Charge injection and tunneling mechanism of solid state reactionsilicon nanocrystal ﬁlm
H. W. Lau and O. K. Tan
a
Microelectronics Center, School of Electrical and Electronic Engineering, Nanyang Technological University, Singapore 639798, Singapore
D. A. Trigg
Institute of Microelectronics, 11 Science Park Road, Singapore 117685, Singapore
Received 8 June 2006; accepted 24 July 2006; published online 15 September 2006
Solid state reaction silicon nanocrystals
Si nc’s
of an average size of 10 nm have been synthesized.Charge transport characteristics have been investigated as a function of temperature and voltage.From 305 to 400 K, it is found that spacechargelimited current
SCLC
, with an exponentialdistribution of trapping states, dominates the conduction mechanism. High resolution transmissionelectron microscope images indicate that microscopic structural defects, such as dislocations, arepresent in this solid state reaction Si nc. These defects are a possible source of trapping states asdescribed in the SCLC model. Using this model, a trap density of
N
t
=1.46
10
18
cm
−3
and acharacteristic trap temperature
T
t
=2057 K can be extracted. The trap density is two orders of magnitude greater than the Si nc density, showing that the structural defects in Si nc, such asdislocations and grain boundaries, are capable of trapping more carriers in a single solid statereaction Si nc. ©
2006 American Institute of Physics
.
DOI: 10.1063/1.2345257
Silicon nanocrystals
Si nc
have been an active area of research for their memory effects.
1–3
Ever since the ﬁrst Sinc memory device was reported,
1
many groups have workedindependently on the electrical properties of Si nc.
2,3
Manymethods of creating Si nc based memory devices have beendemonstrated. They include ion implantation, chemical vapordeposition, and cosputtering. Alternatively, Si nc can be produced by solid state reaction.
4–6
Recently, solid state reactionSi nc has been reported to possess charging trapping effects.
4
This posed another possible alternative fabrication of Si ncmemory devices.Up to the present, there have only been a few investigations of macroscopic electronic conduction mechanismacross Si nc ﬁlms.
7,8
Although there are numerous reportsindicating singleelectron charging effects through a singlenanocrystal,
9
this effect is not clear in the practical caseswhere there are large amounts of nanocrystals. At high bias,it is possible to observe electron emission from thin ﬁlms of nanocrystals.
10
Currently, there are a few models, such as thepercolation model
11
and spacechargelimited currentmodel,
8
reported to describe macroscopic electronic conduction mechanisms in nanocrystal ﬁlms. Although solid statereaction Si nc provides an easy method to fabricate highdensity Si nc ﬁlm, none of these models has been used toinvestigate the macroscopic electronic conduction mechanism of this form of Si nc ﬁlm. In this letter, we report on thedominating conduction mechanism of space charge limitedcurrent
SCLC
in this solid state reaction Si nc ﬁlm. At thesame time, the characteristic temperature and trap density of this form of solid state reaction Si nc ﬁlm are derived usingthe SCLC model.The preparation of Si nc by solid state reaction
5
andtetraethylorthosilicate
TEOS
solution
6
were well describedelsewhere.
5
After milling for 20 h the Si nc was dispersed inethanol. This suspension was centrifuged and the residue wasextracted. After the TEOS solution was hydrolyzed for 48 h,the residue, at a mole ratio of 8:1 with TEOS, was added tothe solution. This mixture was stirred for another 24 h.
p
type
100
Si wafers with a resistivity of 10–20
cmwere used as the substrates. Each layer of ﬁlm, containingsolid state reaction Si nc, was spun onto the substrate at3000 rpm for 30 s
300 nm thick
. The thickness of eachﬁlm layer was characterized using Filmetric F20 from Filmetric Inc. The ﬁlm containing solid state reaction Si nc wasannealed in air for 6 min at 800 °C to densify the ﬁlm. Aluminum
Al
was evaporated to form the top electrodes
150
m in diameter
. The native SiO
2
on the back side of theSi wafer was etched away before the Al bottom electrodewas deposited. Transmission electron microscope
TEM
images were obtained using a JEM 2010 TEM operating at200 kV acceleration. The currentvoltage
IV
measurementswere collected with Keithley 4200 semiconductor characterization system from 305 to 400 K.Figure 1 shows the TEM image indicating solid statereaction Si nc in the ﬁlm. From TEM observation, it is observed that the average size of the Si nc is between 4 and10 nm. This size is consistent with the results obtained fromxray diffraction and Scherrer’s equation
4,5
which gives anaverage grain size of 10 nm. This is the common size rangeused for the study of electrical properties of Si nc.
