Inhomogeneous Charge Distribution in Semiconductor Nanoparticles

Abstract

The inhomogeneous spatial distribution of charge carriers within semiconductor oxide nanoparticles is investigated by taking into account processes involving the interaction of conduction electrons with oxygen donor vacancies in the bulk and with oxygen adsorbates at the surface. The main characteristics of the semiconductor nanoparticles, such as the surface charge, the distributions of positive and negative charges in the bulk, and the temperature dependence of the concentration of conduction electrons, are determined selfconsistently by taking into account the interaction of all charges in the system under conditions of complete thermodynamic equilibrium. The developed statistical mechanics model allows us to determine the net surface negative charge on oxygen atoms, the spatial distributions of the conduction electrons, the positively charged ionized donors, and the electrical potential inside the nanoparticle as a function of nanoparticle radius and temperature.

Sensor Effect in Oxide Films with a Large Concentration of Conduction Electrons

“…The contributions to F include the free energies of electron gas and ionized donor positive charges, the potential energy of the Coulomb interaction between all positive and negative charges in the system, as well as the free energy of electrons captured by oxygen atoms at the surface of the nanoparticles. The minimization of the free energy functional F over unknown functions  radial distribution of the conduction electrons n c ( r ) and positive charges on ionized donors as well as unknown density of oxygen surface traps of electrons  produces the set of equations which allows us to obtain n c ( r ), the key input for calculation of the sensor sensitivity.…”

“…The temperature-dependent concentrations of oxygen atoms in the absence ( n O (0; T )) and the presence ( n O ( P H 2 ; T )) of hydrogen can be found by solving the system of eqs – and –, respectively. Then, these concentrations are used as input to obtain the concentrations of the conduction electrons n c ( R ; T , 0) and n c ( R ; T , P H 2 ) by solving the system of equations obtained in ref by minimizing total free energy F of interacting charges in the nanoparticle, followed by the calculation of the sensor sensitivity Θ­( T ) using formula .…”

“…This condition is valid only if the donors are fully ionized, which is not the case for most of the oxides as their ionization energy ε d > kT . Moreover, the electron distribution in spherical semiconductor nanoparticles was obtained by using an arbitrary concentration of the surface charges and assuming that the positive charges are fixed and distributed uniformly over the volume of nanoparticles. , As was shown, such unphysical constraints produce substantial errors in concentration of the subsurface electrons. More importantly, the uniformly distributed surface charge of substantial concentration does not influence the distribution of the conduction electrons inside the nanoparticles as their electric field is zero according to Gauss law.…”

Absorption of Infrared Radiation by an Electronic Subsystem of Semiconductor Nanoparticles

“…Different scenarios are possible for the quantum dots depending on particle characteristics and temperature. The first case can be solved with the method proposed in a previous study, 14 and the second requires a quantum approach. Thus, for the quantum dot from the data presented in the last column of Table 1, N c is equal to 4.…”

Absorption of Ultrashort Electromagnetic Pulses by ITO Nanoparticles

“…17 These studies used as initial data, the number of electrons in traps and distribution of conduction electrons over the nanoparticle radius. 18 In the present study, the probability of photoabsorption of ultrashort electromagnetic pulses is calculated, and a description is given of the method used for measuring the refractive index of the surrounding medium in which an ITO nanoparticle is placed. This approach, utilizing the measurement of time dependence of photoprocess probabilities, provides the potential for creation of a new class of sensors, namely, optical plasmon sensors based on semiconductor nanoparticles.…”