Electrical Transport Properties of Glass

Abstract

The aim of this chapter is to review the current understanding of various effects, both electronic and ionic transports, in oxide and chalcogenide glasses. Oxide and chalcogenide glasses are classified into an electronic or ionic transport materials depending on the composition of their constituents. Doping of transition metals or alkali atoms into oxide glasses produces electronic or ionic properties in electrical conduction processes. Free carriers (electron and hole) in rigid materials are transported via extended states (band conduction). Localized carriers are transported by a hopping mechanism through localized states. If carrier transport occurs in a deformable lattice, either with strong or weak carrier–phonon interaction, the carrier is accompanied by lattice distortion. This is regarded as a pseudoparticle and is called a polaron, producing a polaronic transport in these media, which is usually discussed for the transition-metal-oxide glasses (s). It is suggested in this article that an alternative explanation for the transport mechanism, instead of the traditional polaron model, is also possible in TMOG. When the conduction, either electronic or ionic, is thermally activated, it is pointed out that the Meyer–Neldel rule () or the compensation law plays the principal role in the transport process in glassy materials. A long-standing puzzle is the mixed alkali effect () in oxide glasses, together with the power-law conductivity behavior. A similar effect, i. e., the mixed cation effect, is also found in chalcogenide glasses. All of these are still matters of debate for electronic and/or ionic transport in glasses and there are many unsolved and important problems on electrical conductions in glasses, which will be finally summarized. Although the principal concern is with physics involved in electrical transport in glasses, nevertheless it should be mentioned at this juncture that electrical transport phenomena also have many technological ramifications.

Appendix

In Sect. 10.1.1, it is stated that the Boltzmann transport theory breaks down when carrier mean free path $l$ closes in on the atomic separation (Ioffe–Regel rule [10.77]). Kawabata [10.78] modified the Boltzmann conductivity by taking into account multiple scattering as follows

$$\sigma=\sigma_{\mathrm{B}}\left\{1-\frac{C}{(k_{\mathrm{F}}l)^{2}}\right\},$$

(10.B56)

where $\sigma_{\mathrm{B}}$ is the Boltzmann conductivity given by $ne^{2}\tau/m^{*}$, where $n$ is the density of the carrier, $\tau$ is the scattering time, $m^{*}$ is the effective mass, $C$ is a constant (order of unity), and $k_{\mathrm{F}}$ is the wave vector at the Fermi energy. Equation (10.B56) was generalized further as

$$\begin{aligned}\displaystyle\sigma&\displaystyle=\sigma_{\mathrm{B}}\left\{1-\frac{C}{(k_{\mathrm{F}}l)^{2}}\left(1-\frac{l}{L}\right)\right\}\\ \displaystyle&\displaystyle\equiv\mathrm{A}+\mathrm{B}\frac{l}{L}\;,\end{aligned} $$

(10.B57)

where $L$ is the inelastic diffusion length when the electron–phonon or electron–electron interaction dominates the electron transport [10.5]. Note that $L> l$ is required in (10.B57).

If electron–electron collisions dominate, the inelastic scattering time $\tau_{\mathrm{i}}$ is proportional to

$$\left(\frac{k_{\mathrm{B}}T}{E_{\mathrm{F}}}\right)^{-2}[10.5]\;,$$

and hence $L$ ($\propto\tau_{\mathrm{i}}^{1/2}$) should be proportional to $T^{-1}$, producing $\sigma\propto T$. If on the other hand electron–phonon collisions dominate, $\tau_{\mathrm{i}}$ is proportional to $T^{-1}$, leading to $L\propto T^{-1/2}$ and $\sigma\propto T^{1/2}$. In amorphous metals, the conductivity is found to follow the above prediction [10.5, 10.79, 10.80, 10.81, 10.82]

$$\sigma=\alpha+\beta T^{\frac{1}{2}}+\gamma T\;.$$

(10.B58)