We investigated influence of carrier lifetime on performance of silicon (Si) p-i-n variable optical attenuators (VOAs) on submicrometer Si rib waveguides. VOAs were fabricated with and without intentional implantation of lattice defects into their intrinsic region. Carrier lifetime was measured by pulse responses for normal incidence of picosecond laser pulse of 775 nm to the VOA, as ~1 ns and ~7 ns for the VOAs with and without defects, respectively. Carrier lifetime is determined by the sum of surface recombination and Auger recombination for VOAs without defects, while Schockley-Read-Hall recombination is dominant for the VOA with defects. As a result, attenuation efficiency (dB/mA) is 0.2 - 0.7 and 0.04 - 0.1, while 3-dB bandwidth is 40 - 100 MHz and over 200 MHz for the VOAs with and without defects, respectively. There is a trade-off relation between attenuation and response speed of the VOAs with respect to carrier lifetime i.e., attenuation efficiency is linearly proportional to the carrier lifetime, whereas response speed is inversely proportional to it.
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A p-i-n diode structure fabricated on Si rib waveguides is a promising platform for active photonic devices, such as Si Raman lasers , electro-optic micro-ring modulators , and variable optical attenuators (VOAs) . In the Si Raman laser, reverse bias is applied to a p-i-n structure to deplete carriers along the Si optical path and thereby suppress propagation loss due to free carrier absorption (FCA) . The operating principles of micro-ring modulators and p-i-n VOAs are based on a strong plasma dispersion effect, which is related to carrier density . In the modulator, carrier density changes the effective refractive index. Since a carrier density that is too large causes severe absorption, the carrier injection level should remain relatively low. In contrast, a high level of carrier injection is essential for optical attenuation in VOAs. The concept of free carrier injection to a Si rib waveguide has been proposed  and commercial VOA products are on the market . However, these Si VOAs consist of rib waveguides with thickness and width of a few micrometers. We have reported Si p-i-n VOAs with submicrometer rib waveguides . Such a submicrometer VOA has many advantages such as small footprint less than a square millimeter and fast response on the order of nanoseconds, compared to MEMS- or planar lightwave circuit- (PLC-) based VOAs [8,9]. Furthermore, convenient electric control of Si VOAs enables monolithic integration with power monitors and feedback circuits .
Recently, implementation of VOAs for wavelength division multiplexing passive optical networks (WDM-PONs) has been extensively studied. In fact, two practical applications can be considered, 1) compensation of gain transient tilt of erbium-doped fiber amplifiers (EDFAs) and 2) signal equalization of upstream optical packets . For these purposes, both the static property (attenuation) and dynamic property (response speed) should be carefully designed to meet specific application demands. So far, there has been an attempt to improve attenuation efficiency of Si VOA by tampering with device designs such as waveguide geometries and electrode configuration .
Furthermore, it appears evident that carrier lifetime is closely associated with attenuation and response speed. Carrier lifetime depends on carrier density, which can be controlled by the injection current. The relation between carrier density and carrier lifetime has been studied for heavily doped Si wafers . In addition, there are several reports on carrier lifetime in Si rib waveguides under reverse bias  as well as under forward bias . However, no study has investigated the relation between carrier lifetime and Si VOA performance with respect to attenuation and response speed.
In this work, we compared the attenuation and response speed of Si p-i-n VOAs with and without implantation of lattice defects into their intrinsic region to investigate relation between carrier lifetime and VOA performance. We measured carrier lifetime of the VOAs under forward bias. We utilized normal incidence of pulsed light to the VOAs for the lifetime measurement. We studied dominant mechanisms governing carrier lifetime against carrier density.
A 4-inch silicon-on-insulator (SOI) wafer was used as a starting substrate. The thicknesses of the top Si layer and buried oxide (BOX) are 200 nm and 3 µm, respectively. Si rib waveguides were defined by e-beam lithography and were transferred by electron cyclotron resonance (ECR) plasma etching. The waveguide core dimensions are 600 nm (width) and 200 nm (thickness), while the slab thickness is 100 nm. To electrically separate adjacent VOAs, we etched the Si slab down to the BOX to form an isolation groove. To couple light from a lensed fiber, adiabatic tapers at the both facets were fabricated with the rib width of 3 µm at the facets. Boron and phosphorous were ion-implanted for n + and p + contacts to make a lateral p-i-n diode. The peak concentration of ion implantation was intended to be ~1020 cm−3. The p-i-n diode has an approximately 4-µm-wide intrinsic region. To activate the implanted impurities, the wafer was annealed at 1000 °C for 60 min in nitrogen ambient. The VOA is overcladded by SiO2 deposited by plasma enhanced chemical vapor deposition (PE-CVD) with thickness ~1 µm. Finally, aluminum was deposited and etched to make electrode pads. The cross-section of the VOA is shown in Fig. 1(a) . To study the effect of short carrier lifetime, we fabricated a VOA with an identical structure but deliberately introduced lattice defects into the intrinsic region. Argon ions were implanted with a dose of 1012 cm−2 at 100 keV, which was followed by annealing at 300°C for 30 minutes, as shown in Fig. 1(b). We refer to the former and latter as “no defects” and “defects” VOAs unless mentioned otherwise. VOA length varied as 0.25, 0.5, 1 mm for the “no defects” VOAs; the “defects” VOAs were 1-mm-long. Figure 1(c) shows an optical microscope image of the fabricated VOAs.
