摘要
在有机电荷迁移晶体中,有一类是由荷正电的施体分子柱与荷负电的受体分子柱交错平行排列而成,如TTF-TCNQ,因为这类晶体具有很强的各向异性,表现为准一维导体.实验得到,在T_P<T<250K(T_P为Peierls相变温度)范围内,这类晶体TTF-TCNQ、TSeF-TCNQ等的电导率的倒数σ^(-1)近似地随T^2增大.本文用形变势理论研究电子-声子相互作用对载流子的影响,得出σ与温度的依赖关系式.并以TTF-TCNQ电导率为算例,得到与实验相一致的结果。
One class of conducting molecular crystals is consisted of the charge transfermolecules crystallizing in segregated stacks of donor and acceptor, such as TTF-TCNQ and its analogues. They behave as quasi-one dimensional conductors. The ex-perimental works gave an approximate law that σ^(-1) increases as T^2 at the temperaturerange T_p<T<250K for TTF-TCNQ and TSeF-TCNQ where T_p is phase transitiontemperature.In this work, we investigated the influence of electron-phonon interac-tion on the behavior of charge carriers by deformation potential theory. By this the-ory, only the seattering of electrons by longitudinal acoustic wave is considered.And the interaction matrix element H_(k, k) has been derived to be |H_(k, k)|=(E_1~2/2LC)[(hω_q)/exp[hω_q/(k_BT]-1]=(E_1~2/2LC)ω~q k′-k±q=0 (1)where E_1 is the proportional constant of deformation potential,L and C are the lengthand stretching modulus of the one dimensional crystal, and L=Na(N is the No. ofunit cells, a is the lattice constant), C=qv_l (v_l is the velocity of longitudinalwaves), ω_q is the angular frequency. Under the approximation of elastic scattering and parabolic bands, from eqn.(1),we have derived the expression of the conductivity of this class of organic con-ductors.The final results are as follows. (1) High temperature region k_BT>>hω~q, ω_q≈k_BT, we got σ=σ_e (acceptor stacks)+σ_h(donor stacks) σ=e^2h^2C/k_BT[[n|E_f-E_(oc)|/(2m_e)^(3/2)E_(ic)~2]+[p|E_f-E_(ov)|^(1/2)/(2m_h)^(3/2)E_(iv)~2]] (2)where Ef is Fermi energy level, n and p are the numbers of electrons and holes perunit volume, m_e and m_h are the absolute values of effective mass of the electronand the hole, e is the electronic charge, E_(oc) and E_(ov) are the energies of bottom ofconduction band an top of valence band respectively. It can be seen that at high temperature range σ∝T^(-1). The result agrees with the temperature dependence of conductivity of three dimensional metals. (2) Low temperature range, k_BT>>hω_q is not valid, although the approximationE(k')=E(k) is still reasonable, the contribution of other modes of vibrations shouldbe considered, hence we used the following expression for ω_qthen we got Erom equation(4), it can be seen at low temperature range σ∝T^(-2). For illustration, we have calculated the conductivities of TTF-TCNQ at differenttemperature by eqs. (2) and (4). The calculated values agree with experimental valueswell. For instance, σ(300K, calc.)=742Ω^(-1)·cm^(-1), σ(300K, expt.)≈630±10Ω^(-1)·cm^(-1),σ(60K, calc,)=8. 84×10~3Ω^(-1)·cm^(-1), σ_(max) (near 60K, expt.)≈0. 3×10~4--1. 5×10~4Ω^(-1)·cm^(-1). Hence we have shown that the dependence of a on temperature for this classof organic conductor can be accounted for by the interaction of electrons with acoustic phonons.
出处
《物理化学学报》
SCIE
CAS
CSCD
北大核心
1992年第6期728-731,共4页
Acta Physico-Chimica Sinica
基金
国家自然科学基金
国家教委优秀年青教师基金
关键词
电荷迁移晶体
电导率
温度
Electron-phonon interaction
One dimensional charge transfer crystal
Temperature dependence of conductivity
