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  1. 1. H. Arabshahi, M. Izadifard and A. Karimi * / International Journal Of Engineering Research And Applications (IJERA) ISSN: 2248-9622 WWW.IJERA.COM Vol. 2, issue 5, september- october 2012, pp.404-407Calculation of Elecron Mobility in WZ-AlN and ZB-AlN at Low Electric Field 1 H. Arabshahi, 2M. Izadifard and 2A. Karimi 1 Physics Department, Payame Noor University, Tehran, Iran 2 Physics Department, Shahrood University of Technology, Shahrood, IranAbstractIn this work the electron mobility of AlN III-V semiconductor with Wurzite crystallineWurtzite and AlN Zincblende semiconductor properties of WZ-AlN , it has a very wide bandgapcompounds were calculated using iterative ,high thermal conductivity and transparency ofmethod in range of 100-600 K. We compare polar ultraviolet LEDs and high-power electronic devicesoptic phonon scattering, deformation-potential for promising material in deep UV devices , whiteacoustic phonon scattering, piezoelectric color LED ,high density medical laser ,scattering and impurity scattering mechanisms. photolithography, photocatalytic decontamination ,Boltzmann transport equation was solved using alternative of Hg lamp and He-Cd laser . They areiterative method. In addition, we took into also applied to high-power electronic devices andaccount the mixing of wave functions and solar cells.With comparison of scattering effect inelectron screening and we investigated ZB-AlN and WZ-AlN structures, we result that fortemperature dependence of mobility of the given deformation potential scattering, the scattering ofcompound. electron increased with increasing the energy. In piezoelectric scattering with increasing of energy theKeywords-: AlN Wurtzite , AlN Zincblende scattering decreased in polar optical phonon,electron mobility , iterative method , III-Nitrides. scattering, the scattering is increasing by increasing temperature however changes differ is not importantI. INTRODUCTION and in impurity scattering, the scattering rate of Recently ,the previous studies about III-V electron due to impurities atom in low-temperaturesemiconductor compounds are considered important is more than high temperature. Thus, the scatteringIII-V semiconductor compounds, InN, GaN and rate of electron in WZ-AlN is more than ZB-AlNAlN, respectively 1.8 ev,3.4 ev , 6.2 ev , have the wide because their bandgap and the effective mass ofband gaps . Because of these properties III-nitrides electron in Γ-valley is different. The Boltzmannare used in the blue and UV light emitting diodes equation is solved iteratively for our purpose, jointly(LED’s) ,blue lasers ,UV detectors and high power , incorporating the effects of all the scatteringhigh temperature field effect transistors [2,3,4,5,6]. mechanisms. This paper is organized as follow asAluminum nitride is a very interesting material follows details of iterative model is presented inbecause of it’s wide band gap (6.3 ev), high Section II and result of iterative calculations carrieddecomposition temperature (2400 c) chemical out on ZB-AlN and WZ-AlN structures arestability (in air up to 700 c) and good dielectric interpreted in Section III [3-5].properties . In the last decade considerable interestarose in the use of thin films of AlN for various II. SOLVING THE BOLTZMANNapplications , from hard coatings and overcoatings TRANSPORT EQUATIONfor magneto- optic media ,to thin films transducers In principle the iterative technique giveand GHz-band surface acoustic wave devices .The exact numerical prediction of electron mobility inbandgap of AlN is direct in the Wurtzite phase and bulk semiconductors. To calculate mobility, we haveindirect in Zincblende phase .The electronic to solve the Boltzmann equation to get the modifiedstructure around the Valence band maximum of AlN probability distribution function under the action of ain the WZ structure around the Valence band steady electric field . Here, we have adopted themaximum of AlN in the WZ structure is different iterative technique for solving the Boltzmannfrom that of the ZB-type crystal. In WZ-AlN ,the transport equation . Under application of a uniformbandgap is 4.3 ev and direct at gamma point and in electric field the Boltzmann equation can be writtenZB-AlN the conduction-band minimum (CBM) is as :located away from the gamma point at the X-pointand in this point the bandgap is 3.2 ev. ZB-AlN is an (1)object of the invention to prepare ZB-AlN OF where f=f(k) and f=f(k ) are the probabilitysufficient quality and thickness to characterize it for distribution functions and s=s(k,k) and s=s(k,k) areits mechanical, optical and electrical properties and the differential scattering rates . If the electric field isto be useful for device fabrication . WZ-AlN is a small ,we can treat the change from the equilibrium 404 | P a g e