6–8
Using
a
Electronic mail: eoktan@ntu.edu.sg FIG. 1. TEM image indicating solid state reaction Si nc in the ﬁlm.
APPLIED PHYSICS LETTERS
89
, 113119
2006
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the LambertBeer law, UVvisible spectroscopy results revealthat the weight ratio of Si nc to ethanol
of the residue
is1:0.12. Using the volume of the thin ﬁlm, weight ratio of Sinc with ethanol, and zincblende structure of Si, it is derivedthat the eventual number density is
1.36
10
16
cm
−3
. Figure 2
a
shows the
IV
characteristics of a 150
m diameterdiode from 305 to 400 K on a loglog plot. The inset of Fig.2
a
shows
IV
characteristics of the device from −10 to1.5 V
linear scale
at 305 K. A positive voltage is applied to thesubstrate contact which corresponds to a forward biased substrate. The
IV
curve reveals a rectifying behavior. The rectifying ratio at 300 K,
I
F
/
I
R
=165 at
V
=2.5 V, and theturnon voltages for forward and reverse biases are
V
F
1.25 V and
V
R
−9.1 V, respectively. This rectifying nature is due to the
p
Si/Si nc/top Al electrode.
8
The
IV
characteristics of this device can be represented by a serial combination of a diode and a resistor.
7,12
I
=
I
0
exp
q
V
−
IR
nkT
,
1
where
I
o
is the saturation current in reverse bias,
n
is theideality factor, and
R
is a resistance usually assumed to beindependent of applied voltage. Figure 2
b
illustrates thecurve ﬁtting of
IV
characteristics at 300 K based on Eq.
1
The general behavior of the
IV
curve is reproduced with anideality factor
n
of
13.1 and a series resistance
R
of
1487
. This high ideality factor suggests that the
IV
characteristic of this device is not limited by the metal/ semiconductor Schottky barrier, but rather by the carriertransport through the solid state reaction Si nc itself.
7,12
The currents, when the voltage applied is above itsturnon voltage, increase along a straight line in the loglogplot, as shown in Fig. 2
a
. This relationship corresponds tothe power law where
I
V
m
. Ranging from 305 to 400 K, it isfound that
m
varies from 2.68 to 1.03, and a correspondingthreshold voltage from 1.25 to 0.42 V. The reduction in
m
leads to a convergence of the
IV
behavior from 305 to 400 Kwhere the curves can be extrapolated to meet at a singlepoint, as shown in Fig. 3
a
. It has been demonstrated
8
thatSi nc, fabricated by plasma decomposition of SiH
4
, exhibitsa similar trend from 200 to 300 K. Rose
13
and Mark andHelfrich
14
explained this behavior by using SCLC modelwith an exponential density of traps. In our devices, freecarriers are injected from the substrate into the transportstates in the Si nc ﬁlm. An exponential distribution of trapswill reduce the amount of free carriers during the transport.
13
With an increasing voltage where the Fermi level is of highermagnitude than the trap levels, free carriers will ﬁll the trapsand there will be an increased amount of free carrier.
8
Assuming a constant mobility with an exponential distributionof traps and majority hole carriers, the current density can bemodeled as
7,8,12,14
J
=
q
1−
l
p
N
v
2
l
+ 1
l
+ 1
l
+1
ll
+ 1
s
o
N
t
l
V
l
+1
d
2
l
+1
,
2
where
N
t
is the trap density,
o
is the permittivity of freespace,
s
is the dielectric constant,
p
is the hole mobility,
N
v
is the density of transport states,
d
is the sample thickness,and
l
=
T
t
/
T
, where
T
t
is the characteristic temperature and
T
is the measurement temperature.
T
t
is, in turn, related to thecharacteristic energy of the trap distribution as
E
t
=k
B
T
t
,where
k
B
is the Boltzmann constant. Equation
2
can be
FIG. 2.
a
IV
characteristics of a 150
m diameter diode from305 to 400 K on a loglog plot. Inset:
IV
characteristics of the devicefrom −10 to 1.5 V
linear scale
at 305 K.
b
Curve ﬁtting of
IV
characteristic at 305 K based on Eq.
1
.FIG. 3.
Color online
a
SCLC power law ﬁts to the data in Fig. 2
a
from305 to 400 K and
b
variation of exponent factor
m
with respect to inversetemperature.
