Thermoelectric properties of highly conducting quasi-one-dimensional organic crystals of ptype TTT2I3 and of n-type TTT(TCNQ)2 are modeled in order to determine the possibility of their applications in the thermoelectric devices. These crystals attract attention of investigators because due to the low dimensionality of carrier spectrum the density of carrier states is increased. From other part, organic crystals have more diverse internal interactions that allows to somewhat overcome the interdependence between electrical conductivity, thermopower and the electronic thermal conductivity. Crystals of p- and n-type are considered because for a p-n-module both materials are needed. Two main electron-phonon interactions mechanisms are taken into account. One is of deformation potential type, and the other is similar to that of polaron. The kinetic equation is deduced applying the method of two particle retarded Green function and analytic expressions are obtained for the electrical conductivity, Seebeck coefficient, the thermal conductivity and the thermoelectric figure of merit. Temperature dependences of these kinetic coefficients are obtained numerically. Introduction The main parameter, which determines the possibility of a given material to be used in the thermoelectric converters of energy, is the dimensionless thermoelectric figure of merit ZT. It is known that ZT = σS 2 T/κ, where σ is the electrical conductivity, S is Seebeck coefficient, κ = κ e + κ L is the thermal conductivity, which consists from electronic κ e and phononic κ L contributions and T is the operating temperature. However, σ, S and κ are not independent one of other. The increase of σ leads to decrease of S and vice versa. Nevertheless, in the last decades, important achievements in the increase of ZT have been obtained in low dimensional inorganic crystals. A value of ZT ~ 2.4 has been measured [1]1 at room temperature in p-type Bi2Te3/Sb2Te3 superlattice structures. ZT ~ 3 has been obtained in PbTeSe quantum dot superlattices [2]2 , and even ZT ~ 3.5 [3, 4]34 . However, such values have been obtained in very sophisticated, technologically complicated and very expensive structures. Nevertheless, it is demonstrated that such high values of ZT are possible. Now the largest commercially applied thermoelectric materials on the base of Bi2Te3 have ZT ~ 1 near room T. It is a rather low value. A value of ZT  3 would make the solid-state convertors economically competitive with the ordinary used ones. Therefore, the commercialization of thermoelectric devices has still limited applications. In the same time, on can mention mass production of miniature thermoelectric modules to maintain constant temperatures in the laser diodes, climate control seats installed in hundreds of thousands of vehicles each year, portable beverage coolers and other applications. In the last years, organic compounds attract more and more attention of investigators. These materials are less expensive, have more diverse and often unusual properties in comparison with their inorganic analogs and their molecular structure can be easily modified to obtain desirable physical and chemical properties. Besides, the organic materials usually have low thermal conductivity. A review of the state of art and the prospects of thermoelectric applications is presented in [5]1 . We have predicted high values of ZT in some quasi-one-dimensional organic crystals, including those of tetrathiotetracene-iodide, TTT2I3 [6], and of TTT(TCNQ)2 [7]. However, in these crystals the polarizabilities of TTT and TCNQ molecules are not well established and in different papers somewhat different values are presented. Therefore, it is interesting to model the thermoelectric properties of these crystals with different values of molecular polarizability. The aim of present paper is to made detailed modelling of electrical conductivity, Seebeck coefficient, thermal conductivity and the thermoelectric figure of merit in above mentioned crystals, taking slightly modified molecular polarizabilities