Calculation of electric field and optical transitions in InGaN∕GaN quantum wells

Abstract

We present analytical expressions for internal electric field and strain in single and multiple quantum wells, incorporating electromechanical coupling, spontaneous polarization, and periodic boundary conditions. Internal fields are typically 2% lower than the fields calculated using an uncoupled model. We point out two possible interpolation routes to calculate the piezoelectric (PZ) constants eij of an alloy from the PZ constants of the constituent materials and show that, for an In0.2Ga0.8N∕GaN quantum well system, the respective internal electric fields differ by 10%. Using an effective-mass model, we explore the effect of the uncertainty in the elastic and PZ constants of GaN on the internal field and optical transitions of InGaN∕GaN quantum wells, and find that the range of published values of eij produces an uncertainty of more than ±20% in the internal field and of more than ±30% in the blueshift in optical transition energy between zero bias and flatband conditions (when the applied field is equal and opposite to the internal field). Using the PZ constants of Shimada et al. [J. Appl. Phys. 84, 4951 (1998)] in our model gives the best fit to results in the literature for internal field and optical transition energy in InGaN∕GaN quantum wells. We find that a well with a smooth In gradient along the growth direction has similar optical properties to a well with constant composition, if the average In content of the two wells is the same.