1. Introduction

Nano-photonic devices fabricated from silicon-on-insulator (SOI) substrates are nowadays employed for a multitude of applications in telecommunication [1,2] and integrated optics. The strong confinement of light in nano-scale waveguides due to the large refractive index contrast between silicon and the underlying substrate is the driving principle behind the interest in silicon photonics because densely packed photonic structures can be realized on a CMOS compatible platform. While strong confinement enables small device footprint, it also provides strong field enhancement within the waveguide which allows for the observation of optical nonlinear phenomena even at moderate optical input powers [3–5]. Among the various non-linear phenomena two-photon absorption (TPA) plays a dominant role because of the (often unwanted) generation of free carriers [4]. Besides providing free-carrier induced dispersion (FCD) [5], TPA also leads to free-carrier absorption (FCA) [6], which limits the power handling capabilities of nano-photonic waveguides. Furthermore, the performance of optical resonators will eventually be limited by FCA in addition to thermo-optically induced instabilities [7–9].

Considerable effort has been devoted to schemes to reduce the life-time of the generated carriers, allowing for faster operation of optical devices based on FCD or faster decay of generated carriers. Among the various schemes are approaches based on carrier depletion [10–14], as well as material modification through ion implantation [15] or chemical recipes to reduce the effects of surface states [16]. Even though it is known that the carrier lifetime is dependent on temperature and enhanced carrier lifetimes have been observed at elevated temperatures [17–20], the properties of FCG have not been investigated in the cryogenic regime, where one would expect the opposite effect.

In this article we show that carrier dynamics are strongly affected by the operation temperature of the photonic circuit. We investigate the dynamics between carrier induced dispersion and carrier induced heating at temperatures from 1.8K to room temperature in a time-domain framework. We find that the underlying carrier lifetime is reduced from 1.9ns at room temperature to less than 50ps below 5K. The reduction in carrier lifetime is accompanied by a prolonged thermo-optical interaction. Thus the time-domain excitation technique presented in [17] is not required to thermo-optically stabilized micro-photonic devices in a cryogenic environment. Our results represent the first study of thermo-optical non-linearities in silicon nano-photonic structures at temperatures below 77K and provide a viable route to achieve ultra-short carrier lifetimes in integrated optical devices.

2. Device fabrication and experimental setup

In order to measure the time-domain response of the silicon micro-ring resonators we investigated integrated photonic chips employing silicon strip waveguides. The fabricated samples are mounted in a liquid helium cryostat which allows for temperature control down to 1.8K. Optical access to the samples is provided by optical fibers fed through the top of the Dewar as illustrated schematically in Fig. 1a ). A feedback controlled heater mounted in the sample chamber allows us to regulate the substrate temperature over a wide range.

 

Fig. 1 a) The cryogenic time-domain measurement setup. The device under test (DUT) is mounted inside a liquid helium cryostat, temperature controllable through a heater stage. Light from a tunable laser source is guided to the sample through optical fibers. Using an optical modulator combined with a pulse generator, the DUT can be read out in the time domain in a wavelength tunable fashion. Two cascaded fiber amplifiers are used to boost the pulse power up by 54dB. b) The measured transmission spectrum for a fabricated sample at room temperature. The best extinction ratio is approaching 30dB at an optical quality factor of 26,000. Inset: An optical micrograph of a typical fabricated device.

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We fabricate nano-photonic circuitry from standard silicon-on-insulator (SOI) substrates with an 110nm thin silicon layer and a 3μm thick buried oxide layer. Optical waveguides and ring resonators are defined by electron beam lithography and subsequent reactive ion etching in inductively coupled chlorine chemistry. A typical fabricated device is presented in the inset of Fig. 1b), showing the input grating couplers connected by a nano-photonic waveguide, which is coupled to a silicon micro-ring resonator.

The optical properties of the nano-photonic circuits are investigated through optical transmission measurements and the time-domain measurement platform described in detail in [17] as shown in Fig. 1a). A wavelength tunable laser (Santec TSL-210) is fed through an optical modulator driven by an electrical pulse generator (HP 8131A). The pulse generator allows us to select the pulse width, while the central pulse wavelength can be adjusted by tuning the input wavelength of the TSL. In addition, the pulse period can be varied from a nano-second to milli-second range, which allows us to control the duty cyle of the pulse train. In order to boost up the pulse amplitude the modulated signal is sent through two cascaded fiber amplifiers, which provide a total gain of 54dB.

The duty cycle of the generated pulses is kept low in order to allow the device to reach thermo-optical equilibrium after the pulse has passed. In addition, a low duty cycle reduces the amount of heat introduced into the cryostat during the measurements.

