1. Introduction

Optical detection via defect-enhanced carrier generation in SOI ridge waveguides is now established as a viable method for sub-bandgap optical to electrical conversion [1–3]. In the previously reported work defects are introduced into the waveguide through ion implantation (with or without a post-implantation thermal anneal), which increases the optical absorption for wavelengths around 1550 nm through the (essentially) mid-gap divacancy or interstitial cluster level [4]. Integrated p-i-n diode structures are used to extract the optically generated carriers from the device volume supporting the optical mode, thus allowing for signal detection directly from the waveguide. The degree of absorption may be changed by varying the concentration of defects, and thus the amount of signal that is sampled may be varied from a few per cent to virtually the entire signal. As a result, defect-enhanced photodetectors may be implemented as both in-line power monitors and as end-of-line signal detectors. Their potential advantages over competing technologies rely on the fact that they are fabricated entirely using standard silicon processing methods and do not involve hybrid integration or the hetero-growth of germanium.

The photodetectors reported to date are fabricated in the intrinsic (or low-doped) silicon overlayer of a silicon-on-insulator (SOI) structure, and therefore the influence of background dopant concentration on device performance has not been studied. In the case of carrier generation via the divacancy defect, the background dopant concentration will affect the charge state of the divacancies, which in turn will influence the defect mediated absorption. Evidence consistent with this postulate has been reported previously [5], and has recently been demonstrated using a waveguide geometry [6].

The divacancy has a deep-level situated in the band gap 0.4 eV below the conduction band and as such, light at a wavelength of 1550 nm may cause charge excitation from the valence band or from the deep-level to the conduction band, albeit at significantly different rates [7]. The variation in cross-section for these two processes results in a measurable difference in absorption coefficient as background doping type and concentration is changed, but there is no doping concentration at which the absorption coefficient related to the defect is reduced to zero [6]. In contrast, a deep level which is positioned in the bandgap such that either the valence band to deep-level, or the deep-level to the conduction band transition is greater than 0.8 eV provides an absorption mechanism which may be reduced to a negligible amount via variation of the deep-level charge state. Doping silicon with indium provides just such a deep-level because indium is well known to have a single acceptor level at 157 meV above the valence band [8]. Strong absorption may be expected when in the neutral charge state (through hole generation), but not when the associated level is in the negative charge state (the threshold wavelength equivalent for such a transition is approximately 1320 nm). Of significance, a large shift in absorption in response to a change in defect charge state is potentially relevant to active devices, where the occupancy may be altered by injecting or removing carriers. In this work we present results which confirm the strong variation in absorption of 1550 nm light via indium doping in SOI waveguides through the variation of background n-type doping. We suggest device structures in which such a mechanism may be used to provide broadband, polarization independent variable attenuation and demonstrate that such devices are significantly more efficient than those of equivalent dimension which rely on free carrier absorption effects alone.

2. Background to charge state mediated absorption

A 4 µm optical absorption resonance exists in indium doped silicon [9]. This absorption results from the excitation of an electron from the valence band onto a neutral indium center where it occupies the single negatively charged state lying 157 meV above the valence band. The cross-section for this optically excited transition is approximately 1.7x10⁻¹⁷ cm² for photons with an energy equivalent 1550 nm wavelengths [8]. The excitation of an electron from the indium into the conduction band requires a photon energy of 0.94 eV, and therefore has a negligible optical cross-section for 1550 nm photons. The absorption strength for this wavelength is then proportional to the concentration of neutral (unoccupied) indium, which is dependent on the position of the Fermi level. The absorption coefficient of the 4 µm resonant band for 1550nm can be described as follows:

For indium doping alone, the device is p-type and the indium acceptors are partially occupied (n_t is a fraction of N_t) and the optical absorption for 1550 nm is maximized, as depicted in the left of Fig. 1 . Whereas, for background doping which is n-type the indium acceptors are compensated and thus have an occupation n_t which approaches N_t, which reduces the absorption coefficient.

 

Fig. 1 The band diagram of silicon containing a constant concentration of deep acceptors N_t and varying concentrations of shallow donor levels N_d. Without the presence of shallow donors (left), many deep acceptors are unoccupied (n_t takes its minimum value n_t^min) and therefore electrons are capable of being optically excited from the valence band. Moving to the right, shallow donors are added in increasing concentrations. These donors supply free electrons that are trapped by the vacant deep level acceptors, thus decreasing the number of sites available for electrons to be optically excited into. On the far right, the shallow donor concentration is large enough to completely compensate the deep levels, making the optical excitation process impossible.

