Hopping Electrical Conductivity in Ferroelectric Pb[(Fe_1/3Sb_2/3)_xTi_yZr_z]O₃

Abstract

Studies on direct current (dc) and alternating current (ac) electrical conductivity in ferroelectric ceramics [Pb(Fe_1/3Sb_2/3)_xTi_yZr_z]O₃ with x + y + z = 1, x = 1 and y = 0.44 and 0.47 have been performed. The measurements were carried out in the temperature range 77–750 K and frequencies 50 Hz–100 kHz. AC conductivity σ(ω) fulfills the relation σ(ω) = Aω^S, where the exponent s depends on temperature T and frequency ω. The exponent s increases with decreasing temperature and in vicinity of 77 K is equal to 0.988 and 0.991 for samples with y = 0.44 and y = 0.47, respectively. At low temperature, the temperature dependence of dc conduction σ(0) is described by Mott's law σ(0)∝ exp[-(T₀/T)^1/4]. T₀ calculated from that relation equals 4.51 × 10⁶ and 2.2 × 10⁶ K for samples y = 0.47 and y = 0.44, respectively. Knowing T₀ and estimating the spatial extend of localized wave function as α⁻¹ = 2.2Å, the density of states at Fermi level N(E_F) was calculated as 2.7 × 10²² cm⁻³ eV⁻¹ (y = 0.44) and 2.54 × 10²² cm⁻³ eV⁻¹ (y = 0.47). The most probable Mott hopping distance R and hopping energy W were determined. At 300 K R = 19.4 Å, W = 0.058 eV for sample with y = 0.47 and R = 18.2 Å, W = 0.071 eV for sample with y = 0.44. Density of states at the Fermi level calculated from dc and ac conductivities are of the same order of magnitude.

Keywords:

• PZT-PFS ceramics
• electrical conductivity
• hopping conduction