Analytical Study of Electron Mobility in Hemts Algangan 2332 0796 1000169 | Semiconductors

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  Research ArticleOpen Access Volume 5 ã Issue 1 ã 1000169J Electr Electron SystISSN: 2332-0796 JEES an open access journal   Open AccessResearch Article Journal of Electrical & Electronic Systems ISSN: 2332-0796           J       o       u          r       n       a                   l     o       f     E      l    e   c    t   r   i  c  a  l   &   E  l   e   c   t    r     o    n    i        c        S         y       s  t      e   m   s Nouacry et al., J Electr Electron Syst 2016, 5:1 *Corresponding author: Nouacry A, Materials Physics Laboratory, Microelectronics,  Automation and Thermal - University Hassan II, Morocco, Tel: 212523485112; E-mail: Received  October 16, 2015; Accepted  December 29, 2015; Published  January 01, 2016 Citation:  Nouacry A, Touhami A, Benkassou A, Bouziane A, Aouaj A (2016)  Analytical Study of Electron Mobility in Hemts Algan/Gan. J Electr Electron Syst 5: 169. doi:10.4172/2332-0796.1000169 Copyright: © 2016 Nouacry A, et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the srcinal author and source are credited. Analytical Study of Electron Mobility in Hemts Algan/Gan Nouacry A 1,2 *, Touhami A 1 , Benkassou A 1 , Bouziane A 2  and Aouaj A 2 1 Materials Physics Laboratory, Microelectronics, Automation & Thermal - University Hassan II, Morocco 2   Automation Laboratory, Energy Conversion and Microelectronics - University Sultan Moulay Slimane, Morocco Keywords: HEM; AlGaN/GaN heterojunction; Mobility; 2DEG; Scattering mechanism Introduction Te power devices based on semiconductor play an important role in the regulation and distribution of energy in the world [1] and have become an essential component in telecommunications systems. Tis sector, which includes both cellular phone base stations as radar and satellite communications applications, requires work in frequency ranges up to several tens of GHz.In these frequency ranges silicon reaches the intrinsic limits (mobility of the inversion layer, saturation velocity,...) and only the reduction in the size of the grid thanks to the use of heterostructure based SiGe allows it to impose. Nevertheless, in the components of power MOSFE, power losses become important because of the finite resistance of the channel in the on state, despite the increase of the surface component, which increases the input capacity and thus switching losses. Tanks to advances in epitaxy, the possibility of making semiconductor heterostructures of III - V opened the way for new components to very rapid field effect: heterostructure field effect transistors HFE and (MODFE, HEM, PHEM...). Te main interest of HFE comes from the spatial separation of electrons from the conducting channel formed by a potential well in the semi-conductor small gap and doping impurity atoms in semiconductor wide band gap. Tis delocalization of the electron gas gives a high electron mobility. Te first structures based on the physics have been achieved using GaAs and its alloys AlInGaAs. Te structure of a HEM, shown in Figure 1, consists essentially of three different materials: Te substrate, a wide bandgap material and a small gap material. We find the source electrodes, gate and drain, in common MESFE [2]. In the case of the HEM, the juxtaposition of a wide bandgap material and a small gap material involves the creation of discontinuity of band conduction at the interface between two materials, Anderson model. In this model, at the junction of two semiconductors with different band gap, the Fermi levels are aligned. Te conservation of physical parameters on both sides of the interface causes bending of the band and valence conduction, and also discontinuities at the interface of these two bands. Tis “heterojunction”, illustrated in Figure 2, involves the formation of a potential well in the material of small gap where to accumulate and transfer electrons from the donor layer. Te heterojunction is characterized by the discontinuity of conduction band ΔEc  between the two materials [3]. Tis causes the accumulation of electrons in this well is called two-dimensional electron gas (2DEG: two Dimensional Electron Gas). Te heterojunction allows the spatial separation of the ionized donor atoms and free electrons.A fundamental criterion for validating such structures is of course the electron