Capacitance spectroscopy of alumina sol–gel capacitors with Al top contacts

Abstract

We measured the complex capacitance C(f) of ITO/sol–gel alumina/Al capacitors deposited on glass (and some on stainless steel foil) in the frequency range 15 Hz–10 MHz. The sol–gel films were deposited by dip-coating and following a two-step process. The capacitance C(f) found was much higher than that of a pure Al₂O₃-film due to the remaining porosity of the film and the uptake of H₂O from the environment. The C(f) curves are useful as a sensitive probe for the porosity of the sol–gel film. In particular the evolution of the capacitance curve with time after drying has been measured. The curves can qualitatively be understood by modelling the capacitor as a (nearly) percolating random insulator/conductor network, using the effective medium approximation. However a detailed understanding of the relation between the C(f,t) curves and the structure of the films requires a more elaborate model. Films sintered at 500–550 °C for 1 h initially behave exactly as not sintered films but in contrast with the latter they improve slowly over time. Fast sintering yields better films.

Appendix

The transmission of an optically flat film deposited on a substrate varies as cos2kd′′, where d′′ = dn is the optical thickness, with d the geometric thickness and n the effective index of refraction which depends on the porosity p (volume fraction of the guest material) and on the refractive indices of the host and guest materials. To simplify the notations we designate the host with index 1 and the guest with index 2. We assume n ₁ = 1.6 and n ₂ = 1.335, corresponding with pores completely filled with water. The relation n ²(p) is given by the Bruggeman equation (2). Since there are 2 unknowns (d and p) we need another independent measurement for determining the thickness. By measuring the capacitance per unit area in the dry state C (at 10 kHz) one obtains $\epsilon_{0}/C=d/\epsilon\triangleq d^{\prime},$ where ε is the effective dielectric constant in the dry state. Again the relation ε(p) is given by the Bruggeman equation and we assume ε₁ = 9 and ε₂ = 1 corresponding with pores filled with air. From both measurements we obtain then d′′/d′ = nε, which can be solved numerically for p. In practice the equations can easily be solved iteratively. Since the optical contrast between guest and host is much smaller than the dielectric contrast, n ₁ is a good starting value for n (corresponding with d ≈ d′′/n ₁). We then obtain ε = d′′/d′/n and p(ε) and finally a new value for n with n ²(p).