In this work, we improved the performance of germanium (Ge) channel Charge Trapping MemTransistors (CTMTs) as synaptic device by using Ti-doped HfO2 as charge trapping layer (CTL). We manipulated the amount of Ti dopant within the HfO2 CTL to perform the band engineering by varying the Hf/Ti cycle ratio in atomic layer deposition (ALD). The content of Ti was quantified and the energy band structures of the gate stack was constructed with the aid of transmission electron microscope (TEM) images and X-ray photoelectron spectroscopy (XPS) analysis. We then fabricated the charge trapping capacitors and characterized their memory characteristics such as memory windows. By the implementation of amphoteric trap model, thermal activated electron retention model and advanced charge decay model, the trap distribution of the CTL was extracted. Finally, we fabricated the CTMTs with Ti-doped HfO2 as the CTL and characterized their performance as synaptic device such as nonlinearity of depression and potentiation and also conductance on/off ratio. We used NeuroSim simulator with multilayer perceptron and convolutional neural network models to evaluate the pattern recognition accuracy of neural network hardware accelerator using CTMTs as synaptic devices and benchmarked the performance of our CTMT with those of other types of synaptic devices.