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Abstract
We report on our study of optical losses due to sub-band-gap absorption in AlGaAs-on-Insulator photonic nano-waveguides. Via numerical simulations and optical pump-probe measurements, we find that there is significant free carrier capture and release by defect states. Our measurements of the absorption of these defects point to the prevalence of the well-studied EL2 defect, which forms near oxidized (Al)GaAs surfaces. We couple our experimental data with numerical and analytical models to extract important parameters related to surface states, namely the coefficients of absorption, surface trap density and free carrier lifetime.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Integrated non-linear photonic waveguides have become a popular platform for achieving several promising functionalities. Through tight confinement of light in precision-engineered waveguide structures, strong light-matter interaction is possible, enabling a myriad of on-chip photonic devices [1–3]. Among the emerging technologies based on planar non-linear photonic waveguides is the generation of optical frequency combs in micro-resonators [4]. This technology utilizes the resonant enhancement of optical intensity in dispersion-engineered waveguides to convert light from a single-wavelength, continuous-wave laser into a frequency comb by cascaded Four-wave Mixing [5].
The efficiency of such non-linear conversion of optical frequencies is proportional to the non-linear index ${n_2}$ of the waveguide material and the degree of spatial and spectral confinement of light, which are quantified by the effective mode area ${A_{\textrm{eff}}}$ and quality factor $Q$, respectively. Therefore, optical materials that possess high refractive index and high non-linear index are prime candidates for building non-linear photonic waveguides. For that reason, interest in III-V-based non-linear photonics has been increasing, and frequency comb generation has been demonstrated in aluminum gallium arsenide (AlGaAs) and gallium phosphide (GaP) with very low threshold power [6,7]. In these devices, the III-V material is embedded in a low-index dielectric cladding using wafer bonding technology, providing very tight confinement of light with sub-square-micron values for ${A_{\textrm{eff}}}$[8]. In the alloy semiconductor AlxGa1-xAs, choosing the mole fraction allows tuning the material band-gap at a value just above twice the optical frequency of the application, thereby providing very high non-linear index ${n_2}$ while eliminating bulk two-photon absorption [9].
In parallel with research on III-V-based photonics, there has also been interest in III-V-based electronic devices owing to the high carrier mobility possessed by compounds such as GaAs. The biggest hurdle III-V-based electronic devices must overcome is the active nature of III-V-insulator interfaces [10,11]. To overcome this hurdle, intensive research has revealed the characteristics of surface states in III-V-insulator interfaces including their origin, density, chemical nature and charging character [11–14]. These investigations paved the way to achieving effective surface passivation techniques [15–18].
In photonic devices, mid-gap states at III-V surfaces and interfaces can interact with light by absorbing photons, resulting in free carrier emission [19]. Furthermore, they dominate free carrier recombination in nanostructures that have high surface to volume ratio [20]. Therefore, since surface states emit free carriers and determine their lifetime, they also affect optical non-linear losses. In addition, when deep level defects capture carriers from the energy bands, the carrier relaxation transfers energy from the defect center to the crystal lattice [21]. The resulting heat is proportional to the rate of free carrier capture by deep traps and is therefore non-linear with optical power. Since a large thermo-optic effect in micro-resonators makes soliton frequency comb generation much more difficult [22], the active role of surface deep levels may explain why it has not been possible so far to generate solitons in a III-V-based device at room temperature [23].
To predict the effect of a semiconductor surface on the properties of photonic waveguides, several surface analysis techniques may be used [24]. These techniques can provide information about the spatial and chemical structure of the surface, the defect species and defect concentration. However, some of the techniques are quite specialized, and they may only provide information on a single flat surface that is normal to the direction of epitaxial growth. While such characterization is adequate for electronic devices, it is not enough to fully characterize a photonic waveguide that includes sidewalls and bends. In addition, a fully optical characterization of surface effects is more available to experimentalists in integrated photonics.
