of the Ge chips and the SiO2 target
were 99.9999% and 99.99%, respectively. During the deposition the substrates were not intentionally heated. For the
as-deposited samples, no trace of crystallites was detectable0021-8979/98/83(3)/1507/6/$15.00© 1998 American Institute of Physics

1507

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

FIG. 1. Typical cross-sectional HRTEM image of a SiO2 film containing Ge
nanocrystals ( f Ge515.3%!. Dark patches correspond to Ge nanocrystals.

by HRTEM observations and detectable Ge nanocrystals
were grown only when the films were annealed. Thermal
annealing was performed in vacuum of the order of 131025
Pa at 800 °C for 30 min. In this method, the size of Ge
nanocrystals can be controlled by changing the number of Ge
chips during the cosputtering. The size (d) and the volume
fraction of Ge nanocrystals ( f Ge) in the films were estimatedby cross-sectional HRTEM ~JEOL JEM-2010! observations
and electron probe microanalyses ~JEOL JXA-8900!, respectively. The samples for the cross-sectional HRTEM observation were prepared by standard procedures including mechanical and ion thinning methods.
The substrates used were n 1 -Si wafers ~0.005–0.018
V cm!. After the cosputtering and the thermal annealing, upper and lower Al electrodes 5 mm in diameter were deposited. The dc current–voltage (I – V) and current-temperature(I – T) measurements in a vertical direction were made in a
two terminal configuration by an Advantest R8340 electrometer. The measurements were performed in a temperature
range between 20 and 300 K in a closed-cycle type He cryostat ~Iwatani Cryomini! at the applied electric fields of up to
53104 V/cm. Note that the current measured for the sample
not containing Ge nanocrystals was smaller than 1310213 A
for the temperature and the electric field range studied.
III. RESULTS
A. HRTEM observation

Figure 1 shows a typical cross-sectional HRTEM imageof the SiO2 film containing Ge nanocrystals ( f Ge515.3%!.
The dark patches seen correspond to Ge nanocrystals. We
can see that the nanocrystals are randomly dispersed in the
SiO2 matrix. The enlarged image of Fig. 1 is shown in Fig. 2.
1508

J. Appl. Phys., Vol. 83, No. 3, 1 February 1998

FIG. 2. Enlarged image of Fig. 1. Lattice fringes corresponding to the $111%
planes of Ge nanocrystals with the diamond structure can clearly be seen.
Ge nanocrystals are well dispersed in SiO2 matrices.

Lattice fringes corresponding to the $111% planes of Ge crystals with the diamond structure can clearly be seen. The crystallinity of the nanocrystals is rather good. We can see thatthe nanocrystals are not aggregated and are isolated by SiO2
layers. It should be noted here that, since the distances between the neighboring nanocrystals are a few nanometers as
can be seen in Fig. 2, electrons can be transferred from one
nanocrystal to another by tunneling. The volume fractions ofGe and the average diameters estimated from HRTEM images are summarized in Table I. We see that the average
diameter increases as f Ge increases.
B. Electrical measurements

Before discussing the electrical properties, it is important
to distinguish between contact and bulk contributions. In thepresent work, we commonly observed rectification properties
for the samples thinner than 1 m m, indicating that the contribution from contacts is non-negligible. In order to separate
the bulk properties from contact ones, we increased thesample thickness until the rectification behavior disappears
TABLE I. Volume fractions of Ge ( f Ge), average diameters (d), and activation energies (T 0 ) obtained from Fig. 4.
f Ge~%!

d ~nm!

T 0 ~K!

4.2
8.8
15.3

3.8
5.6
8.9

197 465
192 774
108 129

Fujii et al.

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

FIG. 3. Logarithmic conductivity of SiO2 films containing Ge nanocrystals
as a function of applied voltage for the samples with three different f Ge . The
conductivity is almost independent of the applied voltage.

