Đây là một bài báo khoa học về dây nano silic trong lĩnh vực nghiên cứu công nghệ nano dành cho những người nghiên cứu sâu về vật lý và khoa học vật liệu.Tài liệu có thể dùng tham khảo cho sinh viên các nghành vật lý và công nghệ có đam mê về khoa học
Trang 1Physica E 40 (2008) 2859–2861
Phonon-assisted tunneling process in amorphous silicon nanostructures
and GaAs nanowires
P Ohlckers , P Pipinys Vestfold University College, Raveien 197, Toensberg N-3103, Norway Received 12 September 2007; accepted 4 January 2008
Available online 14 February 2008
Abstract
Experimental results on the current–voltage (I–V) characteristics of amorphous Si nanostructures reported by Irrera et al [A Irrera,
F Iacona, I Crupil, C.D Presti, G Franzo, C Bongiorno, D Sanfilippo, G Di Stefano, A Piana, P.G Fallica, A Canino, F Priolo, Nanotechnology 17 (2006) 1428] are reinterpreted in terms of a phonon-assisted tunneling model It is shown that temperature dependence
of current can be caused by the temperature dependence of electron tunneling rate from traps in the metal–semiconductor interface to the conduction band of the semiconductor A good fit of experimental data with the theory is achieved in all measured temperature range from
30 to 290 K using for calculation the effective mass of 0.5me, and for the phonon energy the value of 12 meV An advantage of this model over that of Irrera et al used model is the possibility of describing the behavior of I–V data measured at both high and low temperatures with the same set of parameters characterizing this material The temperature-dependent I–V data by Schricker et al [A.D Schricker, F.M Davidson III, R.J Wiacek, B.A Korgel, Nanotechn 17 (2006) 2681.] of GaAs nanowires, are also explained on the basis of this model
r2008 Elsevier B.V All rights reserved
PACS: 73.21.Hb; 78.67.Lt; 72.20.Jv; 73.40.Gk
Keywords: Si; GaAs nanostructures; Electron transport; Phonon-assisted tunneling
1 Introduction
Current density–voltage (I–V) characteristics measured
over a wide range of temperatures (from 30 to 290 K) for a
device containing amorphous Si nanoclusters were
pre-sented in the recently published paper by Irrera et al [1]
The I–V characteristics exhibited substantial dependence
on a temperature The strongest temperature dependence
has been observed at low electric field The authors of
Ref.[1]asserted that none of the known mechanisms based
on tunneling, neither Poole–Frenkel (PF) emission nor
hopping conduction are able to explain fully the observed
peculiarities of the electrical properties of the objects under
investigation Authors of Ref.[1]itemize tunneling process
like the direct tunneling[2], the Fowler–Nordheim
tunnel-ing mechanism [3] and the trap-assisted tunneling [4]
They all are temperature-independent mechanisms, and,
certainly, cannot explain the strongly temperature-depen-dent I–V data We want to note that without above enumerated tunneling mechanisms phonon-assisted tunnel-ing (PhAT) is established [5,6], which is essentially a temperature-dependent process PhAT has been success-fully used for explanation of the temperature-dependent current–voltage data of thin films [7]and Schottky diodes
[8] In the presented work we apply the phonon-assisted tunneling model approach for explanation of the tempera-ture peculiarities of the I–V characteristics in the amor-phous silicon nanostructures and GaAs nanowires recently published in Refs.[1,9]
2 Theory and a comparison with experimental data
If the current is dominated by the process of charge carriers emission from traps, then the current’s value I may
be expressed by the relation[10]:
www.elsevier.com/locate/physe
1386-9477/$ - see front matter r 2008 Elsevier B.V All rights reserved.
doi: 10.1016/j.physe.2008.01.012
Corresponding author Tel.: +47 33037718; fax: +47 33031103.
E-mail address: Per.Ohlckers@hive.no (P Ohlckers).
Trang 2where A is the effective generation volume, e is the
electronic charge unit, N is the traps density and W is the
rate of tunneling Some tunneling theories accounting
the interaction of electrons with phonons are known[5,6],
in which the tunneling is temperature-dependent process
In the presented paper, we will interpret the experimental
results of current dependence on applied voltage and
temperature by analyzing the transition rate W(E,T) of
electron/hole from deep center to conduction band and
using in this manner dependences on the field strength and
on temperature, which follows from the
quantum-mechan-ical phonon-assisted tunneling theory For this purpose, a
relatively simple equation derived for electron tunneling
from deep center to the conduction band derived in Ref.[5]
is used:
Wt¼ eE
ð8mn
TÞ1=2½ð1 þ g2Þ1=2g1=2½1 þ g21=4
exp 4
3
ð2mn
Þ1=2
eE_
3=2
t ½ð1 þ g2Þ1=2g2
ð1 þ g2Þ1=2þ1
2g
where
g ¼ð2m
n
Þ1=2G2
8e_E1=2
T
Here G2¼8að_oÞ2ð2n þ 1Þ is the width of the absorption
band of a center, n ¼ ½expð_o=kBT Þ 11, where _o
is the phonon energy, eTis the energetic depth of the trap, e
is the electronic charge unit, m* is the electron effective
mass, and a is the electron–phonon coupling constant
ða ¼ G20=8ð_oÞ2Þ, where G0is the width of center band at
temperature 0 K
Thus, let us compare the temperature-dependent
char-acteristics extracted from Fig 2(b) in Ref [1] with
