Thermoelectric Properties of Ultrascaled GaN Nanowires
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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 . GaN has been used in electronic devices such as light emitting diodes , high-speed field-effect transistors , lasers , and piezoelectric nanogenerators . 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 . 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 . 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. . 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 . 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.