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Light emitter based on Ge quantum dots embedded in photonic crystal ring resonator is designed and fabricated. Six sharp resonant peaks dominate the photoluminescence (PL) spectrum ranging from 1500 to 1600 nm at room temperature. The light emission enhancement is due to Purcell effect and high collection efficiency of the PCRR verified by calculated far-field patterns. The Purcell factor of the PCRR is estimated from enhancement factor and increased collection efficiency. The linewidth of the emission of a single Ge quantum dot is estimated from the Purcell factor.
© 2014 Optical Society of America
1. Introduction
Silicon based optical interconnect is now considered as a promising solution to overcome the limited bandwidth and high power consumption of traditional electric interconnects [1]. The realization of silicon based light source is still a huge challenge due to the indirect band gap of bulk silicon. Numerous efforts have been explored to solve this problem, including silicon nanocrystals [2], bulk crystalline silicon [3, 4], optically active defects in crystalline Si [5], erbium doping in silicon [6], tensile-strained n-type Ge [7], III-V lasers [8] and so on. Among these methods, Ge self-assembled quantum dots (QDs) attract great interest due to their easy fabrication, light emission between 1.3 and 1.6 μm in the telecom wavelength and compatibility with complementary metal-oxide semiconductor (CMOS) processes [9, 10]. Considering poor spectral purity, low directionality and low luminescence intensity of light emission from Ge QDs, different microcavities were utilized to enhance light emission and select emission wavelength [11–15].
Photonic crystal ring resonator (PCRR) is formed by introducing defects in shape of a hexagon into two dimensional photonic crystals. The PCRR has some advantages, such as high Q factor, small mode volume, scalability in size, flexibility in mode design due to their multimode nature, adaptability in structure design due to numerous design parameters and flexibility design of backward and forward dropping for channel drop filters [16]. In 2002, S. Kim et al. introduced the concept of PCRR in an InGaAsP quantum well laser firstly, and a Q factor around 2000 for lasing mode was observed [17]. In the last ten years, high Q factor PCRR was demonstrated [18, 19] and applied in various devices, such as filters [20], wavelength division demultiplexers [21], lasers [22] and sensors [23]. However, experimental report of light emission from QDs in PCRR was rarely reported.
In this paper, we demonstrate strong resonant luminescence from Ge QDs embedded in PCRR at room temperature. Six sharp resonant peaks are observed to dominate the PL spectrum of the PCRR, and the strongest resonant luminescence peak is located at 1542 nm. Three-dimensional finite-difference time-domain (3D-FDTD) method is applied to calculate the resonant modes for the PCRR and analyze the PL spectrum of the PCRR. The Purcell factor is estimated from enhancement factor and increased collection efficiency. We also estimate the emission linewidth of a single Ge QD from the Purcell factor.
2. Device fabrication and characterization setup
In the experiment, the silicon-on-insulator (SOI) wafer with 160-nm-thick silicon and 2000-nm-thick silica is transferred into gas source molecular beam epitaxy (GS-MBE) for Si and Ge growth. After a 20-nm-thick silicon buffer layer grown at 700 °C, four layers of Ge self-assembled QDs with coverage of 10 monolayers are grown at 700 °C in the Stranski-Krastanov (SK) growth mode. They are separated by 15-nm-thick silicon spacing layers and capped by a 20-nm-thick silicon layer grown at the same temperature. The total thickness of top Si/Ge layer is 245 nm measured by ellipsometer.
E-beam lithography (Vistec EBPG 5000 Plus) is used to define the PCRR structures on the ZEP520A resist. Then the patterns are transferred to the top Si/Ge layer by inductively coupled plasma (ICP) dry etching using SF6 and C4F8 gases. In order to increase the symmetry of the structure and strengthen optical confinement in the normal direction, buried silicon oxide (BOX) is removed by a dilute hydrofluoric acid solution. A scanning electron microscope (SEM) image of fabricated PCRR structure is shown in Fig. 1(a). The ring resonator is formed by removing 20 air holes in shape of a hexagon. The lattice constant a is 420 nm and the radius of air holes r is 0.30a. The depth of the air holes is 245 nm. The radius of the twelve air holes at the corners of the PCRR, which is denoted as r′, is reduced by 15 nm for higher Q factor [19], as shown in Fig. 1(b). The schematic structure of the device is shown in Fig. 1(c). In the top Si/Ge layer, there are four layers of Ge self-assembled QDs, shown with red dots. The BOX under the photonic crystal region is removed to form the freestanding structure.
Fig. 1 (a) the SEM image of fabricated PCRR embedded with Ge QDs. The excitation spot is shown with a green circle. (b) the magnified micrograph of the corner of the PCRR. The radius r′ of air holes at the corner of the PCRR is reduced by 15 nm. (c) the schematic structure of the device. The red dots represent Ge self-assembled QDs in the top Si/Ge layer. The BOX under the photonic crystal region is removed to form the freestanding structure.