mobility of electrons in the wells that form the transistor channel. Many mechanisms of diffusion may limit the mobility of electrons in the gas: Some are defined as elastic scattering centers (donors, interface roughness, alloy disorder, dislocations loaded) and others are inelastic (acoustic and optical phonons). Teory and Model Te calculation of mobility will be in what follows in the approximation of relaxation time. Tis hypothesis assumes that all Abstract The hetero junctions GaN based offer an excellent potential for power applications at high frequency. This is due to the important energy of the bandgap and high saturation velocity of electrons. The high mobility transistors (HEMT - High Electron Mobility Transistor) are based on the heterojunction AlGaN/GaN. Our work is the subject of an analytical study of the carrier mobility HEMTs AlGaN/GaN calculating Ionized impurities scattering, Residual impurities scattering, Interface roughness scattering, Alloy disorder scattering, dislocations scattering, Phonons and Dipoles taking into account the impact of technological parameters (doping, aluminium content) and geometric (thickness barrier, interface roughness). The results allowed us to take account of the variation of carrier density in the wells of 2D electronic gas.   Figure 1: Schematic sectional view of a HEMT AlGaN/GaN structure. The bias elds are represented. Current modulatedby the gate (G) ow through the 2D gas between the source (S) and drain (D).  Citation:  Nouacry A, Touhami A, Benkassou A, Bouziane A, Aouaj A (2016) Analytical Study of Electron Mobility in Hemts Algan/Gan. J Electr Electron Syst 5: 169. doi:10.4172/2332-0796.1000169 Page 2 of 6 Volume 5 ã Issue 1 ã 1000169J Electr Electron SystISSN: 2332-0796 JEES an open access journal relaxation processes are independent of mode of diffusion. Electron mobility calculations for algan channels were done using several scattering mechanisms. Te total mobility was approximated using Matthiessen rule [4]: 1 1 τ τ  = ∑ itotal i For each carrier where With τi mechanism of relaxation time approximation Te mobility µ i  is the contribution due to the i th  scattering mechanism obtained in the effective mass m*   approximation by: * τ µ   =  em With  e electron charge, Whatever the modes of diffusions are, that assumption remains  valid even for acoustic phonons; however, it is no longer for the optical phonons where the analytical expression allows accounting for the mobility limited by this mode. wo sources are responsible for the presence of donors in the wells which join two processes of diffusion. Ionized impurities scattering  Te model presented by Davies [4], which takes account for the mode of diffusion leads to a relaxation time of surface states, is given by: ( ) 2* 2233 0 1*22 τ ε ε π  −  =     Dimpii F GaN  F  m enk h k  ( ) 62 2 2202 1 (2 ) −   ++     − ∫  F   K  q d TF  F  e b q dqb qq q G q q K   (1) With, d is the thickness of the barrier, ε GaN and ε 0  the dielectric constants of GaN and vacuum.  * 2 TF  B qa =  : containing the 2D gas, here the GaN. a * B   the effective Bohr radius of GaN 2* 0* 2 4 πε ε  − =  GaN  B ham e k  F , the electronic wavelength associated at the Fermi level is given for a 2D gas  2deg 2 π  n . G (q)  is called the form factor of the 2D gas screening by free carriers and is given in the variational approximation Fang Howard by: ( )  ( ) 3 2 12 3 38 η η η η    = + + =  +  bG q and b q  (3) b  variational parameter is given by [4]: 1/32 *2deg2 123 ε    = +       depGaN  ne mb N   (4) Residual impurities scattering  Te second model of Davies, related to the diffusion process and characterized by a relaxation time which takes account of residual impurities is given by: 2* 2233 0 1*22 τ ε ε π  −−−  =     Dres impres imp GaN  F  m e N h k   (5) [ ] 2202 11 (2 ) +− ∫  F   K TF  F  qdqq q q K   (6) Interface roughness scattering  For high electron densities, the potential well is dug and the electrons are pushed closer to the surface which makes them very sensitive to defects. Te influence of interface roughness on mobility is not very precise to determine because of the difficulty of modeling the roughness itself. Ferry and Goodnick [5,6] and Zanato [3] have addressed this problem and led to an expression of the scattering rate by this method:  ( ) 2 2 2 212 2 4 * 42deg2 32 20 0 12 2( ) 12 τ  −  =    + −∆ ∫   F  k L uTF  IR F  n L e m u eduqu G u uk  ò  (7)Where the integral is rendered dimonsionless by the substitution u =q/2k F  .  ∆   is the interface roughness and L the correlation length (approximately the average distance between “defects”). In the case of epitaxial structures grown by MBE, the roughness Δ is the order of several Angstroms, typically 2Å. Alloy disorder scattering  In an alloy, atoms (Al) takes the place of atoms of Ga. Using the  virtual crystal approximation one can describe the potential in which the electron is submitted. Te fact that the potential is different from the true potential introduces a “diffusion” of Bloch waves which has an impact on the conductivity of electrons; it is the alloy disorder. Te relaxation time associated with this mode of diffusion is given by 7: 0* 24'0 03 1 (1 )( )  χ τ  χ  χ  −∞ Ω −= ∫  alloy m V  z dz    (8)With x   is the Al mole fraction. Ω 0 is the volume associated with each Al(Ga) atom, χ’( z))  is the modified Fang-Howard wave function which describes the penetration of the electron gas in the barrier and it is given by: 122 *' 2 02deg 20 0 4 1 8( ) exp2 π  χ ε ε   −      = +         depGaN  e m V  z N N z V h  (9)With V 0 =   ∆E(x) : discontinuity of conduction band between the Figure 2: Band structure of a heterojunction in the presence of a gate potential.  Citation:  Nouacry A, Touhami A, Benkassou A, Bouziane A, Aouaj A (2016) Analytical Study of Electron Mobility in Hemts Algan/Gan. J Electr Electron Syst 5: 169. doi:10.4172/2332-0796.1000169 Page 3 of 6 Volume 5 ã Issue 1 ã 1000169J Electr Electron SystISSN: 2332-0796 JEES an open access journal l’  AlxGa1-xN et le GaN.  V 0  is the alloy scattering potential for AlGaN alloys reported ealier to be 1.8 eV [7,8]. our simulations are made from this experimental value. Dislocations scattering  Te absence of substrate adapted into mesh with GaN leads to the presence in the epitaxial layers of GaN threading dislocations. Te model that can be found in the literature to allow time for mailing by dislocations is given by equation 10,11: 1* 2 232 22 4 00 1( ) 116 ( )2 λ τ π ε ε  − =+ − ∫  LdisTF disGaN F  F  m e du N qu uh k  K   (10)Where u is defined previously by u =q/2kF  . kF the Fermi wave  vector which depends on the carrier density of 2D gas ( n 2DEG  ) and N  dis   is the doping density of 2D dislocation lines, λ L = ef  / c 0 where c 0   is lattice constant in GaN along the direction [0001],  f   is the fraction of occupied acceptor states introduced by dislocation. Phonons Te mechanism of diffusion by phonons is dominant at temperatures above 77 K for electrons, but it may be the determining factor at low temperatures in 2D structures made from particularly pure materials. We can distinguish two types of phonons (acoustic and optical). Phonon acoustic scattering: Te acoustic phonons are sound waves that alternately compress and expand the solid. Te variation of lattice parameter induces a change in energy bands which will fall or rise proportionately with the constraint. Davies [4] gives a simplified expression of the relaxation time that allows a relatively easy numerical computation [9,10]. Tis relationship is given by: * 232 1 316 τ  ρ  − =  cac s m bkTav h  (11) 32* 2 2 163( )  ρ µ  − =  sacc e v hm bkTa Where ρ the density, v  s  the speed of sound in the material and b is  the variational parameter using the wave functions of Fang-Howard. Optical phonons scattering: In GaN (same for AlN and InN) energy of polar optical phonons is very large and the phonon scattering is inelastic. Te optical phonon energy is much larger than the thermal energy of electrons even at room temperature [11]. Tus, the majority of electrons do not have sufficient thermal energy to emit an optical phonon. Only the absorption process taking into account the relaxation time is thus reduced to the characteristic time of absorption of an optical phonon, we can then say that the emission process is effectively blocked. Gelmont [12], via this hypothesis, proposes an expression of time associated with this process. ( ) 2 *0 0* 20 ( )12 ( ) ω τ ε  =  op e m N T H qq F y  (12)With ω 0  is the optical phonon frequency, *00 2  ω  =  mq ħ  is the optical phonon wave vector, ( ) 0 1exp( 1) ω  =−   N T kT  is the Bose-Einstein distribution function, ( )  2 *2deg 11 / π  − −= + =  y e F y with y n m KT  y ħ  , H(q0) is the form factor given by : 2 20 00 30  b(8b 9q b 3q )H(q )8(q b) + +=+  (13) Dipoles In heterostructures