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Silicon (Si) monolithic lasers are key devices in large-scale, high-density photonic integrated circuits. Germanium (Ge) is promising as an active layer due to the complementary metal-oxide semiconductor process compatibility with Si. A net optical gain from Ge is essential to demonstrate lasing operation. We fabricated Ge waveguides and investigated the n-type doping effect on the net optical gain. The estimated net gain of the n-Ge waveguide increased from −2200 to −500/cm, namely reducing loss, under optically pumped condition.
© 2016 Optical Society of America
1. Introduction
Optical interconnection for high-speed intra-datacenter networks has attracted much attention due to the progress in cloud services and big data analysis. Higher-density and shorter-reach optical interconnection for on-board or inter-chip data transmission will be more important to process large amounts of data. To meet the expectations for optical interconnection, large-scale photonic integrated circuits are necessary. In such a situation, small photonic devices and this monolithic integration strategy will be important. Silicon (Si) photonics has a great potential as advanced technology for high-density photonic integrated circuits due to the matured complementary metal-oxide semiconductor (CMOS) process and high optical confinement structure. In this technology, germanium (Ge) is popular for infrared photodiodes due to its process compatibility with Si. In addition Ge is promising as a gain material [1] because Ge has pseudo direct band gap characteristics, which means that the energy difference of Ge between direct gap Γ-valley and indirect gap L-valley is less than 0.2 eV. Therefore, Ge is expected to enable monolithic integrated lasers on Si.
To enhance light-emitting efficiency, highly n-type doping and a tensile strain structure have been effective [2–6], and optically and electrically pumped Ge lasers have been demonstrated [7–9]. Several approaches focusing on n-type doping were investigated to improve carrier injection efficiency into a direct gap Γ-valley of the Ge band structure by filling an indirect valley. However, lasing operation is still technically difficult. The reasons for this difficulty are considered as the increase in cavity internal loss due to heating, free carrier absorption (FCA) [10] and inter-valley absorption [11]. For example, the whispering gallery mode cavity power of a Ge micro-disk structure was damped by increasing optically pumped power [12, 13]. In addition, consideration for indirect gap absorption loss with the pseudo direct band gap system, in contrast to direct band gap system, will be important around direct gap energy.
A net gain (g - α), which means total of amplification (g > 0) and loss (-α < 0) elements, of a waveguide including the Ge active layer is essential as well as light-emitting intensity. We believe net gain (g - α) measurement of the Ge cavity structure without spontaneous emission is important to understand actual cavity properties. For example, material gain, direct gap absorption, indirect gap absorption, FCA, inter-valley absorption, and structure fluctuation of the waveguide were assumed as the amplification and the loss elements.
The net gain (g - α) can be experimentally obtained from cavity resonance of GaAs laser [14], transmission intensity of external light through a Ge island [6], or waveguide-length-dependent photoluminescence intensity of Ge wire on GaAs [4]. The net gain (g - α) measurement from the Ge island on Si has been reported by using the transmission light intensity method, and a gain of 56 ± 25 /cm was successfully observed at a wavelength of 1605 nm [6].
For this study, we fabricated a Ge Fabry-Perot (FP) cavity structure and investigated n-type doping-dependent loss and gain characteristics. As a result, n-type doping was effective in reducing waveguide loss in the optically pumped state.
