Analytical modeling of early voltage and common emitter current gain for Si1-yGey heterojunction bipolar transistor

Abstract

The Early voltage describes the output conductance and the load drive capability of bipolar transistors, so high Early voltage is desirable for any device. An increase in the collector–base voltage causes a greater reverse bias across the collector–base junction which increases the collector–base depletion region width, and decreasing the channel width of the base, which is defined as “Early effect”. The Early effect has been studied extensively in conventional bipolar junction transistors (BJTs). In the present work, closed form analytical model were derived for Early voltage (VA) and common emitter current gain (β) for uniform, exponential and Gaussian base doping profiles with arbitrary Germanium (Ge) profiles heterojunction bipolar transistor (HBT). Field dependent mobility (DnSiGe), band gap narrowing (BGN) (due to both heavy doping and presence of Germanium content in the base) and electron velocity saturation effects (vs) were considered in this model. The effects of base doping profiles and Germanium profiles on VA and β are observed in this work. Here it is observed that if Ge mole fraction at emitter end (yE) is 0.01 and it increases at collector end (yC) from 0.01 to 0.3 it increases VA exponentially. It can be found from this analysis that as yC increases due to BGN effect, effective intrinsic carrier concentration (nieSiGe) increases towards base-collector junction which minimizes “Early effect” and increases VA. For a particular yC and yE, VA found highest for uniform base doping profile and lowest for Gaussian base doping profile. The results show that VA is proportional with base doping concentration. Also keeping yC at 0.3 and if yE vary from 0.01 to 0.3 it reduces VA. It was also observed that by keeping yE at 0.01 if yC can be increased from 0.01 to 0.3 it reduces collector current density (JCO). Effects of Ge mole fraction on DnSiGe, nieSiGe and electric field (ElSiGe) were studied. Effect of vs was studied on diffusivity and collector saturation current density (JCO). It is found that vs has significant impact on both JCO and DnSiGe for uniform and exponential base doping profiles; for Gaussian base doping profile it impact is negligible. Cutoff frequency for HBT calculated in this work. The results obtained by using this analytical model compared with the results available in the previous literature and found in good agreement.