The saturation current of silicon bipolar transistors at moderate stress levels and its relation to the energy-band structure

Mechanical stress has a pronounced influence on the saturation current of bipolar transistors, which is called the piezojunction effect. This effect has been adequately modeled from band theory for stresses over 1 GPa. However, this is not the case for stresses below 200 MPa, which are frequently encountered in electronic engineering. This paper presents a band model for this stress range which reproduces measurements in a successful way. The model is based on the idea that the saturation current depends on the conductivity of minority charge carriers in thermodynamic equilibrium. This conductivity is expressed in terms of the energy bands. The influence of stress on the bands is calculated from the deformation potential theory. With this approach calculations are also made of the changes in the mobility and the intrinsic carrier concentration. The presented model naturally includes the theory of the piezoresistive effect, which is well established. It also includes our previous engineering model of the piezojunction effect. This is used to numerically calculate the coefficients of the piezoresistive and the piezojunction effect, which are in good agreement with literature values and measurement results.