Analysis of the induced photothermal conduction in the Mn$_4$Si$_7$–Si$\langle$Mn$\rangle$–Mn$_4$Si$_7$ and Mn$_4$Si$_7$–Si$\langle$Mn$\rangle$–M heterojunctions

The kinetics of photocurrent is studied in the presence of the intrinsic irradiation at $h\nu\ge$ 1.12 eV in the Mn$_4$Si$_7$–Si$\langle$Mn$\rangle$–Mn$_4$Si$_7$ and Mn$_4$Si$_7$–Si$\langle$Mn$\rangle$–M heterojunctions at relatively high applied voltages. It is demonstrated that photocurrent, scattered power, and temperature at the reverse-biased contact of the heterojunction depend on time at dc applied voltage, low temperature, and irradiation at $h\nu\ge$ 1.12 eV. The analysis of the temperature dependences of the photocurrent growth with time is used to demonstrate that the photocurrent pulses consist of two fragments: the first one corresponds to a slowly increasing relatively low current with a slope of (2–4) $\times$ 10$^{-4}$ A/s and the second fragment is characterized by a sharp increase in the current with a slope of 0.1–1.0 A/s. Based on the slopes, the heating rates ($\beta_1$ = 42 deg/s and $\beta_2$ = 3 $\times$ 10$^3$ deg/s) and temperature gradients across the transient layer that corresponds to the Mn$_4$Si$_7$ $\langle$Mn$\rangle$ interface ($\Delta T/\Delta x$ = 6.3 $\times$ 10$^6$ K/cm for $\beta_1$ = 42 deg/s and $\Delta T/\Delta x\ge$ 1.5 $\times$ 10$^8$ K/cm for $\beta_2$ = 3 $\times$ 10$^3$ deg/s) are estimated. It is demonstrated that the Joule self-heating allows relatively high heating rates in the reverse-biased contact of heterojunction, which provides rapid heating similar to the rectangular step excitation that is equivalent to the activation of the long-wavelength (extrinsic) irradiation.