We study electrical transport properties in exfoliated molybdenum disulfide (MoS2) back-gated field effect transistors at low drain bias and under different illumination intensities. It is found that photoconductive and photogating effect as well as space charge limited conduction can simultaneously occur. We point out that the photoconductivity increases logarithmically with the light intensity and can persist with a decay time longer than 10^4 s, due to photo-charge trapping at the MoS2/SiO2 interface and in MoS2 defects. The transfer characteristics present hysteresis that is enhanced by illumination. At low drain bias, the devices feature low contact resistance of 1.4 k{Omega}/{mu}m, ON current as high as 1.25 nA/{mu}m, 10^5 ON-OFF ratio, mobility of 1 cm^2/Vs and photoresponsivity R=1 A/W.
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