Here we present a study of the effects of surface states on the optical properties of our MOVPE AlGaAs-on-Insulator photonic waveguides (Fig. 1). Depending on the epitaxial growth method and growth conditions, the bulk material may have background doping of, e.g., carbon impurities in MOVPE growth [25]. In all cases, a high density of deep levels at the surface will pin the Fermi level near the deep level and in equilibrium, the waveguide is depleted of free carriers that originate from unintentional crystal doping. Under such equilibrium conditions, the lifetimes of electrons and holes are modified dramatically due to a strong surface field that separates the charges. We show that optically generated free carriers reduce the surface field, making the free carrier decay non-linear in time and density. We use time-resolved pump-probe measurements to study these effects in our AlGaAs-on-Insulator waveguides to determine the rate of optical absorption due to transitions involving deep levels and demonstrate their effect in non-linear free carrier decay.
Fig. 1. Demonstration of the effects of surface deep levels in our MOVPE AlGaAs-on-Insulator photonic waveguides. (a) Without surface traps, the AlGaAs layer contains a high density of free holes caused by carbon impurities. (b) Surface traps deplete the AlGaAs layer of free carriers, causing the energy bands to bend and creating a surface potential ${V_\textrm{s}}$ at equilibrium. (c) Hole emission from surface states can occur by absorbing single photons of energy $\hbar \omega $= 0.8 eV. Emitted holes drift towards the layer interior because of the surface field, slowing down their recapture. ${E_\textrm{C}}$: conduction band minimum, ${E_\textrm{V}}$: valence band maximum, ${E_\textrm{A}}$: acceptor energy level, ${E_\textrm{t}}$: surface trap energy level, ${E_\textrm{F}}$:Fermi energy level.
2. Interface states and Fermi level pinning in AlGaAs-on-Insulator waveguides
2.1 Origin and characteristics of interface states
Clean III-V surfaces are not ideally terminated. Instead, they possess a number of reconstructions that reduce the number of dangling bonds by dimerization of surface atoms [26]. Surface states in such clean, reconstructed GaAs surfaces are outside the bandgap [27]. However, when the reconstructed surface is buried under an oxide layer, its surface state energies may lie within the bandgap [17]. One such state is the antibonding state of As-As dimers, a shallow acceptor level close to the conduction band minimum [17]. More importantly, uncontrolled oxidation of GaAs surfaces creates VIII and IIIV anti-sites, which act as donor-like and acceptor-like traps, respectively [28,29]. Owing to their lower electronegativity, preferable oxidation of group III elements (Ga/Al) results in more VIII anti-site defects [27].
The charging character of interface defects helps explain their capture cross-section for trapping free carriers. The VIII anti-site acts as double donor because it contains five valence electrons, two more than the original group III crystal atom. One such defect, the AsGa anti-site in GaAs, contributes two deep levels: one near mid-gap and the other about 0.5 eV above the valence band maximum [29,30]. Consequently, this defect can trap and emit both electrons and holes, and it exists in neutral, singly- and doubly-ionized states [31]. General estimates of the capture cross-section of Coulomb-attractive, neutral, and Coulomb repulsive deep traps are of the order 10−13, 10−16 and 10−21 cm2, respectively [32].
Although many other defects have been shown to affect the electronic and optical properties of AlGaAs [33], we focus on the native surface defects that occur in large numbers as a result of the surface or interface formation itself, hence dominate in structures having large surface-to-volume ratio.
2.2 Flat-band recombination lifetime
To characterize surface effects by optical measurements, one may measure the rate of free carrier emission or capture at sub-band-gap excitation. The rate of carrier capture by surface states determines the carrier lifetime, which may be measured by probing the change in optical loss after excitation with a pulse. When both the bulk and surface of the waveguide are neutral, the energy bands are flat and carrier recombination only depends on the surface state characteristics. When a net charge exists in the waveguide which is balanced by surface charge, the electrostatic potential affects and may dominate the rate of carrier recombination by sweeping carriers towards or away from the surface. In the following, we use a simple model to describe the recombination rate, which we will use to analyze the experimental data.
