Curved nanowire structures and exciton binding energies

Abstract

Growth of quantum-confined semiconductor structures is a complicated process thatmay lead to imperfect and complex shapes as well as geometrical nonuniformitieswhen comparing a large number of intended identical structures. On the otherhand, the possibility of tuning the shape and size of nanostructures allows forextra optimization degrees when considering electronic and optical propertiesin various applications. This calls for a better understanding of size and shapeeffects. In the present work, we express the one-band Schrödinger equation in curvedcoordinates convenient for determining eigenstates of curved quantum-wire andquantum-dash structures with large aspect ratios. Firstly, we use this formulation tosolve the problem of single-electron and single-hole states in curved nanowires.Secondly, exciton states for the curved quantum-wire Hamiltonian problem are foundby expanding exciton eigenstates on a product of single-particle eigenstates. Asimple result is found for the Coulomb matrix elements of an arbitrarily curvedstructure as long as the radius-of-curvature is much larger than the cross-sectionaldimensions. We use this general result to compute the groundstate exciton bindingenergy of a bent nanowire as a function of the bending radius-of-curvature. Itis demonstrated that the groundstate exciton binding energy increases by40 meV as the radius-of-curvature changes from20 to2 nm while keeping the total length (and volume) of the nanowire constant.