AlGaN/GaN, the presence of the electron gas can be entirely due to the polarization field as spontaneous as piezoelectric. Te relaxation time attributed to this type of diffusion can be formulated by equation 13: ( ) 2* 2222 3 302 121 (2 ) τ π  =− ∫   F   K  D tot dipole scr  Ddipole F  F  m q dqn V qk q K   (14) is the two-dimensional Fourier transform of the scattering potential. Te density of 2D gas is the rate of aluminum given by: 20 13( )4 =  Ddipôle na x Results and Discussion Tis study is based on AlGaN/GaN heterostructure whose characteristics are given in able 1. Figure 3   shows for four values of electron gas density wells in the  variation of mobility as a function of the the barrier thickness this structure has a typical thickness of 30 nm; the variation range was set between 1 nm and 10 nm.For the classical values of thickness 30 nm, the mobility values are of the order of 106 cm 2 /Vs. Tis great value shows the low importance of this type of diffusion in these structures [13]. Figure 4 shows the variation of mobility attributed to such distribution as a function of the density of residual impurities for four NomA392 χ  AL (%)26d  AlGaN (Å)291N Hall 300K   (10 12 cm -2 )7,1 µ Hall  300K (cm 2 /Vs)1734N Hall 10-20K   (10 12 cm -2 )7,7 µ Hall 10-20K   (cm 2 /Vs)7350Buffer (µm)1,5Subs.SiDiscloc density (cm -2 )5-7.10 9 Type epitaxyEJM Table 1: Main characteristics of the sample studied.   Figure 3: Mobility limited by ionized impurities on the surface.  Citation:  Nouacry A, Touhami A, Benkassou A, Bouziane A, Aouaj A (2016) Analytical Study of Electron Mobility in Hemts Algan/Gan. J Electr Electron Syst 5: 169. doi:10.4172/2332-0796.1000169 Page 4 of 6 Volume 5 ã Issue 1 ã 1000169J Electr Electron SystISSN: 2332-0796 JEES an open access journal typical of 2D gas densities in our structures. We note that the influence of residual impurities on the mobility is important for the low 2D gas densities (<5.10 12  cm -2 ). But despite this, the mobility is always greater than an order of magnitude (for density of residual donors of about 10 17  cm -3. . For high carrier densities in the well, the mobility would be really affected for doping densities above 10 17  cm -3 . Tis would allow us to conclude that this type of diffusion is not the critical factor for heterostructures where the best conductivity of gas is sought, which impose a gas density higher than 5×10 12  cm -2 . According to the simulation results of Figure 5, where we note the importance of this mode of diffusion on the overall mobility of electrons in the well. Te mobility varies approximately as L -2 . We expect a significant drop of it depending on the length of correlation between defects [14,15]. In fact, we find that the mobility reaches a plateau which depends on the density of electrons and then practically does not vary more. Figure 6 shows the high sensitivity of mobility to the interface quality AlGaN/GaN. Te calculated values of the mobility are the same of those obtained experimentally and of the magnitude of the mobility limited by alloy disorder. Te epitaxial is therefore very sensitive to this parameter that can completely degrade the mobility at low temperature (μ < 1000 cm²/Vs). Figure 7 shows the variation of mobility as a function of electron density for three values of dislocation densities covering the range of  variation for conventional structure, where f is the value unit [16]. Tis figure shows us that for a given dislocation density, the electron mobility increases with the electron population in the well. Tis trend illustrates the screening of scattering centers as well as the population increases. Figure 8 extends the typical dislocation density of structures encountered in the literature, the variation of mobility as a function of n 2DEG  for different filling factors.Te   Figure 9 shows the variation of the mobility limited by acoustic phonons in the densities of electrons. Figure 4: Mobility limited by the residual impurities.   Figure 5: Variation of mobility as a function of parameters representing the surface roughness. Δ is set at 1 Angstrom.   Figure 6: Variation of mobility according to the correlation length for ns= 0.1, 0.5 and 1.10 13 cm -2.  Δis set at Angstrom.   Figure 7:  Variation of mobility depending on the density of 2D gas.   Figure 8: Inuence of load factor on the mobility of dislocations.
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