Relaxations of the surface photovoltage effect on the atomically controlled semiconductor surfaces studied by time-resolved photoemission spectroscopy

We have systematically investigated relaxation of the surface photovoltage effect on the atomically controlled In/Si(111) surfaces with distinctive surface states and different amounts of the surface band bending. The temporal variations were traced in $real$ $time$ by time-resolved photoemission spectroscopy using soft x-ray synchrotron radiation. The relaxation is found to be temporally limited by two steps of the carrier transfer from the bulk to the surface: the tunneling process at a delay time $\le 100$ ns and the thermionic process on the following time scale ($\ge 100$ ns). Crossover of the two mechanisms can be understood by breakdown of the quantum tunneling regime by the increase in width of the space-charge layer during the relaxation.

Figure 1

(a), (b) Evolution of the SPV effect and the following relaxation through the (c) thermionic and (d) tunneling processes. $E_C$ and $E_V$ are the energies of conduction and valence band edges, respectively, while $E_D$ is the energy position of the donor level. The energy level $E_S$ of a surface state ($SS$), is referred from $E_V$ at a surface. The surface potential ($V_S$) is equivalent to the amount of band bending and the energy shift after SPV is indicated with $V_{SPV}$. The region of a space-charge layer (SCL) is indicated with an arrow.

Figure 2

Summary of the eight sample surfaces prepared with different In coverages and annealing temperatures. The surfaces with long-range orders are labeled with the names of the phases. The $\text{Si}\left(111\right)4\times 1$-In surfaces, prepared by room-temperature deposition and postannealing at 673 and 773 K are labeled “$4\times 1$ low” and $4\times 1$, respectively.

Figure 3

Si 2$p$ core-level spectra of various In/Si(111) surfaces, as listed in Table , taken at a photon energy of 252 eV. Each spectrum is labeled with the corresponding sample surface. The dashed black line marks the peak position of the Si(111)$7\times 7$ surface.

Figure 4

SPV shift for each surface phase and fitting with Eq. (1). The difference in the amount of shift comes from the difference in surface charge in the stationary state, i.e., the band bending in the initial state.

Figure 5

Evolution in TRPES spectra of Si(111)$\sqrt{3}\times \sqrt{3}$ In taken at various delay times after the SPV effect, induced with a laser power density of 3.1 $\mu \mathrm{J}/{\mathrm{cm}}^2/\mathrm{pulse}$.

Figure 6

Energy shift of peak position of Si 2 $p_{3/2}$ with delay time on (a) Si(111)$\sqrt{3}\times \sqrt{3}$ In and (b) $\text{Si}\left(111\right)4\times 1$ In. The vertical axis represents relative binding energy with respect to the Si $2p_{3/2}$ peak position before the photoexcitation.

Figure 7

Logarithmic energy shift for the peak position of Si 2 $p_{3/2}$ with delay time on (a) Si(111)$\sqrt{3}\times \sqrt{3}$ In and (b) Si(111)$4\times 1$ In. The linear curve fits are made for the fast and slow processes. The time constants are given in the figure. In each figure, crossing points of the two extrapolated lines are indicated by an arrow.

Figure 8

Measured relaxation process of (a) $\sqrt{3}\times \sqrt{3}$, (b) $\sqrt{31}\times \sqrt{31}$, and (c) $4\times 1$. All the data were taken with a laser power of 3.1 $\mu \mathrm{J}/{\mathrm{cm}}^2/\mathrm{pulse}$. The (red) solid and (black) broken lines are the curve fits for thermionic emission [Eq. (5)] and tunneling [Eq. (4)], respectively. The time constants of the thermal diffusion and tunneling diffusion models for the surfaces are given in the figure. In each figure, crossing points of the two extrapolated lines are indicated by an arrow.

Figure 9

Measured relaxation process of (a) 0.4, (b) 0.8, and (c) 1.2 ML deposition surfaces. The excitation laser power is 3.1 $\mu \mathrm{J}/{\mathrm{cm}}^2/\mathrm{pulse}$ for the 0.8 ML deposition surface, and 0.52 $\mu \mathrm{J}/{\mathrm{cm}}^2/\mathrm{pulse}$ for the 0.4 and 1.2 ML deposition surfaces. The (red) solid and (black) broken lines are the curve fits of thermionic emission [Eq. (5)] and tunneling [Eq. (4)], respectively. The time constants of the thermal diffusion and tunneling diffusion models for the surfaces are given in the figure. In each figure, crossing points of the two extrapolated lines are indicated by an arrow.

Figure 10

$V_S$ dependence of the time constants of (a) ${\tau }_{\mathrm{slow}}$, (b) ${\tau }_{\mathrm{fast}}$, (c) ${\tau }_s$, and (d) ${\tau }_{\mathrm{tunnel}}$ plotted against $V_S$. The data points of ${\tau }_s$ are well fitted with an exponential function (broken line). The sample surfaces are labeled.

Figure 11

$V_S$ dependence of the surface potential that corresponds to the crossing points, $V_{\mathrm{cross}}$, of the extrapolated lines of the fast and slow processes plotted in logarithmic scale, as shown in Fig. 7, for each surface.

Figure 12

Numerical simulations of a band diagram of space-charge layers with different surface potentials, indicated by solid (red) and broken (black) curves.

Figure 13

A schematic drawing of temporal variation of excess electron density distribution under the sharp-front approximation.