Terahertz Stimulated Emission from Silicon Doped by Hydrogenlike Acceptors

Stimulated emission in the terahertz frequency range has been realized from boron acceptor centers in silicon. Population inversion is achieved at resonant optical excitation on the $1{\mathrm{\Gamma }}_8^{+}\to 1{\mathrm{\Gamma }}_7^{-}$, $1{\mathrm{\Gamma }}_6^{-}$, $4{\mathrm{\Gamma }}_8^{-}$ intracenter transitions with a midinfrared free-electron laser. Lasing occurs on two intracenter transitions around 1.75 THz. The upper laser levels are the $1{\mathrm{\Gamma }}_7^{-}$, $1{\mathrm{\Gamma }}_6^{-}$, and $4{\mathrm{\Gamma }}_8^{-}$ states, and the lower laser level for both emission lines is the $2{\mathrm{\Gamma }}_8^{+}$ state. In contrast to $n$-type intracenter silicon lasers, boron-doped silicon lasers do not involve the excited states with the longest lifetimes. Instead, the absorption cross section for the pump radiation is the dominating factor. The four-level lasing scheme implies that the deepest even-parity boron state is the $2{\mathrm{\Gamma }}_8^{+}$ state and not the $1{\mathrm{\Gamma }}_7^{+}$ split-off ground state, as indicated by other experiments. This is confirmed by infrared absorption spectroscopy of Si:B.

Popular Summary

Today’s electronics is dominated by silicon. However, laser generation is difficult to realize with silicon for a fundamental reason: Silicon is a so-called indirect-band-gap semiconductor, in which an electron excited into the conduction band and the hole it leaves behind in the valance band do not have the same momentum. As a result, photon emission (or light generation) from a direct recombination of the electron and hole is forbidden. Doping silicon with either electron-giving ($n$-doping) donor atoms or electron-capturing ($p$-doping) acceptors has been used as a remedy for this problem. $p$-doped silicon (with boron) is a promising candidate because experimental and theoretical investigations indicate that its electronic structure can enable a four-level laser scheme. In this experimental paper, we demonstrate a boron-doped-silicon laser.

Our laser is obtained by optically pumping the boron acceptors into their high-energy excited states. This leads to population inversion between some of these states and, in turn, to laser emission at 1.740 THz and 1.748 THz, respectively. Unexpectedly, the upper laser states are not those with the longest lifetimes but states with rather short ones of approximately 50 ps. This also allows us to draw a few interesting conclusions on the energy structure of the excited states in Si:B, which has not been known very well. In particular, one excited state that was thought to have the second-largest binding energy turns out to have a significantly smaller one.

Our work demonstrates the feasibility of $p$-doped silicon lasers. More types of lasers based on $p$-doped silicon with different dopants and emission frequencies might be realized in the future.

Figure 1

(a) Band diagram of boron impurity levels in silicon (HH, heavy hole subband; LH, light hole subband; SO, spin-orbit split-off subband). Negative energies correspond to the band gap. The narrow arrows up show dipole-allowed boron absorption transitions (ground $\text{state}\to {\mathrm{\Gamma }}_8^{+}$ subband: lines 1, 2, 3, 4, 5) (ground $\text{state}\to {\mathrm{\Gamma }}_7^{+}$ subband: lines $2^{\prime }$, $3^{\prime }$, $4^{\prime }$), which are regularly observed in low-temperature absorption spectroscopy [14]. The $1{\mathrm{\Gamma }}_7^{+}$ ground state of the split-off state series (${\mathrm{\Gamma }}_7^{+}$ band) is expected to occur in between the two horizontal dashed lines: between resonant to the ${\mathrm{\Gamma }}_8^{+}$ band location [14] and the theoretically predicted in the band gap [15]. The light blue dashed line is the position where the $1{\mathrm{\Gamma }}_7^{+}$ ground state should appear according to Raman spectroscopy [17, 18]. (b) Si:B laser scheme. The bold straight arrows indicate the transitions for stimulated emission (red downward arrows) under optical pumping (bold blue upward arrow). Note that the laser transitions end in the lowest even-parity state. The curved green arrow indicates nonradiative relaxation.

Figure 2

Absorption and pump spectra of the Si:B laser samples. The uppermost curve is the transmission spectrum of a $400\text{−}\mu \mathrm{m}$-thick Si:B sample cut from the same crystal as the laser. It was measured at a temperature of 5 K with a FTIR spectrometer with 2 hPa pressure. The impurity transitions are labeled $1,2,3,\dots ,10$ according to Ref. [14]. The middle curve is an absorption spectrum of the Si:B laser crystal at 5 K measured by tuning the wavelength of the FEL and detecting the transmitted radiation behind the Si:B sample. Note the correspondence between the absorption lines measured with the FTIR spectrometer and the FEL. They correspond to boron intracenter transitions originating from the boron ground state. The asterisks indicate positions of the strongest water vapor absorption lines. The lowest curve displays the Si:B laser power as a function of the pump wavelength. Only pumping on the boron lines 4, 4a, and 4b results in laser emission.

Figure 3

Emission spectrum of the Si:B laser when pumped at the boron line 4. The FEL pump photon flux is $4\times {10}^{25}{\mathrm{cm}}^{-2}{\mathrm{s}}^{-1}$. Two emission lines at 1.740 and 1.748 THz are just resolved (inset).

Figure 4

Dependences of the emission from Si:B on the FEL pump photon flux for different photon pump energies, corresponding to boron absorption lines 4 and 4b.

Figure 5

Typical decay of the photoinduced transmission in Si:B. The pump and probe pulses have a Gaussian shape and a wavelength centred at the boron line 4 ($31.3\mu \mathrm{m}$, resonant pumping in the upper laser state). The FEL pump photon energy is 113 pJ per pulse. The inset is a sketch of the pump-probe experiment.

Figure 6

Dependence of decay time of the Si:B sample (the same as in Fig. 5) on the pump pulse energy for pumping on line 4 ($T\approx 5\mathrm{K}$). The straight line indicates the mean value.