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We demonstrate lasing action with a high spontaneous emission factor and temperature insensitivity in InAs/InGaAs quantum dots (QD) embedded in photonic crystal nanocavities. A quality factor (Q) of over 10,000 was achieved by suppressing the material absorption by QDs uncoupled to the cavity mode. High Q cavities exhibited ultra low threshold lasing with a spontaneous emission factor of 0.7. Less frequent carrier escape from the QDs, which was primarily favored by high potential barrier energy, enabled low threshold lasing up to 90 K.
©2008 Optical Society of America
1. Introduction
Quantum dots (QDs) embedded in micropillar [1–2], microdisk [3–4], and photonic crystal (PhC) nanocavities [5–6] have been attracting considerable attention as ultrasmall and highly efficient optical light sources for photonic integrated circuits. It is well known that the light emission dynamics of carriers generated in an active medium is modified by the photonic environment. PhC nanocavities with a large quality factor (Q) and a small mode volume (Vm) are representatives serves as such control of the spontaneous emission. Since the enhancement factor of the spontaneous emission coupling to the cavity mode (β) is proportional to Q/Vm [7], the PhC nanocavities potentially yield a strong enhancement with β~1. Because of its low surface recombination rate and large oscillator strength, a QD exciton two-level system is a primary candidate as quantum emitter coupled to the photonic modes.
QD PhC nanocavities have been intensively studied in terms of the lasing action [8–13]. For efficient lasing, control of the Q value is an important issue. Unlike Si-based passive PhCs, the Q deterioration is not only due to the optical scattering loss caused by structural imperfections in the PhC but also due to material absorption [14]. Thus, we need to clarify these two factors quantitatively to achieve a higher Q. Another important factor is carrier confinement and its temperature stability in the PhC nanocavity. Generally the lasing threshold increases with increasing temperature as a result of the increase in the exciton-phonon or exciton-carrier scattering rate in typical semiconductor quantum-well microcavities [15]. Of the known QD systems, the InAs/InGaAs dot-in-well (DWELL) structure exhibits temperature insensitivity for the carrier lifetime up to 70~100 K. This is aided by the high potential barrier energy at the interface between the dot and the well layers, which effectively prevents the carrier escaping [16–18]. Therefore, both Q control and the stability of the carrier confinement over a broad temperature range are important.
In this paper, we report the Q control and resulting lasing characteristics of PhC nanocavities with an InAs/InGaAs DWELL structure as the active material. By detuning the cavity mode relative to the inhomogeneously distributed QD emission center, we could quantitatively evaluate the contributions of the structural imperfections and the material absorption, which determine the Q values. The lasing characteristics of such high Q nanocavities were then characterized in both frequency- and time-domain measurements from 4 to 100 K.
Fig. 1. Scanning electron microscope images of (a) cross-sectional PhC slab and (b) point defect cavity.
2. Experimental procedure
A single-defect cavity in a 2D PhC consists of a hexagonal array of air holes in a 190 nm-thick GaAs membrane, containing a single InAs/InGaAs DWELL layer as an active region, grown by molecular beam epitaxy, as shown in Fig. 1(a). Since the QDs have a high density of about 1011 cm-2, and are inhomogeneously distributed, a quasi-continuous broad emission spectrum was observed. As the cavity mode is set near the peak of the emission band, the QD loss resulting from the QD responses that yield only vanishingly small coupling to the cavity mode is high. In contrast, as the cavity mode is set far from the center of the emission energy distribution, the loss can be small, although the number of QD excitons coupled to the cavity is accordingly small. This property enables us to vary the loss by tuning the cavity resonance energy relative to the distribution. The designed PhC lattice constant (a) ranged from 314 to 344 nm and the air hole radius (r) was 72 nm. Neighboring holes in the defect were shifted 75 nm outwards from their original positions [19], as shown in Fig. 1(b). The PhC cavities with QDs, mounted in a continuous flow liquid-helium cryostat, were excited by a pulsed Ti:sapphire laser with a repetition rate of 80 MHz and a pulse width of 100 fs. The excitation laser was focused to a spot with a ~1 µm diameter through an objective lens with a numerical aperture of 0.42. The PL signals were detected with a liquid nitrogen cooled InGaAs linear array for spectral-domain measurements and an IR streak camera (Hamamatsu C9510) for time-domain measurements. The resolutions of the two systems were about 80 µeV and 100 ps, respectively.
3. Results amd discussion
3.1 Q control by cavity mode detuning
We can find several cavity modes in the QD emission range, and detune the cavity mode energy by varying the lattice constants of the air holes (Fig. 2(a)). Electric field profiles calculated by using the finite difference time domain (FDTD) method prove these modes to be the dipole (D), hexapole (H) and quadrupole (Q) modes, and the H mode shows the smallest mode volume of V m=0.56 (λ/n)3 and the highest Q of about 73,000 in an ideal case. Therefore we focus on the H mode in this study.
