Clóves G. Rodrigues

Nonlinear transport properties of III-nitrides in electric field

We consider the transport properties of polar direct-gap semiconductors in an electric field, specializing the numerical calculation of the general theory to the case of n-doped III-nitrides, in particular, GaN, AlN, and InN. The nonequilibrium thermodynamic state of these materials—characterized by the variables so-called quasitemperature, quasichemical potential, and drift velocity of the carriers, and the quasitemperatures of longitudinal optical and acoustical phonons—is studied. The evolution equations of these variables—which are highly nonlinear—are derived, and the transient regime and the ensuing steady state are analyzed. The nonlinear transport is characterized and its main properties are discussed. In one case comparison with a recent Monte Carlo calculation is made and good agreement is obtained. In this paper we mainly consider the ultrafast transient, and in the following paper the steady state.

Nonlinear charge transport in III-N semiconductors: Mobility, diffusion, and a generalized Einstein relation

A theoretical study of nonlinear charge transport in polar semiconductors is presented. It is based on a nonequilibrium statistical ensemble formalism which provides a generalized Boltzmann-style nonlinear quantum kinetic theory. The mobility and the diffusion coefficients are obtained and, relating both, a Nernst-Townsend-Einstein relation is derived extended to the nonlinear regime (i.e., outside the Ohmic domain). Numerical calculations are performed considering the particular case of the strongly polar III nitrides, which have application in blue-emitting diodes.

Urbach's tail in III-nitrides under an electric field

We consider electron-hole recombination in wide-gap strong-polar semiconductors of the III-nitride family under high electric fields. The calculated low-energy side of the luminescense spectrum displays the so-called Urbach’s tail, which is characterized as resulting from the presence of sidebands in the form of replicas of the main band, corresponding to recombination with accompanying emission of one, two, etc., LO phonons. The influence of the nonequilibrium macroscopic state of hot carriers and phonons on the luminescence spectrum is evidenced. Our results for a 45 kV/cm electric field intensity point to 50, 120, and 220 meV Urbach tail widths in, respectively, wurtzite InN, GaN, and AlN.

Evolution kinetics of nonequilibrium longitudinal-optical phonons generated by drifting electrons in III-nitrides: longitudinal-optical-phonon resonance

The case of n-doped direct gap polar semiconductors in the presence of moderate to high electric fields is considered. The study is centered on the theoretical analysis of the behavior of LO phonons generated by drifting electrons. The emergence of a kind of “resonance” (or “overheating”) in the LO-phonon distribution which is centered on an off-center region of the Brillouin zone is evidenced. It consists in a preferential concentration of nonthermal populations of LO phonons in the form of a lobular distribution with its axis along the direction of the electric field. Numerical calculations performed for the case of strongly polar GaN accompanied with descriptive figures are presented.

Non-Linear electron mobility in n-doped III-Nitrides

A theoretical study of the mobility of n-doped III-Nitrides in wurtzite phase is reported. We have determined the nonequilibrium thermodynamic state of the bulk n-InN, n-GaN, and n-AlN systems - driven far away from equilibrium by a strong electric field - in the steady state, which follows after a very fast transient. For this we solve the set of coupled nonlinear integro-differential equations of evolution of the nonequilibrium thermodynamic variables, for the three materials, to obtain their steady state values. The dependence of the mobility (which depends on the nonequilibrium thermodynamic state of the sample) on the electric field strength and the concentration (of electrons and impurities) is derived, which decreases with the increase of the electric field strength and the concentration of carriers, evidencing the influence of the nonlinear transport involved.

Nonlinear transport properties of doped III-N and GaAs polar semiconductors: A comparison

In the previous article we have presented a study of the transport properties of doped direct-gap inverted-band polar semiconductors III-nitrides and GaAs in the steady state, calculated with a nonlinear quantum transport theory based on a nonequilibrium ensemble formalism. In the present one such results are compared with calculations using Monte Carlo-modeling simulations and with experimental measurements. Materials of the n-type and p-type dopings in the presence of intermediate to high electric fields, and for several temperatures of the external reservoir, are considered. The agreement between the results obtained using the nonlinear quantum kinetic theory, with those of Monte Carlo calculations and experimental data is remarkably good, thus satisfactorily validating this powerful, concise, and physically sound formalism.

Hole mobility in zincblende c–GaN

We consider the nonequilibrium thermodynamic state of carriers in III-nitrides, and calculate the mobility of holes in cubic GaN layers under electric fields of low intensity. The contribution of different scattering mechanisms to the mobility is analyzed, and the relevance of each one is characterized. Satisfactory agreement with recently published experimental data is obtained.

Drifting electron excitation of acoustic phonons: Cerenkov-like effect in n-GaN

The process of generation of acoustic phonons by way of drifting electron excitation in polar semiconductors is considered. Similarly to what is present in LO phonons, the emergence of a condensation of the pumped energy in modes around an off-center region of the Brillouin zone is evidenced. The phonons are emitted within a lobe-like distribution with an axis along the direction of the electric field. A numerical calculation for the case of GaN is done, which shows that the phenomenon can be largely enhanced at high carrier densities and in strong piezoelectric materials.

Mobility in n-doped wurtzite III-Nitrides

A study of the mobility of n-doped wurtzite III-Nitrides is reported. We have determined the nonequilibrium thermodynamic state of the III-Nitrides systems driven far away from equilibrium by a strong electric field in the steady state, which follows after a very fast transient. The dependence of the mobility (which depends on the nonequilibrium thermodynamic state of the sample) on the electric field strength is derived, which decreases with the strength of electric field. We analyzed the contributions to the mobility arising out of the different channels of electron scattering, namely, the polar optic, deformation, piezoelectric, interactions with the phonons, and with impurities. The case of n-InN, n-GaN, and n-AlN have been analyzed: as expected the main contribution comes from the polar-optic interactions in these strongly polar semiconductors. The other interactions are in decreasing order, the deformation acoustic, the piezoelectric, and the one due to impurities.

Electron mobility in nitride materials

We contribute here a theoretical study of the electron mobility in n-doped GaN, InN, and AlN at moderate to high electric fields. We solve the set of coupled nonlinear integro-differential equations of evolution to obtain the steady-state values of the basic intensive nonequilibrium thermodynamic variables for the three materials. The regions with ohmic and non-ohmic behavior in the electron drift velocity dependence on the electric field strength are characterized in the three nitrides. The electron mobility is calculated, and it is shown that the larger corresponds to InN, and the smaller to AlN.