A transient electron transport analysis of bulk wurtzite zinc oxide

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1 A transient electron transport analysis of bulk wurtzite zinc oxide Walid A. Hadi, Michael S. Shur, and Stephen K. O Leary Citation: J. Appl. Phys. 112, 3372 (212); doi: 1.163/ View online: View Table of Contents: Published by the American Institute of Physics. Related Articles Interband dephasing and photon echo response in GaMnAs Appl. Phys. Lett. 11, 6243 (212) Enhancement of the carrier mobility of poly(3,4-ethylenedioxythiophene) doped with poly(4-styrenesulfonate) by incorporating reduced graphene oxide APL: Org. Electron. Photonics 5, 167 (212) Enhancement of the carrier mobility of poly(3,4-ethylenedioxythiophene) doped with poly(4-styrenesulfonate) by incorporating reduced graphene oxide Appl. Phys. Lett. 11, 5335 (212) Electron and hole transport in an anthracene-based conjugated polymer APL: Org. Electron. Photonics 5, 165 (212) Electron and hole transport in an anthracene-based conjugated polymer Appl. Phys. Lett. 11, 5332 (212) Additional information on J. Appl. Phys. Journal Homepage: Journal Information: Top downloads: Information for Authors:

2 JOURNAL OF APPLIED PHYSICS 112, 3372 (212) A transient electron transport analysis of bulk wurtzite zinc oxide Walid A. Hadi, 1 Michael S. Shur, 2 and Stephen K. O Leary 3,a) 1 Department of Electrical and Computer Engineering, University of Windsor, 41 Sunset Avenue, Windsor, Ontario N9B 3P4, Canada 2 Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, Troy, New York , USA 3 School of Engineering, The University of British Columbia, 3333 University Way, Kelowna, British Columbia V1V 1V7, Canada (Received 6 June 212; accepted 11 July 212; published online 15 August 212) A three-valley Monte Carlo simulation approach is used in order to probe the transient electron transport that occurs within bulk wurtzite zinc oxide. For the purposes of this analysis, we follow O Leary et al. [Solid State Commun. 15, 2182 (21)], and study how electrons, initially in thermal equilibrium, respond to the sudden application of a constant applied electric field. We find that for applied electric field strength selections in excess of 3 kv/cm that an overshoot in the electron drift velocity is observed. An undershoot in the electron drift velocity is also observed for applied electric field strength selections in excess of 7 kv/cm, this velocity undershoot not being observed for other compound semiconductors, such as gallium arsenide and gallium nitride. We employ a means of rendering transparent the electron drift velocity enhancement offered by the transient electron transport, and then use the calculated dependence of the peak transient electron drift velocity on the applied electric field for the design optimization of short-channel high-frequency electron devices. VC 212 American Institute of Physics.[ I. INTRODUCTION Zinc oxide (ZnO) is a II-VI semiconductor that possesses a number of interesting material properties. It has a wide and direct energy gap, about 3.4 ev at room temperature, 1,2 this being comparable with that exhibited by gallium nitride (GaN). 3 It has a large exciton binding energy, about 6 mev, 1,4 which is more than double that exhibited by GaN. 5 It is amenable to wet chemical etching. 6 It is also able to robustly function in extreme radiation conditions. 7 Traditionally, this material was prepared in the form of a powder, 8 as crystalline needles, 9 or in oriented polycrystalline form. 1 Unfortunately, the defective nature of these samples limited the range of applications that could be contemplated In recent years, however, dramatic advances in ZnO fabrication have been achieved, and high-quality bulk wurtzite ZnO crystals have been fabricated. 14 This has greatly expanded the range of opportunities for ZnO in electronic and optoelectronic device applications. With its wide energy gap, large polar optical phonon energy, and large intervalley energy separation, ZnO is expected to exhibit favorable electron transport characteristics. 15 A number of studies of the electron transport within ZnO have been reported over the years. Experimental measurements of the mobility of this material were reported by Hutson 16 in 1957 and Look et al. 17 in Then, in 1999, Albrecht et al. 18 reported on Monte Carlo simulations of the steady-state electron transport within bulk wurtzite ZnO. Further Monte Carlo analyzes of the steady-state electron transport within bulk wurtzite ZnO have been reported by a) Author to whom correspondence should be addressed. Electronic mail: stephen.oleary@ubc.ca. Tel.: (25) Fax: (25) Guo et al. 19 in 26, by Bertazzi et al. 2 in 27, and by Furno et al. 21 in 28. Then, in 21, O Leary et al. 22 reported on a Monte Carlo analysis of the steady-state and transient electron transport