Measurements of bandgap narrowing in Si bipolar transistors

Theory predicts appreciable bandgap narrowing in silicon for impurity concentrations greater than about 10¹⁷ cm^?3. This effect influences strongly the electrical behaviour of silicon devices, particularly the minority carrier charge storage and the minority carrier current flow in heavily doped regions. The few experimental data known are from optical absorption measurements on uniformly doped silicon samples. New experiments in order to determine the bandgap in silicon are described here. The bipolar transistor itself is used as the vehicle for measuring the bandgap in the base. Results giving the bandgap narrowing (ΔV_g0) as a function of the impurity concentration (N) in the base (in the range of 4.10¹⁵–2.5 10¹⁹ cm^?3) are discussed. The experimental values of ΔV_g0 as a function of N can be fitted by:

$\text{δV}{}_{\mathrm{g0}}\text{= V}{}_1\text{ln}\text{N}\text{N}{}_0\text{+}\text{ln}{}^2\text{N}\text{N}{}_0\text{+C}$

where V₁, N₀ and C are constants.It is also shown how the effective intrinsic carrier concentration (n_ie) is related with the bandgap narrowing (ΔV_g0).