We rediscuss the entropy of a charged dilaton-axion black hole for both the asymptotically flat and non-flat cases by using the thin film brick-wall model. This improved method avoids some drawbacks in the original brick-wall method such as the small mass approximation, neglecting the logarithm term, and taking the term L 3 as the contribution of the vacuum surrounding the black hole. The entropy we obtain turns out to be proportional to the horizon area of the black hole, conforming to the Bekenstein-Hawking area-entropy formula for black holes.
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