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3. Experimental and modelled absorption

Rib waveguides of 4 µm width were fabricated on eleven samples cleaved from 2.5 µm thick silicon overlayer SOI, using a KOH wet etching technique described elsewhere [10]. The etch depth was chosen to ensure the resulting waveguide supported single-mode propagation for 1550 nm light. Windows of varying length L (up to a maximum length of 4 mm), centered on each rib, were defined using 4 µm thick photoresist, and used as a mask during ion implantation of indium at 500 keV for doses varying from 10¹³ to 6x10¹⁴cm⁻². The samples were then cleaned of the resist mask and annealed at 1000 C in dry O₂ for 50 minutes. Eight of the unmasked samples were subsequently ion implanted with phosphorus at an energy of 175 keV at doses ranging from 6x10¹² to 2x10¹⁴cm⁻², and annealed at 1000 C in dry O₂ for a further 150 minutes. These implantation and thermal processes were designed to position the resulting indium and phosphorus concentration profiles coincidently, with a peak concentration at ~1 µm. The concentration of the indium and phosphorus doping at their peak of the profiles are provided in Table 1 .

Table 1. Summary of Measured and Simulated Loss for Fabricated Waveguide Chips

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The unmasked phosphorus implantation contributes to free-carrier absorption over the entire waveguide length W, while the masked indium implant contributes to absorption over the window length L, only. Therefore, the total loss measured for each waveguide has the following form:

Laser light close to 1550 nm in wavelength was coupled into each waveguide through a tapered optical fibre, and the transmitted light collected by an objective lens and focused onto a free-space InGaAs photodetector.

The measured variation in the total loss between waveguides on a single sample is due to the variation in L (the waveguides have constant length W). The value of α_d can be extracted from a fit to the total loss vs. L, examples of which are shown in Fig. 2 . The summary of variation in indium and phosphorus doping for each sample and the measured α_d is provided in Table 1 and plotted as Fig. 3 .

 

Fig. 2 Example plots of total loss measured for each waveguide for the chip with indium implanted at a dose of 6x10¹⁴cm⁻², while the various phosphorus doses are also indicated. A fit to the data using Eq. (2) provides the excess loss due to the indium doping, α_d (the slope of the line, which is observed to decrease with increasing phosphorus dose).

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Fig. 3 Extracted values of α_d vs. peak phosphorus concentration for all samples with indium implanted to a dose of 6x10¹³ cm⁻² (black squares) and 6x10¹⁴ cm⁻² (white triangles), illustrating the significant decrease of α_d resulting from co-doping with phosphorus. The solid lines are fits to the data derived from Eqs. (1) and (3).

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The modelled excess optical loss due to the presence of indium doping is shown in the far right column of Table 1. Using the implantation conditions given above the dopant concentration profiles were simulated using the software code ATHENA [11]. The optical cross-section for excitation of an electron from the valence band to the unoccupied indium level, σ_p^opt, was assumed to be 1.7x10⁻¹⁷ cm² [8]. The optical mode profile Φ(x,y) was obtained from commercial Beam Propagation software [12].

The indium occupation n_t(x, y) was calculated by assuming 100% activation of phosphorus (with a concentration N_d), and numerically solving

For example, the calculated n_t/N_t is plotted in Fig. 4 for N_t = 10¹⁷ cm⁻³ and 10¹⁸ cm⁻³ for varying values of N_d.

 

Fig. 4 Occupation fraction of indium vs. donor concentration N_d for N_t = 10¹⁷ cm⁻³ and 10¹⁸ cm⁻³.

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The results in Table 1 indicate that the variation in occupation of the indium dopant caused by the presence of shallow donor atoms manifests as a variation in optical absorption. We note that while the largest indium implantation dose would be expected to produce a peak indium concentration of 6x10¹⁸ cm⁻³, and therefore an absorption in the region of 130 dB/cm, the activated indium concentration is limited by the solid solubility of indium in silicon. This solid solubility has been determined previously to be 1.4 – 1.5x10¹⁸ cm⁻³, for an activation temperature of 1000 C which limits the accessible absorption [14,15]. This effect has been taken into account also in the modelling. Implicit is that indium which is not activated does not support electronic excitation.

