Hydrodynamic transport parameters of wurtzite ZnO from analytic- and full-band Monte Carlo simulation Enrico Furno a , Francesco Bertazzi a,b , Michele Goano a, * , Giovanni Ghione a , Enrico Bellotti b a Dipartimento di Elettronica, Politecnico di Torino, corso Duca degli, Abruzzi 24, 10129 Torino, Italy b ECE Department, Boston University, 8 Saint Mary’s Street, 02215 Boston, MA, USA article info Article history: Received 8 June 2008 Received in revised form 5 August 2008 Accepted 5 August 2008 Available online 1 October 2008 The review of this paper was arranged by Prof. A. Zaslavsky Keywords: ZnO Monte Carlo transport simulation Hydrodynamic transport simulation Electron thermal conductivity Noise diffusivity abstract Analytic-band Monte Carlo simulation of electron transport in bulk wurtzite ZnO, validated against the results of a full-band code and available experimental data, is used to determine the main parameters required by drift-diffusion and hydrodynamic models. Steady-state drift velocity, carrier temperature, energy and momentum relaxation time, noise diffusivity, and electron thermal conductivity are calcu- lated, and their dependence on temperature and electric field or average electron energy is approximated by means of a complete set of fitting models suitable for inclusion in commercial device simulation tools. Ó 2008 Elsevier Ltd. All rights reserved. 1. Introduction Zinc oxide (ZnO) has seen practical applications much earlier than most wide band gap semiconductors, but only recently it has received renewed attention for electronic and optoelectronic applications because of its potential advantages over III-nitrides, including commercial availability of bulk single crystals, amenabil- ity to wet chemical etching, a larger exciton binding energy, and excellent radiation hardness [1,2]. A remarkable feature of ZnO, compared to most direct-gap semi- conductors, is the absence of secondary valleys in the conduction bands at energies lower than 7 eV from the band edge (the interv- alley separation is about 330 meV in GaAs and 2.25 eV in GaN), since saddle points are present in A 1 , C 3 , and along the M–L edge [3]. This means that a simple analytical nonparabolic approxima- tion for the conduction band around the center of the Brillouin zone could be satisfactory even at moderately high electric fields, thus allowing analytic-band Monte Carlo (ABMC) simulation to match full-band (FBMC) results up to several hundred kV/cm. Moreover, the fact that electrons are confined in a single nearly spherical valley suggests that the energy and momentum distribu- tion functions of electrons could preserve a nearly ideal Maxwellian or Gaussian form, respectively, even when the carrier temperature T e is significantly higher than the lattice temperature T. This feature would make standard hydrodynamic models attractive for reliable simulation of electronic devices at low-to-moderate electric fields, provided that accurate estimates of all transport parameters are available. In order to check these hypotheses, Section 2 compares ABMC and FBMC results, determining the range of electric field values where the first approach allows reliable predictions of bulk ZnO electron transport properties. A comparison between ABMC simulations and available experimental information on low-field transport properties is also discussed. After this assessment, ABMC simulations are used in Section 3 to determine a complete set of fitting coefficients for the analytical models of three key transport parameters: steady-state electron velocity as function of temperature, doping density and electric field, and energy and momentum relaxation times as functions of the average electron energy. Finally, Section 4 presents the electric field dependence of the noise and spreading diffusion coefficients and the temperature and electric field dependence of the elec- tron thermal conductivity, which is an essential ingredient for the closure of hydrodynamic models but is usually approximated in terms of the electron conductivity using the Wiedemann– Franz law. 0038-1101/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved. doi:10.1016/j.sse.2008.08.001 * Corresponding author. Tel.: +39 0115644142. E-mail addresses: michele.goano@polito.it (M. Goano), bellotti@bu.edu (E. Bellotti). Solid-State Electronics 52 (2008) 1796–1801 Contents lists available at ScienceDirect Solid-State Electronics journal homepage: www.elsevier.com/locate/sse