## 3 Results and Discussion
### A Model for the Tunnel Photocurrent within the Structure
Figure 6: **(a)** Two-dimensional schematic image of the tip of the emitter nano-edge irradiated by the optical beam (blue arrows from top to bottom), and reflected radiation from the gate (blue arrows from bottom to top), uneven formation of hot electrons (blue dots) both across the depth of the skin layer and across the emitter perimeter (occurrence of spatial localization zones at each given irradiation wavelength); tunneling of hot electrons into the vacuum in the localization zone of the external strong electrostatic field (the scale of the electrostatic field strength is on the left). **(b)** Diagram of the energy levels in the metal within a strong external electrostatic field when the emitter surface is irradiated with optical radiation (blue arrow) with the photon energy \(h\
u\) less than the outcoming energy of electrons \(\varphi\) equal to the difference between the energy in the vacuum level and the Fermi level; probability of electron tunneling depends exponentially on the electron energy (\(E_{F}\) for the field emission, and \(E_{F}+h\
u\) for the photoemission) and the height of the potential barrier, which decreases in the strong electrostatic field by (3). Accounting of the temperature effects carried out in the work of [12] allowed us to obtain the relations needed to determine the tunneling probability of hot electrons that reach the surface of the emitter \(P_{\lambda}\), and the tunneling photocurrent density \(I_{Ph}\) from the metal emitter depending on the electrostatic field \(F\) and the monochromatic light intensity \(I_{\lambda}\). \[P_{\lambda}=\frac{h^{2}F^{2}\beta_{T}{}^{2}}{16\pi m(\varphi-ln)\sigma(\beta_{ T}E_{F})}\cdot D_{\lambda}, \tag{5}\]  
\[I_{Ph}=I_{\lambda}\ (e/l\
u)\ (1-R_{\lambda})\ P_{\lambda}f_{\lambda}\ (1-\exp(-\alpha_{ \lambda}L)), \tag{6}\]  
where \(\beta_{T}=1/(kT)\); \(G\) is the Fowler function; \(R_{\lambda}=|(1-n_{\rm r})/(1+n_{\rm r})|^{2}\), where \((n_{\rm r})^{2}=\varepsilon_{\rm r}\) (the relative permittivity of the metal); \(f_{\lambda}\) is the coefficient taking into account the ratio of the free path \(L_{\tau}\) of hot electrons to the absorption length of electromagnetic radiation at the wavelength \(\lambda\); \(\alpha_{\lambda}\) is the absorption coefficient, and \(L\) is the molybdenum blade thickness. It follows from relations (4)-(6) that the photocurrent of hot electrons depends exponentially on the electrostatic field. This pattern is similar to the dependence of the field emission on the strength of the local field. At the same time, the photocurrent of the hot electrons increases linearly with an increase in intensity of the detected optical radiation. A new design of the photosensor modernized by introducing an additional electrode from the opposite side of the gate will broaden the possibilities to influence the configuration and position of the electrostatic field localization zone (the second type). To make the influence of the potential \(\rm{Ua}\) on the additional control electrode significant, it is necessary to ensure a relatively small gap between the electrode and the plane of the emitter. There is experience in manufacturing the structures of the given type [27; 28]. To make it clear, let us set the gap at 5 nm when simulating a transformed electrostatic field. As can be seen in Figure 7a,b, application of a unit potential to an additional electrode leads to the appearance of the localization zone of the electrostatic field on the surface of the upper curve of the emitter blade and its end portion. However, the amplification level of the local field is noticeably lower than when the same unit potential is applied to the gate. This conclusion follows from comparing the data relating the field strength in Figure 5c,d (on the fragment of the boundary surface between the points 3 and 4) on the lower rounding with relevant data relating the field strength in Figure 7a,b on the upper rounding (between the points 1 and 2).