The micro-photoluminescence (μPL) of the sample is characterized at room temperature using a confocal microscope photoluminescence system. The sample is excited with a diode-pumped solid-state (DPSS) laser at λ = 532 nm, which is focused to a 2-μm spot on the centre of the PCRR by a high numerical aperture (NA = 0.95) microscope objective. The excitation spot is shown with a green circle in Fig. 1(a). The μPL signal is collected by the same objective, then dispersed by a monochromator with 320 mm focus length and detected by a liquid-nitrogen-cooled InGaAs detector array.
3. Results and discussion
Figure 2(a) shows the room-temperature μPL spectra for the sample, the power of the incident excitation laser is 16 μW. Red and black curves represent the PL spectrum of the PCRR and unprocessed Si/Ge membrane, respectively. As seen in Fig. 2(a), several sharp resonant peaks are observed to dominate the spectrum over an almost flat and weak background emission in the PL spectrum of the PCRR. There are clearly six sharp resonant emission peaks in the telecom wavelength range from 1500 to 1600 nm. Compared to the unprocessed membrane, the PL intensity from the PCRR is significantly enhanced at the resonant peaks.
Fig. 2 (a) the experimental room temperature μPL spectrum of the PCRR, the excitation power is 16 μW. (b) the magnified graph of the experimental PL spectrum for the emission peak 4 of the PCRR.
Figure 2(b) shows the magnified graph of the PL spectrum for the emission peak 4 of the PCRR. The wavelength of the peak 4 is 1542.58 nm, and the full-width-half-maximum (FWHM) is 0.5 nm obtained from Lorentz fitting. The corresponding Q factor is 3085.
In order to identify the resonant peaks in the PL spectrum, 3D-FDTD method is performed to simulate the PCRR. The proposed PCRR structure is based on two dimensional photonic crystals of air holes with a triangular lattice and forms by removing 20 air holes in shape of a hexagon, as shown in Fig. 3(a). The geometry parameters are measured from the SEM image. Ge QDs are not taken into account in the simulation due to the thickness of the layer of Ge is very thin (about 1.4 nm). The refractive index of top Si/Ge layer almost equals to that of silicon layer. The photonic bandgap effect is investigated by 3D-FDTD simulation, in which a TE-like polarized light excited by a dipole source propagates through the perfect triangular lattice or the PCRR structure and then is monitored on the other side. The simulated transmission spectrum for a perfect triangular lattice with a hole radius r = 0.30a is shown in Fig. 3(b) (black curve). As seen in Fig. 3(b), wavelength ranging from 1621 to 1680 nm corresponds to the passband (grey region), while a bandgap for wavelength ranging from 1500 to 1621 nm is obtained. When the hexagon defect is introduced to form the PCRR structure, additional resonant peaks are obtained in the bandgap region, shown as blue curve in Fig. 3(b). It can be seen that, the emission peaks 1~6 in the PL spectrum in Fig. 2(a) are well identified by the simulated resonant modes 1~6 shown in Fig. 3(b). Since the wavelength of the mode 0 is beyond the limitation of our InGaAs detector array, the corresponding emission peak is not observed in the experiment. The simulated electric field (Ey) profiles at the plane of z = 0 (the center of the membrane) of the six resonant modes are shown in Figs. 4(a)-(f), respectively. We introduce the notation for the modes in terms of the in-plane parities of their Ey fields [24]. We place the parity along the x axis above the parity along the y axis, and add a numerical index denoting their ordering in terms of energy. As the resonant mode 1 has an Ey field of odd parity along x axis and even parity along y axis and it is the lowest energy mode with such parities, we term it [- + 1]. The resonant modes 2~6 are called [ + -1], [- -1], [ + + 2], [- + 2] and [- -2], respectively. The resonant mode 0 is [ + + 1], its Ey profile is not shown here. Focusing on the resonant mode 4 shown in Fig. 4(d), the calculated Q factor is 8670 and mode volume is 0.324 μm3 = 3.19(λ0/n)3, where λ0 is the wavelength of light in the air. The experimental Q factor is lower than the simulation result, it may be attributed to extra loss induced by tilt of air-holes, fluctuation of air-hole radii, roughness of the inner walls introduced in fabrication and free-carrier absorption of photogenerated carriers in PL measuring.
Fig. 3 (a) Illustration of the PCRR structure. The radius of the twelve air holes at the corners of the PCRR is reduced. (b) Simulated transmission spectra of photonic crystal with a perfect triangular lattice (black curve) and a PCRR structure (blue curve).
Fig. 4 the simulated electric field (Ey) profiles of the six resonant modes supported by the PCRR at the plane of z = 0 (the center of the membrane). (a) 1594.58 nm. (b) 1584.10 nm. (c) 1563.54 nm. (d) 1547.76 nm. (e) 1536.02 nm. (f) 1518.05 nm.