We model the waveguide core as an extended one-dimensional layer bounded by two surfaces. We justify this choice by the dominance of the contribution of {100} surfaces (top and bottom waveguide surfaces) to surface states [27]. Using the Shockley-Reed-Hall model of trap-assisted recombination [34], we consider the recombination rate of electron and hole densities $n$ and $p$ at surface traps of density ${N_{\textrm{st}}}$ at the energy level ${E_\textrm{t}}$ above the valence band edge and whose capture cross-sections for electron and hole trapping are ${\sigma _\textrm{n}}$ and ${\sigma _\textrm{p}}$, respectively. Because of the large bandgap of AlGaAs, we can assume $pn \gg n_\textrm{i}^2$, $n \gg {n_1} = {n_\textrm{i}}\exp [{{{({{E_\textrm{t}} - {E_\textrm{i}}} )} / {kT}}} ]$ and $p \gg {p_1} = {n_\textrm{i}}\exp [{{{({{E_\textrm{i}} - {E_\textrm{t}}} )} / {kT}}} ]$ for any significant carrier density. Thus, we can express the recombination rate of electron-hole pairs, in units of cm-3s-1 as:
Recombination of electron-hole pairs via neutral AsGa anti-sites requires capturing a hole first. The positively charged deep level then quickly captures an electron to complete the recombination process. Therefore, when these donor-like defects are the dominant recombination center, the recombination lifetime is determined by the hole capture cross-section through the relation [35]:
In an AlGaAs layer 300 nm thick, using ${\sigma _\textrm{p}}$=10−16 cm2, ${v_{\textrm{th}}}$≈107 cm s-1 and ${N_{\textrm{st}}}$=1013 cm-2 yields ${\tau _0}$≈ 1 ns. It is worth noting that the value used for the surface state density in this example are typical for oxidized (Al)GaAs [36], and yet it corresponds to only 1% of surface atoms contributing surface states.
2.3 AlGaAs waveguide at equilibrium
Although the AlGaAs layer is not intentionally doped, Hall-effect measurements of our MOVPE-grown AlGaAs layer on GaAs, used for this study, have yielded hole concentration of 1016-1017 cm-3. Impurities are incorporated during MOVPE layer growth from the organic precursors of the alloy metals [25]. Known to exist as a substitutional defect at As sites, carbon atoms act as acceptors [37]. Had the measured level of free carrier density been present in the waveguide structure, it would have resulted in linear losses of 2-20 dB cm-1. Since the total linear loss in our waveguides, which includes scattering and bulk absorption in addition to free carrier absorption, was below 2 dB cm-1, we expect a high level of free carrier depletion by interface trapping. A high density of donor-like VIII anti-site defects on the oxidized surface can account for the depletion of holes in the AlGaAs waveguide [38]. Indeed, this crystal defect, which was identified as the physical origin of the EL2 deep center, is known to compensate acceptors in bulk GaAs to provide SI wafers [39]. When the density of EL2 deep centers is larger than the acceptor density, the Fermi level is pinned at the mid-gap level of the defect. In the opposite case, the Fermi level is pinned at the 0.5 eV level. In the latter case, all deep centers are singly ionized and at least a fraction of them is doubly ionized [40].
The compensating surface defect creates a depletion layer whose width, in the Schottky approximation, is given by [38]:
where ${q_\textrm{e}}$ is the elementary charge, ${Q_{\textrm{SC}}}$ is the surface space charge density in cm-2 and ${N_\textrm{A}}$ is the density of bulk acceptors in cm-3. For a semiconductor layer 300 nm thick and dopant density ${N_\textrm{A}}$=1016 cm-3, the minimum surface state density necessary for total depletion is 3 × 1011 cm-2, which corresponds to less than a fraction 10−3 of the surface atom density.We use a semiconductor physics simulation tool to investigate carrier depletion by surface states [41]. The simulation model solves Poisson’s equation and the semiconductor drift-diffusion equations. The semiconductor layer in the model is uniformly doped p-type at concentration of 1016 cm-3, to account for carbon acceptor impurities. The two bounding surfaces contain donor-like traps, which are neutral when occupied by an electron and positively charged when occupied by a hole. The default material parameters for AlGaAs (x = 0.2) at 300 K are used. We restrict recombination to the boundaries, so that in the bulk, only a numerical generation term G, in cm-3s-1, enters. In this model, the carrier densities are governed by the drift-diffusion model [42]:
We swept the value of surface trap density ${N_{\textrm{st}}}$ between 1011 and 1013 cm-2 and the value of trap energy level ${E_\textrm{t}}$ between 0.2 and 0.8 eV. In each simulation, we obtained the equilibrium solution. Each solution contains the energy band diagram, free carrier concentration and surface state occupancy.