on the data. Figure 3 shows conductivity ( s ) versus voltage
characteristics obtained for the samples with three different
f Ge . The thickness of the films was 3 m m. We can see nearly
symmetric s 2V characteristics. This suggests that the
sample is sufficiently thick, enabling us to discuss the bulk
properties. In order to confirm this fact, we compared I – V
curves for the samples with two different thickness ~3 and 5
m m! and found that s versus electric field relation was almost independent of the film thickness. This also implies thatthe contribution from contacts is negligible and we can study
net conduction properties of the films if the thickness islarger than 3 m m.
In Fig. 3, we can see that s is nearly independent of theapplied voltage and is very sensitive to f Ge . As f Ge increases
from 4.2% to 15.3%, s increases by several orders of magnitude. This systematic increase in s indicates that the conduction in the present samples is governed by the Ge nanocrystals in SiO2 matrices.
In order to study conduction mechanism, it is convenientto plot logarithm of the conductivity @ ln(s)# as a function of
T 21/a , and find a proper value of a which straighten out
experimental curves. We have studied the temperature dependence of the conductivity and first tried to plot ln( s ) as afunction of T 21 (a51, Arrhenius plot!. However, theArrhenius plot did not give a single straight line. This meansthat carriers are not simply activated to a mobility edge
above which extended states exist. To find a proper value ofa, we numerically fitted the experimental results and tried tofind a. The values of a were around 2 independent of theapplied field and f Ge . Figure 4 shows ln( s ) plotted as afunction of T 21/2 for the samples with three different f Ge at
the applied field of 23104 V/cm. The solid lines are theresults of the least squares fitting by straight lines. We cansee that the observed s can be fitted very well with the
J. Appl. Phys., Vol. 83, No. 3, 1 February 1998

FIG. 4. Conductivity s ~in logarithmic scale! as a function of T 21/2 for the
samples with three different f Ge . Solid lines are the results of the leastsquares fitting. For the easier comparison the top axis has the corresponding
temperature scale.

straight lines. We can also find that the slope (T 0 ) of the ln( s )}T 21/2 lines decreases as f Ge increases. The values of T 0
estimated from Fig. 4 are summarized in Table I. It should be
noted that T 0 was independent of the applied voltage and thefilm thickness, and depended only on f Ge .
IV. DISCUSSION
A. Theories predicting the ln„ s …} T 21/2 relation

The relation of ln( s )}T 21/2 at low electric fields hascommonly been observed for metal–insulator composite
films independent of the kinds of metals and insulators.16–19
In the metal–insulator composite films with relatively low
metal concentration, metal particles are dispersed in insulating matrices. The structure is thus very similar to the present
samples. In these films, ln( s )}T 21/2 relation has been observed for a wide range of a volume fraction of metal particles. The slope of the ln( s )}T 21/2 relation depends on thevolume fraction of metal particles and decreases as the volume fraction increases. These films are also known to exhibit
characteristic I – V curves. At high-electric fields, ln( s ) is
proportional to the inverse of the applied voltage, while at
low-electric fields, s becomes independent of the applied
voltage.16
To derive the ln( s )}T 21/2 relation of the metal–
insulator composite films, many theoretical considerations
were made so far.16–19 In all the theoretical treatments, thecurrent transport was considered on the basis of the thermally activated electron tunneling between metal particles.
Abeles et al.16 proposed that the origin of the activation energy necessary to transfer an electron from one nanocrystal
to another is the electrostatic charging energies of particles
Fujii et al.

1509

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

FIG. 5. Illustration of Ge nanocrystals connected via SiO2 barriers, and the corresponding band diagram at zero bias. E d represents the degree of high-energy
shift of the conduction band edge, DE represents the difference of the conduction band edge between the neighboring nanocrystals.

(E c ). They derived the ln( s )}T 21/2 relation under the assumption that the ratio of the particle diameter (d) and theparticle separation (s) is constant throughout a sample. The
theory is criticized by Šimánek.17 He pointed out that thetheory fails to explain the observed ln( s )}T 21/2 relation in awide enough temperature range. The theory developed byŠimánek regards s as a random variable essentially uncorrelated with the particle diameter, because the shape of theparticles is not perfectly spherical and the protrusions on thesurface of the particles are expected to produce strong fluctuations in the effective local spacing. Furthermore, as theorigin of the activation energy they considered not only the
charging energy but also the distribution of the quantizedenergy levels of particles resulting from the fluctuation of theparticle size. Assuming uniform distributions of the activation energies and the tunneling distances, they derived the ln( s )}T 21/2 relation by means of the percolation method.
Similar approach was used by Sheng and Klafter.18 They
assumed a nonuniform distribution of the activation energy,
and also derived the ln( s )}T 21/2 relation by the percolation
method.
Another class of theory which predicts the ln( s )}T 21/2
relation is the variable range hopping conduction with a Coulomb gap derived by Efros and Shklovskii20 for impurity
1510

J. Appl. Phys., Vol. 83, No. 3, 1 February 1998

doped semiconductors. However, the model has been considered to be inappropriate in explaining the conduction properties of metal–insulator composite films.17–19
B. Comparison between experiment and theory