  2. 2. H. Arabshahi, M. Izadifard and A. Karimi * / International Journal Of Engineering Research And Applications (IJERA) ISSN: 2248-9622 WWW.IJERA.COM Vol. 2, issue 5, september- october 2012, pp.404-407distribution function as a perturbation which is first g(k) is equal zero , we get the relaxation timeorder in the electric field. The distribution in the approximation result after the first iteration . Wepresence of a sufficiently small field can be written have found that convergence can normally bequite generally as: achieved after only a few iterations for small electric f(k)=f0(k) + g(k) cos 𝜃 fields.(2) Once g(k) has been evaluated to the required Where f0(k) in the equilibrium distribution accuracy , it is which is given by :function, θ is the angle between k and E and g(k) isan isotropic function of k, wich is proportional to themagnitude of the electric field .Boltzmann transportequation is involved in scattering mechanisms may (5)have occurred in the material . In this work weregarded that it was taken place acoustic phonon Where d is defined as 1/d =m ∇k E / ℏ2 k. We took thedeformation potential scattering, acoustic structure of AlN compound as Wurtzite structurepiezoelectric scattering, ionized impurity scattering and Zincblende structure And we took into accountand polar optic phonon scattering for given electron screening [2].materials. We took acoustic phonon deformationpotential scattering, acoustic piezoelectric scattering,ionized impurity scattering as elastic process ( Sel) III. Resultsand also polar optic phonon scattering as inelastic Effective mobility parameters are such asprocess (Sinel ).The total elastic scattering rate will be temperature , density , coefficient of nonparabolicthe sum of all the different scattering rates . electron effective mass and the energy balance and so on .S(k,k) = Sel(k,k) +Sinel(k,k) 2.6(3) 2.4 T=500 K In this case, Sinel represents transitions from 2.2 Total scattering(s )*(10 ) 13the state characterized by k to k either by emission 2.0[Sem(k,k)] or by absorption [Sab(k,k)] of a phonon . 1.8 -1 1.6And polar optic phonon scattering, we have to 1.4 T=300 Kconsider scattering – in rates by phonon emission and 1.2 1.0 Parameter WZ- ZB-AlN 0.8 AlN 0.6 ZB-AlNBand-gap (eV) 6.25 5.4 0.4 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8Electron effective mass (m* ) 0.31 0.35 Energy (ev)Static relative permitivity 0 8.5 8.07Optical relative permitivity  4.77 4.46 Fig 1. Changes total scattering electron function inDensity (kgm-3 ) 3230 3257 terms of energy in bulk WZ-AlN at the differentSound velocity (ms-1 ) 9060 5740 temperature.Deformation potential (eV) 9.5 9Optical phonon energy (eV) 0.0992 0.099 1.8absorption . T=500 K 1.6 Total scattering(s )*(10 ) 13Table 1. Important parameters used in our 1.4 -1calculations for WZ-AlN and ZB-AlN [6-7-9]. 1.2 T=300 K Using Boltzmann equation and considering 1.0all differential scattering rates , the factor g(k) in the 0.8perturbed part of the distribution function f(k) can 0.6be given by : 0.4 WZ-AlN 0.2 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 Energy (ev) . Fig 2. Changes total scattering electron function in(4) terms of energy in bulk ZB-AlN at the different temperature.Note the first term in the denominator is simply the Figure 1 and 2 show total scatteringmomentum relaxation rate for elastic scattering . It is depends on energy and increasing temperatureinteresting to note that if the initial distribution is causes increasing in bulk ZB-AlN and WZ-AlNchosen to be the equilibrium distribution, for which materials. 405 | P a g e