Figure 2(b) plots the PL linewidth for the H mode as a function of the detuning energy δ=E cav - E QD, where E cav and E QD are the energies of the cavity mode and the QD ensemble peak of 1.027 eV, respectively. The PL linewidth sensitively changes with the detuning energy. When δ reaches its minimum value, the PL linewidth decreases to 0.09 meV, which corresponds to a Q of 10,500. On the other hand, the linewidth increases and its distribution spreads with increases in δ. The spread of measured points at the larger detuning energy is caused by the distortion of the air holes that is induced by the near-field effect in the electron-beam lithography, because the lattice constant is smaller than that of negative detuning.
Fig. 2. (a). PL spectra of fabricated PhC nanocavities with various lattice constants a. Cavity modes labeled D (dipole), H (hexapole) and Q (quadrupole) are identified by FDTD calculation. (b) PL (red circles) and theoretical (blue circles) linewidth of the H mode dependence of detuning energy™. Blue, red and green regions indicate the area of the intrinsic structural imperfection, the re-absorption loss and distortion effect, respectively. The dotted curve shows the PL spectrum of the QD ensemble (right axis).
To reveal the intrinsic Q value change caused by the various r/a ratios, we examined the ideal values calculated with the FDTD method as represented by the filled blue circles in Fig. 2(b). Our FDTD model takes no losses into account. It is ideal structure with no absorption and no structural imperfections. The calculated values increase much more slowly than the experimental values with increases in the detuning energy. This means that the detuning (i.e. the change in the r/a ratio) is not a major factor in the increase of the cavity linewidth.
Now we can assume that there are three factors that degrade the cavity linewidth; (i) intrinsic imperfections in the PhC structure such as sidewall roughness and angles, (ii) additional structural-imperfections due to the distortion of the air holes, and (iii) re-absorption loss by uncoupled QDs. The contribution of the absorption by the GaAs slab and InGaAs QW layers will be much smaller than the above three factors, because the absorption edges are all far from the QD emission around 1.03 eV (1.52 eV for GaAs and 1.27 eV for InGaAs) [20]. If we assume that the order of the intrinsic structural-imperfection is the same over the whole wavelength range and there is no re-absorption at δ=-50 meV, factor (i) can be quantitatively separated from the others by the dashed curve in Fig. 2(b). Moreover the spread in the experimental data as shown in Fig 2(b) should give the quantity of factor (ii), and then the contribution of the re-absorption loss can be obtained. As a result, the contribution of the reabsorption loss by uncoupled QDs cannot be ignored as regards Q factor deterioration, and the cavity detuning energy critically affects the Q values.
3.2 Characteristics of QD nanocavity coupling
We also examined the QD-cavity coupling characteristics in terms of Q factor dependence. For this purpose, we compared two cavities with positive (CavI, δ=+70 meV, Q=3,300) and negative (CavII, δ=-20 meV, Q=9,000) detuning energies as shown in Fig. 3. The excitation power dependence of the PL integrated intensity for CavI shows a clear lasing threshold of about 146 mJ/cm2, which is estimated form an L-L plot, and the spectral narrowing in the PL linewidth. In this case, we estimated β to be 0.05 by using the conventional rate equation for carrier (N) and photon (S) densities as follows [12, 21],
Fig. 3. Integrated PL intensity as a function of excitation power for (a) CavI and (b) CavII. The curves indicate fitting results obtained by using a rate equation. The fitting parameter ® is 0.01, 0.03, 0.05, 0.08, and 0.1 for CavI, and 0.1, 0.3, 0.5, 0.7, 0.9, and 1.0 for CavII.
where R p is the pumping rate, ν g=c/n eff is the group velocity (1.2×1010 cm/s), Γ is the confinement factor (0.01), τ r (τ nr) is the radiative (non-radiative) lifetime of the carriers, and τ p is the photon lifetime. A τ r of 0.9×10-9 s corresponds to the measured lifetime for CavI, and a τ nr of 10 ns does not affect the fitting. A τ p of 2×10-12 s corresponds to a measured Q of 3,300. For the linear gain function G=g(N-N tr), where g is the differential gain and N tr is the transparency carrier density, we used the reported values of g=3×10-16 cm2 and N tr=1× 1018 cm-3 for the InAs DWELL laser [22]. The only fitting parameter in our calculation is β.
On the other hand, CavII does not clearly exhibit a threshold. If CavII exhibits a lasing action, the β value is calculated to be 0.7 and its threshold of 3 mJ/cm2 is estimated by the L-L fitting with a τ r of 0.5×10-9 s and a τ p of 5.9×10-12 s (Q=9,000). No spectral narrowing was clearly observed, because the cavity mode linewidth is about 100 µeV, which is almost the same as the spectral resolution of our PL setup.