The enhancement factor is estimated as 30 for the peak 4, shown in Fig. 2(a). It is defined as the ratio of the resonant peak intensity to the PL intensity of the unprocessed Si/Ge membrane at the corresponding wavelength. The enhancement is attributed to the increased collection efficiency and the Purcell effect in the PCRR. We calculate the collection efficiency (ηc) into the objective lens placed above the photonic crystal membrane by simulating the far-field emission patterns of the resonant modes with the aid of a standard near-to-far-field projection. The near field patterns at the photonic crystal surface used for the projection are simulated by 3D-FDTD method. The simulated far-field emission patterns for the six resonant modes are shown in Figs. 5(a)-(f), respectively. The far-field profiles for the modes 4~6 of PCRR are more concentrated along the vertical out-of-plane direction than the far-field profiles for the modes 1~3. It means, for a given limited NA objective, light emission from the modes 4~6 is easier to collect from the normal out-of-plane direction comparing to the modes 1~3. The calculated collection efficiency ηc for the peak 4 is 0.844 when the NA of the objective is 0.95. The collection efficiency of unprocessed Si/Ge membrane [25] can be given by ηslab = 1–cos[sin−1(NA/n)]~0.058, where n~2.83 is the effective refractive index of Si/Ge membrane and NA = 0.95 is the NA of the objective. The enhancement of collection efficiency is given by ηc/ηslab~14.5. The total enhancement factor α can be given by α = Fp*ηc/ηslab, where Fp is the Purcell factor. Then, Fp = α*ηslab/ηc~2.1.
Fig. 5 the simulated far-field emission patterns for the six resonant modes shown in Fig. 4. (a) 1594.58 nm. (b) 1584.10 nm. (c) 1563.54 nm. (d) 1547.76 nm. (e) 1536.02 nm. (f) 1518.05 nm. White concentric circles correspond to θ = 30þ, 45þ, 72þ, 90þ from the inner one to the outer one, respectively.
The Purcell factor Fp, which indicates the enhancement ratio of spontaneous emission rate with and without an optical resonator, can be expressed as [26]
where λc is the wavelength of the resonant mode, Vc is the mode volume, n is the effective index of the material. Qeff is the effective quality factor, taking into account quality factor of the resonant mode (Qc) as well as quality factor of the emitter (Qe). The simple expression of Purcell factor here is obtained by assuming perfect spatial and spectral overlaps between the resonant mode and the emitter. The Qeff in the expression can be replaced by Qe, when the emission linewidth of the emitter is much broader than the linewidth of the resonant mode. Thus, the Purcell factor depends on 1/Vc and can only be increased by reducing the mode volume Vc for the emitter with broad emission linewidth, such as Ge QD, crystalline silicon. The Purcell factor in a modified L3 cavity we reported before [14] is threefold higher than that in the PCRR here. It can be attributed to the much smaller mode volume of the L3 cavity. The mode volume of fundamental mode for the modified L3 cavity is 0.076 μm3, which is about one quadrant of the mode volume of the PCRR. We believe that, adopting the resonators or cavities with much smaller mode volume and higher collection efficiency, higher Purcell factor and stronger resonant emission can be realized.It is possible and difficult to directly measure the linewidth of a single QD by spectroscopic methods [27]. A rough estimation of the linewidth can be given using the Eq. (1) and (2). According to Fp = 2.1 and Qc = 3085 mentioned above, Qe = 63 can be obtained. If the spatial and spectral imperfect overlaps between the resonant mode and Ge QD were considered, the estimated Qe should be larger. It indicates that, the emission linewidth of a single Ge QD is less than 25 nm at room temperature. The broad linewidth of a single Ge QD is due to the large lateral size of our Ge QD (~90 nm). The Ge QD with smaller lateral size providing stronger quantum confinement of excitons may have narrow emission linewidth. Narrow emission linewidth (~1 nm) from a single Si QD has been reported by reducing the dot lateral size to 4 nm [27]. However, the emission of ensemble of self-assembled Ge QDs observed in the PL spectrum distributes in a large range of 1.3 to 1.6 μm. We attribute it to the size dispersion of the self-assembled QDs. The similar situation occurs in the case of light emission from active defects in silicon [25].
4. Summary
In conclusion, we experimentally demonstrate resonant luminescence from Ge QDs embedded in a PCRR at room temperature. The resonant modes and corresponding far-field patterns are simulated by 3D-FDTD method. Six sharp resonant peaks, which correspond to the resonant modes supported by the PCRR, are observed to dominate the spectrum over an almost flat and weak background emission in the PL spectrum of the PCRR. The strongest resonant luminescence peak is obtained at 1542 nm with a Q factor of 3085. A Purcell factor of 2.1 is estimated from the enhancement factor of PL intensity and collection efficiency. We attribute the low Purcell factor of the PCRR to the relative large mode volume. The higher Purcell factor can be realized in cavities with smaller mode volume. The emission linewidth of a single Ge QD is less than 25 nm at room temperature estimated from the Purcell factor. Our approach can provide narrow light emission in the telecom wavelength range of 1500-1600 nm, which shows a possible way to realize silicon-based light emitters.
Acknowledgments
This work was partly supported by the Major State Basic Research Development Program of China (grant 2013CB632104), the Major State Research Program of China (grant 2013CB933303), the Major State Basic Research Development Program of China (grant 2012CB922103 and 2010CB923204), and National Natural Science Foundation of China (grant 61177049 and 61335002). We thank all the engineers in the Center of Micro-Fabrication and Characterization (CMFC) of WNLO for the support in device fabrication.
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