1. Conduction model

The conduction properties in the present samples arevery similar to those of the metal–insulator composite films.
First, both of them show the ln( s )}T 21/2 relation under
low-electric fields. Second, T 0 decreases as the volume fraction of conductive species increases. Third, the conductivity
is nearly constant under low-electric fields. From the similarities of the conduction properties and the sample structures, i.e., conductive particles are dispersed in insulating
matrices, we can expect the similar conduction mechanism
for the SiO2 films containing Ge nanocrystals and the metal–
insulator composite films.
Figure 5 is the schematic drawing of the structure of thesamples along the direction of a current flow, where Ge
nanocrystals are separated each other by thin SiO2 barriers.
Corresponding energy band diagram at zero bias is also
shown. It should be noted that the band gap of nanocrystals
is widened by the zero-dimensional quantum confinement
Fujii et al.

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

effects and the degree of the widening depends on the size.
Since the SiO2 barriers are very thin, electrons can be transferred from one nanocrystal to another by tunneling as schematically shown in Fig. 5.
In the case of metal particles, the activation energy necessary for tunneling between neighboring particles is mainly
the electrostatic charging energy of particles (E c ). 16 Assuming that a particle is surrounded by many particles, the charging energy of the particle is expressed as16e2
~ s/d !
E c5,
4 p ee 0 d ~ 1/21s/d !

E d5

2m e* ~ d/2! 2

,

~1!

~2!

where m *e is the effective mass for electrons. Taking thetransversal and longitudinal effective masses at L point asm*
t 50.082m 0 and m *l 51.58m 0 , m *e can be estimated as
10*
0.12m 0 using 1/m *5
1/3~1/m
1
2/m *Since theelt ).
present samples have a size distribution, E d varies from one
nanocrystal to another. This results in the energy differenceof the conduction band edge between the neighboring nanocrystals (DE). The definitions of E d and DE are shown in
Fig. 5. In the following, we will assume that the activationenergy necessary for the tunneling is the sum of E c and DE.
As described above, two types of theories are developedin accounting for the ln( s )}(T 0 /T) 1/2 relation of the metal–
insulator composite films. The one assumes particular correlation between particle size and local separation between
particles.16 The other does not make any assumption on
them.17,18 Since we did not find any particular correlation
between the size and the local separation in the HRTEM
observations, we will consider the latter theories. In these
theories, the metal–insulator composite films are modeled as
the three-dimensional resistance networks in which any site
~nanocrystal! is connected by a finite tunneling resistanceonto its neighbors. This model is very much suitable for thepresent samples because Ge nanocrystals in the present
samples are separated each other by SiO2 tunneling barriers
as can be seen in HRTEM images, and the current transport
is considered to be made by the tunneling of electrons between the neighboring nanocrystals. We adopt the theory developed by Šimánek17 and quantitatively compare the experimental results with the theory. Assuming a uniform
distribution of the particle separations and the activation energies, he derived ln( s )}(T 0 /T) 1/2 relation using the percolation approach. The expression of T 0 is
J. Appl. Phys., Vol. 83, No. 3, 1 February 1998

2 P c s maxE max
,
k Ba

~3!

where P c is the percolation threshold, s max is the maximum
separation of particles in the current path, E max is the maximum value of the activation energy for the intergrain tunneling, and a is the effective decay length for the wave functions of electrons in the insulating region.
2. Comparison between experiment and theory

where e is the dielectric constant of SiO2 matrices ('3.9!,
e 0 is the permittivity in vacuum, and s is the distance between the particle and the surrounding particles. In the caseof the semiconductor nanocrystals, we also have to take into
account the discreteness of the energy levels, because thedegree of the size quantization for semiconductors is expected to be larger than that of metals.21 The degree of thehigh-energy shift of the conduction band edge (E d ) from thebulk edge due to the size quantization can be roughly estimated by the effective mass approximation as\ 2p 2