1131192 Lau, Tan, and Trigg Appl. Phys. Lett.
89
, 113119
2006
Downloaded 15 Sep 2006 to 155.69.4.4. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp
simpliﬁed into a power law dependence where
J
V
m
, wherethe exponent factor
m
=
l
+1. In this way, the gradient in theloglog plot of the
J

V
relationship will directly give thecharacteristic temperature and thus the characteristic energy.Figure 3 shows
a
the SCLC power law ﬁts to the datain Fig. 2
a
from 305 to 400 K and
b
the variation of exponent factor
m
with respect to inverse temperature. Uponthe power law ﬁtting of Fig. 2
a
results, Fig. 3
a
revealsthat
m
decreases as temperature increases
or inverse temperature decreases
. This is as predicted by the SCLC theory.Using Fig. 3
b
, the gradient of the straight line reveals thatthe values of
T
t
and
E
t
are 2056 K and 0.17 eV, respectively.Kumar
et al.
15
has further approximated Eq.
1
to anArrhenius form,
J
=12
qV
p
N
v
d
exp
−
E
t
kT
ln
qN
t
d
2
2
s
o
V
,
3
where the activation energy is
E
a
=
E
t
k
ln
qN
t
d
2
2
s
o
V
.
4
Using Eq.
3
a plot of ln
J
vs 1/
T
at a constant voltage willgive a gradient of
E
a
, as shown in Eq.
4
From Eq.
4
, thetotal trap density can be determined. Using this method, agraph using ln
I
vs 1/
T
is plotted and
N
t
is found to be1.46
10
18
cm
−3
at a bias of 1 V. By a further examinationof Eq.
3
, it is revealed that the current is almost independent of temperature, where
E
a
=0, at a crossover voltage,
7,8
V
c
=
qN
t
d
2
2
s
o
.
5
Extrapolation of the curves from Fig. 2
a
results in the convergence of the curves. The corresponding voltage is thecrossover voltage
V
c
100 V, as shown in Fig. 3
a
. FromEq.
5
, it is derived that
N
t
is 1.44
10
18
cm
−3
, which isclose to the
N
t
determined from Eq.
4
.The value of
N
t
is 100 times larger than the Si nc density.This is quite unlike the results reported by Ratiq
et al.
8
whoobserved that the values of
N
t
and the nanocrystal density
N
nc
were similar. For solid state reaction Si nc, other thanthe potential well existing in the Si nc,
8,16
defect states alsoplays a major role in the contribution to the trap density. Ithas been reported
17
that traps present at the interfaces, grainboundaries, and defects in Si nc
Ref. 5
are capable of inducing charge trapping as well. Lu and Lai
18
have reportedthat high energy ball milling is often capable of creatingstructural defects such as surface defects, dislocations, grainboundaries, etc. Figure 4 shows high resolution TEM imagesrevealing
a
dislocations and
b
grain boundaries in thesolid state reaction Si nc. Dislocations and grain boundariesare evident in the Si nc. These dislocations and grain boundaries may be deep traps that contribute to the approximately100 traps per Si nc. It has been reported that in CdSe nanocrystals, an
N
t
/
N
nc
ratio of 100 was observed for deeptraps.
19
This is similar to solid state reaction where dislocations are prominent. This explains why a higher
E
t
at0.17 eV, as a result of higher
T
t
at 2057 K, is required to“free” the trapped holes as compared to the
E
t
of 0.14 eV forSi nc by plasma decomposition
8
and 0.08 eV for amorphousSi nc.
7
Though defects in Si nc are presented, they are reported to be efﬁcient charge trapping centers.
17
In conclusion, the SCLC theory can be used to model themacroscopic electronic conduction mechanism of solid statereaction Si nc thin ﬁlm.
N
t
and
E
t
values are found to be1.46
10
18
cm
−3
and 0.17 eV. The
N
t
/
N
nc
ratio is
100 dueto the existence of structural defects. This is attributed to thedislocations which exist as deep traps. The higher
E
t
value,as compared to Si nc synthesized by plasma deposition andamorphous Si,
8
shows that higher trap energy is required forthe release of holes in these deep traps. The high
N
t
/
N
nc
ratioand
E
t
values provide evidences of larger charge trappingability and longer retention times which is of high importance to Si nc memory devices.
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.FIG. 4. High resolution TEM images revealing
a
dislocations and
b
grainboundaries in the solid state reaction Si nc.
1131193 Lau, Tan, and Trigg Appl. Phys. Lett.
89
, 113119
2006
Downloaded 15 Sep 2006 to 155.69.4.4. Redistribution subject to AIP license or copyright, see http://apl.aip.org/apl/copyright.jsp