## Thermoelectric Properties of Ultrascaled GaN Nanowires

##### Date

2011-12-15##### Author

Davoody, Amirhossein

##### Advisor(s)

Knezevic, Irena

##### Metadata

Show full item record##### Abstract

In recent years, there have been a number of studies done on gallium nitride (GaN) because of
its promising electronic and thermal properties. Its characteristic features are a wide bandgap,
high electron mobility, and high thermal stability [1]. GaN has been used in electronic devices
such as light emitting diodes [2], high-speed field-effect transistors [3], lasers [4], and piezoelectric
nanogenerators [5]. One of the major concerns before establishing a new material in
everyday technology is the reliability of the devices that are made from it. Among all the factors
that affect the reliability of a device, one is the working temperature of the device. This
is especially important for GaN technology because of its special use in high power, high mobility
devices. An integrated thermoelectric cooling solution has been proposed for electronic
and optoelectronic devices [6]. The need for the integration of the thermoelectric cooler in the
integrated circuit provides a motivation to use GaN as the base material of the thermoelectric
cooler. In addition to spot cooling application, thermoelectric devices are good for micro-power
generation where temperature gradients are present. High temperature stability of GaN makes
it a good candidate for high temperature applications [7].
While theoretical and experimental work has been done on electrical conductivity [8, 9, 10]
as well as thermal conductivity [11, 12, 13, 14] of bulk GaN, there have been very few experimental
efforts to investigate the thermoelectric potential of GaN and its alloys [7, 15, 16, 17]. To the best of our knowledge, the only theoretical attempt to study the thermoelectric properties of
GaN was the work of Liu et al. [18]. In their work they use the relaxation-time approximation
to calculate thermal conductivity (k), electrical conductivity (s), and the Seebeck coefficient
(S) of bulk GaN and AlxGa1 xN alloys. Using these calculated quantities, they found out that
the thermoelectric figure of merit ZT = S2sT=k, can reach values as high as 0.0017 at temperature
T = 300 K. For comparison, the ZT values of the commercial thermoelectric materials
such as Bi2Te3 is about 0.7-0.9 at room temperature [19]. It is obvious that GaN based thermoelectric
devices need much further improvement to have a chance to compete these devices at
room temperature. On the other hand, because of high thermal stability of GaN it is worthwhile
to look at the thermoelectric figure of merit at high temperatures around 1000 K to see if there
is any improvement at those temperatures.
The ultimate goal in improving ZT is to increase the power factor S2s while we decrease
thermal conductivity. Using nanostructures has the benefit of providing scattering sources for
phonons which will decrease thermal conductivity by orders of magnitude. Early works of
Hicks and Dresselhaus [20, 21] showed that spatial confinement can enhance the Seebeck coefficient
which leads to a higher power factor. Effectiveness of using silicon nanowires as
thermoelectric devices has been demonstrated experimentally by Hochbaum et al. and Boukai
et al. [22, 23].
The electrical properties of GaN nanowires have been investigated experimentally several
times [3, 24, 25, 26]. The electron mobility values reported in these papers are very disperse
depending on the nanowire thickness, doping, and the fabrication process which requires us
to do a through study of the electron mobility. So a Monte Carlo simulation of the electron
transport in GaN nanowires is done to clarify the role of these parameters. In the thermal conductivity
part the situation is worse. Very little work has been done on the thermal conductivity
of GaN nanowires [27, 28]. So we performed a Monte Carlo simulation of thermal transport as
well.
In this paper, we have shown an ensemble Monte Carlo simulation of electronic and thermal
transport in GaN nanowires over a range of thicknesses (from 3 nm 3 nm to 15 nm 15 nm),
n-type doping densities (from 1018 cm 3 to 1020 cm 3), and a large temperature domain (from
200 K to 1000 K). Also, the Seebeck coefficient and the thermoelectric figure of merit have
been calculated for all these cases. We have solved the Boltzmann transport equation (BTE)
for electrons and phonons by the ensemble Monte Carlo technique. The electronic states are
calculated by solving the Schr�odinger equation coupled with the Poisson equation. The calculated
wavefunctions were used to calculate the scattering rates of electron between different
energy states. We have included acoustic phonon , impurity, surface roughness, polar optical
phonon (POP), and piezoelectric (PZ) scattering mechanisms for electrons. Bulk phonons have
been adopted in this paper. Phonon scattering mechanisms included in simulation are normal
phonon scattering (N), Umklapp phonon scattering (U), isotope impurity scattering, and surface roughness scattering. The results of the simulation showed that increasing the temperature
from 300 K to 1000 K makes a five-fold enhancement to ZT. The optimum nanowire thickness
for getting the highest ZT is 4 nm. The highest value of ZT occures at 3 1018 cm 3 doping
concentration.
This paper is organized as follows: The models used to calculate the electron scattering
rate are discussed in section 2 and the results of the simulation for the electron mobility are
shown after that. Section 3 goes through the phonon scattering models used in this paper and
then shows the calculated values of phononic and electronic thermal conductivity. Section 4
contains calculated values of the electronic and phononic Seebeck coefficients and discusses
their variation under doping, temperature, and the wire cross section changes. Section 5 shows
calculation of the thermoelectric figure of merit from its elements, obtained in the previous
sections, and discusses its variations. Section 6 gives a summary of the work done in this
paper.