3. Measurement results

We determine the optical properties of fabricated devices at room temperature to select suitable circuits for subsequent cooldown. Here we consider optical ring resonators with a radius of 40μm coupled to a feeding waveguide as shown in the inset of Fig. 1b). The waveguides are 500nm wide and the gap between the ring and the input waveguide is set to 250nm to achieve near critical coupling. From the transmission spectrum in Fig. 1b) we find a best extinction ratio of almost 30dB, while the optical quality factor determined from fitting the resonance dip with a Lorentzian is 26,000. The sample is subsequently mounted in the cryostat and cooled to a base temperature of 1.8K.

3.1 The thermo-optical resonance shift

Because the input wavelength of the pulsed source needs to be tuned closely to one of the resonance dips at any given temperature we first monitor the drift of the resonance wavelength when the working temperature is reduced. Since the refractive index of the sample material is dependent on the operation temperature, the effective mode index of the resonance and thus resonance condition is dependent on temperature as well. When reducing the base temperature from room temperature to the cryogenic limit of the cryostat we observe a total wavelength shift of 9.5nm while keeping the optical power constant. The wavelength shift then converts to a thermo-optical coefficient for the effective mode index of ~32pm/K under steady-state conditions in most of the temperature range.

In order to examine the time-domain thermo-optical properties of the selected ring resonator we compare the resonator dynamics when the pulse wavelength is slightly blue-detuned from the resonance wavelength. As explained in our previous work and the introduction, two competing mechanisms determine the value of the ring resonance for a given input power: the generation of free-carriers due to TPA provides a reduction of the refractive index of silicon, while the generation of heat due to absorption increases the refractive index through the thermo-optical effect. The two processes occur on different time-scales and can thus be differentiated in a time-domain measurement as shown in Fig. 2 .

 

Fig. 2 a) The resonance dynamics of the ring resonator at liquid nitrogen temperature. Shown is the pulse profile of a slightly blue detuned pump wavelength in dependence of input power (amplifier current ranging from 650mA to 900mA, bottom to top). When the output power is increased, the thermo-optical effect is increases leading to a pronounced thermal shift of the ring resonance during the pulse. The spike at the initial position of the pulse is due to carrier generated absorption and FCD. b) The influence of thermal heating on device transmission in the temperature range from 5K to 293K, taken at 700mA amplifier current. When the temperature is decreased, the thermal heating effect slows down, leading to a slower shift of the resonance during the pulse duration. c) The measured thermo-optical rise time shifting the resonance out of the pulse wavelength.

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The detuning of the resonance wavelength in dependence of free-carrier density and temperature is governed by the following equation [17]

Here $g_{to}$is the thermo-optical coefficient of silicon and $g_{FC}$is the coefficient describing the free carrier-induced change of the refractive index n of silicon. $\mathrm{\Delta }{\omega }_i$is the initial detuning of the driving laser wavelength, with respect to the ring resonance. T(t) is the temperature of the resonator and N(t) the carrier density in the waveguide. Because g_to and g_FC have opposite signs the two effects provide resonance shifts in opposite directions. The effects can be differentiated in the time-domain, because the two phenomena occur on sufficiently different time-scales.

We employ pulses of 40ns length with a repetition rate of 1μs (1MHz). The pulse amplitude, i.e. the pulse power is controlled by adjusting the driving current of the fiber amplifiers. In Fig. 2a) we present the measured results for a pump wavelength tuned to the resonance wavelength. The curves are taken for varying input power, where the lowest power is the bottom curve and the highest power is at the top. The initial phase of the pulse is marked by a sharp spike, which results from carrier generated dispersion and subsequent carrier-induced absorption. Due to the blue shift resulting from FCD the resonance wavelength is moved away from the central pulse wavelength and thus the power inside the ring decreases, leading to rapid decay of the carriers. Subsequently, the much slower thermo-optical effect moves the resonance back through the pulse wavelength and thus the output increases as a result of the thermal red-shift. When the input power is increased thermal heating is more pronounced, leading to a faster thermal shift of the resonance during the pulse. By setting the pulse power to a level where the free-carrier dispersion induced resonance shift is minimal (amplifier current of 700mA, second trace from the bottom in Fig. 2a)), we can record the thermal rise time in dependence of temperature. This is illustrated in Fig. 2b), where we show the time-domain profile of the thermo-optical resonance shift in dependence of temperature. It is apparent, that the thermo-optical shift slows down significantly when the sample temperature is reduced.

