Impurity photoionization cross-section and intersubband optical absorption coefficient in multilayer spherical quantum dots

Energy spectrum, wave functions and binding energies of the electron to the donor impurity ion located in the center of a multilayer spherical quantum dot (MSQD) consisting of a core and two spherical shells were studied within the effective mass approximation. Based on the exact wave functions of the electron expressed in terms of Coulomb functions of the first and second kind, the spectral dependences of the photoionization cross section of the impurity (PCS) and the intersubband optical absorption coefficient (OAC) for various geometric dimensions of the nanostructure were calculated. It is shown that the decrease in the width of the external potential well changes the localization of the electron in the nanosystem which significantly affects the binding energy of the electron with the impurity, photoionization cross section and interband absorption coefficient. The position of the PCS peak associated with the quantum transition of an electron from the ground state to the 1p0 state shifts to the region of higher energies, and its height decreases. At the same time, the height of PCS peaks associated with quantum transitions to higher excited states (2p0, 3p0) increases.The presence of impurities and changes in the MSQD size significantly affect the intersubband absorption coefficient. Decrease of the external potential well width in the absence of impurities leads to a monotonous increase in OAC through the first excited state, and in the presence of a central impurity, absorption through states with higher energy increases.

On hydrodynamics in the presense of strong external potential field

On the base of the Boltzmann kinetic equation, hydrodynamics of a dilute gas in the presence of the strong external potential field is investigated. First of all, a gravitational field is meant, because the consistent development of hydrodynamics in this environment is of great practical importance. In the present paper it is assumed that it is possible to neglect the influence of the field on the particle collisions. The study is based on the Chapman–Enskog method in a Bogolyubov’s formulation, which uses the idea of the functional hypothesis. Consideration is limited to steady gas states, which are subjected to a simpler experimental study. Chemical potential μ0 of the gas at the point where the external field has zero value and its temperature T are selected as the reduced description parameters of the system. In equilibrium, in the presence of the field, these values do not depend on the coordinates. It is assumed that in thehydrodynamic states T and μ0 are weakly dependent on the coordinates and therefore their gradients, considered on the scale of the free path length of the gas, are small. The kinetic equation, accounting for the functional hypothesis, gives an integro-differential equation for a gas distribution function at the hydrodynamic stage of evolution. This equation is solved in perturbation theory in gradients of T and μ0. The main approximation is analyzed for possibility of the system to be in a local equilibrium by means of comparing it with an equilibrium distribution function. Next, the distribution function is calculated in the first approximation in gradients and it is expressed in terms of solutions Ap , Bp of some first kind integral Fredholm equations. An approach to the approximate solution of these equations is discussed. The found distribution function is used to calculate the fluxes of the number of gas particles and their energy in the first order in gradients T and μ0 . Kinetic coefficients, which describe the structure of these fluxes, are introduced. Matrix elements of the operator of the linearized collision integral (integral brackets) are used for their research. It is a question of validity of the principle of symmetry of kinetic coefficients and definition of their signs.