Correlation between emission intensity of self-assembled germanium islands and quality factor of silicon photonic crystal nanocavities

We present a comparative microphotoluminescence study of the emission intensity of self-assembled germanium islands coupled to the resonator mode of two-dimensional silicon photonic crystal defect nanocavities. The cavity-mode intensity is investigated for L3 and hexapole cavities with a range of different mode quality factors. For each type of cavity, many nominally identical samples are probed to obtain reliable statistics. As the cavity-mode quality factor increases, we observe a clear reduction of the average mode emission intensity under conditions of strong optical pumping. This clear trend is compared with simulations based on a dissipative master-equation approach that describes a cavity weakly coupled to an ensemble of emitters. We obtain direct evidence that reabsorption of photons in the cavity is responsible for the observed trend. When combined with the observation of cavity linewidth broadening in power-dependent measurements, we conclude that free carrier absorption limits the cavity-mediated light enhancement under conditions of strong excitation.

Figure 1

(a) Left panel: Schematic cross-sectional representation of the photonic crystal nanocavity structures investigated. Right panel: layer sequence in the active region. (b) Atomic force microscope image of the Ge islands investigated. (c) SEM image showing a L3 photonic crystal cavity with shifted outer holes from the top. (d) $\mu$PL spectrum from Ge islands in the unpatterned region at $T=25\mathrm{K}$. The grey line is a Gaussian fit to the data.

Figure 2

(a) $\mu$PL spectra recorded at $T=25\mathrm{K}$ from a series of L3 PhC cavities with different air-hole radii, increasing from bottom to top. (b) Mode emission in the spectral range from 0.915 to $0.935\mathrm{eV}$ [marked grey in (a)] for different cavity modes: (i) fundamental L3 cavity mode (M1), (ii) first higher energy L3 mode (M2), (iii) second higher energy L3 mode (M3), (iv) fifth higher energy L3 mode (M6), and (v) fundamental dipole mode of a hexapole cavity (Hex M1).

Figure 3

Average mode emission intensity as a function of inverse cavity $Q$ factor (cavity linewidth ${\gamma }_a$) for excitation power densities of 100 kW/cm${}^2$ (open triangles, dotted line as guide for the eye) and 600 kW/cm${}^2$ (filled circles, solid line as guide for the eye), normalized to the maximum value for each set of data points. Each point is obtained by averaging over several modes emitting in the spectral range between 0.915 and $0.935\mathrm{e}\mathrm{V}$. The error bars display the standard deviation. The (red) shaded area marks the region that cannot be accessed by our experimental setup due to the limited spectral resolution.

Figure 4

(a) Schematic illustration of the parameters used for the theoretical model of $N$ emitters coupled to a cavity: cavity linewidth ${\gamma }_a$, emitter linewidth ${\gamma }_b$, emitter distribution $\sigma$, and effective ensemble cavity detuning $\tilde{\Delta }$. (b) Theoretical trends in various limiting cases of the cavity QED light-matter coupling: (i) cavity at resonance ($\tilde{\Delta }=0$) and (ii) at finite detuning ($\tilde{\Delta }=1.5\mathrm{m}\mathrm{e}\mathrm{V}$) to a spectrally narrow emitter ensemble with a FWHM of ${\Gamma }_b+\sigma =0.01\mathrm{m}\mathrm{e}\mathrm{V}$. (iii) Cavity at large detuning ($\tilde{\Delta }=30\mathrm{m}\mathrm{e}\mathrm{V}$) to a broad emitter ensemble with an effective ensemble linewidth of ${\Gamma }_b+\sigma =50\mathrm{m}\mathrm{e}\mathrm{V}$, which corresponds to our system.

Figure 5

Mode emission intensity as a function of cavity linewidth ${\gamma }_a$: (dotted line) Theoretically predicted trend for our system with an emitter ensemble distribution with ${\Gamma }_b+\sigma =50\mathrm{m}\mathrm{e}\mathrm{V}$ and an ensemble cavity detuning of $\tilde{\Delta }=30\mathrm{m}\mathrm{e}\mathrm{V}$, in the absence of photon reabsorption and (solid line) including reabsorption of photons with an absorption of ${\gamma }_{\mathrm{abs}}=0.27\pm 0.05\mathrm{m}\mathrm{e}\mathrm{V}$ together with the experimental data points obtained at an excitation power density of 600 kW/cm${}^2$ from Fig. 3.

Figure 6

(a) Cavity-mode linewidth of M2, ${\gamma }_a^{\text{M2}}$, as a function of optical excitation power density. The vertical line marks the optical excitation power density that we used in our comparative study (600 kW/cm${}^2$). The horizontal dotted line marks the intrinsic linewidth ${\gamma }_{\mathrm{esc}}^{\mathrm{M}2}$ of M2. (b) ${\gamma }_{\mathrm{abs}}$, extracted from ${\gamma }_a^{\text{M2}}$, as a function of optical excitation power density. The vertical line marks the optical excitation power density we used in our comparative study (600 kW/cm${}^2$). The horizontal dotted line marks the extracted absorption linewidth of ${\gamma }_{\mathrm{abs}}^{☆}=0.23\pm 0.04\mathrm{m}\mathrm{e}\mathrm{V}$ at this power.