We carried out current-voltage (I-V) measurement at various temperatures in a cryostat chamber to study the energy level of the defect states. The “no defects” VOAs show very low current even at 300 K under reverse bias. Therefore, we could not obtain the temperature dependence i.e., an Arrhenius plot, for them. On the other hand, the “defects” VOA shows temperature dependence in Fig. 2(a) . In Fig. 2(b), we show an Arrhenius plot for estimating the activation energy of the lattice defects implanted in the intrinsic region. The activation energy is approximately 0.5 eV, indicating that the defect implantation created a defect level in the Si band gap.
3. Characterization results
Continuous wave (CW) infrared light with peak wavelength of 1560 nm was guided along the Si rib waveguide to measure optical attenuation as forward current was injected to the VOA. Excessive propagation loss at the p-i-n region was ~2 dB/cm for the “no defects” VOAs and ~4 dB/cm for the “defects” VOA. Since we investigated VOAs shorter than 1 mm in length, extra losses caused by the p-i-n structure and defect implantation is negligible. We calibrated the attenuation to be 0 dB for different VOAs at injection current of 0 mA. Figure 3(a) shows attenuation with respect to injection current of four different VOAs. To give a more quantitative perspective, injection current and attenuation in Fig. 3(a) were normalized by VOA length. The values on the x axis of Fig. 3(b) correspond to current density because the rib core height is identical. To estimate free carrier density, we used Soref’s plasma dispersion relation for silicon as in Eq. (1) . Attenuation due to FCA is expressed asFig. 3(b). Therefore, Fig. 3(b) is a plot of carrier density as a function of injection current density. This graph shows how many free carriers are converted from injection current. As a result, the data points for the “no defects” VOAs lie on the same curve in spite of the different VOA length because the VOA cross-section and the crystal quality of Si rib waveguides are nearly identical. On the other hand, the “defects” VOA shows approximately one degree of magnitude lower attenuation than the “no defects” VOA for the same VOA length. This indicates that the conversion rate from injection current to free carriers is smaller for the “defects” VOA because injected carriers are readily recombined at the lattice defects.
3.2 Frequency response
To evaluate the response speed of the VOAs, the frequency responses of the VOAs was measured using the setup shown in Fig. 4(a) . While CW light of 1560 nm is guided through Si VOA at various injection currents, sinuous signals modulate the VOA. The signal was launched at 0 dBm of power with 50-Ω impedance matching. For 50-Ω impedance matching between VOAs and RF cables, resistors for which resistance sums with VOAs are nearly 50 Ω, were connected to micro-probe near the VOA. Output optical signals through the VOA chips were converted to electrical signal at the O-E converter and were collected by a network analyzer (Agilent E5071C). We varied the injection current from 1 to 150 mA. However, frequency response cannot be obtained when attenuation at the VOAs exceeds 30 dB because output optical signal is too small. This corresponds to the maximum detectable injection current of 50, 75, and 100 mA for the “no defect” VOAs with length of 1, 0.5, and 0.25 mm, respectively. The “defect” VOA has no injection current limit for the measurement because of small attenuation. Figure 4(b) shows typical measurement results at injection current of 50 mA.
In Fig. 5 , 3-dB cut-off frequencies are summarized as a function of carrier density. For the “no defects” VOAs, it is difficult to estimate 3-dB cut-off frequencies at low injection current. From I-V curves of the VOAs, we estimated 4 - 10 Ω of device resistances above the threshold voltage of ~0.7 V. However, at low carrier density, in other words, at low injection current (up to ~5 mA), the VOAs have large resistance ranging from 0.1 - 1 kΩ. A fixed resistor was connected to the VOAs to become series resistance of ~50 Ω for impedance matching at high injection current. However, there must be large impedance mismatch at low injection current. As a result, the sweeping voltage range must be wide and thus, the measured speeds must be incorrect. Excluding the large impedance mismatching data, we can extrapolate the 3-dB cut-off frequency to be around 40 MHz at carrier density of 1017 - 1018 cm−3. For the “defects” VOA, 3-dB cut-off frequencies are around 200 MHz at carrier density of 1017 - 1018 cm−3. In this carrier density range, the “defects” VOA shows higher response speed than the “no defects” VOAs. However, the 3-dB cut-off frequency of the “no defects” VOAs becomes larger as carrier density increases above 5×1018 cm−3. These results are further discussed later.
