Ultrafast carrier thermalization and trapping in silicon-germanium alloy probed by extreme ultraviolet transient absorption spectroscopy

Abstract

Semiconductor alloys containing silicon and germanium are of growing importance for compact and highly efficient photonic devices due to their favorable properties for direct integration into silicon platforms and wide tunability of optical parameters. Here, we report the simultaneous direct and energy-resolved probing of ultrafast electron and hole dynamics in a silicon-germanium alloy with the stoichiometry Si_0.25Ge_0.75 by extreme ultraviolet transient absorption spectroscopy. Probing the photoinduced dynamics of charge carriers at the germanium M_4,5-edge (∼30 eV) allows the germanium atoms to be used as reporter atoms for carrier dynamics in the alloy. The photoexcitation of electrons across the direct and indirect band gap into conduction band (CB) valleys and their subsequent hot carrier relaxation are observed and compared to pure germanium, where the Ge direct [Formula: see text] and Si_0.25Ge_0.75 indirect gaps ([Formula: see text]) are comparable in energy. In the alloy, comparable carrier lifetimes are observed for the X, L, and Γ valleys in the conduction band. A midgap feature associated with electrons accumulating in trap states near the CB edge following intraband thermalization is observed in the Si_0.25Ge_0.75 alloy. The successful implementation of the reporter atom concept for capturing the dynamics of the electronic bands by site-specific probing in solids opens a route to study carrier dynamics in more complex materials with femtosecond and sub-femtosecond temporal resolution.

FIG. 1.

XUV transient absorption spectroscopy on the silicon-germanium alloy. (a) Scheme of the experimental setup. A time-delayed visible-to-near infrared (VIS-NIR) pump pulse and an extreme ultraviolet (XUV) probe pulse are collinearly focused onto the sample. A shutter blocks the pump pulse for acquiring differential absorption spectra that are measured in transmission through a sample with a grating spectrometer. An aluminum filter removes residual pump light before the spectrometer. (b) Band structure and pump-probe scheme in silicon-germanium alloy. A calculated band structure of Si_0.25Ge_0.75 is schematically shown [detailed band structure in supplementary material, Fig. S2(a)]. The VIS-NIR pump pulse (red arrow) can excite an electron (filled red circle) assisted by a phonon (black undulating arrow) from the valence (red shaded area) to the conduction band (blue shaded area), here typified into the L valley, leaving a hole behind (open red circle). Likewise, indirect excitation assisted by a phonon is possible into the X and K valleys as well as a direct excitation into the Γ valley by the blue tail of the spectrum (not shown here). The germanium atoms act as reporter atoms for the kinetics with XUV transitions (violet arrows) to both the valence and conduction band from the 3d core-levels. The dashed black line beneath the X valley indicates possible locations for trap states in the midgap. (c) M_4,5 absorption edge of germanium in pure germanium (blue dashed line) and silicon-germanium alloy (blue dotted line) normalized to the pre-edge region. Absorbances were measured relative to an uncoated Si₃N₄ membrane of the same thickness. The signal ratio above the edge supports the material fraction of 75% Ge in the alloy. The broadband XUV pulse (shaded orange area) covers the spectral regions associated with the valence and conduction band allowing simultaneous capture of the carrier and band shift kinetics. (d) Raman spectra of the samples used in this work. The monatomic germanium sample shows a strong single Raman peak at 302 cm⁻¹ (gray dashed dotted line) corresponding to the transverse-optical (TO) phonon mode. The silicon-germanium sample exhibits three Raman peaks (blue solid line) associated with the optical vibrations of the Ge-Ge, Si-Ge, and Si-Si bonds in the alloy. Comparison of relative peak positions to literature suggests an $\mathit{x}=0.75$ alloy, i.e., Si_0.25Ge_0.75, in the experiment (see the text for details).

FIG. 2.

Density of states in Si_0.25Ge_0.75 calculated using density functional theory (DFT). Bands with 4p orbital character can be probed via transitions from the 3d core-levels. Similar to pure germanium (Ref. 13), the valence band is almost primarily of 4p orbital character, while the conduction band is a mix of 4s and 4p orbital character. Midgap features are not included in this calculation, since a crystalline super-cell containing 75% Ge atoms and 25% Si atoms was assumed and defects causing trap states were not considered.

FIG. 3.

Time-resolved state blocking in germanium and silicon-germanium alloy measured in the XUV and spin-orbit separated, so that only the signal probed from the Ge 3d_5/2 core-level is shown. (a) Carrier dynamics in nanocrystalline germanium reveal the decays of the valence band (VB) and conduction band (CB) populations. Adapted from Ref. . (b) Direct comparison with silicon-germanium alloy shows that the Ge M_4,5-edge can be employed to study carrier dynamics in the alloy. In the silicon-germanium alloy, an additional weak feature in the midgap (indicated by the black arrow), which is assigned to trap states, can be observed at longer time delays (detailed analysis in Fig. 5). The three colored rectangles on the left in (a) indicate the energies of the line profiles in Fig. 5.

FIG. 4.

Comparison of the state blocking following photoexcitation after ∼10 fs in germanium and silicon-germanium alloy. A time slice of the state blocking averaged from τ = 8,…,12 fs is shown, which precedes the onset of carrier relaxation. Although the valence band (VB) distribution features a similar shape, the conduction band (CB) onset in silicon-germanium is shifted to higher energies indicating a larger band gap. At the zero-crossing, an increase of the band gap by 0.17 eV compared to germanium can be measured. The letters designate valley assignments for germanium (blue letters) and silicon-germanium (red letters, cf. Fig. S5). The letters L, Γ, X, and K designate the conduction band minima in the respective valleys calculated for $\mathit{x}=0.75$ in relation to the valence band maximum at Γ_25'.

FIG. 5.

Kinetic analysis of electrons, holes, and midgap feature. Panels (a) to (c) analyze the conduction band (CB) kinetics in silicon-germanium. (a) At each energy, a single exponential is fit to the experimental data. (b) Using the retrieved initial amplitudes and time constants as a function of energy, the dynamics of the transient signal are captured. (c) The initial amplitude of the fit (green line with shaded error bar) depicts the initial electron distribution over energy. The two maxima correspond to an indirect excitation to the X and L as well as the direct excitation into the Γ bands. The time constant (blue line with a shaded error bar) over energy indicate the average life times of the carriers. (d) After hot carrier relaxation (τ = 1.4 ps), a weak negative feature (indicated by the black arrow) becomes visible in the midgap region of the alloy (black line with shaded error bars). For comparison, in germanium, no significant signal is observed (blue dotted line) at these time delays. Initially the midgap region between 29.1 eV and 29.4 eV in silicon-germanium (red dashed line) exhibits a near-zero signal indicative of the absence of carrier population in the band gap region. (e) In silicon-germanium alloy, a faster decay of the electrons (time constant ∼0.9 ps) and slower decay for the holes are observed. At the same time, a midgap feature grows in. Note that here the absolute value of the signals is plotted for better comparison of the temporal behavior. The energy ranges for extracting the line profiles are indicated by the three rectangles in respective colors in Fig. 3(a). The signal of the midgap feature has been amplified by a factor of two to increase visibility.