  3. 3. H. Arabshahi, M. Izadifard and A. Karimi * / International Journal Of Engineering Research And Applications (IJERA) ISSN: 2248-9622 WWW.IJERA.COM Vol. 2, issue 5, september- october 2012, pp.404-407 effective mass of ZB-AlN is more than WZ-AlN, with increasing the effective mass , the electron 2.0 mobility decreases with increasing electron effective 1.8 WZ-AlN mass increases the moment of it which reduces the Total scattering(s )*(10 ) 13 1.6 electron acceleration in an electric field is uniform, which ultimately reduces mobility in an electric field 1.4 -1 is present . Increasing the non parabolic electron 1.2 ZB-AlN energy bands are meant to be paved. 1.0 Smooth energy bands, effective mass of electrons and thus increase the mobility reduction in the crystal is. 0.8 0.6 0.4 T=300 K 340 0.2 320 T=300 K 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 300 Energy (ev) Electron mobility (cm /v s) 280 WZ-AlN 2 260 Fig 3. Changes total scattering electron function in 240 220 terms of energy in bulk ZB-Aln and WZ-AlN at 200 different temperature. 180 Figure 3 shows comparison of totals 160scattering in WZ-AlN and ZB-AlN at the different 140 ZB-AlNtemperature .Our calculation results show that the 120totals scattering rate in WZ-AlN is more than ZB- 100 0.00E+000 2.00E+018 4.00E+018 6.00E+018 8.00E+018 1.00E+019AlN . Only a weak electric field the electrons in the -3 electron concentration (cm )Γ-valley electric transportation involved. Becausethey no longer have the energy to go to the valley.Hence transitions between valley occurs. In weak Fig 5. Changes the electron mobility function inelectric field piezoelectric scattering and ionized terms of electron concentration in bulk ZB-AlN andimpurity scattering play an important role and they WZ-AlN at T=300 K.can not be ignored. 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 2800 impurity centers is also increasing the number of times that electron feels coulomb potential, therefore Electron mobility(cm /Vs) 2400 the ionized impurity scattering rate increases. So, 2 2000 WZ-AlN electron mobility decreases. 1600 We result that electron mobility at the definite temperature 300K for the WZ-AlN semiconductor is 1200 gained about 337.61cm2 v-1s-1 and for ZB-AlN about 800 152.254 and the electron mobility WZ-AlN is more than ZB-AlN. This increasing is because of small 400 effect mass. ZB-AlN 0 100 200 300 400 500 600 REFERENCES Temperature (K) [1] S. AYDOĞU, M. AKARSU and Ö. ÖZBAª. Calculation of the electron Fig 4. Changes the electron mobility function in mobility of GaN Osmangazi University, Artterms of temperature in bulk ZB-AlN and WZ-AlN at and Science Faculty, Department of different temperature. Physics, Eskiºehir, Figure 4 shows the electron mobility of,akarsu@oguWZ-AlN is more than ZB-AlN at the different, . We see the electron mobility [2] H. Arabshahi, Z. Moodi and A.decreases with increasing temperature . Because of a PourhasanInternational NUMERICALphonon scattering rate increased with increasing CALCULATION OF THE ELECTRONtemperature and increasing temperature also MOBILITY IN GaAs SEMICONDUCTORincreases the energy of the phonons . Because the UNDER WEAK ELECTRIC FIELD APPLICATIONJournal of Science, 406 | P a g e
  4. 4. H. Arabshahi, M. Izadifard and A. Karimi * / International Journal Of Engineering Research And Applications (IJERA) ISSN: 2248-9622 WWW.IJERA.COM Vol. 2, issue 5, september- october 2012, pp.404-407 Environment and Technology, Vol. 1, No 2, APPLICATION, VOL. 1, NO.1, 80 - 87, 2012 JANUARY, 2012[3] N. A. Masyukov and A. V. Dmitriev. Hot [6] Fabio Bernardini and Vincenzo Fiorentini. electrons in wurtzite indium nitride. Spontaneous polarization and piezoelectric JOURNAL OF APPLIED PHYSICS 109, constants of III-V nitrides . PACS: 023706 _2011_ 77.65.Bn, 77.84.Bw, 77.22.Ej. 23 Jul 1997[4] F Litimein1, B Bouhafs1,2†, Z Dridi1,2 [7] S.Loughin and R.H.French –Electronic and P Ruterana2The electronic structure structure of ALN :Theory and experiment . of wurtzite and zincblende AlN: an ab Appl . phys , lett ,63(9),30 August 1993 initio comparative study. New Journal of [8] P.Jonnard , N.Capron –F.Semond ,J Physics 4 (2002) 64.1–64.12 .Massies . Electronic structure of wurtzite[5] H. Arabshahi. Modeling Low Field and zinc-blende ALN ,February 2,2008 Electron Mobility in Group III Nitride Materials . COMPUTER SCIENCE AND 407 | P a g e