Abstract: A model for the built-in electric field in the base is developed and calculated analytically.The model is suitable for a base with a Gaussian doping distribution and different Ge profiles (e.g.,triangle,box-triangle).A new formula for the valence band effective states is obtained,and the effect of the conduction band effective states on the built-in electric field is considered for the first time.It is found that the effect of the Ge fraction on the built-in electric field is larger than that of impurities.When the Ge fraction profile is triangular,the built-in electric field increases gradually from emission to collector with the total Ge fraction.At a given location x,the built-in electric field becomes larger and larger with the increasing of the total Ge fraction.When the Ge fraction profile is box-triangular,the built-in electric field increases from emission junction to collector for a given x1 and a given Ge fraction yc.For an invariable Ge fraction profile,the built-in electric field is nearly invariable.For a linearly graded Ge fraction profile,the built-in electric field becomes larger and larger with the increasing of x1.In addition,there is a sharp drop near x1.

Key words: SiGe alloy,  built-in electric field, triangular Ge profile, box-triangular Ge profile,  Gaussian doping distribution