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{\Large \bf Path integral Monte Carlo simulations of bound states in
semiconductor quantum wells:  excitons, trions and biexcitons}

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{\large A.V.~Filinov$^{1,2}$,
M.~Bonitz$^1$, and Yu.E.~Lozovik$^2$}

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$^{1}$FB Physik, Rostock University, D-18051 Rostock, Germany\\
$^2$ Institute of Spectroscopy, Russian Academy of
Sciences, 142190 Troitsk

%\\%$^{*}$e-mail: afilinov@id.ru

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%\centerline{\large Abstract}
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We present first-principle path integral Monte-Carlo (PIMC)
studies of strongly correlated electron-hole complexes
such as excitons, trions (charged excitons) and biexcitons
in $Al_{x}Ga_{1-x}As$ quantum-well structures.
The correlation and binding energies are calculated as function of
quantum well width and compared with available experimental~[1,2] and
theoretical~[3] data. The only approximation made in our simulations
is the seperation of particle motion parallel and perpendicular to the
quantum well plane. The obtained very accurate 
PIMC results for experimantally measured binding energies validates
the applicability of our approximation in the wide range of quantum well
widths $10 \rm \AA < L < 250 \rm \AA$. As in the experiments,
we observe a maximum of the binding energies in GaAs/AlGaAs quantum well samples 
around $L = 40 \rm \AA$. We clearly show that the physical reason
is non-monotonic dependence of the electron (hole) confinement on the well
width.

The developed method is a powerful tool for further inverstigation of temperature
and many-body effects on bound states in heterostructures (e.g. depedence
on finite exciton, biexciton densities). 

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[1] S.~Adachi, T.~Miyashita, S.~Takeyama et al., Phys. Rev. B {\bf 55},
1654 (1997)

[2] D.~Birkedal, J.~Singh et al., Phys. Rev. Lett. {\bf 76}, 672 (1996)

[3] C.~Riva, F.M.~Peeters, and K.~Varga, Phys. Rev. B {\bf 61}, $13\; 873$ (2000)

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