T 05

Although the Šimánek’s model is very simple, it is possible to roughly estimate T 0 using Eq. ~3! and compare theresults with experimental ones at the order-of-magnitudelevel. To estimate T 0 from Eq. ~3!, the maximum separationof neighboring nanocrystals (s max) and the maximum activation energies (E max) in a current path are required. Since theprecise information on the actual current path is not available, we roughly estimate s max as 3 nm from HRTEM images. We also assume that the activation energy becomesmaximum when electrons are transferred from the largest to
the smallest nanocrystals in the size distribution. In the caseof the sample with f Ge515.3%, the smallest nanocrystal we
found from HRTEM images was about 4 nm and the largest
one was about 15 nm. Using Eq. ~2!, E d of the 4 and 15 nm
particles can be calculated to be 0.78 and 0.06 eV, respectively. The energy difference (DE max) is thus 0.72 eV. From
Eq. ~1!, the charging energy necessary to add an electron to ananocrystal 4 nm in diameter (E cmax) is 0.06 eV, if the particle is surrounded by many particles with the separation of 3
nm. Assuming that E max is the sum of DE max and E cmax ,E max for the sample with f Ge515.3% becomes 0.78 eV. It
should be noted here that DE max of the present samples ismuch larger than E cmax . This is opposite to the case of themetal–insulator composite films, in which the effect of thecharging energy is much more important and the intragrain
level splitting is negligible.16
In order to estimate T 0 , we need the value of the percolation threshold P c . Since P c of the present samples is unknown, we adopt that of the simple cubic lattice of particles.
In this case P c becomes 0.25.22 Assuming a 50.1 nm17 andE max50.78 eV, T 0 becomes 136 000 K. This value is in good
agreement with the experimental results shown in Table I,
indicating that the conduction properties of the present
samples can be well explained by the Šimánek’s theory. Itshould be noted here that the observed T 0 in the present
samples is very large and the large T 0 cannot be explained
without taking into account DE.
As can be seen in Fig. 4 and Table I, T 0 increases as f Ge
decreases. From Eq. ~3!, the increase in T 0 is caused by theincreases of s max and/or E max with decreasing f Ge . We havestudied the samples with a wide range of f Ge by HRTEM andfound that the average separation of nanocrystals is not sosensitive to f Ge , provided that the annealing condition is thesame. On the other hand, the average diameter depends
strongly on f Ge as can be seen in Table I. Since E c and E dare proportional to d 21 and d 22 , respectively, the reductionof the size causes significant increases in E c and E d . DE isalso considered to increase significantly, because E d becomes very sensitive to the size as the size decreases. ThereFujii et al.

1511

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp

fore, we believe that the observed increase in T 0 is caused by
the decrease in the size of Ge nanocrystals with decreasingf Ge .
In the present work, I – V characteristics were nearly
Ohmic ( s is nearly constant! as shown in Fig. 3. In the caseof metal–insulator composite films, s is nearly constant at
low electric fields and at high electric fields, ln( s ) is proportional to the inverse of the applied field. We tried to measure
the conduction at high electric fields. However, the present
samples were vulnerable and the maximum electric field we
could apply was 53104 V/cm. In this electric field range, theconductivity was almost constant.
3. Conduction properties of SiO2 films containing Ge
clusters

In our previous work,23 we have studied I – T characteristics of Si, Ge, or C doped SiO2 films prepared by cosputtering of Si, Ge, or C with SiO2 ~without any thermal treatment!. We demonstrated that these films generally exhibit a
T 21/4 dependence of ln( s ). Since previous optical studies forthese films indicated that they are the systems of Si, Ge, or C
clusters much smaller than 2 nm dispersed in SiOx
matrices,8,24–26 the conduction is considered to be mediatedby the electronic states associated with the clusters distributed in the films.
The results of the present work demonstrate that the I – T
characteristics of the films change from ln( s )}T 21/4 to ln( s )}T 21/2 relation as the clusters grow to nanocrystals several nanometers in diameter by the thermal annealing. In aprevious theoretical work for the metal–insulator composite
films, the crossover of ln( s )}T 21/2 and ln( s )}T 21/4 ispredicted.18 It was suggested that the temperature at which
the crossover occurs depends on the particle size. As the size
decreases ~activation energy increases!, the temperature region of the ln( s )}T 21/4 extends and this becomes a betteroverall fit than T 21/2. On the other hand, increasing the grain
size ~decreasing the activation energy! has the effect of extending the T 21/2 region to lower temperature. Therefore, theobserved change from ln( s )}T 21/4 relation to ln( s )}T 21/2
relation by the thermal annealing may be explained by thedecrease of the activation energy due to the growth of thenanocrystals.
V. SUMMARY

In summary, we have studied electrical transport properties of SiO2 films containing Ge nanocrystals. We found thatthe present samples exhibit the T 21/2 dependence of ln( s ) at
relatively low electric fields for a wide range of the volume
fraction of Ge nanocrystals. We also found that as the volume fraction of Ge nanocrystals increases, the slope of the ln( s )}T 21/2 relation decreases. From the conduction properties and sample structures, we concluded that carrier transport in the present samples is carried out via Ge nanocrystals

