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Physica E 40 (2008) 2859–2861 Phonon-assisted tunneling process in amorphous silicon nanostructures and GaAs nanowires P. Ohlckers à , 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 0.5m e , 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. r 2008 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 densit y–voltage (I–V) charact eristics 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 explanat ion 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]: I ¼ 1 2 AeNW , (1) ARTICLE IN PRESS 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 à Corresponding author. Tel.: +47 33037718; fax: +47 33031103. E-mail address: Per.Ohlckers@hive.no (P. Ohlckers). where 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 experi mental 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: W t ¼ eE ð8m n T Þ 1=2 ½ð1 þ g 2 Þ 1=2 À g 1=2 ½1 þ g 2 À1=4  exp À 4 3 ð2m n Þ 1=2 eE_ 3=2 t ½ð1 þ g 2 Þ 1=2 À g 2 Âð1 þ g 2 Þ 1=2 þ 1 2 g , (2) where g ¼ ð2m n Þ 1=2 G 2 8e_E 1=2 T . (3) Here G 2 ¼ 8 a ð_oÞ 2 ð2n þ 1Þ is the width of the absorption band of a center, n ¼½expð_o=k B TÞÀ1 À1 , where _o is the phonon energy, e T is 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 G 2 0 =8ð_oÞ 2 Þ, where G 0 is 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 0.5m e , 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 in Fig. 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  10 15 cm À3 , 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 J$V l+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 0.067m e for 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 T ¼ 0. ARTICLE IN PRESS 3.6 -20 -15 -10 -5 0 5 0 5 10 15 20 25 iln J (A/cm -2 ) ln E (MV/m) 30K 80 130 180 230 290 Irrera, 2006 Si nano ln E (MV/m) ln W (s -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 0.74eV, m* ¼ 0.5m e , _o ¼ 12 meV. P. Ohlckers, P. Pipinys / Physica E 40 (2008) 2859–28612860 15 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 advantag e 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, S ˇ . Kudzˇ mauskas, 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. ARTICLE IN PRESS -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 I (nA) ln V (V) 260K 220K 190K 160K Schrick 2006 GaAs nanwr 220 160 260 190 ln W (s -1 ) ln E (MV/m) -2.0 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 -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. P. Ohlckers, P. Pipinys / Physica E 40 (2008) 2859–2861 2861 . 40 (2008) 2859–2861 Phonon-assisted tunneling process in amorphous silicon nanostructures and GaAs nanowires P. Ohlckers à , P. Pipinys Vestfold University. 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