To ensure that CavII exhibits lasing action, we measured the temporal characteristics of the PL emission. The time evolution of the photon and carrier density given by the rate equation can also provide evidence of lasing. If the contribution of the non-radiative recombination is linear with N at low temperatures, the decay rate of the photon density should be dominated by the radiative recombination (photon leakage) rate at well below (above) the threshold. In the time domain, the photon lifetime should be asymptotic in τ r with single-exponential decay below the threshold. After reaching the threshold, excessive carriers that exceed N tr immediately recombine at a rate of ∝(ν g gS) and emit photons. These photons leak to the outside of the cavity with a shorter lifetime of τ p. Then the carriers that fall below N tr exhibit spontaneous emission with longer lifetime of τ r. Therefore the decay curve above the threshold should show the double-exponential decay (Fig. 4).
Fig. 4. Time evolution of the photon density solved by a rate equation with the same parameters as Fig. 3(b) and ® of 0.7. The carrier density varied from 0.5 to 30N th.
Fig. 5. (a)~(c) Time decay spectra with various excitation powers, and (d) carrier lifetime as a function of excitation power for CavII (red circles). The lifetime value calculated by a rate equation (green chains) is also shown. The black circles and dotted line indicate the lifetime of the non-lasing device and the temporal resolution limit.
Figures 5(a)–5(c) show the PL decay curve of CavII at various excited powers. Below the threshold, the lifetime is about 500 ps and the spontaneous emission rate is enhanced by a factor of 2 when compared with the lifetime of a bare QD emission without a PhC nanocavity. We also observed the decay of two components with lifetimes of 120 and 500 ps well above the threshold in CavII. These values correspond to the temporal resolution limit of the streak camera and the recombination lifetime τ r. The lifetime values of the two components in CavII at various excitation powers are shown in Fig. 5(d). The behavior of the lifetime values, which are calculated with a rate equation with the same parameters as Fig. 3(b), agrees well with the experimental results. Moreover, to confirm the contribution of the non-radiative recombination, we also measure the lifetime of a non-lasing device. As a result, we obtained a constant lifetime at various excitation powers and this implies that the contribution of non-radiative recombination is not predominant in this excitation range. These results indicate that an ultra low threshold lasing with a very soft turn-on is achieved in PhC nanocavities with higher Q factors.
3.3 Temperature dependence
We also examined the temperature dependence of these lasing characteristics. Figure 6 shows the integrated intensity as a function of the excitation power and the carrier lifetime below the threshold of CavII at various temperatures. The increasing of the lasing threshold below 100 K is smaller than that above 100 K and the lifetime is almost constant up to 90 K. Similar behavior can be observed even in CavI. Note that the Q factor is also constant over the entire temperature range as shown in Fig. 6(b). In addition, the energy band gap change of InAs is less than 10 meV in the 4 to 90 K temperature range. These facts indicate that the properties of QD coupling to the cavity mode, i.e. the coupling efficiency and the gain, are maintained constantly, and the temperature dependence of the lasing threshold is mainly characterized by the carrier dynamics. Therefore the characteristics of temperature insensitive lasing are reflected in the prevention of the carrier escaping from the InAs QD to the InGaAs well due to the high energy potential between them.
Fig. 6. (a). Integrated PL intensity as a function of the excitation power of CavII at various temperatures. The arrows and dashed curves are the estimated threshold and an eye guide, respectively. (b) Carrier lifetime of CavII below the threshold (red) and bare QD (blue circles). The excitation power is the same in both cases. The green asterisks show the cavity mode linewidth (right axis).
4. Summary
We demonstrated lasing with high spontaneous emission factor β and temperature insensitivity in an InAs/InGaAs DWELL embedded in PhC nanocavities. The Q can be controlled by detuning the cavity mode to the inhomogeneous broadening of the QD emission, and a value of over 10,000 can be achieved. Such a high Q cavity exhibits ultra low threshold lasing with a spontaneous emission factor of 0.7. Moreover, these lasing characteristics are maintained up to 90 K, because the high energy potential barrier of InGaAs prevents the carriers escaping from the InAs QDs. These results indicate that using an InAs/InGaAs DWELL as an emitter for the PhC nanocavity will enable us to obtain highly efficient light sources such as lasers or single photon emitters that can work even at liquid nitrogen temperature.
Acknowledgments
The authors thank M. Gotoh and K. Kimura for their help with the time-domain measurements, and Drs. H. Nakano, Y. Tokura, and J. Yumoto for their encouragement throughout the course of this work. This work was partially supported by Strategic Information and Communications R&D Promotion Programme (SCOPE) Grant No. 072103004 and National Institute of Information and Communication Technology (NICT) Grant No. 7801.
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