2. Experimental method
Schematic structures and a cross-sectional scanning electron microscope (SEM) view of a single-mode Ge waveguide on Silicon on insulator (SOI) substrate is shown in Fig. 1. A 500-nm-thick Ge layer was grown on a 70-nm-thick SOI layer. The Ge layer was in situ doped with phosphorus during low pressure chemical vapor deposition (CVD). Depending on the tensile strain, required doping level for positive net gain (g - α > 0) is expected to exceed 1 × 1019 /cm3 [5, 15]. Then, three types of doping concentrations were prepared, unintentionally doped (i-, Nd << 1 × 1018 /cm3), n-type doped (n-, Nd = 2 × 1018 /cm3), and highly n-type doped (n+-, Nd = 2 × 1019 /cm3). Carrier concentrations were measured with Hall-effect measurement. Activated dopant is almost 100% for lightly doped n-Ge and 70% for heavily doped n+-Ge, respectively. The doping of n+-Ge almost reaches maximum saturation level with our CVD equipments. The i-Ge showed p-type characteristics with the Hall-effect measurement, which is explained by acceptor-like defect at the Si/Ge interface [16]. Estimated dislocation density of Ge was approximately 1 × 108 /cm2. Three 500-nm-wide Ge waveguides were patterned with electron beam lithography and a dry etching process. Uniform reflectivity at the dry-etched waveguide edge facets was expected due to the matured Si process technology compared to the dicing or polishing method. The uniform facet condition is useful to analyze the device characteristics of a waveguide or Fabri-Perot (FP) cavity. The Ge waveguides were buried with 1-µm-thick CVD-SiO2. Reflection between the edge of Ge and SiO2 is ideally about 19% from an equivalent refractive index of the waveguide of 3.95 and side wall angle of the 85 degrees, which is not critical for reflectivity in sub-micron scale Ge waveguide [17]. Tensile stress of 0.2% introduced during the Ge-CVD was reduced to 0.1% after waveguide formation. Additional stressor will be necessary to enhance tensile strain of the Ge waveguide.
Fig. 1 (a) Schematic structure, (b) cross sectional structure, and (c) cross sectional SEM view of Ge waveguide.
We investigated the waveguide transmission properties under passive and optically pumped conditions. Figure 2(a) shows the layout of the experimental setup. For the transmission measurement, either a 1650-nm-wavelength, transverse-electrical (TE) mode polarized, super luminescence diode (SLD), tunable laser diode for a 1950-nm wavelength, or 1600-nm single-wavelength laser diode were used as a probe light. The SLD wavelength was aligned to cover the direct and indirect bandgap wavelength of the Ge band structure for inter-band absorption and the 1950-nm wavelength was applicable to analyze intra-band absorption such as FCA of doping impurity. The transmission light was detected using an optical spectrum analyzer (OSA) with a resolution of 70 pm and 1 nm, or power monitors (PMs). Figure 2(b) shows a schematic of a Ge waveguide and fiber alignment. In this experiment, the external probe light was coupled to one waveguide facet with lensed single mode fiber (SMF). We collected an output light from another facet. For optical pumping, the Ge waveguides were partially excited using a continuous wave 1480 nm-wavelength pump laser. The Ge waveguide was irradiated from the top surface by using the pump laser through a flat end single mode fiber with a core diameter of 10 µm to enhance power density, and the fiber faced was closely adjusted to around 20 µm from the sample surface. We estimated the excited waveguide length to be 15 µm by taking into account the fiber numerical aperture and the core diameter. Optical coupling of the pumping light and spontaneous emission of the Ge waveguide into the lensed fiber was negligible.
Fig. 2 (a). Experimental setup for transmission measurement under optical pumping. (b) Schematic of optical pumping with SMF
3. Passive waveguide loss
In a Ge waveguide in the un-excited state, material gain (g) is zero; in other words, the net gain (g - α) is equal to the waveguide loss (-α). Based on the passive waveguide loss value, we discuss the analysis of the absolute net gain values from the relative transmittance change between the un-excited and excited states in Section 4.
For passive waveguide loss estimation, we combined the FP cavity resonance analysis [14] and transmission power analysis. Figure 3 shows the fiber-to-fiber spectrum of the SLD light and propagation spectra of the i-Ge, n-Ge, and n+-Ge waveguides. The intensity of the SLD light was compensated with a coupling loss of −22 dB (−11 dB/facet) from fiber to waveguide. A decrease in transmittance was observed below a wavelength of 1630 nm for the i-Ge waveguide and 1670 nm for the n-Ge waveguide. This change point discrepancy suggests a wavelength shift of the absorption edge of the energy band structure. We observed clear FP cavity resonances in the longer wavelength region, which means relatively low cavity loss. On the other hand, the n+-Ge waveguide transmittance was quite low over the full wavelength range from 1550 to 1750 nm compared to those of the two other waveguides, and we did not observe cavity resonance.
