Polarization doping—Ab initio verification of the concept: Charge conservation and nonlocality

Abstract

In this work, we study the emergence of polarization doping in AlxGa1−xN layers with graded composition from a theoretical viewpoint. It is shown that bulk electric charge density emerges in the graded concentration region. The magnitude of the effect, i.e., the relation between the polarization bulk charge density and the concentration gradient is obtained. The appearance of mobile charge in the wurtzite structure grown along the polar direction was investigated using the combination of ab initio and drift-diffusion models. It was shown that the ab initio results can be recovered precisely by proper parameterization of drift-diffusion representation of the complex nitride system. It was shown that the mobile charge appears due to the increase of the distance between opposite polarization-induced charges. It was demonstrated that, for sufficiently large space distance between polarization charges, the opposite mobile charges are induced. We demonstrate that the charge conservation law applies for fixed and mobile charge separately, leading to nonlocal compensation phenomena involving (i) the bulk fixed and polarization sheet charge at the heterointerfaces and (ii) the mobile band and the defect charge. Therefore, two charge conservation laws are obeyed that induces nonlocality in the system. The magnitude of the effect allows obtaining technically viable mobile charge density for optoelectronic devices without impurity doping (donors or acceptors). Therefore, it provides an additional tool for the device designer, with the potential to attain high conductivities: high carrier concentrations can be obtained even in materials with high dopant ionization energies, and the mobility is not limited by scattering at ionized impurities.

Polarization Doping in a GaN-InN System—Ab Initio Simulation

“…Ab initio simulations reported in this paper employed the density functional theory (DFT) package SIESTA. SIESTA uses numeric atomic orbital series to solve Kohn–Sham equations [ 23 , 24 ]. The following atomic orbitals were used: for In—3s: DZ (double zeta), 3p: TZ (triple zeta), 3d: DZ; N—2s: DZ, 2p: TZ, 3d: SZ (single zeta) and for Ga- 4s: DZ (double zeta), 4p: TZ (triple zeta), 3d: DZ.…”

“…The transition between two chemically different substances may be also more or less diffuse. Predictably, the diffuse interface generates the extended charge density [ 17 , 18 , 19 , 20 , 21 , 22 , 23 ]. The nitride alloys concentration change leads to the polarization difference and creation of a bulk charge density, inducing a phenomenon known as polarization doping [ 18 , 19 , 20 , 21 , 22 , 23 ].…”

“…Predictably, the diffuse interface generates the extended charge density [ 17 , 18 , 19 , 20 , 21 , 22 , 23 ]. The nitride alloys concentration change leads to the polarization difference and creation of a bulk charge density, inducing a phenomenon known as polarization doping [ 18 , 19 , 20 , 21 , 22 , 23 ]. Since the polarization is proportional to metal concentration, linearly graded materials have a uniform bulk charge density.…”

“…In insulating systems, without screening the potential profile, it can be used to determine the polarization-related charge density via the Poisson equation. The method was successfully used to determine the polarization density constant for the Al-Ga-N system in [ 23 ]. In addition, the mechanism for the generation of the mobile charge was described and used to design the UV laser diode (LD).…”

“…The best possible remedy is to use Mg and polarization doping simultaneously [ 30 ]. In this work, we will use the methods developed in [ 23 ] for the Ga-In-N system to obtain polarization-doping constants, verify the creation of mobile charge and its application to device design.…”