Excitation Enhancement of Hot Electrons by Ultrafast Optical Pumping in Heavily $p$-Doped Graphene Stacks

Energetic photoinduced hot electrons have been attracting increased scientific attention owing to their potential applicability in numerous photoelectrical and photochemical processes. Normally, the energy of electrons quickly converts into heat by ultrafast cooling, which is considered as the bottleneck for high-efficiency utilization of hot electrons. In this work, we explore intentionally heavily $p$-doped graphene stacks by degenerate femtosecond pump-probe spectroscopy, and observe an excitation enhancement of hot electrons at weak pump fluence. The time scale of hot-electron excitation is of the same order as that of fast decay via electron-electron and electron-optical-phonon scattering in our experiments. Physically, both Auger processes and population inversion are suppressed in this system, yet it becomes possible for the conduction bands to be effectively evacuated within the pulse duration through the ultrafast cooling of hot electrons, which may lead to an enhanced excitation of hot electrons. This excitation enhancement can be further strengthened by multiple layer-stacking processes or a thermal annealing pretreatment. The optical absorption of graphene stacks increases correspondingly, exhibiting a value larger than the linear limit at low pump fluence. Furthermore, the absorption modulation depth can reach approximately 0.79% in monolayer graphene for a small pump-fluence change ($<20\mu {\mathrm{J/cm}}^2$), further increasing to approximately 1.2% and approximately 2.5% in double- and triple-stacking graphene layers, respectively, indicating that the absorption can be sufficiently altered by an extremely small variation of pump fluence. These outcomes can be applied for low-cost pulse operations. We suggest that this effect can have potential applications to harvesting energy from excited hot electrons, and may provide a unique way to achieve high-speed modulators, photodetectors, solar cells, and photocatalysts.

Figure 1

(a) The measured source-drain current ($I_{SD}$) versus gate voltage ($V_G$) for SG with channel length of 50 $\mu \mathrm{m}$. The source-drain voltage ($V_{SD}$) is 0.1 V. The inset is a schematic cross section of graphene electric-double-layer device with positive gate voltage. (b) Schematic illustration of monolayer graphene under ultrafast optical excitation. The optically induced hot electrons cool down via electron-electron scattering and electron-phonon scattering. (c) Schematic of the setup for our femtosecond optical pump-probe measurement. (d) Delay-time dependence of the normalized transient differential reflection spectra measured for SG, while increasing the pump power from 2.74 to 19.18 $\mu {\mathrm{J/cm}}^2$. The curves are shifted for clarity. (e) The deduced photoinduced hot electron density of SG from experimental data (black cross). The dark purple solid line represents the linear relation between $N_L$ and pump fluence. The light purple area marks the region where $N>N_L$, as a guide to the eye. The inset shows the peak intensities of the measured signals in SG below 2.74 $\mu {\mathrm{J/cm}}^2$. (f) The differences of $N$ (i.e., the density of photoinduced hot electrons) and its linear limit $N_L$ with pump fluence. The light purple area marks the region where $N>N_L$, as a guide to the eye.

Figure 2

(a) Schematic of the evolution of photoinduced hot carriers in heavily $p$-doped graphene after ultrafast optical excitation. The pump pulse creates a short-lived electron and hole distribution at energy levels of $\epsilon =\pm 1/2\hslash \omega$. The gray dashed line corresponds to the chemical potential ${\mu }_e$ of the heavily $p$-doped graphene. Then the hot electrons are cooled via fast (e-e and e-OP scatterings) and slower (e-AP scattering) decay processes, which are indicated by the blue arrows. (b) The corresponding measured transient differential reflection spectrum, placed at the same time axis as (a). The black solid curve is an analytical fit to the data using a biexponential function. (c) The fast decay time (${\tau }_1$) and slower decay time (${\tau }_2$) of SG under various pump fluences.

Figure 3

(a) Optical image of layer-by-layer graphene stacks (SG, DG, and TG) transferred on ${\mathrm{Si}\mathrm{O}}_2$/$\mathrm{Si}$ substrate. (b) Raman spectra for differently stacked graphene layers. Black, red, and blue curves represent SG, DG, and TG, respectively. (c),(d) The measured transient differential reflection signal versus delay time plotted when increasing the pump fluence from 2.74 to 19.18 $\mu {\mathrm{J/cm}}^2$.

Figure 4

(a) Pump fluence dependence of the difference between the density of photoinduced hot electrons ($N$) and its linear limit ($N_L$). The gray, red, and blue areas mark the regions where $N>N_L$ for graphene stacks (SG, DG, and TG, respectively), as a guide to the eye. (b) The fast decay time (${\tau }_1$) and the slower decay time (${\tau }_2$) are plotted with varying pump fluences in the upper and lower panels, respectively. Black, red, and blue represent graphene stacks (SG, DG, and TG, respectively). (c) The contribution weights in the fast decay process ($A_1$) and the slower decay process ($A_2$) are plotted at different pump powers. Black, red, and blue represent SG, DG, and TG, respectively.

Figure 5

(a) The photoinduced hot-electron density of graphene stacks (SG, DG, and TG) under a pump fluence of 5.48 $\mu {\mathrm{J/cm}}^2$ before or after annealing in an Ar-${\mathrm{H}}_2$ environment at 200 ${}^{\circ }\mathrm{C}$ for 2.5 h. (b) Upper panel: the fast decay time (${\tau }_1$) of graphene stacks (SG, DG, and TG) before or after annealing. Lower panel: the slower decay time (${\tau }_2$) of graphene stacks (SG, DG, and TG) before or after annealing.

Figure 6

Raman spectra measured for monolayer graphene with increasing temperature, illustrated using different colors.

Figure 7

(a) The measured normalized transient differential reflection signal versus delay time when varying the substrate temperature from 30 to 150 ${}^{\circ }\mathrm{C}$ under a pump fluence of 5.48 $\mu {\mathrm{J/cm}}^2$. The curves are shifted for clarity. (b) The fast (${\tau }_1$) and slower (${\tau }_2$) decay times under a pump fluence of 5.48 $\mu {\mathrm{J/cm}}^2$ while varying the substrate temperature of graphene stacks (SG, DG, and TG). (c) The contribution weights versus substrate temperature of graphene stacks (SG, DG, and TG).

Figure 8

(a) The absorption coefficients of SG from experimental data in Fig. 1. The linear limit of absorption coefficient ${\alpha }_0$ for SG is marked by the dashed line. (b) Pump fluence dependence of the absorption coefficients for SG, DG, and TG in black, red, and blue, respectively. The linear absorption coefficients for SG, DG, and TG are marked by dashed lines with corresponding colors.