We define the degree of free carrier depletion as the ratio of bulk acceptor density ${N_\textrm{A}}$ to the average free hole density $\bar{p}: = {1 / d}\int_d {p(x)\textrm{d}x}$, at equilibrium. Figure 2 shows the simulation results. It is evident from the simulation results that deep traps deplete the semiconductor of free carriers very effectively, even at moderate surface trap densities.
Fig. 2. Results of numerical simulation of a one-dimensional semiconductor model of 300 nm thick AlGaAs layer with two bounding surfaces containing donor-like traps. (a) The degree of free hole depletion is defined as the ratio between acceptor density ${N_\textrm{A}}$ and average free hole concentration in the AlGaAs layer at equilibrium, $\bar{p}: = {1 / d}\int_d {p(x)\textrm{d}x}$ and is calculated from the equilibrium solution for varying values of ${N_{\textrm{st}}}$ and ${E_\textrm{t}}$. (b) The surface charge density. The simulation temperature is $T = 300\;\textrm{K}$.
2.4 Band bending and the surface photo-voltage
Due to surface charging by free carrier trapping, there is an electric field pointing towards the center of the semiconductor layer. This surface-induced field can affect the free carrier lifetime significantly [43,44]. The lifetime given in Eq. (2) accounts for free carrier trapping resulting from random thermal motion that is equal in all directions. However, a potential barrier that significantly exceeds the carrier thermal energy between the layer center and boundary modifies the free carrier flux to the surface dramatically. When surface recombination dominates, as it does in our AlGaAs waveguides, this effect of surface charging affects the carrier lifetime significantly.
Under illumination, generated free carriers by band-to-band or trap-to-band transitions respond to the surface potential by forming a carrier density distribution that reduces the field strength across the semiconductor layer. This sort of carrier relaxation is much faster than recombination [45]. Consequently, the free carrier lifetime becomes dependent on carrier density and significantly different for electrons than holes [46]. We investigate this effect numerically by simulating the semiconductor layer under homogenous and constant electron-hole pair generation, to appreciate the dynamic band-bending under illumination. We note, however, that the presence of surface states can result in uneven generation of electrons and holes. The model solves Poisson’s equation and the semiconductor drift-diffusion equations as mentioned above, but here the non-equilibrium, steady-state solution is obtained, and the initial conditions are that of the equilibrium solution in the previous subsection. We calculate the carrier lifetime ${\tau _\textrm{N}} = {{\bar{N}} / G}$ at every value of carrier creation rate $G$, which we vary between 1017 and 1027 cm-3 s-1.
The simulation results are plotted in Fig. 3. The results indicate that, at low carrier generation rates, the large surface potential due to the charged surfaces causes the hole lifetime to increase and electron lifetime to decrease by more than two orders of magnitude compared to the ‘flat band’ value ${\tau _0}$ given by Eq. (2). It is only beyond a certain generation rate that the free carrier density in the semiconductor layer becomes big enough to reduce the surface field. At higher generation rates, the electron and hole lifetimes are equal to ${\tau _0}$ since the relaxation of the free carrier density profiles shields the surface field.
Fig. 3. Results of numerical simulation of one-dimensional semiconductor model of 300 nm thick AlGaAs layer with two bounding surfaces containing donor-like traps under constant and homogenous electron-hole pair generation. The steady-state solution for the surface potential ${V_\textrm{s}}$, electron and hole lifetimes, and the average electron and hole carrier density are plotted against bulk generation rate $G$.
For comparison with experimental results, it is useful to obtain an analytical model that allows fitting the data and extracting parameters. To do that, we use the following expression for the dependence of the hole lifetime on the potential barrier height [35,43]:
Fig. 4. Simulation results of (a) steady-state solutions for hole lifetime vs. average carrier density and (b) normalized surface potential vs. normalized generation rate. The simulation results in (a) and (b) are plotted along with analytical models given in Eq. (6) and Eq. (7), respectively.
