Bull. Mater. Sci., Vol. 37, No. 7, December 2014, pp. 1603–1606. c Indian Academy of Sciences. Electric field dependence of the electron mobility in bulk wurtzite ZnO K ALFARAMAWI Science Department, Teachers College, King Saud University, Riyadh 11451, Saudi Arabia Physics Department, Faculty of Science, Alexandria University, Alexandria 21511, Egypt MS received 7 November 2013; revised 1 January 2014 Abstract. The electric field dependence of the electron mobility in bulk wurtzite zinc oxide (ZnO) material is stud- ied. The low-field electron mobility is calculated as a function of doping concentration and lattice temperature. The results show that above nearly 50 K the electrical conduction is governed by activation through the bulk material and the conduction is then influenced by both lattice and impurity scattering mechanisms. The high-field charac- teristics are also considered. The transition between the low-field and high-field regions is specified. The negative differential mobility for bulk ZnO at room temperature is observed at electric fields above 280 kV/cm. Keywords. Electron drift velocity; low-field mobility; saturation velocity. 1. Introduction the effects of lattice scattering, screened Coulomb charges, carrier–carrier scattering and impurity clustering effects at Recently, zinc oxide (ZnO) semiconductor has received a high concentrations are considered. great attention for electronic and optoelectronic applications In this paper, the electric-field dependent electron mobil- because of its noticeable advantages over GaN and other III- ity in bulk wurtzite ZnO is studied. The low-field elec- nitrides. ZnO has unique properties with possible applica- tron mobility, as a function of doping concentration and lat- tion to ultraviolet light emitters, gas sensors, surface acoustic tice temperature, is computed. High-field electron mobility wave devices and transparent electronics (Ozgur et al 2005). and the electron saturation velocity are also studied. The A distinguished characteristic of ZnO, compared with transition between the low-field and high-field regions is many other direct gap semiconductors, is the large interval- determined. ley separation which is approximately 3·23 eV, while this is 330 meV in GaAs and 2·25 eV in GaN. This may lead to a use of a simple analytical nonparabolic approximation for 2. Theory the conduction band around the centre of the Brillouin zone even at moderately high electric field up to several hundred The low-field mobility models are best understood by starting kV/cm (Goano et al 2007). with the modelling approach of Caughey and Thomas (1967), The electron mobility in bulk ZnO as a function of electric μmax − μmin field is important parameter for device design and analysis. μ0 = μmin + α , (1) At low-field level, the bulk sample carriers are almost in equi- 1 + (N/C) librium with the lattice vibrations and the low-field mobil- where C and α are fitting parameters, N the total doping den- ity is mainly affected by phonon and Coulomb scattering sity and μ and μ the ‘maximum–minimum’ behaviour (Schroder 1987). At higher electric fields, mobility becomes max min of the mobility. field-dependent parameter. To match the experimental findings, at doping levels There are many theoretical models to describe the low- greater than 5 × 1019 cm−3, Masetti et al (1983) assumed field mobility for bulk materials. Those include the con- that: stant mobility model, Caughey and Thomas (1967) model and Arora model (Arora et al 1982). In such models, the μ − μ μ μ = μ + max min − 1 , (2) 0 min α1 α2 low-field mobility is temperature- and doping-concentration- 1 + (N/C1) 1 + (C2/N) dependent. On the other hand, Dorkel and Letureq (1981) presented a model, where the dependence on the carrier– where μ1,C1,C2,α1 and α2 are new fitting parameters. carrier scattering was considered in the low-field mobil- According to Arora (Arora et al 1982), the temperature ity formulation. Klaassen (1992) model provided unified (T)and ionized impurity concentration (Ni) dependence of description of majority and minority carrier mobility, where the low-field mobility is given by: μ μ = μ + d , 0 om r (3) ([email protected]) 1 + (Ni/N0) 1603 1604 K Alfaramawi where Figure 1 shows the low-field electron mobility vs tempe- α α T m T d rature for ZnO in a temperature range from 10 to 400 K. μ = r ,μ= r , om m T d d T The mobility was calculated at different values of donor 0 0 × 16 × 17 −3 α α concentration from 3 10 up to 5 10 cm .In T N T a figure 1, two main regions can be distinguished. In