Tham khảo tài liệu 'electromotive force and measurement in several systems part 2', kỹ thuật - công nghệ, cơ khí - chế tạo máy phục vụ nhu cầu học tập, nghiên cứu và làm việc hiệu quả | Quantum Theory of Thermoelectric Power Seebeck Coefficient 5 where ụ is the chemical potential whose value at 0K equals the Fermi energy ep. The voltage difference AV LE with L being the sample length generates the chemical potential difference A ụ the change in f and consequently the electric current. Similarly the temperature difference AT generates the change in f and the current. At 0K the Fermi surface is sharp and there are no conduction electrons. At a finite T electrons holes are thermally excited near the Fermi surface if the curvature of the surface is negative positive see Figs. 2 and 3 . We assume a high Fermi degeneracy Tp T. Consider first the case of electrons . The number of thermally excited electrons Nx having energies greater than the Fermi energy 8f is defined and calculated as Nx r de N eV . 1 N0 r de - JeF v V-ụ kBT 1 0 eF e e-ụ kBT 1 -No kBT ln 1 e- e-ụ kBT e ln2 kB .V No N eF Fig. 2. More electrons dots are excited at the high temperature end T2 Tj. Electrons diffuse from 2 to 1. Fig. 3. More holes open circles are excited at the high temperature end T2 Tj. Holes diffuse from 2 to 1. 6 Electromotive Force and Measurement in Several Systems where N e is the density of states. The excited electron density n Nx V is higher at the high-temperature end and the particle current runs from the high- to the low-temperature end. This means that the electric current runs towards away from the high-temperature end in an electron hole -rich material. After using Eqs. and we obtain S 0 for electrons S 0 for holes . The Seebeck current arises from the thermal diffusion. We assume Fick s law j qjparticle -qDVn where D is the diffusion constant which is computed from the standard formula D 4 vl 4 vF2T v VF l vt d d F where d is the dimension. The density gradient Vn is generated by the temperature gradient V T and is given by Vn ỉnl bNqVT Vd where Eq. is used. Using the last three equations and Eq. we obtain A V2 qvịk