2.5 Single carrier emission from deep levels
Band-to-band optical transitions in the bulk of AlxGa1-xAs (our samples have 0.17 ≤ x ≤ 0.21) require simultaneous absorption of three photons of wavelength 1550 nm [9]. However, in the presence of surface states within the band-gap, trap-to-band and band-to-trap transitions that require sub-band-gap energy may exist. Because of their abundance and their role in compensating p-type AlGaAs, we postulate that carrier emission from the EL2 defect is dominant. In GaAs, the EL2 center has two energy levels, one near mid-gap and the other 0.5 eV above the valence band maximum. Therefore, the interaction of neutral EL2 centers with 0.8 eV light is limited to electron emission. Singly ionized centers (EL2+) interact with the valence band, where hole emission takes place, reverting the center to its neutral state (EL2°). EL2+ centers exhibit an intra-center absorption line at 0.76 eV, which is caused by an excited state of the electron occupying the 0.5 eV state [40]. Finally, 0.8 eV light excitation from the valence band to the 0.5 eV level takes place in EL22+ centers and in an EL2+ center while its dangling electron is in excited state. In AlxGa1-xAs (0.17 ≤ x ≤ 0.21), the higher electron energy level of EL2° is very close to mid-gap, whereas the lower level is well inside the lower half of the bandgap [47,48].
3. Time-resolved pump-probe non-linear loss measurement
Here we experimentally study the effects of surface states expected from the theoretical and numerical modelling presented in the previous section. Precisely, we measure the rates of sub-band-gap absorption in our AlGaAs waveguides and the decay dynamics of free carriers.
We use time-resolved pump-probe measurements to determine the contributions of single- and two-photon absorption in non-linear loss and free carrier generation in AlGaAs-on-Insulator waveguides and to study the dynamics of free carrier decay.
3.1 Experiment and samples
Our pump-probe experimental setup is schematically illustrated in Fig. 5. As pump source, we use a picosecond laser (Calmar FPL-02LFFCUT11) emitting at 1586 nm with repetition rate of 16 MHz. We use a variable optical attenuator to control the pump power coupled into the sample. The probe light is emitted from a CW laser (Toptica DLC CTL 1550) tuned to a wavelength in the C-band. The pump and probe light are combined in an optical directional coupler before coupling into the chip waveguide by a lensed fiber. The polarization of pump and probe is tuned by fiber polarization controllers and calibrated to match the TE mode of the waveguide. We use a photonic crystal waveguide, on a separate sample, which exhibits TE transmission bandgap, to calibrate the polarization. Output light, collected by a lensed fiber, is passed through a band-pass filter (1 nm) at the probe wavelength. The probe light is then amplified and passed through a similar band-pass filter. A fast photodiode and RF modules (40 GHz) detect the probe signal. In each measurement, the probe signal is averaged by acquiring 700 data sets.
Fig. 5. Schematic of the pump-probe experimental setup used to measure non-linear loss and carrier decay in AlGaAs-on-Insulator waveguides. VOA: variable optical attenuator.
In part of the measurements, the pump laser light is amplified by an L-band EDFA. We measure the pulse width at the lensed fiber input in each case using an autocorrelator (APE PulseCheck). Without amplification, the pulse width ${\tau _{\textrm{pul}}}$(full width at half maximum) is 3 ps, and the maximum coupled pump average power in the waveguide is -9.0 dBm. With amplification, the pulse width is 25 ps and the maximum coupled pump average power in the waveguide is 3.4 dBm.
Figure 6 shows a typical probe transmission trace. Evident from the data is the clear distinction between loss within the duration of the pulse, where absorption due to optical transitions is significant, and after the pulse ($t > {t_0}$), where the loss is caused by free carrier absorption and follows the decay of free carrier density. We define the free carrier loss as the attenuation in probe transmission at $t = {t_0}$ compared to its pre-pulse level.
Fig. 6. Part of a typical probe transmission trace. Beyond $t = {t_0}$, the probe loss is caused by free carrier absorption.
