Nernst theorem and entropy of dirac field in Reissner-Nordstrom black hole

A Reissner-Nordstrom (R-N) black hole is regarded as a composite thermodynamic system composed of inner and outer horizons. The free energy and entropy of Dirac fields inside and outside the black hole are calculated via brick-wall method. It is found that the entropy is proportional to the area of inner and outer horizons. The entropy of Dirac field is 7/2 times of Klein-Gordon field. The total entropy of R-N black hole contributed by inner and outer horizons satisfies Nernst theorem.