A Deterministic and Self-Consistent Solver for the Coupled Carrier-Phonon System in SiGe HBTs

A stationary deterministic solver based on a spherical harmonics expansion of the Boltzmann transport equations for electrons, holes, and phonons is presented to study self-heating in ultrascaled bipolar transistors. With the electrothermal device simulator, a state-of-the-art toward-terahertz SiGe heterojunction bipolar transistor is analyzed and the simulation results are verified against experimental data. To investigate nonequilibrium effects for the carrier-phonon system, the impact of hot longitudinal optical phonons on steady-state carrier transport is discussed. Furthermore, the self-consistent and deterministic solution of the coupled set of equations allows to extract the junction temperature by making use of a method based on the simulated DC characteristics. The resultant junction temperature is compared with the value obtained from the temperature profile within the nanoscale device. Good agreement is obtained for the average temperature in the base-emitter junction verifying the analytical approach used to extract the thermal resistance of the device by experiments.