1512

J. Appl. Phys., Vol. 83, No. 3, 1 February 1998

by tunneling between adjacent nanocrystals. The activationenergies obtained from I – T characteristics were in good
agreement with that estimated by the Šimánek’s theory. It
was found that not only the charging energy but also the
distribution of the quantized conduction band edge between
the nanocrystals play significant roles in determining the
conduction properties. We observed very similar conduction
properties for SiO2 films containing Si nanocrystals. The results will be published elsewhere.
ACKNOWLEDGMENTS

The authors are grateful to M. Kayahara for his valuableassistance in the experiment. This work was supported by aGrant-in-Aid for Scientific Research, from the Ministry of
Education, Science, Sports and Culture, Japan, and a grantfrom the Takayanagi Foundation for Electronics Science andTechnology.
L. T. Canham, Appl. Phys. Lett. 57, 1046 ~1990!.
H. Takagi, H. Ogawa, Y. Yamazaki, A. Ishizaki, and T. Nakagiri, Appl.
Phys. Lett. 56, 2379 ~1990!.
3
H. Morisaki, F. W. Ping, H. Ono, and K. Yazawa, J. Appl. Phys. 70, 1869
~1991!.
4
K. A. Littau, P. J. Szajowski, A. J. Muller, A. R. Kortan, and L. E. Brus,
J. Phys. Chem. 97, 1224 ~1993!.
5
Y. Kanzawa, M. Fujii, S. Hayashi, and K. Yamamoto, Solid State Commun. 100, 227 ~1996!.
6
Y. Kanzawa, T. Kageyama, S. Takeoka, M. Fujii, S. Hayashi, and K.
Yamamoto, Solid State Commun. 102, 533 ~1997!.
7
K. S. Min, K. V. Shcheglov, C. M. Yang, H. A. Atwater, M. L. Brongersma, and A. Polman, Appl. Phys. Lett. 68, 2511 ~1996!.
8
M. Fujii, S. Hayashi, and K. Yamamoto, Jpn. J. Appl. Phys., Part 1 30,
687 ~1991!.
9
M. Fujii, M. Wada, S. Hayashi, and K. Yamamoto, Phys. Rev. B 46,
15 930 ~1992!.
10
Y. Maeda, Phys. Rev. B 51, 1658 ~1995!.
11
L. Yue and Y. He, J. Appl. Phys. 81, 2910 ~1997!.
12
M. Zacharias, R. Weigand, B. Dietrich, F. Stolze, J. Bläsing, P. Veit, T.
Drüsedau, and J. Christen, J. Appl. Phys. 81, 2384 ~1997!.
13
D. C. Paine, C. Caragianis, T. Y. Kim, Y. Shigesato, and T. Ishahara,Appl. Phys. Lett. 62, 2842 ~1993!.
14
M. Nogami and Y. Abe, Appl. Phys. Lett. 65, 2545 ~1994!.
15
V. Craciun, C. Boulmer-Leborgne, E. J. Nicholls, and L. W. Boyd, Appl.
Phys. Lett. 69, 1506 ~1996!.
16
B. Abeles, P. Sheng, M. D. Coutts, and Y. Arie, Adv. Phys. 24, 407~1975!.
17
E. Šimánek, Solid State Commun. 40, 1021 ~1981!.
18
P. Sheng and J. Klafter, Phys. Rev. B 27, 2583 ~1983!.
19
G.-F. Hohl, S. D. Baranovskii, J. A. Becker, F. Hensel, S. A. Quaiser, and
M. T. Reetz, J. Appl. Phys. 78, 7130 ~1995!.
20
A. L. Efros and B. I. Shklovskii, J. Phys. C 8, L49 ~1975!.
21
D. V. Averin, A. N. Korotkov, and K. K. Likharev, Phys. Rev. B 44, 6199
~1991!.
22
J. M. Ziman, J. Phys. C 1, 1532 ~1968!.
23
M. Fujii, Y. Inoue, S. Hayashi, and K. Yamamoto, Appl. Phys. Lett. 68,
3749 ~1996!.
24
Y. Kanzawa, S. Hayashi, and K. Yamamoto, J. Phys.: Condens. Matter 8,4823 ~1996!.
25
S. Hayashi, M. Kataoka, and K. Yamamoto, Jpn. J. Appl. Phys., Part 2 32,
L274 ~1993!.
26
S. Hayashi, M. Kataoka, Y. Kanzawa, and K. Yamamoto, Proceedings ofthe 22nd International Conference on the Physics of Semiconductors,
1995, p. 2023.
1
2

Fujii et al.

Downloaded 10 Jun 2002 to 133.30.106.15. Redistribution subject to AIP license or copyright, see http://ojps.aip.org/japo/japcr.jsp