CALCULATION OF ELECRON MOBILITY IN WZ-AlN AND AT LOW ELECTRIC FIELD

In this work the electron mobility of AlN Wurtzite and AlN Zincblende semiconductor compounds were calculated using iterative method in range of 100-600 K. We compare polar optic phonon scattering, deformation-potential acoustic phonon scattering, piezoelectric scattering and impurity scattering mechanisms. Boltzmann transport equation was solved using iterative method. In addition, we took into account the mixing of wave functions and electron screening and we investigated temperature dependence of mobility of the given


I. INTRODUCTION
Recently, the previous studies about III-V semiconductor compounds are considered important III-V semiconductor compounds, InN, GaN and AlN, respectively 1.8 ev , 3.4 ev , 6.2 ev , have the wide band gaps . Because of these properties III-nitrides are used in the blue and UV light emitting diodes (LED's) ,blue lasers ,UV detectors and high power , high temperature field effect transistors [2,3,4,5,6]. Aluminum nitride is a very interesting material because of it's wide band gap (6.3 ev ), high decomposition temperature (2400 c) chemical stability (in air up to 700 c) and good dielectric properties. In the last decade considerable interest arose in the use of thin films of AlN for various applications , from hard coatings and overcoatings for magneto-optic media ,to thin films transducers and GHz-band surface acoustic wave devices .The bandgap of AlN is direct in the Wurtzite phase and indirect in Zincblende phase .The electronic structure around the Valence band maximum of AlN in the WZ structure around the Valence band maximum of AlN in the WZ structure is different from that of the ZB-type crystal. In WZ-AlN, the bandgap is 4.3 ev and direct at gamma point and in ZB-AlN the conduction-band minimum (CBM) is located away from the gamma point at the X-point and in this point the bandgap is 3.2 ev .
International Journal of Science, Environment and Technology, Vol. 1, No 5, 2012, 395 -401 ZB-AlN is an object of the invention to prepare ZB-AlN OF sufficient quality and thickness to characterize it for its mechanical, optical and electrical properties and to be useful for device fabrication. WZ-AlN is a III-V semiconductor with Wurzite crystalline properties of WZ-AlN, it has a very wide bandgap, high thermal conductivity and transparency of ultraviolet LEDs and high-power electronic devices for promising material in deep UV devices, white color LED, high density medical laser, photolithography, photocatalytic decontamination, alternative of Hg lamp and He-Cd laser . They are also applied to high-power electronic devices and solar cells.With comparison of scattering effect in ZB-AlN and WZ-AlN structures, we result that for deformation potential scattering, the scattering of electron increased with increasing the energy.
In piezoelectric scattering with increasing of energy the scattering decreased in polar optical phonon scattering, the scattering is increasing by increasing temperature however changes differ is not important and in impurity scattering, the scattering rate of electron due to impurities atom in low-temperature is more than high temperature. Thus, the scattering rate of electron in WZ-AlN is more than ZB-AlN because their bandgap and the effective mass of electron in -valley is different. The Boltzmann equation is solved iteratively for our purpose, jointly incorporating the effects of all the scattering mechanisms. This paper is organized as follow as follows details of iterative model is presented in Section II and result of iterative calculations carried out on ZB-AlN and WZ-AlN structures are interpreted in Section III [3][4][5].

SOLVING THE BOLTZMANN TRANSPORT EQUATION
In principle the iterative technique give exact numerical prediction of electron mobility in bulk semiconductors. To calculate mobility, we have to solve the Boltzmann equation to get the modified probability distribution function under the action of a steady electric field. Here, we have adopted the iterative technique for solving the Boltzmann transport equation. Under application of a uniform electric field the Boltzmann equation can be written as: (1) where f=f(k) and f'=f(k' ) are the probability distribution functions and s=s(k,k') and s'=s(k',k) are the differential scattering rates . If the electric field is small, we can treat the change from the equilibrium distribution function as a perturbation which is first order in the electric field. The distribution in the presence of a sufficiently small field can be written quite generally as: Where f 0 (k) in the equilibrium distribution function, is the angle between k and E and g(k) is an isotropic function of k, wich is proportional to the magnitude of the electric field .Boltzmann transport equation is involved in scattering mechanisms may have occurred in the material . In this work we regarded that it was taken place acoustic phonon deformation potential scattering, acoustic piezoelectric scattering, ionized impurity scattering and polar optic phonon scattering for given materials. We took acoustic phonon deformation potential scattering, acoustic piezoelectric scattering, ionized impurity scattering as elastic process (S el ) and also polar optic phonon scattering as inelastic process (S inel ). The total elastic scattering rate will be the sum of all the different scattering rates.
In this case, S inel represents transitions from the state characterized by k to k' either by emission [S em (k,k')] or by absorption [S ab (k,k')] of a phonon . And polar optic phonon scattering, we have to consider scattering -in rates by phonon emission and absorption. Using Boltzmann equation and considering all differential scattering rates , the factor g(k) in the perturbed part of the distribution function f(k) can be given by : Note the first term in the denominator is simply the momentum relaxation rate for elastic scattering . It is interesting to note that if the initial distribution is chosen to be the equilibrium distribution, for which g(k) is equal zero , we get the relaxation time approximation result after the first iteration . We have found that convergence can normally be achieved after only a few iterations for small electric fields.
Once g(k) has been evaluated to the required accuracy , it is which is given by : Where d is defined as 1/d =m k E / 2 k. We took the structure of AlN compound as Wurtzite structure and Zincblende structure And we took into account electron screening [2].

III. Results
Effective mobility parameters are such as temperature, density, coefficient of nonparabolic electron effective mass and the energy balance and so on .         WZ-AlN Figure 5 shows the electron mobility of WZ-AlN is more than ZB-AlN in range of electron concentration .In this case we see the electron mobility decreases with increasing the electron concentration. Because of the increasing number of electrons ionized impurity centers is also increasing the number of times that electron feels coulomb potential, therefore the ionized impurity scattering rate increases. So, electron mobility decreases.
We result that electron mobility at the definite temperature 300K for the WZ-AlN semiconductor is gained about 337.61cm 2 v -1 s -1 and for ZB-AlN about 152.254 and the electron mobility WZ-AlN is more than ZB-AlN. This increasing is because of small effect mass.