Laser Action of Trions in a Semiconductor Quantum Well

We report on the observation of optical gain and lasing at the trion transition of $n$-doped ZnSe quantum wells. Specifically, the (stimulated) emission-absorption net rate of this transition is controlled by the difference of trion and electron occupation in momentum space. As the mass of the trion is larger than that of the electron, gain occurs on the low-energy side of the line center without degeneracy and inversion in the total particle numbers. The scenario is reminiscent of a three-level system. At higher injection levels, carrier heating sets on and limits the available gain to values of about ${10}^4\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{1}}$.

Figure 1

Schematics of the trion transition. $E_t\left(k\right)$ and $E_e\left(k\right)$ represent the trion and electron band dispersion, respectively, assumed to be parabolic. The Fermi distribution functions (dashed curves) are plotted for $T=12\mathrm{K}$, $m_e=0.15m_0$, $m_t=0.9m_0$, and a ratio $n_t/n_e=0.8$. The vertical dash-dotted lines mark the crossover from absorption to gain.

Figure 2

Upper panel: Reflectivity spectra of a quarter-wavelength-cap sample without and with resonant pumping at the exciton transition. Dashed lines: calculated spectra using two Lorentzian-like resonances [6]. Lower panel: PL spectra for excitation resonant to the exciton and trion transition with an excitation intensity $I_{\mathrm{e}\mathrm{x}\mathrm{c}}=2\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$.

Figure 3

Lower panel: Surface (solid line) and edge (dashed line) PL of a moderately doped wave guide sample. For comparison, the linear reflectivity spectrum is given by the dash-dotted line. Inset: Derived gain spectra for excitation resonant to the exciton with ($a$) $I_{\mathrm{e}\mathrm{x}\mathrm{c}}=5\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$ and ($b$) $20\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$. Upper panel: Edge emission of a cleaved resonator of $l=240\mu \mathrm{m}$ made from the same sample for excitation resonant to the exciton ($E_x$), $I_{\mathrm{e}\mathrm{x}\mathrm{c}}=8\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$, and the trion ($E_t$), $30\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$. The width of the laser modes is limited by the spectral resolution.

Figure 4

Lower panel: Optical gain of two QWs recalculated from the modal gain measured for different excitation photon energies $\mathrm{\hbar }{\omega }_{\mathrm{e}\mathrm{x}\mathrm{c}}$ and $I_{\mathrm{e}\mathrm{x}\mathrm{c}}$. (i) $n_0=3\times {10}^{10}\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{2}}$, ($a$), ($b$) as in Fig. 3, ($c$) $\mathrm{\hbar }{\omega }_{\mathrm{e}\mathrm{x}\mathrm{c}}=E_t$, $I_{\mathrm{e}\mathrm{x}\mathrm{c}}=30\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$, ($d$) $\mathrm{\hbar }{\omega }_{\mathrm{e}\mathrm{x}\mathrm{c}}=2.87\mathrm{e}\mathrm{V}$, $I_{\mathrm{e}\mathrm{x}\mathrm{c}}=40\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$. (ii) $n_0=3\times {10}^{11}\mathrm{c}{\mathrm{m}}^{\mathrm{-}\mathrm{2}}$, (e) $\mathrm{\hbar }{\omega }_{\mathrm{e}\mathrm{x}\mathrm{c}}=E_x$, $I_{\mathrm{e}\mathrm{x}\mathrm{c}}=40\mathrm{k}\mathrm{W}/\mathrm{c}{\mathrm{m}}^{\mathrm{2}}$. The photon energy is measured relative to the position of the trion peak in reflectivity. Inset: Real part of the refraction index $n$ and intensity of the wave guide mode along growth direction $z$. Upper panel: Calculated gain spectra.