as compared with [6, 7]23 , and to determine, haw the thermoelectric figure of merit will be affected. Physical model of crystals In TTT2I3 crystals, only TTT chains are conductive, due to considerable overlap of π – wave functions along chains, and the carriers are holes. In the transversal to chains direction the overlap of wave functions is small and the electrical conduction in theses directions is almost by three order of magnitude smaller than along TTT chains. In TTT(TCNQ)2 crystals the TCNQ chains are much more conductive than TTT chains and the carriers are electrons. The charge and energy transport are described in these crystals in the tight binding and nearest neighbors approximations as the most suitable for this class of materials. In the 3D model the energy of the electron with the quasi-wave vector k and projections (kx, ky, kz) has the form ( ) 2 [1 cos( )] 2 [1 cos( )] 2 [1 cos( )], E k  w1  kx с  w2  kyb  w3  kza (1) where w1, w2, w3 are transfer energies of the electron from the given molecule to the nearest ones along lattice vectors b, a, c, the axes x, y, z are directed along b, a, c, the conductive chains are directed along c, and the energy is measured from the bottom of conduction band. Respectively, w1 is much bigger than w2 and w3. For holes the conductive chains are directed along b and the energy is measured from the top margin of conduction band. ( ) 2 [1 cos( )] 2 [1 cos( )] 2 [1 cos( )], 1 2 3 E w k b w k a w k c k    x   y   z (1a) The frequencies of longitudinal acoustic phonons are for TTT(TCNQ)2 and TTT2I3, respectively, are: sin ( / 2) sin ( / 2) sin ( / 2), 2 2 3 2 2 2 2 2 1 2 q  ω qx c  qyb  qza (2) sin ( / 2) sin( / 2) sin( / 2), 2 3 2 2 2 2 1 2 x y z q   bq  aq  cq (2a) where, ω1, ω2 and ω3 are the limit frequencies in the x, y and z directions. Due to the same quasi-one-dimensionality, ω1 is much bigger than ω2 and ω3. The square of matrix element module of carrier-phonon interaction has the form ( , )  2 /( ){  [sin( ) sin((  ) )  sin( )]    [sin( )  2 2 2 1 2 1 2 A k q  MNq w kx c kx qx c  qx c w kyb sin(( ) ) sin( )] [sin( ) sin(( ) ) sin( )] } 2 3 2 3 2 ky  qy b  2 qyb  w  kya  ky  qy a  qya (3) Here M is the mass of TCNQ or TTT molecule, N is the number of molecules in the basic region of crystal. The parameters 1, 2 and 3 have the means of the ratios of amplitudes of second interaction to the first one in the direction of chains and in transversal directions and depend on molecule polarizability. The sign (+) in face of 1, 2 and 3 refers to electrons and the sign (–) to holes. Besides, the TCNQ chains are directed along c, as in (3), but TTT chains are directed along b. The impurity and defect scattering processes are described by a dimensionless parameter D0, which may be rather small in very perfect crystals. Results and discussion Let consider that a weak electrical field and a weak temperature gradient are applied along the conductive chains. The kinetic equation is deduced using the two-particle temperature dependent retarded Green function. The linearized kinetic equation is solved analytically and the electrical conductivity σ, the Seebeck coefficient S, the electronic thermal conductivity e  and ZT along the chains can be expressed through the transport integrals Rn as follow σxx = σ0R0, (2 )/( ( ) ) 2 1 2 0 3 2 1 2 1 2  0  e Mvs w r  abc k T w  , 0 1 0 1 0 S  (k / e)(2w / k T)R / R , [4 /( )]( / ) 0 2 2 1 2 0 2 w1 e T R R R e     , /( ) 2 L e ZT S T   , (4) where vs1 is the sound velocity along chains, r = 2 for TTT(TCNQ)2, and r = 4 for TTT2I3 crystals, and Rn are the transport integrals        3 -1 sin ( ) [ ( ) ] (1 ) k k nk nk Mk R abc d k c n n x F   (5) Here ε(k) = E(k)/2w1 and εF = EF/2w1 are the dimensionless carrier and Fermi energy, respectively, nk is the Fermi distribution function and Mk is the dimensionless mass operator of twoparticle retarded Green function: ] [1 2sin ( ) 2 cos( ) ]}/ 8sin ( ) . [1 cos( )] { [1 2sin ( ) 2 cos( ) 0 2 2 3 3 2 2 2 2 2 2 2 2 1 2 1 d k a k a k c D M k c d k b k b z z x x y y                 