Phonon spectra in quantum wires

Green's function method, adjusted to bound crystalline structures, was applied to obtain the phonon dispersion law in quantum wires. The condition of the existence of small mechanical atom movements defining phonon spectra can be found by solving the secular equation. This problem was presented graphically for different boundary parameters. The presence of boundaries, as well as the change of boundary parameters, leads to the appearance of new properties of the layered structure. The most important feature is that, beside the allowed energy zones (which are continuous as in the bulk structure), zones of forbidden states appear. Different values of the boundary parameters lead to the appearance of lower and upper energy gaps, or dispersion branches spreading out of the bulk energy zone. The spectra of phonons in corresponding unbound structures were correlated to those in bound structures. U radu je izvrsena analiza fononskih spektara i dozvoljenih fononskih stanja kvantne zice sa prostom kubnom kristalnom strukturom primenom dvovremenskih temperaturskih retardovanih Grinovih funkcija, a potom je izvrseno njihovo poredjenje sa energetskim spektrima fonona u neogranicenim kristalnim strukturama i tankim filmovima. Rezultati istrazivanja predstavljeni su graficki za razne vrednosti granicnih parametara. Sprovedene analize su pokazale bitne razlike u zakonu disperzije fonona u pomenutim sistemima, kao iskljucivu posledicu postojanja granica odgovarajuce strukture, u kojima energetski spektri poseduju energetske gepove. Jos jedan vazan rezultat je diskretnost zone dozvoljenih fononskih energija u konfiniranim kristalnim strukturama, za razliku od prakticno kontinualnih fononskih spektara u balkovskim materijalima.