The modelling also takes into account the decrease of free-carrier absorption within the implantation window as a consequence of electron trapping by indium centers. This is manifest as an added component to Eq. (1) that in certain cases causes α_d to take on apparent negative values, as shown in the far-right column of Table 1. A revision to Eq. (1) accounting for this effect yields:

4. Potential designs for a modulator structure

It is of interest to consider how the phenomenon described in sections II and III (specifically for the case of indium doping) might be used to produce a modulation effect in a silicon waveguide. It is envisaged that a modulator may function by varying n_t (the number of occupied indium acceptors) over a large range to vary α_d as described in Eq. (1). For example, if a concentration of indium centres, N_t, is introduced into a waveguide with negligible background doping, n_t will be a small fraction of N_t (controlled by the electrical activation of indium) and α_d will be a maximum. Subsequent application of an electric field to the waveguide would then cause a depletion effect with the result that holes would be emitted from the indium centres, increasing n_t and decreasing the absorption to a minimum level. Alternatively, if N_t indium centers are introduced into a waveguide which is co-doped with shallow donors (such as phosphorus atoms) to a concentration of N_d, such that N_d ≥ N_t, the indium dopant will be fully compensated with the result that n_t = N_t (as in Fig. 3) so that minimum absorption occurs. An application of a forward bias causes n_t to decrease and thereby enhance absorption. Investigation of these two alternative device designs is the focus of the remainder of this paper. Each design is subsequently referred to as the depletion or injection methods.

Simulations were performed using the commercial software ATLAS [11]. A silicon waveguide structure shown schematically in Fig. 5 was described in the Deckbuild environment and electronic levels, having the characteristics of the indium center, were added into the entire overlayer region of the SOI. The structure was subsequently modelled for electrical performance using ATLAS. For each bias condition, the two-dimensional profile of the ionized acceptor trap density, n_t(x, y), was determined. The normalized optical mode profile Φ(x,y), obtained from the waveguide propagation simulator BeamPROP, was used to calculate the overlap integral of Eq. (1). As a result, it was possible to acquire α_d as a function of electrical bias applied to the device. In addition, free carrier concentration distributions were simulated and used to calculate their absorption contribution. This was also incorporated into a transient simulation, whereby the total absorption was computed at various time intervals following bias application in order to determine the bandwidth of the device.

 

Fig. 5 Cross-sectional view of the device modelled in this study, described previously by Geis et al. The p + and n + regions correspond to doping levels of 10¹⁸ cm⁻³, and the p + + and n + + correspond to doping levels of 10¹⁹ cm⁻³ [2].

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The device used for this study, shown in Fig. 5, utilises a sub-micron sized structure used previously, for example, to form waveguide photodetectors as described by Geis et al. [2]. Both contact regions are in close proximity to the optical mode, which is beneficial in that any carrier depleted volume or injected hole distribution overlaps strongly with the optical mode.

Depletion Method: A limitation of the depletion method when applied to the device structure shown in Fig. 5 is that it is restricted to relatively small values of indium concentration, N_t. The use of high concentrations of indium severely limits the volume of the waveguide that could be depleted. For instance, α_d increases with N_t at a rate given by Eq. (1), but the bias required to achieve n_t = N_t increases also. To demonstrate this effect Fig. 6 plots simulated optical absorption as a function of reverse bias for two values of N_t. The achievable modulation depth is limited to ~5 dB/cm for a relatively large bias of −20 V, while it is difficult to achieve zero loss using the depletion method, even for N_t = 2x10¹⁷cm⁻³. Although the large insertion loss and limited modulation depth limits its applicability, this ‘normally off’ device can provide substantially reduced power consumption over traditional optical modulators, particularly in the case of multiple channel devices where the majority of the channels are required to be in the ‘off’ state for a given time interval.

 

Fig. 6 Absorption coefficient α_d plotted as a function of applied reverse bias, for two uniform indium concentrations, N_{t .}

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A transient study was also performed using the depletion method. For the case of N_t = 2x10¹⁷ cm⁻³ the results are shown in Fig. 7 . The turn-on time is 0.6 ns, and becomes larger as N_t is increased. The turn-off time is 0.3 ns, and was found to be independent of the value of N_t (for the two values in Fig. 6). There is no significant impact of the magnitude of the reverse bias on the turn-on and turn-off times.

 

Fig. 7 Simulated absorption coefficient following the application of a −20 V bias, and following the removal of the bias after 10 ns.

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Injection Method: Relative to the depletion method, the modulation achievable via carrier injection is considerable. The ability of ionized acceptors to decrease n_t via hole capture is largely dependent on the difference between the capture rates for electrons and holes. For indium the capture cross-section of holes (8x10⁻¹⁵ cm²) is much larger than the capture cross-section for electrons (2x10⁻²² cm²) [8]. As a result, the injected holes will be preferentially captured over the injected electrons in a bipolar device. This disparity in carrier trapping rates can be enhanced by placing the p-type contact in a closer proximity to the optical mode than the n-type contact, allowing more holes in the modal volume than electrons. This injection method then can be used as an enhancement to a variable optical attenuator (VOA) which relies on free carrier absorption alone, achieving a significantly larger extinction ratio with a negligible increase in dissipated power.

