Ultrafast dynamics of the surface photovoltage in potassium-doped black phosphorus

Black phosphorus is a quasi-two-dimensional layered semiconductor with a narrow direct band gap of 0.3 eV. A giant surface Stark effect can be produced by the potassium doping of black phosphorus, leading to a semiconductor to semimetal phase transition originating from the creation of a strong surface dipole and associated band bending. By using time- and angle-resolved photoemission spectroscopy, we report the partial photoinduced screening of this band bending by the creation of a compensating surface photovoltage. We further resolve the detailed dynamics of this effect at the pertinent timescales and the related evolution of the band structure near the Fermi level. We demonstrate that after a fast rise time, the surface photovoltage exhibits a plateau over a few tens of picoseconds before decaying on the nanosecond timescale. We support our experimental results with simulations based on drift-diffusion equations.

Figure 1

(a) Crystal structure of BP plotted with the VESTA visualization program [54] showing the two inequivalent in-plane directions, namely the ZZ and AC directions. (b) Corresponding three dimensional BZ and its 2D projection on the (001) plane (green). (c) ARPES spectrum along the $Z-L-Z$ high-symmetry line [thick red line in (b)] measured at T = 300 K and $h\nu$ = 21.2 eV. (d) Bulk projected electronic band structure [red plane in (b)] calculated from DFT in the SCAN approximation.

Figure 2

ARPES spectra recorded at pump-probe delays of [(a) and (c)] $-1$ ps and [(b) and (d)] $+2$ ps for bare BP and K-doped BP. In panel (b), the intensity at high KE has been multiplied by a factor 100 with respect to the low KE part in order to visualize the CB and the VB on the same linear color scale. The data have been acquired along the ZZ direction, i.e., the $M-Z-M$ high symmetry direction of the BZ. (e) EDCs at $-1$ ps (red) and $+2$ ps (blue) integrated $\pm 2^{\circ }$ around the normal emission for K-doped BP. We highlight the position of the leading edge inflexion point of the VB, which is the marker we use in the following to obtain the evolution of the energy shift induced by the SPV. (f) Difference between the ARPES spectra of panels (c) and (d). Red and blue colors respectively correspond to an increase and a depletion of photoemission intensity. (g) and (h) are sketches of K-doped BP photoemission spectra from panels (c) and (d) at negative and positive pump-probe delays.

Figure 3

Schematic diagram of electron energy levels near the surface of (a) p-doped BP sample and (b) K-doped BP with and without illumination. For the p-doped (K-doped) BP surface, an upward (downward) long-range BB and consequently a negative (positive) SPV are expected. In the K-doped case, the CB is confined at the surface and experiences an additional Stark potential which is not screened by the pump excitation in our fluence regime. This Stark potential is responsible of the progressive collapse of the surface band gap as a function of K coverage. Note that the scales in panels (a) and (b) are not respected.

Figure 4

Temporal evolution of the surface photovoltage (SPV) at the surface of K-doped BP for (a) the CB and (b) the VB. Panels (c) and (d) represent EDCs taken at normal emission, respectively for the CB and the VB, corrected by the SPV determined from panels (a) and (b) for a few pump-probe delays. (e) Temporal evolution of the integrated intensity $I_{\mathrm{CB}}$ under the EDCs in panel (c) (gray area). The inset corresponds to a zoom over the first ps. (f) Same for $I_{\mathrm{VB}}$ [red area in panel (d)].

Figure 5

[(a) and (b)] Cartoon representation of the band structure before and after K deposition on BP as measured by ARPES. The strong surface dipole originating from alkali deposition leads to a progressive surface semiconductor to semimetal transition named giant surface Stark effect. (c) Cartoon of the temporal evolution of K-doped BP band structure at the pertinent timescales as measured by Tr-ARPES: $➀$ Photoelectrons acceleration before time zero, $➁$ SPV build up, band structure modification and excited electrons thermalization, $➂$ Plateau, and $➃$ SPV relaxation and band structure recovery. (d) Schematic representation of the evolution of the SPV only, as experimentaly measured with Tr-ARPES (red) and as expected from theory (blue).

Figure 6

Nonequilibrium dynamics of photoexcited carriers obtained by solving the DDEs. (a) The SPV as a function of time after the pump for different recombination rates $B_r$. When $B_r=0$ (blue dashed line), there is no recombination. The inset shows the fast initial dynamics in the range $0\le t<10$ fs. (b) The band energy as a function of $x$ at different times. The upper panel is for $B_r\ne 0$ and the lower panel is for $B_r=0$ [similarly in panels (c) and (d)]. The red-dashed line in the lower panel shows the solution of the steady state after the pump when $B_r=0$. (c) The internal electric field as a function of $x$ for different $t$. (d) The net excess carrier density ($\delta n-\delta p$) as a function of $x$ for different $t$. The parameters used in the simulation are shown in Table 1.

Figure 7

Tr-ARPES measurements of BP along the ZZ direction at $-1$ ps pump-probe delay for a pump fluence of (a) 0 $\mu \mathrm{J}/{\mathrm{cm}}^2$ and (b) of 160 $\mu \mathrm{J}/{\mathrm{cm}}^2$. (c) Corresponding EDCs taken at normal emission. A negative SPV of $-13$ meV is observed due to the compensation of the upward ${\varphi }_{\mathrm{BB}}$ as depicted in Fig. 3.

Figure 8

Tr-ARPES measurements of K-doped BP along the AC direction at $-1$ ps pump-probe delay for a pump fluence of (a) 0 $\mu \mathrm{J}/{\mathrm{cm}}^2$ and (b) of 160 $\mu \mathrm{J}/{\mathrm{cm}}^2$. (c) Corresponding EDCs taken four degrees off normal emission. A positive SPV of $+200$ meV is observed due to the compensation of the downward ${\varphi }_{\mathrm{BB}}$ as depicted in Fig. 3.

Figure 9

Tr-ARPES measurements of K-doped BP along the AC direction using a pump fluence of 160 $\mu \mathrm{J}/{\mathrm{cm}}^2$ for pump-probe delays of (a) $-1$ ps and (b) $+2$ ps. (c) Intensity difference between the panels (b) and (a). Red and blue colors respectively correspond to an increase and a depletion of photoemission intensity. The transient dynamics is the same at the one observed in Fig. 2 of the main text.

Figure 10

(a) EDCs of the K-doped BP ARPES spectra taken at normal emission for a few pump-probe delays. These EDCs show both a time dependent energy shift and VB spectral shape evolution. (b) Temporal evolution of the low energy electron cutoff position.

Figure 11

Temporal evolution of the SPV at the surface of K-doped BP for (a) the CB and (b) the VB. (c) Temporal evolution of $I_{\mathrm{CB}}$ and [(d) and (e)] $I_{\mathrm{VB}}$ as defined in the Fig. 4 of the main text. For all these spectra, solid lines are the exponential fit used to extract the characteristic time constants discussed in the text.

Figure 12

The static equilibrium-state solution before the laser pump and the photoexcited carriers distribution at $t=0_{+}$.