We note that although the waveguide transmission spectrum contains Fabry-Perot oscillations, these oscillations would be limited to some 0.1 dB if caused by free carrier dispersion for carrier densities below 1017 cm-3. A thermo-refractive shift, on the other hand, is much slower than the nano-second timescales we measure.
We performed pump-probe measurements on MOVPE AlGaAs waveguides fabricated by our standard process [8]. During the process, all AlGaAs structure surfaces were exposed to air during processing, before they were finally encapsulated, so a thin layer of native oxide exist between the core and cladding. The cladding material was SiO2 in samples I and II, except for the top and side surfaces of sample II, which were clad by an ALD Al2O3 layer 240 nm thick. This ALD layer enhanced the waveguide power handling so that higher-power measurements could be performed. The enhancement of power handling may be due to the better thermal conductivity of Al2O3. We did not remove the native oxide or chemically passivate the samples. A scheme of the waveguide cross-section and the optical intensity profile of the waveguide mode is given in Fig. 7.
The AlGaAs waveguides under study are 300 nm high, 630 nm wide and 3 mm long. Input and output coupling is achieved by inverse tapers, which consisted of a taper section 300 µm long and a uniform section 200 µm long at the taper final width of 140 nm. The effective area of the TE mode is ${A_{\textrm{eff}}}$≈ 0.2 µm2.
In the following, we attribute all free carrier loss to free holes, since free electron absorption is much smaller except for excited electrons in the X-valley band of AlGaAs [49], and since free hole emission is expected to dominate in p-type samples. The free hole absorption cross section we use is ${\sigma _\textrm{h}}$= 4 × 10−17 cm2.
3.2 Source of free carriers
In this measurement we use pump pulses without amplification to find the source of free carrier generation in Sample I. The probe laser was tuned to 1530 nm. The 3 ps pulses coupled into the waveguide have maximum peak power around 1.6 W. The maximum free carrier density generated by these pulses via three-photon absorption is ${p_{\textrm{3PA}}} = {{\sqrt {{\pi / 2}} {\alpha _3}{\tau _1}({{{\overline {P_0^3} } / {A_{\textrm{eff}}^3}}} )} / {({3\hbar \omega } )}}$ where ${\alpha _3}$ is the coefficient of three-photon absorption, ${\tau _1} = {{{\tau _{\textrm{pul}}}} / {\left( {2\sqrt {2\ln (2)} } \right)}}$, ${P_0}$ is the pump peak power coupled into the waveguide and $\overline {P_0^n} = {1 / L}\int_0^L {P_0^n(z)\textrm{d}z} $ denotes the average over the waveguide length, $L$. Using ${\alpha _3}$≈ 0.08 cm3 GW-2 [9], we find ${p_{\textrm{3PA}}} \sim $ 1014 cm-3. Therefore, free carrier generation by three-photon absorption is negligible at such pump power.
We denote the free carrier absorption loss, measured at $t = {t_0}$, as ${\alpha _{\textrm{fca}}}$, in units of m-1. ${\alpha _{\textrm{fca}}}$ can be expressed in terms of pump peak power in the waveguide through the following relation [50]:
The coefficients ${a_1}$ and ${a_2}$ are used to extract the single-photon absorption coefficient ${\alpha _1}$ and the two-photon absorption coefficient ${\alpha _2}$ by the following relations [50]:
Figure 8 shows the measured free-carrier absorption loss. We plot the quantity ${{{\alpha _{\textrm{fca}}}} / {{P_0}}}$ and fit a model ${{{\alpha _{\textrm{fca}}}} / {{P_0}}} = {a_1} + {a_2}{P_0}$ to the data. The error in the data points of ${{{\alpha _{\textrm{fca}}}} / {{P_0}}}$ are calculated using the root-mean-square of the fluctuations in the measured probe transmission. We also plot the percent loss in probe transmission, which indicates that the bigger uncertainty in the loss measurement occurred when the change in probe transmission was a fraction of a percent.
Fig. 8. Pump-probe measurement results of sample I. The quantity ${{{\alpha _{\textrm{fca}}}} / {{P_0}}}$ is the measured free carrier loss divided by probe peak power in the waveguide, and the fit model is ${{{\alpha _{\textrm{fca}}}} / {{P_0} = {a_1} + {a_2}{P_0}}}$.
