  A theory of the trion and biexciton in a nanowire (NW) in the framework of
the effective-mass model using the Born-Oppenheimer approximation is presented.
We consider the formation of trions and biexcitons under the action of both the
lateral confinement and the localization potential. The analytical expressions
for the binding energy and eigenfunctions of the trion and biexciton are
obtained and expressed by means of matrix elements of the effective
one-dimensional cusp-type Coulomb potentials whose parameters are determined
self-consistently by employing the same eigenfunctions of the confined electron
and hole states. Our calculations for the ZnO/ZnMgO, CdSe/ZnS and CdSe/CdS
core/shell cylindrical shaped NWs show that the trion and biexciton binding
energy in NWs are size-dependent and for the same input parameters the
biexciton binding energy in NWs is always larger than the binding energy of the
trion. The trion and biexciton remain stable in CdSe/ZnS NW with the increase
of the dielectric shell, while in ZnO/ZnMgO NW they become unstable when the
surrounding dielectric shell exceeds 2.5 nm and 2 nm for each, respectively.
The associative ionization of biexciton antibonding states into trion bonding
states is studied. Based on the results for size dependence of biexciton
binding energy and probability associative ionization an optimal radius for
optoelectronic application NW is suggested.