temper- N0 = rN ,r= ra , (4) T0 T0 ature range, between 10 and approximately 50 K (the value depends on the carrier concentration), the electron mobility with T = 300 K and the quantities r ,r ,r ,r ,α ,α , 0 m d N a m d increases with the increase of temperature. The second range α and α are fitting parameters. N a is from 50 up to 400 K in which the mobility decreases with The high-field electron characteristics are well understood the elevation of temperature. by studying the relationship between the drift velocity ν(E) Above approximately 50 K, the conduction is assumed and the electric field. By the aid of Arora model, one can to be dependent on the activation processes of electrons write between donor sites and the conduction band. In that range β μ E + ν (E/E ) 1 of temperature, scattering of electrons determines the mobil- ν(E) = 0 sat c , (5) β1 β2 1 + (E/Ec) + a (E/Ec) ity behaviour. Scattering by acoustic and optical phonons are probably the dominant processes at higher temperatures, μ where 0 is the temperature- and doping-dependent low-field while at lower temperatures, the ionized impurity scattering ν electron mobility given from (3), sat the saturation velocity, process might be the dominant one. E c the critical field corresponding to the maximum steady Below 50 K, the mobility data are assumed to be deter- a,β ,β state velocity and 1 2 the fitting parameters. mined by both band and hopping conduction (Look et al The temperature dependence of the drift velocity is prop- 1998). The experimental data of low-field mobility on erly specified by considering the model which suggested that bulk wurtzite ZnO at carrier concentration 6 × 1016 cm−3 the fitting parameters could be modified to be temperature- shows that the critical temperature between the two types dependent according to the equation (Yang et al 2010) of conduction is about 40 K, which may be considered in a good agreement with our calculations (Bertazzi et al 2 par(T ) = par(300) × a + bT + cT , (6) 2009). where par(300) is a parameter at T = 300 K and a,b and c In order to study the temperature-dependent electronic are constants. behaviour, the low-field mobility is plotted as a function of T for temperatures above 100 K at some selected values of the donor concentration, see figure 2. Experimental Hall 3. Results and discussion mobility data extracted from Bellotti and Bertazzi (2007)are also included as well as results from Monte Carlo simulation Calculations of the low-field electron mobility and high- (ABMC) data from Furno et al (2008). Inspection of figure 2 field electron characteristics as a function of temperature and reveals that the present calculated results fit well with the doping concentration for bulk wurtzite ZnO were carried experimental results of Bellotti and Bertazzi (2007). out according to (3)and(4). The numerical values of the parameters used in the calculations are given in table 1. 7000 16 -3 310× cm 6000 16 -3 Table 1. Parameters used in the field- 510× cm 16 -3 dependent electron mobility calculations 810× cm 5000 17 -3 using (3)and(4) for bulk wurtzite ZnO 110× cm 17 -3 × (extracted from Furno et al 2008). 4000 310 cm 17 -3 / V.s) 2 510× cm (cm 3000 Parameter Value o 2 2000 rm 98·92 cm /V·s r · 2 · d 304 1cm /V s 1000 17 −3 rN 1·92 × 10 cm ra 1·058 0 αm −0·698 0 50 100 150 200 250 300 350 400 450 α −3·386 d T (K) αN 2·718 α −0·125 a Figure 1. Low-field electron mobility vs temperature for ZnO in a E 290 kV/cm c temperature range from 10 up to 400 K. The curves are calculated a 2·4 at different values of donor concentration from 3 × 1016 up to β 4·5 1 5 × 1017 cm−3. Peak mobilities are noticed at approximately β 0·85 2 50 K (the value depends on the carrier concentration). Electric field dependence of the electron mobility in bulk wurtzite ZnO 1605 1800 17 −3 2.5×107 Our calculations at N =10 cm 1600 d Experimental Hall mobility from 1400 7 Bellotti and Bertazzi (2007) 2.0×10 1200 ABMC from Furno et al (2008) 1000 1.5×107 / V.s) 2 800 (cm 1.0×107 600 400 Electron drift velocity (cm/s) 5.0×106 200 0 0.0 0.0 2.0×105 4.0×105 6.0×105 8.0×105 100 150 200 250 300 350 400 E (V/cm) T (K) Figure 2. Low-field electron mobility at temperatures above Figure 4. Electron drift velocity vs electric field at room temper- 100 K for bulk wurtzite ZnO calculated at donor concentration ature for bulk wurtzite ZnO. of 1017 cm−3 (solid line). The calculated results are compared to experimental work from Bellotti and Bertazzi (2007) (symbols) and Monte Carlo simulation from Furno et al (2008) (dashed line).