3.2.2 Electron Transport

Using the established setup of models and model parameters, MC simulation results for different physical conditions are obtained (doping, temperature, field, etc.) for bulk GaN. Fig. 3.1 shows the low-field electron mobility in hexagonal GaN as a function of free carrier concentration. The mobility depends on the sound velocity via the piezoelectric and the acoustic deformation potential (ADP) scattering mechanism. A higher sound velocity reduces the ADP scattering rate, which results in an increased mobility.

Figure 3.1: Low-field electron mobility as a function of carrier concentration in GaN:
Comparison of the MC simulation results and experimental data.

The simulations show, that the piezoelectric scattering is the dominant mobility limitation factor at low concentrations even at room temperature, beside the commonly accepted importance at low temperatures.

The MC simulation is in fairly good agreement with experimental data from collections or single point measurements from [175,176,177,178,179]. The electron mobilities selected for comparison, consider bulk material and are measured using the Hall effect. The discrepancy between the simulation results and the measured data might be attributed to dislocation scattering which is not considered here. This mechanism is considered to be a source of mobility degradation for GaN samples.

Numerous publications on GaN heterostructure devices (see e.g. a summary in [180]) provide inversion layer mobilities which are higher. These values are derived from transit frequency and device dimensions. However, two-dimensional electron gas heterostructures are plagued, among others, by surface scattering effects, and are not considered in this work.

Fig. 3.2 shows the low-field electron mobility as a function of lattice temperature in GaN at 10$^{17}$ cm$^{-3}$ concentration. The experimental data are from [179,181,182]. Note, that mobility increased over the years because of the improved material quality (reduced dislocation density).

Figure 3.2: Low-field electron mobility as a function of lattice temperature in GaN at carrier concentration of 10$^{17}$ cm$^{-3}$.

Fig. 3.3 provides the electron drift velocity versus the electric field. We compare our MC result with other simulations [146,147,110,153,155,113], and with the available experimental data [183,184]. The low field data points are in qualitatively good agreement, at higher fields experimental values are significantly lower. Both experiments [183,184] of electron velocities in bulk GaN, employed pulsed voltage sources. Many devices with etched constrictions were measured and the peak electron drift velocity $v_\ensuremath{\mathrm{d,max}}$ was typically found to be about 2.5$\times$10$^7$ cm/s at electric fields $E_\ensuremath{\mathrm{pk}}$=180 kV/cm. The discrepancy in the reported MC results is due to various uncertainties of parameter values and considerations of scattering mechanisms.

Figure 3.3: Electron drift velocity versus electric field in wurtzite GaN: Comparison
of MC simulation results and experimental data I.

While the low-field transport has been profoundly studied, reports on the high-field transport properties are inconsistent. Several groups observe a negative differential mobility (NDM) in their experiments [185,184], while others do not obtain any saturation below 200 kV/cm [186] (Fig. 3.4). MC simulation results are contradictory too: some simulations yield a maximum of the electron velocity at 140 kV/cm [187,109], while according to others the maximum velocity is at 180 kV/cm [146,111]. Those again are in a disagreement with the NDM as observed in experiments at over 320 kV/cm [185].

Figure 3.4: Electron drift velocity versus electric field in wurtzite GaN: Comparison
of MC simulation results and experimental data II.