The temporal responses of the undoped, n-type, and p-type delta-doped GaAs metal-semiconductor-metal photodetectors were systematically studied. The full-width at half-maximum of the temporal response is significantly improved at low bias for the F-doped detectors compared to the conventional undoped one. The p-type delta-doped detector exhibits the smallest fall-time, and hence the highest bandwidth, because the induced electric field in the absorption region facilitates the transport of the photogenerated holes. In addition, the p-type delta-doped detector also gives the highest peak amplitude of the temporal response. Two dimensional simulation on the internal electrical field distribution in the detectors is consistent with the experimental results.