A Model for the Mechanisms of Charge Transport Controlled by the Short-range Mobility
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A Model for the Mechanisms of Charge Transport Controlled by the Short-range Mobility Valerio Dallacasa Department of Computer Science, University of Verona, Italy ABSTRACT Studies of carrier motion in a variety of nanostructures have indicated that a modified Drude model can be applied, by considering carrier bound motion from backscattering mechanisms and localized oscillator modes. Based on the results of these studies a model of damped harmonic oscillation modes is suggested to evaluate transport parameters in piezotronic devices. Here, the case of a system subject to static and low frequency piezoelectric fields is considered which corresponds to typical working conditions of nanogenerators and, as a working example, the response of ZnO nanowires excited by sound waves is analyzed.
INTRODUCTION Nanogenerators based on piezoelectric semiconductor nanostructures are a promising technique for self-powering of nanosystems. Enhancement of the power generation is needed to commercial applications of devices with low operating power consumption. A strategy of applying acoustic and ultrasonic waves on ZnO nanowires devices has proved successful [1,2]. Recently, engineered ZnO structures have shown an output power at the level suitable to drive electrophoretic ink displays [3]. For realizing highly efficient nanogenerators the control of transport parameters is one of the most important issues. A number of studies in systems at nanoscale [4-9] have indicated that the dynamics of carriers shows departures from the Drude model, with the real part of the conductivity displaying a minimum at zero frequency and a transfer of oscillator strength to higher frequency and with the imaginary part of the conductivity being negative at small frequency. It is impossible to explain these data with the mathematical form of the Drude model. It has been suggested that carrier bound motion from backscattering mechanisms and localized oscillator modes are the origin of this behaviour. The Smith model [10], based on backscattering, has been used successfully to explain data in TiO2 nanoparticles and ZnO nanowires [7], silicon nanocrystal films [8] and gold films at the metal-insulator transition [9]. Carbon nanotube films [4,5] have been described by a multioscillator Drude-Lorentz model. On the basis of such evidences, in order to get insight into the possible power enhancement of nanostructures, we apply these models to piezoelectric nanodevices. Results are presented for the conductivity and mobility as a function of frequency of ZnO nanowires and for the current density of a typical nanodevice.
THEORY The Drude model is the straighforward model for conductivity in metals and semiconductors. This model considers a free electron gas with complete randomization in scattering events.
Departures from Drude behaviour can be accommodated in the Drude-Smith (D-S) and DrudeLorentz (D-L) models . The complex conductivity at a frequency in the Drude-Smith model has the form [10]
( )
ne 2 / m c 1 1 i (1 i )
(1)
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