Direct-bandgap InAs quantum-dots have long-range electron-hole exchange whereas indirect gap Si dots have short-range exchange.

Excitons in quantum dots manifest a lower-energy spin-forbidden "dark" state below a spin-allowed "bright" state; this splitting originates from electron-hole (e-h) exchange interactions, which are strongly enhanced by quantum confinement. The e-h exchange interaction may have both a short-range and a long-range component. Calculating numerically the e-h exchange energies from atomistic pseudopotential wave functions, we show here that in direct-gap quantum dots (such as InAs) the e-h exchange interaction is dominated by the long-range component, whereas in indirect-gap quantum dots (such as Si) only the short-range component survives. As a result, the exciton dark/bright splitting scales as 1/R(2) in InAs dots and 1/R(3) in Si dots, where R is the quantum-dot radius.