k (6) Here w1 = 0.125 eV for TCNQ chains and w1 = 0.26 eV for TTT chains. The transfer energies w2 = d1·w1 and w3 = d2·w1 are small. The parameters d1 = d2 = 0.015 were estimated for TTT2I3 crystals by comparing the experimental and numerical results of transversal electrical conductivity. The internal structure of TTT(TCNQ)2 crystals is similar to that of TTT2I3 and one can put d1 = 0.015 and d2 = 0.01 for y and z directions. The transport integrals (Eq. 5) can be calculated only numerically. Let consider the thermoelectric properties of TTT2I3 crystals. The basic crystal parameters were taken from [8, 9]12 . It is important that in quasi-one-dimensional organic crystals the Wiedemann-Franz law is violated [10]3 and high carrier mobility may be achieved [11]4 . Now let take 1 = 1.6 instead of 1.7 in [6]. This means that the polarizability of TTT molecule is reduced from 453 to 42 3 . Note that the value of molecule polarizability slightly differs in different papers [12, 13]5 . 6 In Fig. 1 the dependences of electrical conductivity along chains σ as functions of dimensionless Fermi energy εF in units of 2w1 are presented for three values of D0: 0.1 which correspond to crystals grown by gas phase method [14] 7 with stoichiometric electrical conductivity  ~ 104  -1 cm-1 ; 0.05 and 0.01 which corresponds to more perfect crystals with higher  not obtained yet. It is seen that only in the most perfect crystals the interaction between the conduction chains becomes important and it is necessary to apply more complete 3D crystal model. In Fig. 2 the dependences of thermopower (Seebeck coefficient) along chains S on Fermi energy at room temperature are presented. One can observe that in this case the results of models 3D and 1D are very close in the whole interval of εF variation and that S may achieves rather high values. In Fig.3 the dependences of the electronic thermal conductivity along chains κ e on Fermi energy at room temperature are presented. It is seen that the contribution of κ e to the total thermal conductivity has increased considerably. The dependences of the thermoelectric figure of merit along chains ZT on Fermi energy at room temperature are presented in Fig.4. One can observe that in stoichiometric crystals (with F  ~ 0.35) ZT takes very small values even in the most perfect crystals. But if εF is decreased up to 0.2 (the carrier concentration is decreased by 1.5 times, from 1.2x1021 cm-3 down to 0.81x1021 cm-3 ) ZT is expected to achieves the value of 1.0 in existing crystals with stoichiometric ~ 104  -1 cm-1 and even value of 3 in the most perfect crystals. The parameters of TTT(TCNQ)2 crystals were taken from [151 , 6], 1 = 1.8. The stoichiometric concentration of electrons in TTT(TCNQ)2 crystals was estimated as n = 1.1·1021 cm-3 or εF = 0.35.The electrical conductivity as function of dimensionless Fermi energy is presented in Fig.5. If the concentration of electrons increases, the electrical conductivity grows rapidly, especially in the most perfect crystals. As it is seen from Fig.6, in stoichiometric crystals Sxx ≈ -120 μV/K is expected. The electronic thermal conductivity κ e is shown in Fig.7. In stoichiometric crystals ZT = 0.02 for D0 = 0.1 and it remains small, even in the purest crystal (Fig.8), but achieves pronounced maximums for εF = 1.2 ÷ 1.3. It is expected that at εF = 1.05 (the concentration of electrons is increased up to 2.2 · 1021 cm-3 ) a value of ZT ~ 1 can be obtained. Conclusions The crystals of p-type TTT2I3 and of n-type TTT(TCNQ)2 are very prospect materials for thermoelectric applications after their purification and optimization of carrier concentrations. In TTT2I3 the carrier concentration must be reduced by ~ 1.5 times. It is possible, because these crystals admit nonstoichiometric concentrations. Values of ZT ~ 3 are predicted. In TTT(TCNQ)2 the carrier concentration must be increased. It is possible by additional doping with donors and further purification of the crystal. Values of ZT ~ 1 are expected for crystals with σ ≈ 1.2·104 Ω -1 cm-1 .