within this material. A more detailed follow-up analysis, focused on how the steady-state electron transport within bulk wurtzite ZnO responds to variations in the non-parabolicity coefficient, was subsequently reported by Hadi et al. 23 in 211. Steady-state electron transport is the dominant electron transport mechanism within electron devices with larger dimensions. For devices with smaller dimensions, however, transient electron transport must also be considered when evaluating electron device performance. Ruch 24 demonstrated, for both silicon and gallium arsenide (GaAs), that the transient electron drift velocity may exceed the corresponding steady-state electron drift velocity by a considerable margin for appropriate selections of the applied electric field strength. Shur and Eastman 25 explored the device implications of transient electron transport, and demonstrated that substantial improvements in the electron device performance may be achieved as a consequence. The benefits of transient electron transport were further highlighted by O Leary et al. 26 In this paper, we will further develop our understanding of the nature of the transient electron transport that occurs within bulk wurtzite ZnO. In particular, within the framework of a three-valley model for the conduction band associated with this material, ensemble semi-classical Monte Carlo simulations of the transient electron transport that occurs within this material will be pursued. By examining the dependence of the transient electron drift velocity on the applied electric field strength selection, for a fixed selection of the time elapsed since the onset of the applied electric /212/112(3)/3372/5/$3. 112, VC 212 American Institute of Physics

3 Hadi, Shur, and O Leary J. Appl. Phys. 112, 3372 (212) field, a quantitative means of rendering transparent the electron drift velocity enhancement provided through transient electron transport is provided. The electron device implications of these results are then commented upon. This paper is organized in the following manner. In Sec. II, the three-valley Monte Carlo simulation approach, that is used for the purposes of this analysis, is presented. Then, in Sec. III, we study how electrons, initially in thermal equilibrium, respond to the sudden application of a constant applied electric field. A means of rendering transparent the electron drift velocity enhancement offered by the transient electron transport is presented in Sec. IV, the calculated dependence of the peak transient electron drift velocity on the applied electric field being subsequently used for the design optimization of short-channel high-frequency electron devices. Finally, conclusions are drawn in Sec. V. II. MONTE CARLO SIMULATION APPROACH For this analysis of the electron transport within bulk wurtzite ZnO, we employ ensemble semi-classical threevalley Monte Carlo simulations. The scattering mechanisms considered are: (1) ionized impurity, (2) polar optical phonon, (3) piezoelectric, and (4) acoustic deformation potential. Intervalley scattering is also considered, each valley being treated through the application of the Kane model. 27,28 We assume that all donors are ionized and that the free electron concentration is equal to the dopant concentration. For our transient electron transport simulations, the motion of ten thousand electrons is considered. Electron degeneracy effects are accounted for by means of the rejection technique of Lugli and Ferry. 29 Electron screening is also accounted for following the Brooks-Herring method. 3 Further details of our Monte Carlo simulation approach are presented in the literature. 22,31 39 Most of the material and band structural parameter selections, used for our simulations of the transient electron transport within bulk wurtzite ZnO, are from Albrecht et al. 18 ; we adopt the same material and band structural parameter selections as O Leary et al. 22 and Hadi et al. 23 Unfortunately, as Albrecht et al. 18 did not provide an exhaustive list of all of the material parameters needed for our Monte Carlo simulations, some of the material parameters employed by us are drawn from other sources in the literature, 4 or through a direct fit with the results of Albrecht et al., 18 i.e., we tweaked the material parameters until the resultant velocity-field characteristic corresponded with that found by Albrecht et al. 18 With the exception of the second order non-parabolicity factor, which we neglect for the purposes of our analysis, 27,28 we employ the same three-valley band model as that employed by Albrecht et al. 18 The lowest energy conduction band valley electron effective mass selection, :17 m e, where m e denotes the free electron mass, while smaller than the selections of Adachi et al. 4 (:234 m e ), Guo et al. 19 (:54 m e ), and Furno et al. 21 (:21 m e