Figure 2(a) shows the dark current of the device and the photocurrent when excited by white light changes with the bias voltage, and the change of the current with voltage when 2 Hz white light is applied. It can be seen from the Fig. 2(a) that the device has obvious rectification effect. The positive direction of the applied voltage is from the silicon side to the graphene side, which indicates that the main built-in electric field of the device comes from the silicon-titanium oxide junction, and the built-in electric field constructed by weak p-type graphene and weak n-type TiO2 can be ignored. Under the negative bias voltage, the built-in electric field is further enhanced by the external bias voltage. Light is incident from the graphene side, and a large number of photogenerated carriers are collected by the graphene and quickly transmitted out, which results in an imbalance between the photo-generated carriers on the graphene side and the silicon side, thereby obtaining a strong optical guide gain under high bias. When 2 Hz white light is applied, the current coincides with the dark current when no light is applied, and coincides with the photocurrent when light is applied, which shows that the device has a high response speed and good repeatability. As shown in Fig. 2(b), graphene/TiO2/p-Si has obvious photoelectric response under light from 350 nm to 1050 nm wavelength at a bias of -2 V. It can be seen from the figure that the dark current of the device does not change much under different wavelengths of laser irradiation. However, the dark current increases slightly with the increase of time, which is caused by the heat loss when the device is working. As the working time of the device is extended, there is a local temperature rise, which causes the increase of the leakage current. The photocurrent of the device change obviously under different light waves (350 nm-1050 nm). The photoresponse currents (Ion-Ioff) at 350 nm, 550 nm, 750 nm, 950 nm and 1050 nm are 126.29, 213.35, 189.67, 335.93, and 102.46 µA, respectively.
Figure 3(a) and Fig. 3(b) exhibits the spectra-dependent of Responsivity (R), external quantum efficiency (EQE) and Detectivity (D*) of the heterojunction. R, EQE and D* are important parameters to evaluate the performance of photodetectors. Responsivity (R) is defined as R=(Ion-Ioff)/Pin, where Ion, Ioff and Pin are photocurrent, dark current and incident light power. External quantum efficiency (EQE) refers to the number of electron-hole pairs excited by the unit incident photon, which reflects the sensitivity of photodetectors to photons and can be calculated as EQE = Rhc/λ, where h, c and λ are Plank’s constant, elementary charge and wavelength of incident light, respectively. Detectivity (D*) can be expressed as D* = R/(2qId/A)1/2, where Id is the dark current and A is active area (0.5 cm2). The highest responsivity and EQE of 3.6 A/W and 6001% was observed under light with 0.417 mW/cm2 intensity and 750 nm wavelength. Detectivity is 4×1013 Jones at 750 nm light, about 520 times higher than the graphene/Si photodetector.  Light is incident from the graphene side, and the carriers excited by the short-wavelength are near the TiO2 side. At this time, the electrons are quickly collected by the graphene under the negative bias voltage. However, holes need to travel a long distance before received by the electrode on the silicon side, which causes serious recombination and reduces the photoresponse of the device. Insufficient absorption of long-wavelength light by Si will also reduce the photoresponse of the device. The excitation light near 750 nm wavelength can be completely absorbed by Si, and the distribution of photogenerated carriers in the thickness direction of the device is relatively uniform, so the best responsivity is obtained.
The THz wave transmittance of the THz wave of the graphene/TiO2/p-Si heterojunction in the range of 0.3 to 1 THz is shown in Fig. 4(a). It can be seen from the Fig. 4(a) that when a positive bias voltage of 5 V and 10 V is applied, the transmittance of the THz wave hardly changes compared to 0 V. When negative bias voltages of -10 V, -15 V, and − 20 V are applied, the THz wave transmittance changes significantly. The direction of the applied negative bias electric field is consistent with the direction of the built-in electric field of p-Si and TiO2. As the negative bias voltage increases, the space charge region widens, and the device gradually becomes fully depleted. Meanwhile, there is no carrier accumulation inside the device, the carriers move in the external circuit, and the transmission of the terahertz wave increases. Modulation depth is an important performance parameter of terahertz modulators,which can be calculated by (Texcitation – Tno excitation)/Tno excitation, where the Texcitation and Tno excitation represent the intensity of THz transmission with and without photoexcitation respectively. The variation of the modulation depth of the device under different bias voltages in the range of 0.3-1.0 THz is calculated, and the result is shown in Fig. 4(b). It can be seen from the figure that when 5 V and 10 V are applied, the modulation depth is approximately zero. The modulation depth is about 23% at -15 V. At -20 V, the modulation depth decreases slightly, about 22.6%. This is because when the voltage is extremely high, the device will break down in the reverse region and the current will increase. Continuing to increase the voltage will not further broaden the space charge layer to increase THz transmission, but will increase the temperature of the device and increase the carrier concentration due to the thermal effect caused by the increase in current, which cause the decrease of the terahertz wave, resulting in the decrease of the modulation depth.
The time-domain signals of the graphene/TiO2/p-Si THz modulator with various bias voltages are plotted in Fig. 5(a). We can see that the time-domain graph when positive gate voltage is applied almost coincides with the graph when 0 V is applied. When a negative bias is applied, the THz transmission peak increases significantly. The peak value at 0, 5, 10, -10, -15 and − 20 V is about 72.49, 73.39, 72.49, 79.7 88.66 and 87.15 respectively. In order to show this change more intuitively, we plot the change of the device's terahertz transmission peak under different voltages in Fig. 5(b). It is clear that the device allows terahertz waves to pass under negative bias, but prevents terahertz waves from passing under positive bias. It represents that our terahertz modulator can also function as a diode for terahertz waves.