Modeling the hole transport in GaN is hindered by the lack of high
quality -type material. Several dopants such as Mg, Zn, Cd, and Be
[188,189,190,191] have been investigated. Of
all those dopants Mg is known to have the lowest ionization energy
[192]. The first
-type conduction in magnesium-doped GaN
grown by MOCVD was realized by Amano et al. [188]. The
as-grown high-resistivity GaN:Mg is converted into
-conductive
material by hydrogen depassivation [193]. Due to the high
activation energy of Mg of 150 to 250 meV [194,192] only
a few percent are active at room temperature. The highest reported
efficiency is around 10% [195]. In order to reach a useful
hole concentration of 10
-10
cm
a Mg doping as high
as 2
10
-10
cm
is needed
[196]. However, such high doping concentrations lead to a
deterioration of the hole transport properties
(Fig. 3.5). Kozodoy et al. [197] suggest
that at very high doping levels the degree of compensation and
self-compensation [198] increases, which suppresses the hole
mobility. On the other hand the hole concentration is extremely
dependent on the temperature as demonstrated in [199].
One way of improving the performance is by using a -doping as
suggested by Nakamari et al. [200]. The
dislocation density is significantly reduced, and a higher conductivity
is achieved in both the lateral and vertical directions. The latter is
an issue for Mg-doped heterostructures, where the super-lattice
introduces also potential barriers in vertical direction. Such an
approach was used by several
groups [201,202,203,204]. The variation of
the valence band energy caused by the modulation of chemical
composition leads to a reduction of the acceptor activation
energy. The polarization fields increase the band bending, and the
hole concentration rises in addition [202]. The acceptors
in the Al
Ga
N are energetically closer to the
valence band edge and are therefore ionized easier [205].
Another problem, which bipolar GaN-based devices face, is the high resistivity of the p-type ohmic contacts. They are sometimes referred to as closer to leaky Schottky contacts in their characteristics [84]. Introduction of InGaN/AlGaN super-lattices greatly improves the contact sheet resistance [206], due to the large oscillations of the valence band.
A parameter also crucial for the modeling of hole transport is the
effective hole mass. Estimation of the hole effective masses and their
anisotropy was the subject of numerous studies (a comprehensive review
is found in [207,208,209,210]). Values ranging
from 0.3m[211] to 2.2m
[212] are reported. Kasic
et al. [208] suggest that the effective hole mass
depends on the hole concentration: 1.0m
for
=5
10
cm
, and 1.4m
for
=8
10
cm
[213]. In this work a
value of 1.4m
is assumed as reported in [208], lower than
the one used in [199] (1.6m
), and slightly higher than
the one recommended by Vurgaftman et al. (1.0m
)
[209].
Fig. 3.7 shows the hole drift velocity as a function
of the electric field as calculated by two groups. Rodrigues et
al. [214] use a rather high hole mass (2.0m) and a
doping concentration of 10
cm
. The calculation of Chen
et al. [157] relies on a standard ensemble Monte Carlo
approach and accounts for various scattering effects including impact
ionization. Again the hole velocity is limited by the high density of
states of the heavy band (1.8m
).