3.3 Measurement of carrier recombination lifetime
To associate the measured performances of VOAs, i.e., attenuation and 3-dB cut-off frequency with carrier lifetime, the carrier lifetime of VOAs at the current injection condition needs to be obtained. For bulk material, FCA transient decay has been used to measure effective carrier lifetime . For Si waveguides, on the other hand, one of the most straightforward methods is to guide 1550-nm light to generate two-photon absorption (TPA) through the waveguides. However, the output optical signal was too low for our VOAs because the p-i-n region was too lossy under forward bias. Instead, we chose to employ normal incidence of a picosecond-pulsed laser with 775-nm wavelength. Because Si has 12,900 cm−1 of absorption coefficient at 775 nm , a 200-nm-thick Si slab would absorb ~20% of the light power. 775 nm of pulse light signal was produced by passing pulse signal from picosecond fiber mode-lock laser (MML) with pulse duration of ~5.5 ps through a second-harmonic generator (SHG). The initial wavelength of the MML is 1550 nm. The SHG consists of periodically poled lithium niobate (PPLN). Single mode fiber (SMF) was positioned above the sample at a distance of 50 µm. The optimal position was found by moving the fiber with a stepping motor to produce maximum peak height. A block diagram of the measurement setup is illustrated in Fig. 6(a) . While varying the injection currents, we obtained pulse responses. Typical peak responses are shown in Fig. 6(b). By fitting the tail of the peak to exponential decay, we derived the lifetime, which corresponds to the carrier recombination lifetime.
The measured carrier lifetimes are plotted in Fig. 7 as a function of carrier density. For the “no defects” VOAs, all the data are on the same curve regardless of VOA lengths. Note that there is lack of data near 1018 cm−3. The reason is that the peak response was extremely small around ~1018 cm−3 in carrier density to compensate for the built-in potential of p-i-n VOAs, and thus we could not estimate the carrier lifetime. In addition, gradual decrease of lifetime is shown at carrier density of over 5×1018 cm−3. Carrier lifetime of the “defects” VOA is ~1 ns, whereas carrier lifetime of the “no defects” VOAs is ~7 ns at carrier density of 1017 - 1018 cm−3.
4.1 Carrier recombination lifetime
Attenuation properties and 3-dB cut-off frequency of Si p-i-n VOAs have been presented as a function of carrier density. Measured carrier lifetime against carrier density has been presented as well. It is quite clear that there is a close relation between VOA performance and carrier lifetime. In this section, the most influential mechanism to determine carrier lifetime with respect to carrier density is discussed.
We begin with the general formula of carrier recombination lifetime (τrec). Recombination lifetime depends on several parameters, such as Schokley-Read-Hall (SRH) recombination τSRH, radiative recombination τrad, and Auger recombination by τAuger. In addition, SRH surface recombination velocity should be taken into account because a surface effect, rather than bulk one becomes critical for submicrometer Si rib waveguides fabricated on SOI substrate. These parameters can be summarized as
For Si, τrad is ignorable. τSRH is proportional to trap density (NT) but independent of carrier density (n). For the “no defects” VOAs, τSRH is 1 µs or larger , and thus the SRH recombination term is ignorable. The Auger recombination is expressed as τAuger = 1/γn 2. Auger recombination coefficient for Si at 300 K is 3.8×10−31 cm6s−1 . In Fig. 7, Auger recombination lifetime against carrier density is shown by a blue dotted line. Surface recombination velocity of SOI BOX/Si interface (Slower) is reported to be 500 - 1800 cm/s . Supper is, on the other hand, definitely larger than Slower due to surface damage from the etching process and the poor interface between the waveguide and PE-CVD SiO2 overclad. Therefore, we ignore surface recombination of the BOX/waveguide (Slower) as well. In fact, we need to take into account a complicate geometrical consideration and carrier diffusion at Si rib waveguides [13,18]. For simplicity, only Supper was considered as a single variable for the WG/overclad interface with SOI slab thickness of H = 200 nm. As a result, effective carrier recombination lifetime for the “no defects” VOAs is associated with Auger recombination and surface recombination at the waveguide/overclad interface. When Supper is 4000 cm/s, the effective carrier lifetime (dashed line in Fig. 7) shows good agreement with measured lifetime. For the “defects” VOA, SRH or multiphonon recombination through lattice defects is expected to be dominant. From Fig. 2(b), the activation energy of lattice defects is ~0.5 eV. This corresponds to half of the band-gap energy of Si. We can assume that the trap level is located at half of the band gap. Furthermore, it is known that τSRH ≈τn + τp = vth −1 NT −1(σn −1 + σp −1) at high carrier injection, where σn and σp are capture cross-sections of electrons and holes and vth is average thermal velocity . Substituting the values found in , NT for the “defects” VOA is estimated as 4×1017 cm−3. This value corresponds to the effective density of electrically active traps.
