the electron  phonon interaction in semiconductor heterostructures is of greater interest in comparison to bulk materials . this is due to the fact that the quasi - particle space localization leads to the modifications of the energy spectrum . the all - important factor is the rise of new vibration branches of optical spectrum , namely , the interface optical phonon . this interaction is of considerable importance in the understanding of the properties of heterostructures based on material with high ionicity . it can lead to self - consistent bond state of a charge particle and phonons , that is , the large radius polaron . currently , an investigation on the part played by interface phonons has attracted considerable interest in polaron state formation study . the contributions to polaron binding energy both of interface and of bulk optical phonons are the same value order in the quantum dots [ 3 - 5 ] . taking into account , alternatively , the interface phonon role dominates in polaron binding energy for quantum well case . in response to this fact , the strong electron phonon interaction can be realized in the quantum wells based on non - polar material with high iconicity barrier material . in addition , from the results , it follows that profound polaron effects should be expected , e.g. , in the si / sio2 compounds . although there are no polar optical phonons in the material of such quantum well , these may be produced at the heteroboundary . as a result , the strong interaction of charged particles with interface phonons becomes possible . phonon interaction is possible when the quantum well is made of polar material and for the barriers is taken non - polar material . in recent years , varied technologies of semiconductor quantum wire growth with assorted barriers are progressing rapidly . the most success has been achieved for the quantum wires based on iii  v compounds [ 8 - 12 ] . it is in these structures that the polaron states can arise . at the same time , no extended theoretical study of the polaron states in such structures is available . proper allowance must be made for the interaction of charge particles with interface optical phonons for an understanding of this problem . in this paper , we develop a theory of polarons in the quantum wires , taking into account the interaction of charged particles with all branches of the optical phonon spectrum . the general equations have been obtained to describe the phonon spectrum taking into account the interaction of polarization and deformation potentials . in materials with high ionicity degree , the charge particle interaction with polar optical phonons is of crucial importance in polaron state formation . this has led us to use the model which takes into account this phonon type in the quantum wire . optical - phonon modes in the quantum wire are determined using the classical electrostatics equations : together with conventional boundary conditions at heterointerfaces , where   is the polarization field ,   the electric field ,   the scalar potential ,   the total charge density , and   is the dielectric susceptibility of the material i ( i = 1 , 2 ) . the dielectric function   is given by : where   and   are the frequencies of longitudinal - optical ( lo ) phonons and transverse - optical ( to ) phonons , respectively , and   is the high - frequency dielectric constant . 1 ) for the cylindrical quantum wire leads to the equation defining the dispersion law for interface optical phonons : here , i m is the m - th order modified bessel function of the first kind , km is the m - th order modified bessel function of the second kind , k is the wave vector , 0 is the quantum wire radius . 3 . in fig . 1 is shown the wave - vector dependence of the interface phonon frequencies . this dependence is calculated for the quantum wire based on cdse surrounded by znse barriers with m = 0 in eq . the wave - vector dependence of interface optical phonon frequencies for znse / cdse / znse quantum wire the hamiltonian operator for phonon subsystem is conveniently written in terms of the phonon creation and annihilation operators : where the operators   describe the creation of bulk phonons localized inside the quantum wire ,   are the interface phonon creation operators . phonon interaction for the cylindrical quantum wire can be represented by the method supposed in : here , the coefficients   are defined as : here , n(m ) is n - th order root of the equation jm( ) = 0 , jm is the m - th order bessel function of the first kind . the interaction parameters m(k ) have the form : the expressions ( 6 ) , ( 7 ) do not require in the region . the reason is that we suppose the total electron localization within the quantum wire . in eq the general equations have been obtained to describe the phonon spectrum taking into account the interaction of polarization and deformation potentials . in materials with high ionicity degree , the charge particle interaction with polar optical phonons is of crucial importance in polaron state formation . this has led us to use the model which takes into account this phonon type in the quantum wire . optical - phonon modes in the quantum wire are determined using the classical electrostatics equations : together with conventional boundary conditions at heterointerfaces , where   is the polarization field ,   the electric field ,   the scalar potential ,   the total charge density , and   is the dielectric susceptibility of the material i ( i = 1 , 2 ) . the dielectric function   is given by : where   and   are the frequencies of longitudinal - optical ( lo ) phonons and transverse - optical ( to ) phonons , respectively , and   is the high - frequency dielectric constant . 1 ) for the cylindrical quantum wire leads to the equation defining the dispersion law for interface optical phonons : here , i m is the m - th order modified bessel function of the first kind , km is the m - th order modified bessel function of the second kind , k is the wave vector , 0 is the quantum wire radius . 3 . in fig . 