## 3 Results
### Relationship between THz Time-Domain Waveform and Photocurrent  
When the photon energy is higher than the band gap of the SI-GaAs materials, each photon that is absorbed induces the formation of one electron-hole pair. The external bias electric field drives the photogenerated carriers to form a transient photocurrent. The SI-GaAs PCA transient photocurrent is generated at the gap between the anode and cathode. Then, a THz wave is generated by transient photocurrent. For an elementary Hertzian dipole antenna in vacuum, the radiation field \(E_{\text{THz}}(r,t)\), at a distance r and time t, can be described as [3; 4; 19]. \[E_{\text{THz}}(r,t)=\frac{\mu_{0}}{4\pi}\frac{\sin\theta}{r}\frac{d}{dt}[I_{ \text{PC}}(t)]*\theta=\frac{1}{k}\frac{d}{dt}[I_{\text{PC}}(t)], \tag{1}\]  
Here, \(I_{\text{PC}}(t)\) is the photocurrent in the SI-GaAs PCA, \(\mu_{0}\) is the permeability in vacuum, \(\theta\) is the angle representing the direction of the antenna, and \(k\) is the conversion ratio. Equation (1) indicates that the THz-radiation electric field intensity is mainly proportional to the first derivative of the photocurrent \(I_{\text{PC}}(t)\) with respect to time [20]. The motion of the photogenerated electron-hole pairs can be described using the Drude-Lorentz model. Because the electron mobility is much larger than the hole mobility in GaAs photoconductive material, we consider photogenerated electrons are the main charge carriers. The time-varying photocurrent is expressed as a convolution of the optical pulse envelope and the photocurrent response [21]:  
\[I_{\text{PC}}(t)=\int I_{opt}(t-t^{\prime})[en(t^{\prime})*v(t^{\prime})]dt^{ \prime}, \tag{2}\]  
In (2), \(I_{opt}\) is the intensity parameter of the optical pulse, \(e\) is the charge of a single electron, \(n(t^{\prime})\) is the density of the photogenerated carriers, and \(v(t^{\prime})\) is the average electron-drift velocity. In the experiment, because the optical excitation energy of the femtosecond laser remains constant, the change of photocurrent is mainly determined by the change of the average electron drift speed. It means that with the increasing of bias electric field, the change of the average electron-drift speed is the main reason of photocurrent change. The effective mass increases, and the carrier mobility decreases when the carriers enter the satellite valley from the \(\Gamma\) valley. In this paper, the relationship between THz time-domain waveform and the average electron drift velocity rate is detected by using THz-TDS. Then, the electron transfer rate at different bias voltage is obtained. Based on the relationship between the electric field \(E_{\text{THz}}(r,t)\) of the terahertz time-domain waveform and the THz photocurrent \(I_{\text{PC}}(t)\), the corresponding photocurrent is obtained by integration (reverse derivation) of the terahertz time-domain waveform signal, as shown in Figure 4a. In the meantime, the change of GaAs-PCA photocurrent is measured by an oscilloscope. The THz photocurrent and GaAs-PCA photocurrent are equivalent, except that they are obtained in different ways. The integrated photocurrent curve with the GaAs PCA photocurrent curve as measured with an oscilloscope are compared as shown in Figure 4b. With the bias voltage increasing, the photocurrent amplitude increases, but the conversion ratio \(k\) of the THz electric field decreases. The mean value and standard deviation of conversion ratio \(k\) for repeated multiple measurements are shown in Figure 5.  
In case the bias voltage is set to 30 V and the gap of the SI-GaAs PCA is 150 \(\upmu\)m, the electric field bias is \(E=~{}2\) kV/cm. Because the electric field is weak, there is not enough energy to make the photogenerated carrier produce valley scattering. It can be considered as all carriers in the \(\Gamma\) valley; therefore, a bias voltage of 30 V can be used as a starting point to determine the rate of carriers transferred to the satellite valley. The carrier occupancy for the \(\Gamma\) valley calculation can be described using Equation (3).