Thermosize effects and thermodynamic analysis of a macro/nano scaled refrigerator cycle
Changes in the metal properties, caused by periodic indents in the metal surface, have been studied within the limit of quantum theory of free electrons. It was shown that due to destructive interference of de Broglie waves, some quantum states inside the lowdimensional metal become quantum mechanically forbidden for free electrons. Wave vector density in k space, reduce dramatically. At the same time, number of free electrons does not change, as metal remains electrically neutral. Because of Pauli exclusion principle some free electrons have to occupy quantum states with higher wave numbers. Fermi vector and Fermi energy of low-dimensional metal increase and consequently its work function decrease. In experiment, magnitude of the effect is limited by the roughness of metal surface. Rough surface causes scattering of the de Broglie waves and compromise their interference. Recent experiments demonstrated reduction of work function in thin metal films, having periodic indents in the surface. Experimental results are in good qualitative agreement with the theory. This effect could exist in any quantum system comprising fermions inside a potential energy box of special geometry.8530 St *
In this study, the quantum state depression (QSD) in semiconductor quantum well (QW) is investigated. The QSD emerge from the ridged geometry of the QW boundary. Ridges impose additional boundary conditions on the electron wave function and some quantum states become forbidden. State density reduces in all energy bands, including conduction band (CB). Hence, electrons, rejected from the filled bands, must occupy quantum states in the empty bands due to Pauli Exclusion principle. Both the electron concentration in CB and Fermi energy increases as in the case of donor doping. Since quantum state density is reduced, the ridged quantum well (RQW) exhibits quantum properties at widths approaching 200 nm. Wide RQW can be used to improve photon confinement in QW-based optoelectronics devices. Reduction in the state density increases the carrier mobility and makes the ballistic transport regime more pronounced in the semiconductor QW devices. Furthermore, the QSD doping does not introduce scattering centers and can be used for power electronics.
Carrier capture by attractive centres has been discussed in a number of papers.The principal results a r e reviewed in /1/ where a criticism of the fundamental papers /2, 3/ is given. The calculation of capture cross sections is carried out by the Pitaevski method in which the expressions for cross sections in high and low temperature ranges, respectively, a r e given in the form
Thanks to recent development of nanoelectronics, devices such as resonant tunneling diodes and transistors, super-lattices, quantum wells, and others, based on wave properties of electrons are fabricated. We discuss what happens when low dimensional regular indents are fabricated on the surface of a thin metal film. Using corresponding theoretical methods, we study the free electron inside a potential-energy box with ridged wall and compare the results to the case with plane walls. It was shown that, ridged geometry of the wall leads to Quantum Interference Depression (QID), or reduction of the density of quantum states for the electron. Results obtained for the potential-energy box were extrapolated to the low-dimensional metals (thin metal films). QID leads to increase of the Fermi level and corresponding reduction of the work function. Experimental possibility of fabricating such indents on the surface of a thin metal film was studied.Assume a rectangular potential-energy box, with one of the walls modified as shown in Fig.1. The indents on the wall have the shape of strips of depth of a and width w. We name the box shown on Fig.1 as Ridged Potential-Energy Box (RPEB) to distinguish it from the ordinary Potential-Energy Box (PEB). The time-independent Schrödinger equation for an electron wave function inside the RPEB can be rewritten in the form of Helmholtz equationwhere Ψ is wave function and k is wave vector. For the case a/2L x <<1 we use the volume perturbation method to solve the Helmholtz equation [1]. The big rectangular box is regarded as the Main Volume (MV) and the total volume of strips is regarded as the Additional Volume (AV) (Fig.2). Let Ψ m (x, y, z) be the wave function of electron in the MV and Ψ a (x, y, z) in the AV. The matching conditions will be Ψ m = Ψ a , and an equation of partial derivatives of Ψ from two sides, for all points of the connection area. Analysis show that maximized spectrum of wave vector k in RPEB is following:
Optical I' impurity-band" transitions have been studied in various models. For example, optical transitions in which shallow impurities take part a r e well described within the frames of a hydrogen-like model /l/. Deep acceptor photodeionization is considered in the delta-function potential model of Lucovsky /2/. Optical transitions involving not too deep and not too shallow impurities are calculated using the Hulten potential /3/.Thus, optical transition problems with shallow donor levels created by group V elements and with deep donor levels created by singly ionized ions of group VT are solved by means of various approaches, though from the physical viewpoint there is no difference between these defects except for the central charge. The same is true for shallow and deep acceptors created by group ITI elements and singly charged group I f ions, respectively. Besides, the above mentioned theories suffer from a serious disadvantage -introduction of a fitting parameter taking into account the increase of the optical transition amplitude due to the fact that the effective local field exceeds the averagemacroscopicfield in the crystal.Tn /4/ we proposed a model in which the impurity centre potential can be presented in the formwhere z* is the effective charge of the impurity centre which is estimated according to the Slater rules. Since this z* corresponds to the free atom ionization energy differing sufficiently from its experimental value, we make a correction to the Slater rules, so that z* found with allowance for this correction 1) Prospekt Chavchavadze 1, 380028 Tbilisi, USSR.
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