The data and fit point to the dominance of single-photon and two-photon free carrier generation within the range of peak power in the measurement. The corresponding coefficients of absorption calculated using the fit parameters ${a_1}$ and ${a_2}$, by Eq. (9), are ${\alpha _1}$= 0.09 ± 0.02 cm-1 and ${\alpha _2}$= 0.98 ± 0.08 cm GW-1.
3.3 Free carrier decay
Here we used amplified pump pulses to characterize free carrier decay in Sample II. The amplified pump pulses caused free carrier loss amounting to more than 60% at $t = {t_0}$. Within the period $t > {t_0}$ of probe transmission, we define the instantaneous free carrier lifetime as:
We calculate the waveguide average of free hole density using the relation [51]:
where ${T_\textrm{p}}(t)$ is the normalized probe transmission, $S$ is the slow-light factor and $\eta$ is the overlap factor of the waveguide mode and core.Figure 9 shows the measurement results. Figure 9(a) shows the carrier density data calculated by Eq. (11) using the measured probe transmission data. We calculate the instantaneous lifetime in Eq. (10) using piecewise linear fits to $\bar{p}(t)$. The result is given in Fig. 9(b), plotted against the carrier density. The measured data indicates that free carrier decay is strongly non-linear, starting at a fast rate and slowing down by more than two orders of magnitude. Figure 9(b) indicates that the lifetime decreases exponentially with carrier density at low density levels but approaches a constant value at high density levels.
Fig. 9. Pump-probe characterization results of free carrier decay in sample II. (a) Average free hole density calculated by Eq. (11) using the measured non-linear loss data. (b) Instantaneous free hole lifetime calculated by Eq. (10) using the free hole density data in (a).
4. Discussion
The measured dependence of free carrier lifetime on carrier density, given in Fig. 9(b), is qualitatively identical to the simulation and analytical models in Fig. 4(a). In other words, both the exponential decrease of lifetime at low carrier density levels and its approaching a constant value at high carrier density levels are marks of surface-dominated recombination and the existence of a high surface potential barrier at equilibrium. Although the simulation and analytical models apply to the stationary state, the readjustment of carrier distribution in response to changes in the surface electric field can be considered instantaneous compared to the time scale in the carrier decay measurement, because of the high carrier mobility and small size of the waveguide structure. Experimental measurement of the dynamics of surface photo-voltage have indeed shown that carrier transport occurs under one picosecond of the optical excitation and the subsequent relaxation within tens of picoseconds at the surface of doped GaAs [45].
We can use our model and experimental data further to extract information about our devices pertaining to background doping and surface states. The high carrier density fit in Fig. 9(b) gives a constant lifetime of 1.2 ns. Using Eq. (2) we find ${N_{\textrm{st}}}$≈ 1012 cm-2. The low carrier density fit ${\tau _\textrm{p}}(\bar{p}) = \exp [{6 - 2{{\bar{p}} / {({{{10}^{16}}\;\textrm{c}{\textrm{m}^{ - 3}}} )}}} ]$ns predicts ${\tau _\textrm{p}}(0)$≈ 400 ns. Using Eq. (6), the equilibrium surface potential follows as ${{{V_\textrm{s}}(0)} / {kT}}$≈ 5.8. We used our simulation model to find the value of the surface potential at varying p-type doping levels. The result, given in Fig. 10, gives an acceptor density of ${N_\textrm{A}}$≈ 1016 cm-3 for this value of surface potential and ${N_{\textrm{st}}}$= 1012 cm-2.
Fig. 10. Simulation results for the magnitude of the surface voltage at varying background acceptor density. The values ${N_{\textrm{st}}}$= 1012 cm-2 and ${E_\textrm{t}}$ = 0.8 eV are used here.
Our investigation of the source of free carrier generation indicates that single-photon and two-photon absorption are dominant up to 1.6 W of optical power. Since we attribute free carrier loss to free holes, hole emission from surface deep levels by absorption of light must account for the measured carrier density. Considering the deep levels associated with the EL2 defect, these surface states can indeed emit holes by absorbing photons of energy 0.8 eV (1550 nm) when they are ionized in EL2+ or EL22+ states (Fig. 11 processes 2 and 4) [30,31]. The trapped holes that originate from p-type impurities make this transition possible.
