The reason is that the decay time is hole recombination dependent. As the holes have larger effective mass (i.e. small mobility) than electrons, the decay time takes more time compared with rising time.
Rise time of signal of photodetector is determined by rise time of exciting light pulse.
Decay time of signal of photodetector is determined either by decay time of photosignal (photoresponse) of photodetector if this time is longer than decay time of light pulse or by decay time of light pulse if this time is longer than decay time of signal of photodetector.
Another reason may be carrying out pulse measurements of photosignal at low and very high power of exciting light pulse. In first case you perform measurement within linear part of dependence photosignal-light power (this is obligatory condition to provide correct measurement of rise time and decay time of photodetector), in second case you put photodetector in saturation, decay time of saturated photosignal is indefinite (measurement of rise time and decay time of photodetector in saturation condition is wrong!).So you can get absolutely different ratio of rise and decay times using exciting light pulse of same timing form if in one case its power will be within linear part of photoresponse and in another case - out of linear part (in saturation region of photoresponse) Please be aware that. Every time before pulse measurement please check linear part of dependence photosignal-light power and carry out measurements within this region.
Therefore, you can see in the experiment two ratios between rise time and decay time of photodetector, because as usual you register pulse of photosignal only.
materials, it is observed that the recovery time is longer compare to response time since the
absorption and desorption kinetics is different for many of materials. The presence of surface defects
mainly in TMDCs, functional groups in organic materials, porous morphology of some oxide
materials acts as trapping centres which eventually trap atmospheric molecules in photo/gas/humidity sensor and hydronium ion in case of humidity sensor for more time. These trap centres enhance the sensitivity of the sensor and also make
recovery time longer...the same mechanism is observed in the case of photodetector..where the carriers are trapped by surface defects or Deep Level Defect States called oxygen assisted mechanism...
The difference in rise time and decay is probably due to bio-molecular adsorption at defect sites on surface of materials. As surface to volume ratio of nano structured device is exceptionally high, they tend to absorb large number of oxygen atoms on surface defect states. The absorbed oxygen atoms become negatively charged by absorbing electrons from active material of device. In this way, photo-generated holes are captured in oxygen adsorbed on surface defect states and recombination of trapped holes and photo-generated electrons is delayed which leads to a prolonged carrier life time.
Also, the response time of devices greatly affected by defect states and adsorbents. The defect state nearer Fermi level, called deep-level-defect-state (DDLS), trapes the photo-generated charge carriers, leading the reduced photocurrent and prolonged the response time of detectors.
You can refer following articles for the detailed study of the mechanism of the photodetector: