The SiO2/SiOx/SiO2 strip-loaded waveguide on Si substrate with buried Si nanocrystals (Si-ncs) in SiOx layer is demonstrated to show the Si-nc dependent optical gain. The amplified spontaneous emission (ASE) spectrum at 750-850 nm is observed with central wavelength of 805 nm and 3dB spectral linewidth of 140 nm. The optical net modal gain and loss coefficients of 85.7 cm−1 and 21 cm−1, respectively, are determined from the waveguide length dependent ASE intensity. By attenuating 785-nm laser diode signal to inject the pumped SiO2/SiOx/SiO2 strip-loaded waveguide, a small-signal power gain of 13.5 decibel (dB) is obtained. Increasing the laser diode power shows a significantly reduced power gain with a saturated output power due to the finite density of the optically pumped Si-ncs. The fitting of power-dependent gain with a gain-saturated amplifier model reveals a peak gain of 35 dB and a saturation power of 1.1 nW for the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide. Similar output saturation is also observed with increasing pumping power. With the presence of optical gain in the optically pumped Si-ncs, the intended application will be the monolithic integration of the Si-nc based optical waveguide amplifier with the other on-board photonic integrated circuits for the future optical interconnect communication.
©2010 Optical Society of America
The main challenge left for realizing the all-Si based photonic integrated circuits (ICs) at current stage is to demonstrate Si material based amplifiers and lasers. The expected breakthrough on adding the photonic functions within or between Si-based IC chips could provide a leap on data-transmission speed for a revolutionary progress in current IC industry. However, the light emission in bulk Si material is a phonon assisted process with a relatively low probability due to the indirect band geometry of Si, which results in a competitive non-radiative recombination process and causes an extremely low internal quantum efficiency for the photoluminescence (PL). Since 1990, the room-temperature PL at near-infrared wavelengths was preliminarily observed from nanocrystallite Si structure prepared by chemical dissolution of anodized porous Si  or by Si-ion implantation on SiO2 substrate [2–4]. Subsequently, the size dependent PL response has been correlated with the quantum confinement effect occurred in Si nanocrystals (Si-ncs) [5,6]. Later on, the stimulated emission of Si-ncs grown by plasma enhanced chemical vapor deposition (PECVD) was characterized [7,8], and the electroluminescence of an ITO/SiOx/p-Si diode was reported with micro-watt (0.13 mW/cm2) output and >0.1% external quantum efficiency [9,10]. Numerous works have claimed that the optical gain can be obtained from such kind of low-dimensional Si-ncs buried in SiOx or SiNx films [11,12]. Until 2005, the convincing argument on the existence of optical gain from Si-ncs was concluded by analyzing the planar waveguides made by PECVD grown SiOx or Si ion-implanted SiO2 with Si-ncs  by using the variable strip length (VSL) method  and the shifted excitation-spot (SES) method . In this work, we demonstrate the SiO2/SiOx/SiO2 based strip-loaded waveguide on Si substrate with dense Si-ncs buried in the SiOx film (hereafter referred to as SiOx:Si-nc) for small-signal power amplification of a directly modulated Fabry-Perot laser diode (FPLD) signal at 785 nm. The optical gain and loss coefficients are characterized by using the small-signal power gain analyses. The gain saturation effect observed either by increasing the injection power or by enlarging the pumping power is elucidated with a model developed for standard waveguide amplifiers.
2. Experiment setup
The geometric structure of a SiO2/SiOx:Si-nc/SiO2 strip-loaded waveguide with buried Si-ncs on a 2-cm2 Si substrate by PECVD is shown in Fig. 1(a) . To prevent optical leakage, the 1μm-thick SiO2 buffer layer was deposited on Si substrate for 14 min with standard SiH4/N2O flow ratio of 0.05 and RF plasma power of 200 mW. After the SiO2 buffer layer deposition, the 1μm-thick Si-rich SiOx film was grown at substrate temperature of 350°C for 30 min with anomalous SiH4/N2O flow ratio of 0.15 and RF plasma power of 30 mW. The SiOx film with a refractive index of 1.8 was annealed in a quartz furnace with flowing N2 at 1100°C for 90 min to precipitate Si-ncs. The HRTEM image of Si-ncs in SiOx film and their size distribution were shown in Fig. 1(b). Afterwards, a 1.5μm-thick SiO2 capped layer was grown upon the top of SiOx film to form the asymmetric planar waveguide. The photolithography process with a 50-μm wide and 3-cm long mask pattern was performed to form the SiO2/SiOx:Si-nc/SiO2 strip-loaded waveguide after buffered oxide etching for 20 min.
