Theory of Point Defects and Complexes in GaN
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ABSTRACT We have studied the electronic and energetic properties of native defects, impurities and complexes in GaN applying state-of-the-art first-principles calculations. An analysis of the numerical results gives direct insight into defect concentrations and impurity solubility with respect to growth parameters (temperature, chemical potentials) and into the mechanisms limiting the doping levels in GaN. We show how compensation and passivation by native defects or impurities, solubility issues, and incorporation of dopants on other sites influence the acceptor doping levels. The role of hydrogen in enhancing the p-type doping is explained in detail. We also discuss the mechanisms responsible for the experimentally observed limitation of the free-carrier concentration in p-type GaN. INTRODUCTION During the past few years interest in GaN-based devices has grown rapidly, stimulated by the accomplishment of bright, highly-efficient green/blue light-emitting diodes [1]. However, despite the progress in devices, doping problems remain an important issue. Current doping levels are sufficient for producing light-emitting diodes, but the lack of high p-type doping levels may be a major obstacle in achieving III-V nitride laser diodes. Native defects are often invoked to explain the shortcomings in doping. With the advent of increasingly fast computers and methodical improvements, firstprinciples calculations have evolved into a powerful tool to study various properties of
defects and impurities in semiconductors. With the capability to calculate accurate total energies and electronic structure, it became possible to investigate the character and the position of defect levels, the atomic structure of the defect, as well as the energy to create
the defect. More recently, formalisms have been developed to use the total energy of the defect to calculate defect concentrations, under the assumption of thermodynamic equilibrium [2, 3]. The same formalism can also be extended to the calculation of impurity solubilities [4, 5]. In the present paper we will give an overview about theoretical results for native defects and impurities in GaN. We will mainly focus on the problem of acceptor doping limits in GaN, particularly for Mg, which is presently the acceptor of choice to obtain p-type con-
ductivity. However, hole concentrations are still lower than desired. We therefore discuss various mechanisms which may limit the hole concentration: compensation by native de-
fects and impurities, solubility limits, and incorporation of the Mg acceptor on other sites. The role of hydrogen, in particular its ability to enhance the p-type doping, is discussed in detail.
645 Mat. Res. Soc. Symp. Proc. Vol. 395 0 1996 Materials Research Society
FORMALISM The equilibrium concentration c of an impurity or defect at temperature T is determined by its formation energy, El: c = Nsites g expS/kB exp-E
(1)
/kBT
where Nsite, is the number of sites the defect can be built in. g is a degeneracy factor representing the number of possible configu
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