^{1}

^{2}

^{1}

^{2}

The cross-section of light absorption by size-quantized semiconductor quantum dots (QD) is
calculated in the case of a resonance with an exciton

Study of the resonant reflection and absorption of light by low-dimensional semiconductor objects is a simple and reliable way of the determination of exciton parameters [

The light elastic scattering on a QD of arbitrary form and sizes in a resonance with excitons is investigated in [

In the present work, a semiclassical method [

There are two variants of the semiclassical method. The first of them assumes using of boundary conditions for electric and magnetic fields on the semiconductor object boundaries (see, e.g., [

First of all, we calculate the current

The induced electric and magnetic fields are represented with the help of the vector

The quantum theory of conductivity of low-dimensional objects is elaborated in [

We assume

We apply (

Let us consider an exciton consisting of an electron from twofold degenerated conductive band

According to determinations of [

We assume that the QD radius

Let us consider light scattering by a QD near the resonance with some energy level of

With the help of (

Using (

To obtain precise induced electric and magnetic fields on large distances from a QD, we have to calculate the vector

Using the formulas for retarded potentials, we obtain the induced field

Let us substitute (

Equation (

Let us consider a special case when the system of three equations is reduced to one equation. It happens if the function

The precise results for the fields distinguish from the results of the lowest approximation on the light-electron interaction only by the substitution

For the case (

The Pointing vector on large distances from the QD equals

The results for the cross-sections of light scattering on QD, obtained with the help of the quasiclassic method, coincide with the lowest approximation on the light-electron interaction with the results of the quantum perturbation theory [

It was shown at calculations of light absorption by a QW that the interference of stimulating and induced electromagnetic fields must be taken into account (see, e.g., [

Let us calculate an interference contribution into the Pointing vector at

Since (

Let us calculate the energy flux

Further we substitute variable

Since

Comparing (

Thus, the electric and magnetic fields induced at the light irradiation of QDs are calculated in the resonance of the stimulating light and excitons with the help of the semiclassical method of the retarded potentials. The fields on the large distances are calculated exactly.

The concrete calculations are performed for the excitons

The light scattering and absorption cross-sections by QDs are obtained for arbitrary QDs under condition