However, the isotropic wet-etching solution could over-etch the side wall of the capped SiO2 layer, such that the strip width must keep sufficiently large to ensure the modal gain and to prevent waveguide disconnection. Otherwise, the buffered oxide etchant inevitably breaks up the capped oxide layer to destroy a narrow strip-loaded waveguide along the propagating direction. Theoretically, the simulation with beam-propagation method (BPM, supported by R-Soft Company) reveals that the optical leakage is significantly enlarged when the strip height is smaller than 0.7 μm [see Fig. 2 (a) ]. The waveguide propagation loss can be reduced to 3 × 10−3 cm−1 with a buffered SiO2 thickness up to 0.7 μm. In addition, the cross-sectional view of the fundamental mode amplitude profile within the SiOx layer is shown in Fig. 2(b) and 2(c), in which X = 0 represents the center of the horizontal direction.
In experiment, the VSL diagnosis for the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide pumped by He-Cd laser at 325 nm and 40 mW is depicted in Fig. 3(a) , which clearly shows the photoluminescence with dark-red pattern [see Fig. 3(b)]. The laser beam is expanded by UV lens and focused by uni-axis cylindrical lens to top pumping the waveguide. The ASE is received by a lens-collimated fiber with a core diameter of 400 μm located very close to the waveguide edge.
3. Results and Discussion
By moving the slit to change the pumping length, the length-dependent ASE spectra are obtained and shown in Fig. 4(a) . The ASE ranged between 750 and 850 nm exhibit a central wavelength around 805 nm and a 3-dB spectral linewidth of 140 nm. Besides, the slightly red-shifted ASE spectrum of the waveguide by lengthening the pumping length is also observed. This is mainly attributed to the slightly deviated power density at different pumping segment, and is correlated with the transverse intensity distribution of the He-Cd laser with a Gaussian shape. In experiment, the He-Cd laser beam is focused into a line for top-pumping the strip-loaded waveguide, and the central spot of the focused He-Cd laser line was aligned to coincide with the strip-loaded waveguide edge for obtaining larger ASE. Owing to the non-uniformly distributed power density of the He-Cd laser line, the power density illuminated at lengthened pumping segment of the waveguide becomes attenuated when comparing with that at waveguide edge. As a result, the ASE obtained at waveguide edge is blue-shifted by the band-filling effect occurred at higher pumping power density, whereas the ASE spectrum red-shifts lengthening the pumping segment with its power density gradually attenuated by the Gaussian distributed pumping line power.
The pumping length is fixed at 1-cm and the pumping power is gradually attenuated to record different ASE spectra shown in Fig. 4(b). It clearly indicates a wavelength blue-shift for the Si-nc related normalized ASE spectrum due to the enhanced band-filling effect with increasing pumping power. The peak wavelength of ASE spectrum is blue-shifted by 2 nm as the pumping power enlarges from 1.6 to 42.4 mW. The short-wavelength photons are injected to excite the valence-band electrons in Si-ncs and to cause the filling of the conduction-band states, such that the PL could happen at higher energies to blue-shift the Si-nc gain spectrum accordingly. In comparison, the normalized PL and ASE spectra are slightly different from each other [see Fig. 5(a) ], the peak PL wavelength of the non-guiding SiOx:Si-nc layer is red-shifted by 6 nm as compared to the ASE from the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide with guiding modes. Only specific modes can be confined within the strip-loaded waveguide, and the gain profile of the waveguide amplifier is also reshaped under gain competition.
The ASE intensity (IASE) versus pumping length shown in Fig. 5(b) reveals an exponential growth at very beginning and saturate at pumping length longer than 1.5 mm. The gain coefficient of the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide can be fitted from the VSL analyzed plot in Fig. 5(b), which is based on the relationship of IASE = ISPE[e(g-α)L-1]/(g-α) among the pumping length (L) dependent ASE intensity (IASE), the spontaneous emission intensity (ISPE), and the gain (g) and loss (α) coefficients. The VSL fitting of the ASE response with the one-dimensional amplifier model provides the optical net modal gain and optical loss coefficients of 85.7 cm−1 and 21 cm−1, respectively, for the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide. The total optical gain coefficient of 106.7 cm−1 confirms the record of g = 100 cm−1 reported in earlier work . The main contribution of such a loss coefficient larger than α = 9 cm−1 ever reported by another group  may be attributed to the larger Rayleigh scattering induced by Si-ncs with diameter much smaller than optical wavelength. In our sample, the Si-ncs exhibit larger diameter of about 5 nm could cause a more pronounced scattering effect for the light propagating along the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide. In addition, the SiOx film roughness could introduce additional interfacial scattering loss.
To characterize the small-signal amplification by seeding a 785 nm laser signal into a 1-cm long strip-loaded waveguide under pumping power of 40 mW at wavelength of 325 nm, the small signal amplification experimental setup is shown in Fig. 6 . The TO-can packaged and fiber-pigtailed Fabry-Perot laser diode (FPLD) at 785 nm is directly modulated by combining a sinusoidal-wave signal of Vpp = 1 volt at 250 Hz with a DC biased current of 50 mA in a bias-tee. The FPLD input power is varied with an attenuator for small-signal power amplification analysis, and the amplified traces at different input powers are monitored by a digital oscilloscope. With FPLD injection, the stimulated emission occurs owing to the population inversion established in the pumped waveguide amplifier, as shown in Fig. 7(a) . The small-signal power gain as a function of the laser signal output power from the waveguide is illustrated in Fig. 7(b), which shows a small-signal gain of 13.5 dB obtained at output power of 8.7 nW.
