  We present current-voltage studies of very thin (ca. 77 nm) barium titanate
single crystals up to 1.3 GV/m applied field. These show that the mechanism of
leakage current at high fields is that of space charge limited conduction
(SCLC) in a regime with a continuous distribution of traps, according to the
original model of Rose [Phys. Rev. 97, 1537 (1955)]. This study represents a
factor of x5 in field compared with the early studies of BaTiO3 conduction [A.
Branwood et al., Proc. Phys. Soc. London 79, 1161 (1962)]. Comparison is also
given with ceramic multilayer barium titanate capacitors, which show similar
SCLC behaviour. The data are shown to be completely incompatible with variable
range hopping [B. I. Shklovskii, Sov. Phys. Semicond. 6, 1964 (1973)], despite
the recent report of such mechanism in SrTiO3 films [D. Fuchs, M. Adam, and R.
Schneider, J. Phys. IV France 11, 71 (2001)].
