Hot electron transport phenomena in semiconductors occur when charge carriers, typically electrons, gain sufficient kinetic energy from a high electric field to reach energies significantly above the thermal equilibrium of the lattice. This regime is characterized by non-equilibrium conditions where the electron temperature exceeds the lattice temperature. In materials like gallium nitride (GaN) and silicon carbide (SiC), hot electron effects are particularly pronounced due to their high critical electric fields and strong polar optical phonon scattering. Understanding these phenomena is essential for optimizing high-frequency and high-power electronic devices, even when excluding power device specifics.
At low electric fields, electron transport in semiconductors follows Ohm’s law, where the drift velocity is proportional to the applied field. However, as the electric field increases, deviations from linear behavior occur due to energy-dependent scattering mechanisms. In GaN and SiC, the primary scattering mechanisms include acoustic phonon scattering, polar optical phonon scattering, and ionized impurity scattering. At high fields, electrons gain enough energy to emit optical phonons, leading to energy loss and a reduction in mobility. This marks the onset of hot electron transport.
Velocity saturation is a key phenomenon in hot electron transport. As the electric field increases beyond a critical value, the electron drift velocity no longer increases linearly but instead saturates. In GaN, the saturation velocity is approximately 2.5 × 10^7 cm/s, while in SiC, it is around 2.0 × 10^7 cm/s. This saturation occurs because the rate of energy gain from the electric field balances the rate of energy loss due to phonon emission. The saturation velocity is a fundamental parameter for high-field operation, as it limits the maximum current density and switching speed of devices.
Intervalley scattering further complicates hot electron transport in multi-valley semiconductors like GaN and SiC. In these materials, the conduction band consists of multiple energy minima (valleys) with different effective masses and densities of states. At high electric fields, electrons can gain enough energy to transfer from the lower-energy Γ-valley to higher-energy satellite valleys, such as the L or X valleys. This transfer is accompanied by a reduction in mobility because the effective mass in the higher valleys is larger. In GaN, the Γ-valley to L-valley separation is approximately 1.5 eV, while in SiC, the Γ-valley to X-valley separation is around 0.8 eV. Intervalley scattering leads to negative differential resistance (NDR) in some cases, where increasing the electric field results in a decrease in current due to the reduced mobility in the higher valleys.
Impact ionization is another critical high-field phenomenon where energetic electrons collide with the lattice and generate additional electron-hole pairs. This process becomes significant when the electron energy exceeds the bandgap of the material. In GaN, the threshold energy for impact ionization is about 3.3 eV, while in SiC, it is approximately 2.9 eV for 4H-SiC and 3.2 eV for 6H-SiC. Impact ionization can lead to avalanche breakdown, which is undesirable in most device applications due to the resulting uncontrolled current flow. However, it can also be harnessed in specialized devices like avalanche photodiodes.
High-field Hall measurements are a powerful tool for studying hot electron transport. The Hall effect is traditionally used to measure carrier concentration and mobility at low fields, but under high-field conditions, it provides insights into the energy distribution and scattering mechanisms of hot electrons. In high-field Hall measurements, the Hall voltage is measured as a function of the applied electric field, revealing deviations from classical behavior due to hot electron effects. For example, the Hall mobility may decrease at high fields due to increased phonon scattering or intervalley transfer.
In GaN, high-field Hall measurements have shown that the electron mobility drops significantly at fields above 10 kV/cm due to polar optical phonon scattering. Similarly, in SiC, the mobility reduction is observed at fields above 20 kV/cm, with additional contributions from intervalley scattering. These measurements also reveal the onset of velocity saturation and the energy thresholds for intervalley scattering and impact ionization.
The following table summarizes key parameters for hot electron transport in GaN and SiC:
Parameter GaN SiC (4H)
Saturation velocity (cm/s) 2.5 × 10^7 2.0 × 10^7
Γ-valley to satellite valley (eV) 1.5 (L-valley) 0.8 (X-valley)
Impact ionization threshold (eV) 3.3 2.9
Hot electron transport and high-field Hall measurements are essential for understanding the limits of semiconductor performance. In GaN and SiC, the interplay of velocity saturation, intervalley scattering, and impact ionization defines the high-field behavior, influencing device design and operational boundaries. By characterizing these phenomena, researchers can optimize material properties and device architectures for applications requiring high-speed and high-power operation, even without delving into power device specifics. The insights gained from these studies are critical for advancing semiconductor technology in fields ranging from RF electronics to optoelectronics.