As the gain saturation caused by the finite population inversion density at specific pumping condition, the small-signal power gain is exponentially decreased with increasing power of the injected FPLD signal. The power gain of the waveguide amplifier can be calculated by using the equation of G = 10log(Pon/Poff) = Pon,dB−Poff,dB = 10log(Aon/Aoff) = 10log[egL], in which Pin and Pout are the waveguide input and output power defined by Pon,dB = 10log[ηPine(g-α)L] and Poff,dB = 10log[ηPine-αL], where η denotes the total coupling loss are the waveguide output power obtained with and without pumping, the corresponding amplitudes of Aon and Aoff are determined from the digital oscilloscope. The gain coefficient can be modeled by assuming g = g0/(1 + P/Ps), where g0 is the peak gain, P is the amplified output power, and Psat is the saturated output power. The rate equation of dP/dz = g0P/(1 + P/Psat) obtained by substituting g with dlnP/dz is solved by integrating over the length L. As a result, the saturated gain under the initial conditions of P(0) = Pin and P(L) = Pout = GPin = e(g-α)LPin is derived as  G = G0exp[-(G-1)Pout/GPsat]. The fitting of the G vs. Pout curve in Fig. 7(b) provides the peak gain (G0, without considering the waveguide loss) of 35 dB with an input below the saturated power (Ps) of 1.1 nW.
Alternatively, the monitored oscilloscope traces of small-signal power amplified responses from the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide shown in Fig. 8(a) are obtained by fixing the input small-signal power and enlarging the pumping power. The Fig. 8(b) plots the small-signal gain versus pumping power to elucidate a pumping saturation effect based on the insufficient concentration of the buried Si-ncs with finite density of states. The small-signal gain slowly increases and eventually saturate with increasing pumping power. With the conduction-band states of all Si-ncs completely filling by the photo-excited electrons, the small-signal gain becomes saturated as no more ground electrons with can contribute to population inversion within the Si-ncs. Therefore, the net modal gain of the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide saturated at 13.5 dB even though the pumping rate linearly increases. The relaxation of pumping saturation and the enhancement on small-signal power gain thus relies strictly on promoting the volume density of buried Si-ncs with larger size within SiOx.
The small-signal power gain of a SiO2/SiOx:Si-nc/SiO2 strip-loaded waveguide amplifier synthesized on Si substrate with dense Si-ncs buried in SiOx layer is characterized. Under the pumping of He-Cd laser at 325 nm, the waveguide amplifier reveals an ASE spectrum at 750-850 nm with central wavelength around 805-810 nm and 3dB spectral linewidth of 140 nm. The slightly red-shifted ASE spectrum is observed when lengthening the optical pumping length, which is caused by slightly detuning the power density at different pumping segment. By increasing the He-Cd laser power up to 42.4 mW, the ASE spectrum is blue-shifted by 2 nm due to the band-filling effect, which further shows a blue-shift up to 6 nm as compared to PL spectrum due to the mode guiding mechanism of the strip-loaded waveguide. The optical net modal gain and loss coefficients are 85.7 cm−1 and 21 cm−1, respectively, as determined by using VSL method. In particular, the small-signal power amplification is demonstrated by injecting a 785-nm FPLD signal into the SiO2/SiOx:Si-nc/SiO2/Si strip-loaded waveguide amplifier. By comparing the receiving small-signal power with and without He-Cd optical pumping, the small-signal gain is 13.5 dB in experiment. The small-signal gain of 35 dB is derived by fitting the power-dependent curve, and the gain saturation effect caused by injection small-signal is observed. The effect of pumping power on the small-signal gain saturation effect of the SiO2/SiOx:Si-nc/SiO2 strip-loaded waveguide is also observed, which can be elucidated by the finite density of states in the buried Si-ncs of insufficiently large size. Due to the finite population inversion can be established in the Si-ncs to cause the small-signal gain limiting at a finite value. The SiO2/SiOx:Si-nc/SiO2 strip-loaded waveguide is successfully performed as the optical amplifier in our small-signal experiment. Furthermore, by detuning the size of Si-ncs, the amplification of different optical wavelength will be achieved. The potential application by integrating the SiO2/SiOx:Si-nc/SiO2 strip-loaded waveguide amplifier with the other on-board photonic datacom integrated circuits for optical interconnect communication networks in the future.
This work is partially supported by the National Science Council of Republic of China and National Taiwan University Center for Information and Electronics Technologies under grants NSC98-2221-E-002-023-MY3, NSC 98-2623-E-002-002-ET, NSC 98-2622-E-002-023-CC3 and 98R0062-07.
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