We analyzed the wavelength dependence of waveguide loss from the spectra of FP cavity resonance. We first estimated waveguide loss and reflectivity from the resonance peak and valley ratio observed in the i-Ge transmission spectrum at various wavelengths, as shown in Fig. 3. Figure 4(a) shows the waveguide length dependence of the i-Ge resonance amplitude at various wavelengths by using Eq. (1) [14].
Fig. 4 (a) Wavelength-dependent waveguide loss and reflectivity of i-Ge waveguide measured using transmission resonant spectra. (b) n-type doping-dependent waveguide loss and reflectivity measured using transmission resonant spectra of 70μm-length cavity around 1950 nm
These slopes and y-intercepts show passive waveguide loss (g - α, g = 0) and reflectivity (r). The waveguide loss had wavelength dependence between 1600 and 1700 nm; however, a reflectivity of around 18% was not sensitive to wavelength. The wavelength-dependent waveguide loss is mainly considered to be derived from indirect-gap absorption. The reflectivity of 18% showed good agreement with reflectance at the Ge/SiO2 interface of the waveguide facet, as mentioned above. We also analyzed the passive transmission characteristics around a wavelength of 1950 nm. Figure 4(b) shows waveguide loss and reflectivity depending on n-type doping. The inset shows resonant spectra of 70 µm-length cavity around a wavelength of 1950 nm. Although FP resonance amplitude decreased with increasing doping concentration, the peak valley ratio could be detected even from the n+-Ge waveguide. The waveguide losses of the i-Ge, n-Ge, and n+-Ge waveguides at 1950 nm were experimentally obtained as 4, 53, and 250 /cm, respectively, as shown in Fig. 4(b). Photon energy of the 1950-nm wavelength (630 meV) is so small compared to the bandgap (660 meV) of the Ge band structure that interband light absorption can be ignored. Considering intraband transition, the estimated waveguide loss showed good agreement with losses described in previous studies [18, 19].
Figure 5 shows waveguide loss spectra for various doping concentrations (solid lines) by simply converting the transmittance in Fig. 3 by using Eq. (2).
Fitting curves of wavelength dependent direct and indirect absorption were also plotted [20]. The inter-band absorption derives from mainly electron heavy-hole transition, which interacts with TE polarized field. The open circles of i-Ge, which denote the estimated waveguide loss from cavity resonance shown in Fig. 4(a), correspond to the waveguide loss spectrum. These equivalent magnitudes of the waveguide loss estimated by two different analysis support the validity of the measurement results in Fig. 5, for example fiber alignment accuracy. The dashed lines show FCA elements based on waveguide loss at a wavelength of 1950 nm and the study by Spitzer et al. [18]. Increasing waveguide loss associated with n-type doping cannot be explained by FCA alone. A red-shift of the waveguide loss spectra was confirmed by impurity doping due to the reduced bandgap [21]. Direct gap band edges estimated by the fitting curves in Fig. 5 are 1596 nm, 1617 nm, and1675 nm for the i-Ge, n-Ge, and n+-Ge waveguides, which means band gap narrowing (BGN) of 10 meV for n-Ge, and 36 meV for n+-Ge, respectively. These BGN values are consistent with previous study [22].4. Waveguide characteristics under optical pumping
Figure 6(a) shows the transmission spectra of the i-Ge and n+-Ge waveguides obtained with the SLD probe light under optical pumping as shown in Fig. 2(b). Photon energy of the pump signal is about 0.84 eV and slightly higher than direct gap energy. The transmission power of the i-Ge waveguide decreased in the 1600 to 1700 nm wavelength range, and we confirmed the reduction in the transmission intensity of the n+-Ge waveguide in the long wavelength side of 1650 nm by optical pumping. Though all over the waveguide should be irradiated by pump laser ideally for the net gain (g - α) measurement, the excited area was limited about 15 µm-length in order to enhance pump power density. In this study, net gain shift (Δg - Δα) values were simply estimated from transmission power ratio between on and off state of the pump laser using Eq. (3) and the transmission spectra in Fig. 6(a).
