A simplified model for graded-gap heterojunctions

A simplified method for calculating the energy band profiles of graded-gap heterojunctions, based on the generalized model of Oldham and Milnes, is presented. The profiles are derived by superposing an energy band grading function and the electrostatic potential in the heterojunction. The latter is obtained by using the depletion layer approximation as for conventional p-n homojunctions. The energy band profiles of hypothetical p(GaAs)-n(Al_0·4Ga_0·6As) heterojunctions are calculated using the simplified method. For small grading layer widths, the results are in good agreement with the generalized model. The barrier lowering factor η as a function of the graded layer width l is calculated for such heterojunctions. It is found, for acceptor and donor densities of 10¹⁸ and 10¹⁶ cm^?3 respectively, that the barrier height is reduced from 0·47 eV to zero as l increases from zero (abrupt case) to ≈300 Å. The applications of these analyses to practical heterojunctions are discussed.