From the fit of the resonance drift we can extract a thermo-optical “rise time”, yielding a characteristic time scale on which the ring resonance moves away from the pulse wavelength. This is illustrated in Fig. 2c), where we plot the fitted rise time in dependence of temperature. We find that down to the lowest temperature the thermo-optical rise time drops monotonically. This behavior is related to the temperature dependence of the heat capacity of silicon [18,21], which follows a typical Debye model. When the temperature is reduced the heat capacity is reduced, leading to prolonged phonon interaction times and thus slower thermal relaxation. At our base temperature the rise time reaches 133ns. The slow thermal drift of the resonance makes it possible to stabilize the resonance wavelength of the resonator for prolonged periods in the cryogenic regimes. Compared to room-temperature the burst excitation scheme reported previously [17] is not required, because the slow drift allows for pulses 10s of nanoseconds long to remain on resonance.

3.2 Temperature dependence of the free-carrier lifetime

We then determine the carrier lifetime by investigating the initial stage of a time-domain pulse slightly blue detuned from the resonance wavelength. The micro-ring resonator is now excited by 40ns long pulses with a pulse period of 100μs, in order to ensure that the resonator has reached thermal equilibrium before each subsequent pulse.

The resonance wavelength is tuned such that the spike due to free-carrier generation is isolated from the thermal resonance shift, which amounts to a detuning of 10pm. The resonator is pumped with an amplifier current of 700mA, corresponding to a peak pulse amplitude of 1.2mW. As described in [17], the carrier lifetime can be extracted from the decay time-constant of the initial spike. The spike amplitude is reduced from the initial amplitude because of the build-up of free-carriers at the pulse front. After build-up, which happens almost instantaneously, the carriers decay with a characteristic time-constant, which is temperature dependent. While the pulse is travelling through the carrier-active region, the pulse-profile provides a temporal mapping of the spatial carrier profile along the waveguide. The lifetime is then determined from the exponential fit of the decay of the initial spike amplitude.

Results for representative pulses are shown in Fig. 3a ) for stage temperatures ranging from 5K to 45K. When the temperature is low the number of generated carriers is reduced due to thermal freeze-out. As a result, the spike amplitude is also reduced, because the blue shift induced by FCD is smaller. Thus the ring resonance shifts only slightly away from the minimum and the increase in transmission in the through port is less pronounced. When the base temperature is increased, more carriers are generated, leading to a strong resonance shift and subsequently an enhanced pulse height.

 

Fig. 3 a) Zoom into the carrier induced spike during the initial stage of a 40ns pulse. Shown are traces taken at temperatures from 5K to 45K. With increasing temperature the decay time of the pulse increases which is the signature of increased carrier life-times. b) The measured dependence of the free carrier lifetime on temperature. Between 10K and room temperature the lifetime increases almost linearly from 55ps to 1.9ns, while the low temperature lifetime saturates at 43ps.

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By fitting the slope of the decay curve we obtain the carrier lifetime in dependence of temperature as shown in Fig. 3b). At room temperature we find a carrier lifetime of 1.9ns. In the regime down to 5K the carrier lifetime decreases monotonically to 55ps, which is equivalent to similar behavior reported previously above room temperature in [19,20]. We find that below 10K the carrier lifetime reduction slows down to 43ps at 5K and saturates around 40ps below 5K, as shown by the plateau region in Fig. 3b).

The main phenomenon contributing to the reduction of the carrier lifetime at low temperature is likely related to the availability of recombination sites for the photo-generated carriers. Following Shockley–Read–Hall theory, the thermally excited carrier density partially neutralizes existing ionized impurities by increasing the occupation of empty energy states. Therefore, the photo-injected density of free carriers increases with temperature, which consequently increases the plasma recombination emission.

This is directly associated with an increase of free carrier lifetime, as shown in Fig. 3b). Previous measurements using conventional photo-thermal infrared radiometry led to the same conclusion [20] when measured at elevated temperatures. At low temperatures the process works in the opposite direction. Because plasma recombination is reduced at lower temperatures, more recombination sites are available. Therefore the lifetime of the carriers generated by TPA is reduced when the sample temperature is lowered, because the generated carriers can reach a neutralization site more efficiently.

4. Conclusion

In conclusion we have investigated the thermo-optical properties as well as carrier and thermal dynamics of silicon microresonators at cryogenic temperatures. By performing pulsed time-domain measurements of silicon ring resonators we determined the lifetime of free carriers generated by two-photon absorption. The lifetime decreases from 1.9ns at room temperature to below 100ps at liquid Helium temperature. At the same time, the decrease in carrier lifetime is accompanied by an increase in thermo-optical relaxation time. This combination implies that the resonance condition of optical ring resonators is stable for much longer times at low temperatures and thus the resonator is photo-thermally stable on a 10s of nanoseconds timescale, during which the resonance wavelength does not shift significantly with respect to the optical linewidth. Our results represent the first study of the nonlinear optical properties of integrated silicon devices at cryogenic temperatures. Operating silicon nano-photonic devices at low temperatures provides an efficient route to reduce the lifetime of optically generated carriers to ultrashort timescales.