1 is shown the wave - vector dependence of the interface phonon frequencies . this dependence is calculated for the quantum wire based on cdse surrounded by znse barriers with m = 0 in eq . the wave - vector dependence of interface optical phonon frequencies for znse / cdse / znse quantum wire the hamiltonian operator for phonon subsystem is conveniently written in terms of the phonon creation and annihilation operators : where the operators   describe the creation of bulk phonons localized inside the quantum wire ,   are the interface phonon creation operators . phonon interaction for the cylindrical quantum wire can be represented by the method supposed in : here , the coefficients   are defined as : here , n(m ) is n - th order root of the equation jm( ) = 0 , jm is the m - th order bessel function of the first kind . the interaction parameters m(k ) have the form : the expressions ( 6 ) , ( 7 ) do not require in the region . the reason is that we suppose the total electron localization within the quantum wire . in eq . let the quantum wire be surrounded with compositionally identical barriers . in order to separate the effect of exactly dielectric irregularities , we assume that the potential well for electrons is rather deep , so that the penetration of the wave functions under the barrier can be disregarded . in this case , the interaction of charged particles with barrier phonons is weak . we write the hamiltonian of the system as here ,   is the electron hamiltonian for which the interaction of the electron with phonons is disregarded . the hamiltonian is given by where   is the quantum wire potential and m is the electron effective mass . if the interaction of an electron with polar optical phonons is strong , the polaron binding energy can be determined with the use of adiabatic approximation . in so doing , the adiabatic parameter here is the ratio of the quantum wire radius 0 to the polaron radius a0 : the exact expression for polaron radius a0 is obtained below . the condition ( eq . 13 ) implies that the main contribution to the polaron binding energy is given by small values of the wave vector k such that if condition ( eq . 13 ) is satisfied , the wave function of an electron localized in the n - th size - quantization level can be represented as : where the wave function   describes the two - dimensional electron motion not disturbed by electron the wave function   represents the electron localization in the self - consistent potential well created by phonons . the quantum numbers n , m define not disturbed electron state in the quantum wire . in the case of total electron localization in the cylindrical quantum wire , the wave function   has the form : here   is n - th root of m - th order bessel function . the wave function   is to be obtained by solving self - consistent problem . in so doing , the total wave function from eq . 12 ) takes the form after this procedure : here   is the energy of an electron on relevant size - quantization level , m is the electron mass inside the quantum wire . phonon interaction   can be written as : here ,   and   are the coefficients   and m(k ) from eq . we obtain average hamiltonian   it can be brought to the form diagonal in phonon variables by the unitary transformation   where the unitary transformation application gives the following equation : from expression ( eq . 21 ) , we can see that , in the adiabatic approximation used here , the bulk phonon spectrum and the interface phonon spectrum remain unchanged . 21 ) presents the energy of a large radius polaron . in the general case , the energy   involved in ( eq . 21 ) depends on the dielectric properties of the materials of both the quantum wire and the barriers . in the general case , the polaron binding energy ee depends on electron size - quantization level number and on optical - phonon spectrum properties . after the procedure of angle averaging which is expressible in explicit form , we obtain this energy ee as : the energy ( eq . 22 ) is defined by the electron interaction with phonon modes correspond to m = 0 only . this equation ( eq . this contribution is caused by the interaction of localized electron with confined and interface phonons . however , the electron energy and wave function can be obtained analytically on condition the unequality ( eq . the most significant contribution to the polaron binding energy in the parameter ( eq . 14 ) gives the interaction of an electron with interface phonon mode of the frequency close to barrier frequency   the largest contribution to the energy in the parameter ( eq . this quantity comes about from taking into account the interaction of an electron with interface optical phonons . 23 that the quantum wire material properties have no effect on the polaron state formation . the part of quantum wire material dielectric properties can be obtained in higher orders in the parameter ( eq . 23 that the characteristic values of the phonon wave vector k which describe the value of electron phonon interaction is of the order reciprocal to polaron radius a0 the logarithmic function changes weakly in this region . therefore , we can consider with the same accuracy in parameter ( 14 ) that the energy is equal to : the substitution of the energy from eq . 19 leads to the expression for polaron binding energy as the functional of unknown yet wave function (z ) . it can be written as : the following equation is obtained by variational method using wave functions (z ) : this nonlinear eq . 26 has the solutions which can be written in the form with any energy values epol : the polaron binding energy is found by substitution of eq . 27 to 26 : the polaron radius a0 is obtained by solving the transcendental equation . it has the form : it is this quantity from eq . 29 which contains the adiabatic parameter ( eq . 13 ) . substituting material parameters   into eq . 29 for the quantum wire znse / cdse / znse leads one to expect that the strong polaron effects for these structure should be observed when the quantum wire radius 0 < 40  . it might be well to point out that both the polaron binding energy ( eq . 29 ) depend on effective electron mass inside the quantum wire and barrier dielectric properties . this clearly demonstrates the prevailing role of the interaction of an electron with interface optical phonons . the availability of the surface phonons leads to widening the range of materials in which the strong polaron effect should be expected . phonon interaction may exist near the interface between polar and non - polar materials . among other things phonon interaction is determined significantly by interface optical phonons in narrow quantum wires corresponding to the condition ( eq . is meant that the interface phonons can produce the effective canal of excitation transfer in the structures with several quantum wires . this work was supported by russian foundation for basic research , grant 09 - 02 - 00902-a and the program of presidium of ras  the fundamental study of nanotechnologies and nanomaterials  no . 27 . this article is distributed under the terms of the creative commons attribution noncommercial license which permits any noncommercial use , distribution , and reproduction in any medium , provided the original author(s ) and source are credited .