First-principles calculation of hot-electron scattering in metals

We analyze hot-electron scatterings in metals within a first-principles approach based on density-functional-theory band-structure calculations and on Green-function calculations within the $GW$ approximation. Results for hot-electron lifetimes and the differential cross section of the underlying scattering process are presented for Al, Cu, Au, and Pd, and analyzed with emphasis on the differences and similarities with respect to the predictions of the homogeneous electron-gas model. The electron-gas results can nicely explain the scattering characteristics in aluminium, whereas in copper and gold a strong enhancement of the hot-electron lifetimes is found and attributed to $d$-band screening. Finally, in palladium $d$-band scatterings are responsible for a drastic modification of the scattering characteristics, which no longer can be explained by the homogeneous electron-gas results.

Figure 1

(Color online) Band-structure (left panel) and density-of-states (right panel) plots for aluminium as calculated within the LAPW method.

Figure 2

(Color online) Hot electron lifetimes in aluminium as computed from Eq. (1) by including local field effects and dynamic screening. The inset shows the total scattering rate ${\tau }^{-1}$. The symbols + and ◁ report the scattering rates which are obtained by neglecting local field effects and using a static approximation for the screening, respectively. The results clearly reveal a minor importance of local-field effects and dynamic screening, and support the electron-gas description of hot-electron scatterings in aluminium.

Figure 3

(Color online) Intensity plot of the averaged differential cross section $P_i\left(\omega \right)$ in arbitrary units for the hot electron transitions in aluminium. The intensity of each square corresponds to the magnitude of the corresponding cross section. The inset reports the integrated differential cross section as a function of the energy $\omega$ transferred in the transitions.

Figure 4

(Color online) Integrated differential cross section in arbitrary units for different initial state energies and for aluminium.

Figure 5

(Color online) Band-structure (left panel) and density-of-states (right panel) plot for copper as calculated within the LAPW method.

Figure 6

(Color online) Band-structure (left panel) and density-of-states (right panel) plot for gold as calculated within the LAPW method.

Figure 7

(Color online) Hot-electron lifetimes for copper (top) and gold (bottom) as computed from Eq. (1). For details see figure caption 2.

Figure 8

(Color online) Same as Fig. 3 but for copper (top) and gold (bottom).

Figure 9

(Color online) Band-structure (left panel) and density-of-states (right panel) plot for palladium as calculated within the LAPW method.

Figure 10

(Color online) Hot electron lifetimes in palladium as computed from Eq. (1). The inset shows the total scattering rate ${\tau }^{-1}$ and the symbols + and ◁ report the scattering rates which are obtained by neglecting local field effects and using a static approximation for the screening, respectively. For details see text.

Figure 11

(Color online) Same as Fig. 3 but for palladium.

Figure 12

(Color online) Integrated differential cross section in arbitrary units for different initial state energies and for palladium.

Figure 13

(a) $s$-like, (b) $p$-like, and (c) $d$-like band characteristics for palladium. The sizes of the circles indicate the degree of $s$, $p$, and $d$-like characteristics for a given $\mathit{k}$ point.