Fig. 11. Possible origins of single-photon and two-photon carrier generation in AlGaAs involving prominent surface defects at 1550 nm.
Possible origins of two-photon absorption loss, for photon energy less than half the bandgap energy, include band tail states, two-photon excitation from the valence band to an empty trap level (Fig. 11 process 6), and two-step single-photon excitation from the same deep level to both bands (Fig. 11 process 5). In the latter case, a mid-gap level is ionized by emitting an electron to the conduction band followed by emitting a hole by an excitation to the same level from the valence band. Alternatively, an EL2+ level is excited to its intra-center higher electronic state followed by hole emission from the 0.5 eV level before the excited electron relaxes to the ground state (Fig. 11 process 3).
For band tail states to become significant, there must be an extremely high bulk impurity concentration in the AlGaAs layer [52], or significant spontaneous ordering of group III atoms in the crystal [53], both unlikely conditions in our AlGaAs layers. Two-step single-photon electron and hole emission from the same deep level is also unlikely, since it requires the sum of the two photon energies exceed the bandgap energy, or the significant energy deficit be supplied by phonons. Two-photon excitation from the valence band to a shallow center close to the conduction band is more likely. One such center is the As-As dimer, which has an empty anti-bonding electronic state acting as shallow acceptor. However, we could not find measurements or calculations of the strength of this transition in the literature. The most likely scenario is the two-step single-photon excitation within the same EL2+ center, first to the higher electronic state, and then from the valence band to the 0.5 eV state.
Surface state absorption was identified to be a significant contributor to losses in GaAs photonic waveguides by Parrain et al. [54], and in nano-mechanical oscillators by Hamoumi et al. [55]. It was mitigated considerably by surface passivation by Guha et al. [56], who achieved huge enhancement in GaAs micro-disk quality factor as a result of surface passivation, and by Weiqiang et al. [57], who passivated AlGaAs-on-Insulator waveguides with Al2O3. In our study, we expand on these efforts by providing a detailed analysis of surface state absorption and how it affects optical linear and non-linear losses. Using optical transmission measurements only, we measure the loss coefficients and carrier lifetime as a function of carrier density, which are necessary to evaluate the power-dependent loss under CW pumping of a non-linear resonator. We show that surface absorption and band bending are necessary to model III-V nano-waveguides under high optical excitation.
We summarize the effects of surface states on our MOVPE AlGaAs-on-Insulator waveguides in the following. Although surface states deplete the AlGaAs waveguide core of free holes, the surface-induced band bending dramatically increases the free hole lifetime and, consequently, it increases the free hole absorption loss. The use of ultralow doped wafers, such as optimized MBE-grown AlGaAs, will eliminate band bending at equilibrium and ensure that EL2 levels are filled by electrons and, hence, single-photon hole emission becomes not possible (Fig. 11 process 1). In such a pure AlGaAs layer, however, electron emission from EL2° level and other defect-related carrier emission may contribute to non-linear losses. Optimally, the significant reduction of the density of surface states will bring the performance of AlGaAs-on-Insulator waveguides closer to the three-photon absorption limit. Surface passivation that employs ALD of ternary oxides, such as Al2O3, can reduce the density of surface states significantly [15,58], and it can be employed in the fabrication of III-V photonic waveguides.
5. Conclusion
We have presented a study of the effects of surface states on the linear and non-linear losses of AlGaAs-on-Insulator photonic nano-waveguides. Our study includes the interaction of surface states with free holes originating from background doping resulting from MOVPE growth. We have combined analytical and numerical models with experimental pump-probe measurements to find the surface state density, surface potential, surface absorption coefficients and background doping level, and to explain the effect of the surface and background doping on the non-linear decay of free carriers.
Funding
Danmarks Grundforskningsfond (DNRF123); European Research Council (853522).
Acknowledgments
The authors acknowledge the contribution of E. Stassen and Y. Zheng to sample fabrication.
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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