perpendicular and :23 m e parallel), is in keeping with the relation between the electron effective mass and the direct energy gap found in other III V and II VI semiconductors, as was shown in Figure 1 of O Leary et al. 22 ; given Drift Velocity (1 7 cm/s) ZnO 1 kv/cm 9 kv/cm 8 kv/cm 7 kv/cm 6 kv/cm 5 kv/cm 4 kv/cm 2 kv/cm 3 kv/cm 1 kv/cm.1.2 Time (ps).3.4 FIG. 1. The electron drift velocity as a function of the time elapsed since the onset of the applied electric field for the case of bulk wurtzite ZnO, for various applied electric field strength selections. For all cases, we have assumed an initial zero-field electron distribution, a crystal temperature of, and a doping concentration of 1 17 cm 3. the considerable overlap in authorship between Bertazzi et al. 2 and Furno et al., 21 it will be assumed that the choice of electron effective mass is similar. As with Albrecht et al., 18 anisotropy in the bands is neglected, the simulations of Bertazzi et al. 2 and Furno et al. 21 demonstrating that the anisotropy that is present only leads to a slight correction in the results. The material and band structural parameter selections, employed for the purposes this analysis of the transient electron transport within bulk wurtzite ZnO, are tabulated in Tables I and II, respectively. III. TRANSIENT ELECTRON TRANSPORT ANALYSIS For our analysis of the transient electron transport that occurs within bulk wurtzite ZnO, we follow the approach of O Leary et al., 22 and study how electrons, initially in thermal equilibrium, respond to the sudden application of a constant TABLE I. The material parameter selections corresponding to bulk wurtzite ZnO that are employed for the purposes of this analysis. The source for each parameter is identified. Parameter ZnO Reference Mass density (g=cm 3 ) Longitudinal sound velocity (cm/s) 4: 1 5 Determined through fit Transverse sound velocity (cm/s) 2: Acoustic deformation potential (ev) Static dielectric constant High-frequency dielectric constant Effective mass (C 1 valley) :17 m e 18 Piezoelectric constant, e 14 (C=cm 2 ) 3: Determined through fit Direct energy gap (ev) Polar optical phonon energy (mev) Intervalley deformation potentials (ev/cm) Intervalley phonon energies (mev)

4 Hadi, Shur, and O Leary J. Appl. Phys. 112, 3372 (212) TABLE II. The band structure parameter selections corresponding to bulk wurtzite ZnO. These band structure parameter selections are mostly from Albrecht et al. 18 Valley number ZnO Valley location C 1 (Ref. 18) C 1 (Ref. 18) L-M (Ref. 18) Valley degeneracy Effective mass :17 m e (Ref. 18) :42 m e (Ref. 18) :7 m e (Ref. 18) Intervalley energy separation (ev) 4.4 (Ref. 18) 4.6 (Ref. 18) Energy gap (ev) 3.4 (Ref. 18) Non-parabolicity (ev 1 ).66 (Ref. 18).15 (Ref. 18). (Ref. 18) applied electric field. For our material and band structural parameter selections, i.e., those tabulated in Tables I and II, with the crystal temperature set to and the doping concentration set to 1 17 cm 3, in Figure 1 we plot the electron drift velocity as a function of the time elapsed since the onset of the applied electric field, for a number of different applied electric field strength selections. We note that for the applied electric field strength selections 1 and 2 kv/cm, the electron drift velocity reaches steady-state very quickly, with little or no velocity overshoot. In contrast, for applied electric field strength selections in excess of 3 kv/cm, significant velocity overshoot occurs. This result suggests that in bulk wurtzite ZnO, for this particular selection of parameters, that 3 kv/cm is close to the critical applied electric field strength required for the onset of velocity overshoot effects. Earlier, O Leary et al. 22 pointed out that the onset of overshoot effects is approximately correlated with the applied electric field strength at which point the peak in the steady-state velocity-field characteristic associated with bulk wurtzite ZnO is achieved, i.e., approximately 27 kv/cm, as is seen in Figure 2(a) of O Leary et al. 22 ; we henceforth refer Drift Velocity (1 7 cm/s) GaN 56 kv/cm GaAs 16 kv/cm ZnO 18 kv/cm Time (ps) FIG. 2. The electron drift velocity as a function of the time elapsed since the onset of the applied electric field for the cases of bulk wurtzite ZnO, bulk wurtzite GaN, and bulk zinc-blende GaAs. For all cases, the applied electric field strength selection is set to four times the peak field, i.e., 18, 56, and 16 kv/cm for the cases of bulk wurtzite ZnO, bulk wurtzite GaN, and bulk zinc-blende GaAs. For all cases, we have assumed an initial zero-field electron distribution, a crystal temperature of, and a doping concentration of 1 17 cm 3. These results were all determined from Monte Carlo simulations of the electron transport. to this field as the peak field. This suggests that velocity overshoot is related to the