In the simulation results that follow the value of the n-type background doping N_d of the waveguide were fixed such that N_d = N_t. The extinction ratio of the modulator will increase with increasing N_t. Figure 8 plots this increase as a function of N_t, showing the seemingly unbounded improvement over a modulator without indium and with a background doping concentration of 10¹⁵cm⁻³ (this is equivalent to a device using free-carrier injection alone to achieve modulation). The limit on modulation improvement will in fact be determined by the solid solubility of indium in the silicon waveguide. For larger devices (on the order of 10 μm² cross-section), the large donor concentrations will limit the penetration of holes into the device cross-section.

 

Fig. 8 Simulated α_d following application of 1 V forward bias as a function of N_t = N_d (dotted line: performance of free-carrier absorption alone).

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In practice, N_d is unlikely to be matched to N_t, which may lead to an excess insertion loss. If N_d > N_t, the insertion loss will increase due to free carrier absorption; while if N_t > N_d, the insertion loss will increase due to absorption from uncompensated indium. Since the optical cross-section for indium absorption is approximately double that for absorption of free electrons, it is preferred to overcompensate the background doping such that N_d > N_t, as is the case in the passive loss data described in section III. For example, overcompensating such that N_d = 1.1 x 10¹⁸ cm⁻³ while N_t = 10¹⁸ cm⁻³, an insertion loss of 2.6 dB/cm will be present.

The turn-on and turn-off times for the injection modulator are plotted as a function of N_t = N_d in Fig. 9 . The horizontal lines indicate the turn-on and turn-off times for a device containing no indium and again represents the performance of a device relying on free-carrier absorption alone. It is possible to improve the turn-on time (t_on) by applying a reverse bias rather than a zero bias to switch to the non-absorbing state. However, this decreases the modulation depth because the electric fields not only sweep out free-carriers but also decrease the indium occupancy. Regardless, t_on cannot be reduced below t_off, which is related to the capture and emission rate of free carriers at the indium centers and represents the fundamental limit in the speed of these devices. Compared to the case of free carrier absorption alone then, the modulation bandwidth is degraded by the introduction of indium. We note though that for indium doping levels < 3x10¹⁷cm⁻³ the speed of the device remains close to 1 GHz.

 

Fig. 9 Turn-off time (t_off) and turn-on time (t_on) plotted as a function of N_t = N_d, showing the decrease in device speed concurrent with the increase in absorption.

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The Extinction Ratio vs. Dissipated Power for two indium doping concentrations, one having N_t = N_d = 10¹⁸ cm⁻³ and a second having N_t = N_d = 10¹⁷ cm⁻³, is plotted as Fig. 10 , together with that for a device without enhancement from indium absorption.

 

Fig. 10 Extinction ratio vs. Power (both normalized to length) for the enhanced VOA for two levels of indium doping, plotted with the performance of an undoped device operating solely by free-carrier absorption.

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At N_t = N_d = 10¹⁷ cm⁻³, the enhancement in modulation relative to the undoped device is such that the addition of indium barely compensates for the degradation in absorption from free holes. For N_t = N_d = 10¹⁸ cm⁻³, the increase in absorption is however significant. For example, a device of 1 mm in length would require 40 mW of power to achieve an extinction ratio of 10 dB. Alternatively, a 1 mm VOA using only free-carrier absorption would require approximately 400 mW to achieve a 10 dB extinction ratio.

Assuming the device is sufficiently small, the limiting factor on both extinction ratio and speed is the deep level characteristics, specifically the optical cross-section for excitation of electrons from the valence band to the defect level, σ_p^opt, and the relative capture cross-sections of electrons and holes at the defect level. For instance, the larger the difference in hole and electron cross-sections, the more effective the current injection for changing the occupancy. The speed of the device could be increased by selecting a defect level with larger capture cross-sections of both electrons and holes, while maintaining a significant superiority of holes over electrons for the reasons outlined above.

5. Conclusion

We have investigated the effects of doping type and concentration on the absorption of deep level defects in silicon waveguides using the indium center as an example. The dependence has been shown to be correlated with the defect occupancy, which in turn depends on the location of the Fermi level, and can be changed by depleting or injecting a device with charge carriers. This presents a novel means for fabricating a “normally off” VOA device or enhancing more traditional forms of carrier injection VOA operation. We have shown that both the speed and modulation depth of a sub-micron cross-sectional device depends primarily on the defect characteristics.