Fig. 6 (a) Transmission spectra of Ge waveguides under optical pumping (liner scale). (b) Net gain shift (Δg-Δα) of Ge waveguide under optical pumping obtained with Fig. 6(a) and Eq. (3).
Figure 6(b) shows relative net gain shift (Δg - Δα) in the optically pumped state of the i-Ge waveguide. In the excited state, the net gain shift (Δg - Δα) trends of the i-Ge waveguide differed between short and long wavelength regions. A sharp drop-off around 1600 nm was considered as the red-shift of the direct-gap absorption due to heating. On the other hand, less wavelength-dependent change in the longer wavelength region was derived from the FCA due to pumped excess carriers. Considering the FCA-loss increase [18, 19], excess carrier density was estimated to be approximately 1 × 1019/cm3 under optical pumping intensity of 11.7 kW/cm2.
Figure 7(a) shows the transmission power change of the 1600-nm-wavelength laser used as the probe light because the transmission light intensity of the n+-Ge waveguide with SLD probe light around 1600 nm was too low to observe the transmittance change as shown in Fig. 6(a). The 1600-nm wavelength is expected to have the material gain from the n-Ge waveguide [6]. The transmission power in the i-Ge waveguide decreased due to optical pumping, as expected from previous results shown in Fig. 6(b). The reasons for the negative net gain shift (Δg - Δα) were mainly considered due to the red-shift of the absorption spectrum and FCA included in the waveguide loss. However, the n-Ge and n+-Ge waveguide transmission light was amplified by irradiating the pump laser. Signal amplification of the n+-Ge waveguide was larger than that of the n-Ge waveguide. Figure 7 (b) shows the estimated net gain (g - a) as a function of excitation power using Eq. (4). The waveguide transmittance change ratio in Fig. 7(a) was converted to net gain change by using Eq. (3). The net gain (g - α) in the un-excited state, which means equal to the passive waveguide loss, was referred from the estimated waveguide loss mentioned in section 3.
Fig. 7 (a). Transmission power change by optically pumping. (b) Loss and gain analysis of Ge waveguides depending on pumping power density
The estimated net gain (g - α) of the n-Ge and n+-Ge waveguides increased from −800 to −200/cm and −2200 to −500/cm at a power density of 27 kW/cm2, respectively. An increase in the net gain occurred, although increase in FCA loss was assumed simultaneously. These results showed that the optical property of Ge changed from an absorber into transparent or gain medium around a wavelength of 1600 nm. There is the potential for larger material gain (g) at longer wavelength with n+-Ge waveguide due to the band gap narrowing. Based on a difference in net gain slope of i-Ge and n-type Ge shown in Fig. 7(b), we confirmed the effectiveness of n-type doping to inject carriers into the Γ-valley efficiently and enhancing carrier recombination at direct transition points.
5. Conclusion
We reported on the Ge waveguide transmission characteristics for Si monolithic laser diodes. We carefully measured the passive waveguide loss as a reference to estimate absolute values of the net gain (g - α). For an n-type doped waveguide, we confirmed an increase in waveguide loss due to free carrier absorption and bandgap narrowing. We then estimated the net gain (g - α) from transmission power change. The net gain (g - α) of the n-Ge waveguide with a donor concentration of 2 × 1018 /cm3 increased from −800 /cm to −200 /cm under the optically pumped condition at a power density of 27 kW/cm2. The net gain (g - α) of highly doped n+-Ge waveguide with donor concentration as high as 2 × 1019 /cm3 also increased from −2200 /cm to −500 /cm at a wavelength of 1600 nm. These results showed the effectiveness of n-type doping to inject carriers into the Γ-valley and the potential for positive optical gain from Ge by increasing the n-type doping level and optical pumping power.
Acknowledgments
We would like to thank Professors Yasuhiko Arakawa, Satoshi Iwamoto, and Dr. Satoshi Kako of the University of Tokyo and Professor Shinichi Saito of the University of Southampton for their helpful advice. This work was supported by the Project for Developing Innovation Systems of the Ministry of Education, Culture, Sports, Science and Technology (MEXT), Japan.
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