peak in the velocity-field characteristic associated with ZnO. Similar results were found for the cases of GaAs and GaN by Foutz et al. 34 It is interesting to note that the transient electron transport results that exhibit the greatest velocity overshoot also exhibit a region of undershoot. A detailed examination of Figure 1 indicates that velocity undershoot, i.e., transient electron drift velocities that are below the corresponding steady-state electron drift velocity following a period of velocity overshoot, are observed when the applied electric field strength is set to 8, 9, and 1 kv/cm. We have performed a similar transient electron transport analysis for the cases of wurtzite GaN and zinc-blende GaAs and find no evidence to suggest that velocity undershoot occurs for these cases, although a distinct velocity overshoot is observed in all cases when the applied electric field strength exceeds the corresponding peak field. A representative comparative transient electron drift velocity result is depicted in Figure 2, in which we plot the electron drift velocity as a function of the time elapsed since the onset of the applied electric field, for the cases of wurtzite ZnO, wurtzite GaN, and zinc-blende GaAs. For all cases, we set the applied electric field strength to four times the corresponding peak field, the peak fields being 27, 14, and 4 kv/cm for the cases of ZnO, GaN, and GaAs, respectively. We note that only ZnO exhibits a distinctive velocity undershoot. While the exact origins of this velocity undershoot remain unclear at the present moment, we note that wurtzite ZnO exhibits polar optical phonon emission scattering rates that are considerably higher than their wurtzite GaN and zinc-blende GaAs counterparts. In Figure 3, we plot the steady-state polar optical phonon emission scattering rates associated with these materials as a function of the applied electric field strength, for the case of the temperature being set to and the doping concentration being set to 1 17 cm 3, these scattering rates being determined from Monte Carlo simulations of the electron transport; the zincblende GaAs polar optical phonon emission scattering rate has been extrapolated out to high-fields as impact ionization effects were neglected. The dramatic enhancement in the polar optical phonon emission scattering rate associated with GaN as opposed to GaAs primarily arises as a consequence of the larger electron effective mass associated with GaN. The further enhancement in the polar optical phonon scattering rate associated with ZnO primarily arises as a consequence of the enhanced differences between the static and

5 Hadi, Shur, and O Leary J. Appl. Phys. 112, 3372 (212) 2 polar optical phonon emission 6 ZnO Scattering Rate (1 1 3 s 1 ) ZnO GaN GaAs Drift Velocity (1 7 cm/s) steady state.7 ps.1 ps Electric Field (kv/cm) FIG. 3. The steady-state polar optical phonon emission scattering rate as a function of the applied electric field strength for the cases of bulk wurtzite ZnO, bulk wurtzite GaN, and bulk zinc-blende GaAs. For all cases, we have assumed, a crystal temperature of and a doping concentration of 1 17 cm 3. These results were all determined from Monte Carlo simulations of the electron transport. high-frequency relative dielectric constants, i.e., ZnO is more ionic. We speculate that this dramatically enhanced polar optical phonon scattering rate, observed at the higher applied field strengths for the case of wurtzite ZnO, will lead to reductions in the energy relaxation time, so much so that the energy relaxation time becomes shorter than the amount of time required for the transient electron drift velocity to attain steady-state values, and, as a consequence, a region of velocity undershoot is observed. Further investigation would need to be performed in order to confirm the validity of our premise. IV. THE ADVANTAGE OFFERED BY TRANSIENT ELECTRON TRANSPORT AND DEVICE DESIGN CONSIDERATIONS We now plot the dependence of the transient electron drift velocity on the applied electric field strength for a fixed selection of the time elapsed since the onset of the applied electric field. In Figure 4, we plot this dependence for the case of bulk wurtzite ZnO. The time elapsed since the onset of the applied electric field is set to.7,.1, and.13 ps for the cases considered in our analysis, these times spanning over the range of times over which transient electron transport effects occur for the case of bulk wurtzite ZnO; recall Figure 1. The corresponding steady-state electron drift velocity dependence on the applied electric field strength is also depicted in this figure. As was noted previously by O Leary et al., 22 transient electron transport effects are particularly evident for applied electric field strength selections beyond the peak field, i.e., 27 kv/cm for the case of bulk wurtzite