Finite-width quantum-well exciton ($V(\rho )=-\frac{e^2}{4\pi {ϵ}_0{ϵ}_r}\int \frac{|{\chi }_e(z_e){|}^2|{\chi }_h(z_h){|}^2}{\sqrt{{\rho }^2+(z_e-z_h{)}^2}}d{z}_{e}d{z}_h$)

In the envelope approximation, a quantum well confines electron and hole motion perpendicular to the plane. Averaging their screened attraction over the confinement envelopes gives the displayed effective in-plane potential. Its narrow-well limit approaches the ideal two-dimensional exciton; finite width softens the short-distance attraction. Dielectric mismatch, nonparabolic bands and strong electron–hole confinement mixing require more than this single-subband model.