Stimulated Terahertz Stokes Emission of Silicon Crystals Doped with Antimony Donors

Stimulated Stokes emission has been observed from silicon crystals doped by antimony donors when optically excited by radiation from a tunable infrared free electron laser. The photon energy of the emission is equal to the pump photon energy reduced by the energy of the intervalley transverse acoustic (TA) $g$ phonon in silicon ($\approx 2.92\mathrm{THz}$). The emission frequency covers the range of 4.6–5.8 THz. The laser process occurs due to a resonant coupling of the $1s(E)$ and $1s(A_1)$ donor states (separation $\approx 2.97\mathrm{THz}$) via the $g\mathrm{\text{−}}\mathrm{TA}$ phonon, which conserves momentum and energy within a single impurity center.

Figure 1

Typical Si laser thresholds. The pumped Sb states or pump photon energy are shown in the left corner (inset: sketch of the experiment).

Figure 2

Emission spectra from $\mathrm{Si}:\mathrm{Sb}$ taken at different pump frequencies (same symbols as in Fig. 1). The accuracy of the central wavelength of the FEL pump pulse is $<0.01\mathrm{meV}$ and the FWHM is $\sim 0.1–0.2\mathrm{meV}$. The instrumental resolution for the emission spectra is $\sim 0.06\mathrm{meV}$. The dip in the emission spectrum (when pumped in the $2s$ state) is due to atmospheric absorption at $\sim 21.8\mathrm{meV}$.

Figure 3

Schematic energy diagram of the intracenter ($I$ laser) and the Brillouin-type ($B$ laser) mechanisms in $\mathrm{Si}:\mathrm{Sb}$. The two parts of the graph represent two opposite equivalent valleys of the silicon conduction band. Gray bold arrows are for stimulated emission; hollow up arrows indicate optical pump transitions. Diagonal arrows indicate intervalley phonons. Curved arrows are for cascade relaxation of electrons due to intravalley acoustic phonon-assisted transitions. Donor states are labeled as in Ref. 24; $1s^{\mathrm{EL}}(E)$ and $1s^{\mathrm{PH}}(E)$ represent the electronic (black thin line) and phonon-related (graded gray rectangle) contributions, respectively, in the mixed $1s(E)$ donor state [separation of the $1s^{\mathrm{EL}}(E)$ and $1s^{\mathrm{PH}}(E)$ states is not to scale].

Figure 4

Typical silicon laser emission pulses (black lines) with the corresponding pump Sb states. The flat top of the emission pulse when pumped in the $2p_0$ impurity state is due to saturation of the $\mathrm{Ge}:\mathrm{Ga}$ detector. The FEL macropulse (gray) is recorded using a fast infrared photodetector.