ZnO. Indeed, for the time elapsed since the onset of the applied electric field being set to.1 ps, transient electron drift velocities as high as 5:4 1 7 cm=s (for an applied electric field strength selection of around 5 kv/cm) may be.13 ps Electric Field (kv/cm) FIG. 4. The dependence of the electron drift velocity on the applied electric field strength for the case of bulk wurtzite ZnO. Steady-state results are depicted with the solid line. The transient electron transport results are indicated with the solid colored points. These transient electron transport results are determined for.7,.1, and.13 ps following the onset of the applied electric field. For the purposes of these simulations, we have assumed an initial zero-field electron distribution, a crystal temperature of, and a doping concentration of 1 17 cm 3. achieved while the corresponding steady-state electron drift velocity is found to be only around 2:5 1 7 cm=s. It is noted that as the time elapsed is increased that the transient electron drift velocity approaches the corresponding steadystate result, as would be expected; as the time elapsed since the onset of the applied electric field goes to infinity, the transients expire, and the results settle into their steady-state form. The velocity undershoots that are observed in Figure 1 for the higher applied electric field strength selections, i.e., 8, 9, and 1 kv/cm, are responsible for the undershooting of the steady-state electron drift velocity by the transient electron drift velocities for applied electric field strength selections in this range of values. These results have important implications in terms of the performance of electron devices. Noting that the cut-off frequency for a device f T ¼ 1 2ps ; (1) where s represents the transit-time across the device, we can use our results to suggest the device length required in order to satisfy a desired cut-off frequency requirement. Figure 4, for example, suggests that for the case of wurtzite ZnO that cut-off frequencies of around 1.59 THz may be achieved for device lengths of at most 5 nm; for a set transit-time of.1 ps, i.e., f T 1.59 THz, a rough estimate for the maximum electron range, i.e., the maximum device length, may be obtained by multiplying the peak transient electron drift velocity by this transit-time. The non-idealities of an actual device, such as non-uniformities in the electric field distribution, must be considered when evaluating the performance of any particular device configuration, of course.

6 Hadi, Shur, and O Leary J. Appl. Phys. 112, 3372 (212) V. CONCLUSIONS In conclusion, a three-valley Monte Carlo simulation approach is used in order to probe the transient electron transport that occurs within bulk wurtzite zinc oxide. For the purposes of this analysis, we followed the approach of O Leary et al., 22 and studied how electrons, initially in thermal equilibrium, respond to the sudden application of a constant applied electric field. We found that for applied electric field strength selections in excess of 3 kv/cm that an overshoot in the electron drift velocity is observed. An undershoot in the electron drift velocity is also observed for applied electric field strength selections in excess of 7 kv/cm, this velocity undershoot not being observed for other compound semiconductors, such as GaAs and GaN. We employed a means of rendering transparent the electron drift velocity enhancement offered by the transient electron transport, and then used the calculated dependence of the peak transient electron drift velocity on the applied electric field for the design optimization of short-channel high-frequency electron devices. At the present moment, a comparison with experiment is difficult, as currently ZnO is predominantly being considered for use in thin-film transistor device applications, where the fields are low and the materials are typically deposited on foreign substrates. An attempt to determine the velocity-field characteristic associated with crystalline ZnO was made by Sasa et al. 41 Unfortunately, inhomogeneities in the electric field, the presence of a two-dimensional electron gas, and a strong electron confinement at the heterointerfaces that are present, resulting in greater roughness scattering and a substantial reduction in the obtained electron drift velocities, make a direct comparison with the case of bulk ZnO difficult. As the field develops, however, and the quality of ZnO improves, as experimental measurements of greater precision are made, a direct comparison with the results of experiment will eventually become possible. ACKNOWLEDGMENTS The authors gratefully acknowledge financial support from the Natural Sciences and Engineering Research Council of Canada. The work at Rensselaer Polytechnic Institute (M. S. 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