Band-gap shrinkage calculations and analytic model for strained bulk InGaAsP

Band-gap shrinkage is an important effect in semiconductor lasers and optical amplifiers. In the former it leads to an increase in the lasing wavelength and in the latter an increase in the gain peak wavelength as the bias current is increased. The most common model used for carrier-density dependent band-gap shrinkage is a cube root dependency on carrier density, which is strictly only true for high carrier densities and low temperatures. This simple model, involves a material constant which is treated as a fitting parameter. Strained InGaAsP material is commonly used to fabricate polarization insensitive semiconductor optical amplifiers (SOAs). Most mathematical models for SOAs use the cube root bandgap shrinkage model. However, because SOAs are often operated over a wide range of drive currents and input optical powers leading to large variations in carrier density along the amplifier length, for improved model accuracy it is preferable to use band-gap shrinkage calculated from knowledge of the material bandstructure. In this letter the carrier density dependent band-gap shrinkage for strained InGaAsP is calculated by using detailed non-parabolic conduction and valence band models. The shrinkage dependency on temperature and both tensile and compressive strain is investigated and compared to the cube root model, for which it shows significant deviation. A simple power model, showing an almost square-root dependency, is derived for carrier densities in the range usually encountered in InGaAsP laser diodes and SOAs.