A mathematical model based on the one dimensional diffusive transport of bismuth atoms has been used to study the concentration profile of the bismuth atoms during the liquid phase epitaxial growth of InPBi. This model is used to determine the growth kinetics at equally spaced layers in the proximity of the grown epitaxial interface. Various growth parameters such as growth temperature, melt supercooling and the continuous cooling ramp applied during growth have been optimized to find out the suitable conditions of growth. The thickness of the epitaxial layers as a function time is also estimated. Valence Band anticrossing (VBAC) model is used to determine the reduction in band gap and increase in spin-orbit splitting energy for InP1−xBix. The valence band structure of InPBi is modified due to the interaction of the Bi related impurity levels with the light hole (LH), heavy hole (HH) and spin-orbit split-off (SO) sub bands. A 12 × 12 Hamiltonian is solved to find out the valence band structure of InPBi in the <100> direction. © Springer International Publishing Switzerland 2017.