The assessment above strongly suggests that carrier lifetime for Si VOAs without defect implantation is determined by the sum of 1) surface recombination at the WG/overclad interface and 2) Auger recombination. In particular, Auger recombination becomes prominent at high carrier density of over 5×1018 cm−3, which leads to reduced lifetime. On the other hand, in Si VOAs with defect implantation, carrier lifetime is mainly determined by SRH bulk recombination, which is independent of carrier density.
4.2 Influence of carrier recombination lifetime on VOA performances
First, we discuss attenuation of optical power, which is the main function of VOAs. In particular, attenuation efficiency in dB/mA is a useful criterion for evaluating the performance of VOAs because it is closely related to their power consumption. To see the relation between carrier lifetime and attenuation efficiency, we considered effective carrier lifetime, τrec :Eq. (1), and thus attenuation efficiency is linearly proportional to carrier lifetime. Figure 8 plots attenuation efficiency as a function of carrier lifetime. The data points well fit the line with the slope = 1. This graph supports the theoretical prediction. Attenuation efficiency of the “no defects” VOAs is almost one order of magnitude larger than that of the “defects” VOA for the same length in proportion to carrier lifetime. The carrier lifetime of our VOAs, particularly the “no defects” ones are mainly determined by surface recombination at the waveguide/overclad interface. Therefore, we should reduce surface recombination centers in Si waveguides to increase attenuation efficiency. One solution is to minimize surface damage from the etching process.
Second, we discuss the effect of carrier lifetime on VOA’s speed. In Fig. 5, the 3-dB cut-off frequency of the “defects” VOA is ~200 MHz as carrier lifetime is ~1 ns. In contrast, that of the “no defects” VOAs is ~40 MHz as carrier lifetime is ~7 ns. Another important phenomenon for the “no defects” VOAs is that the 3-dB cut-off frequency begins to rise at carrier density larger than 5×1018 cm−3, which matches the point where carrier lifetime begins to decrease via Auger recombination. In other words, response speed increases as carrier lifetime become short and vice versa.
Thus, we found that there is a trade-off relation between attenuation efficiency and response speed at a given carrier lifetime. In this work, carrier lifetime depends on the density of lattice defects and carrier density which depends on injection current and VOA length. Therefore, it is important to determine those parameters according to application specifications. For instance, an attenuation range of 10 - 20 dB and response speed of ~10 ns are required for level control of burst-mode signals in 10 Gbps WDM-PONs [11,22]. To meet these requirements, at least 100 MHz in 3-dB cut-off frequency is necessary. For the “no defects” VOA, it is relatively easy to achieve a large attenuation range, but carrier density should exceed 5×1018 cm−3 in order to achieve over 100 MHz of speed. For that purpose, VOA length even smaller than 0.25 mm is needed. More variations of the samples are necessary to find the optimum device design for the application. For the “defects” VOA, we implanted an extremely high density of defects in this work. Owing to that, fast speed of ~200 MHz could be achieved. However, attenuation is insufficient. Possibly, a moderate dose and elaborate post-annealing would offer 10-20 dB of attenuation range. From a technical viewpoint, we believe that the introduction of lattice defects to VOAs is an effective way to increase response speed.
We fabricated and characterized two types of VOAs based on submicron Si rib waveguides. One contains the intrinsic region of p-i-n VOAs with lattice defects by ion-implantation while the other does not. Carrier recombination lifetime was measured under forward bias and its influence on attenuation and speed of VOA was investigated by using normal incidence of pulsed laser at 775 nm on the intrinsic layer of p-i-n diodes. For the VOA without defects, carrier lifetime is dominated by surface recombination at waveguide/overclad interface at low injection while Auger recombination becomes dominant at high injection. For the VOA with intentional defects implantation, SRH bulk recombination is dominant. There is a trade-off relation between attenuation efficiency and response speed at a give carrier lifetime. Ultimately, VOAs with sufficient attenuation and fast speed can be achieved with moderate defect implantation.
The authors are very grateful to Dr. Yukinori Ono of NTT Basic Research Laboratories for helping with the low-temperature I-V measurement.
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