Direct-Gap Gain and Optical Absorption in Germanium Correlated to the Density of Photoexcited Carriers, Doping, and Strain

Direct-gap gain up to $850{\mathrm{cm}}^{-1}$ at 0.74 eV is measured and modeled in optically pumped Ge-on-Si layers for photoexcited carrier densities of $2.0\times {10}^{20}{\mathrm{cm}}^{-3}$. The gain spectra are correlated to carrier density via plasma-frequency determinations from reflection spectra. Despite significant gain, optical amplification cannot take place, because the carriers also generate pump-induced absorption of $\approx 7000{\mathrm{cm}}^{-1}$. Parallel studies of III–V direct-gap InGaAs layers validate our spectroscopy and modeling. Our self-consistent results contradict current explanations of lasing in Ge-on-Si cavities.

Figure 1

Simplified band structure of unstrained Ge, illustrating the $k$-space distribution of photoexcited carriers. $E_{F,e}$ and $E_{F,h}$ are the conductance-band and valence-band quasi-Fermi energy levels, respectively. The vertical HH-SO transition in the valence band thought to be responsible for most of the PIA is also indicated.

Figure 2

(a) Brewster transmission spectra of unpumped ($U$) and pumped ($P$) Ge1 as a function of $\Delta t$ with fits. (b) NI transmission spectra and fits of pumped InGaAs1 showing thin film interference effects and optical amplification. (c) and (d) The differential direct-gap absorption ($\Delta {\alpha }_{\mathrm{DG}}$) and pump-induced absorption (${\alpha }_{\mathrm{PIA}}$) extracted from the fits to spectra in (a) and (b), respectively. Optical amplification ($\Delta {\alpha }_{\mathrm{DG}}+{\alpha }_{\mathrm{PIA}}<0$) and gain ($\Delta {\alpha }_{\mathrm{DG}}<0$) ranges are highlighted.

Figure 3

(a) Mid-IR reflection spectra of pumped InGaAs2 expressed as the ratio of pumped ($R_P$) and unpumped ($R_U$) reflection, fitted with a Drude model. The inset shows the deduced injected carrier density in Ge1 as a function of pumping intensity. (b) Near unity correlation between injected carrier density values for InGaAs1 as deduced independently from Drude modeling and transmission modeling. The observed variation in electron effective mass in InGaAs [16] from conductance-band nonparabolicity has been included in these calculations.

Figure 4

(a) Comparison of measured and modeled peak gain values ($-\Delta {\alpha }_{\mathrm{DG}}$) from the Ge samples as a function of carrier injection. (b) The magnitude of the PIA at the direct-gap energy, for the three Ge samples, expressed as a function of total carrier density, fitted by using a linear cross-section model. Note that $\Delta {\alpha }_{\mathrm{DG}}+{\alpha }_{\mathrm{PIA}}(E_{\mathrm{DG}})\gg 0$ in all cases, meaning that optical amplification cannot occur.