An Investigation of the Electron Escape Time within a Biased AlGaN/GaN Quantum Well
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Biased AIGaN/GaN Quantum Well
Kevin R. Lefebvre and A.F. M.Anwar Electrical and Systems Engineering, University of Connecticut, Storrs, CT 06269-2157 Abstract In this paper, the electron escape time from an AI.2sGa.75N/Ga`N/Al.2sGa.75N quantum well system is calculated as a function of electric field. The calculation includes the piezoelectric field induced by the material system, the continuous density of states within a quantum well as a result of the applied electric field, the change in the group velocity and the proper partitioning of between the tunneling and thermionic emission currents. The calculation of the escape time is achieved by solving Schroedinger equation, through the logarithmic derivative of the wavefunctions, and Poisson's equation self-consistently. Introduction GaN based wide bandgap semiconductors are primary candidates for high temperature electronic applications or optoelectronic devices [1-4]. In the area of optoelectronic devices, the focus was primarily on the realization of light emitting diodes. The optical properties of GaN based devices using inter-subband transitions are also of interest. In this paper, electron escape time from AIGaN/GaN quantum wells is calculated as a function of electric field. The room temperature calculation shows two orders of magnitude improvement in the escape time when compared to it GaAs/AIGaAs counterpart [5,6]. The model presented in this paper in calculating the electron escape time from a quantum well takes into account the partitioning of the current into to components: the tunneling and thermionic emission components [5,6]. This calculation requires the density of states, energy levels and average local velocity for a biased quantum well. Based upon the Green's function treatment, as presented in Ref. [5-9], of solving Schroedinger equation through the logarithmic derivative of the wavefunction, the redistribution of the density of states and the average group velocity is obtained as a function of applied electric field. It is assumed that the electrons are in thermal equilibrium with each other and that the energy bands are parabolic as well as the system is in steady state. Theory The one electron Schroedinger equation under effective mass approximation can be written as: 2 dz, m(z)
dz
J+vz-)q)E')0
where V(z) = Va +V,•(z) +AE• +V,-h +V1,,~,. Vw is the applied potential, V,•(z) is the space charge potential, AE• is the bandoffset, Ye.h is the potential due to the separation of electrons and holes in the quantum well and Vpio0 is the potential due to the piezoelectric field. The calculation
827 Mat. Res. Soc. Symp. Proc. Vol. 482 ©1998 Materials Research Society
of the piezoelectric field is based upon Ref. [4] where
ýpiez,
P
= :C
2d3 68
+C
C33 ]
u1,
and the values for the elastic constants (Cij), the piezoelectric constant (d31) and the strain tensor component (u,=) [4]. Also, E, is the z-directed carrier energy, m*(z) is the effective mass at position z, h is the reduced Planck's constant, and 9(Ez,z) is the envelope function at en
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