theoretical W(E,T) dependences calculated using the
Eq (2) The calculation was performed using the traps
depth value of 0.74 eV The effective mass of carrier m* was
taken to be equal to 0.5me, and for the phonon energy the
value of 12 meV was taken The value of the parameter a
was chosen to get the best fit of simulated W(T,E) curves
with a set of experimental data The theoretical ln W
versus 1/T dependences fitted to the experimental data
are depicted by solid lines inFig 1 It is seen that in whole
range of temperatures, the experimental data fit well with
computed dependences, with exception of only low voltage
tails of curves obtained at 230 and 290 K temperatures The
traps density evaluated from the fit of the experimental
data with the theory was found to be equal to
1.5 1015cm3, the thickness of Si layer being 70 nm
Very similar temperature-dependent I–V data have
been obtained by Schricker et al for GaAs nanowires[9]
The I–V curves became increasingly nonlinear with
decreasing temperature and followed the scaling
relation-ship JVl+1 In the low bias region, the curves were ohmic
(i.e l+1 ¼ 1) The authors of Ref [9] suggested that at lower temperatures, space charge-limited currents dom-inate with l increasing as T decreases We will show that observed peculiarities of the I–V data can be also described
by PhAT model In Fig 2, the experimental results extracted from Fig 7a in Ref.[9] are fitted to computed W(T,E) data
The calculation of W(T,E) was performed by using the value of 0.067mefor effective mass[11], and by selecting the value of 13 meV for the phonon energy The electron– phonon coupling constant a was chosen so that the best fit
of the experimental data with the calculated dependences should be received on the assumption that the field strength
at the junction is proportional to the square root of the applied voltage, i.e the tunneling occurs in the high field region of the Schottky barrier In this case, the source of charge carriers are traps in the electrode–GaAs nanowire interface layer from which the electrons emerge to the conduction band of semiconductor due to the phonon-assisted tunneling The electron population in the traps is assumed to be independent of bias voltage due to the continuous filling the traps in the interface layer from the electrode The center depth (activation energy) of e ¼0
3.6 -20 -15 -10 -5 0 5
0 5 10 15 20 25
-2 )
ln E (MV/m)
30K 80 130 180 230 290
Irrera, 2006
Si nano
ln E (MV/m)
-1 )
3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8 3.6 3.8 4.0 4.2 4.4 4.6 4.8 5.0 5.2 5.4 5.6 5.8
Fig 1 Current versus E dependences for Si nanostructure at different temperatures from ( [1] , Fig 2b (symbols)) fitted to theoretical W(E,T) versus E dependences (solid curves), calculated for parameters: a ¼ 20,
e T ¼ 0.74 eV, m* ¼ 0.5m e , _o ¼ 12 meV.
Trang 315 eV was extracted for this sample from Table 1 in
Ref [9] The comparison shows a good agreement of the
experimental data with the calculated ln W(T,E) versus ln E
curves in at all measured temperatures
3 Conclusion
In conclusion, it has been shown that the phonon-assisted tunneling model describes well the peculiarities of the temperature-dependent I–V data in thin films of Si nanostructures and GaAS nanowires for explanation elsewhere [1,9] were invoked different mechanisms The comparison of experimental data with calculated depen-dencies allows to estimate the field strength at which the free charge carriers are generated, and the density of charged centers An advantage of the PhAT model is the possibility to describe the behavior of I–V data measured at different temperatures with the same set of parameters characterizing the material
Thus, the phonon-assisted tunneling mechanism must
be taken into account in explaining the temperature-dependent I–V characteristics of devices on the basis of Si nanostructures and GaAs nanowires
References
[1] A Irrera, F Iacona, I Crupi1, C.D Presti, G Franzo, C Bongiorno,
D Sanfilippo, G Di Stefano, A Piana, P.G Fallica, A Canino,
F Priolo, Nanotechnology 17 (2006) 1428.
[2] S.M Sze, Physics of Semiconductor Devices, Wiley, New York, 1981 [3] R.H Fowler, L Nordheim, Proc R Soc A 119 (1928) 181 [4] B Ricco, G Gozzi, M Lanzoni, IEEE Trans Electron Devices 45 (1998) 1554.
[5] A Kiveris, Sˇ Kudzˇmauskas, P Pipinys, Phys Status Solidi (a) 37 (1976) 321.
[6] F.I Dalidchik, Zh Eksp Teor Fiz 74 (1978) 472 [Sov Phys JETP
47 (1978) 247].
[7] P Pipinys, A Rimeika, V Lapeika, Phys Status Solidi (b) 242 (2005) 1447.
[8] P Pipinys, V Lapeika, J Appl Phys 99 (2006) 093709.
[9] A.D Schricker, F.M Davidson III, R.J Wiacek, B.A Korgel, Nanotechnology 17 (2006) 2681.
[10] P Migliorato, C Reita, G Tallarida, M Quinn, G Fortunato, Solid-State Electron 38 (1995) 2075.
[11] J.S Blakemore, J Appl Phys 53 (1982) R123.
-2.5
-9
-8
-7
-6
-5
-4
-3
-2
-1
0
1
2
9 10 11 12 13 14 15 16 17 18 19
ln V (V)
260K
220K
190K
160K
Schrick 2006 GaAs nanwr
220
160
260
190
-1 )
ln E (MV/m)
-0.2 0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6
Fig 2 Current versus V dependences for GaAs nanowires at different
temperatures from (Ref [9] , Fig 7a (symbols)) fitted to theoretical W(E,T)
versus E dependences (solid curves), calculated for parameters: a ¼ 1.7,
e T ¼ 0.154 eV, m* ¼ 0.067m e , _o ¼ 12 meV.