1. Introduction

GaSb/GaAs based quantum dots (QDs) exhibit a type-II (staggered) band alignment [1] and have proved promising in applications such as charge-based memories [2, 3] and solar cells [4–6]. The spatial separation between unbound electrons and confined holes that occurs in these structures modifies significantly the emission properties when compared with their type-I counterparts. Previous time-resolved photoluminescence spectroscopy revealed a strong blue-shift of the emission energy accompanied by a significant reduction of the radiative lifetime at elevated carrier densities [7, 8]. In addition, two-colour pump-probe spectroscopy provided wavelength dependent carrier recombination timescales at room temperature and identified a novel ultrafast feature unique to type-II carrier dynamics [9].

In this paper, we utilise single colour pump-probe spectroscopy to further investigate the absorption and phase dynamics of these structures and reveal the existence of a ∼5 ps timescale that is unique to type-II structures. We numerically analyse the structure and conclude that this timescale is due to the capture of high energy carriers generated by pump-induced multi-photon absorption. By comparing absorption and phase dynamics at different wavelength we conclude that the strength of this component is due to complicated cancellation dynamics that can occur in type-II structures as a result of the strong carrier dependence of emission frequency.

2. Experimental results

The structure comprises 5 layers of GaSb QDs grown on n-type GaAs substrate by molecular beam epitaxy. Each QD layer was formed on a wetting layer (WL) by depositing 2.5 monolayers (MLs) of GaSb with a growth rate of 0.12 ML/s followed by a 25 nm thick GaAs barrier. This multi-layered structure is surrounded by 115 nm thick GaAs cladding layers, 1.25 μm Al_0.3Ga_0.7As p/n doped waveguide layers and finally covered with 100 nm of p-type GaAs. A piece of wafer was processed into 1 mm long semiconductor optical amplifiers (SOA) with a 4 μm wide angled ridge. In order to provide good thermal conductivity the SOA was then attached to a copper heat sink in a manner that allows access from both facet sides to couple and collect the light from the device.

Transmission spectra of the SOA at room temperature for various reverse bias (RB) voltages and the amplified spontaneous emission spectra (ASE) spectra for various forward bias (FB) currents are shown on Figure 1. The transmission spectrum does not display a strong voltage dependence from 0 − 4 V; note however the strong blue-shift in peak ASE over the current range which is typical of type-II based devices and has been attributed to band bending [10], capacitive charging [11,12] and state filling [12,13] effects.

 

Fig. 1 Transmission spectra of SOA for various RB voltages. Inset: ASE spectra for various forward bias currents. The WL transition is expected to occur around 950 nm [9].

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Single colour differential pump-probe spectroscopy was used to measure the room temperature dynamical properties of the SOA [14]. Briefly, in this technique the femtosecond pulses beam from an Optical Parametric Oscillator (OPO) (<300 fs, bandwidth 20 nm) is split into reference, pump and probe beams. After applying a suitable delay between beams and propagating through the SOA, low and high frequency lock-in amplifiers measure the relative change of the probe intensity and phase due to pump-induced gain change. The OPO wavelength was initially set to 1020 nm and moved to 1050 nm for later measurements.

The resulting RB experimental time traces reveal two distinct recovery stages: slow (>100 ps) and fast (<5 ps). As is the case for type-I QD recovery under RB [16, 17], the slow stage fits well with an exponential decay ∼ exp(−t/τ_s), where τ_s reduces exponentially with voltage (see inset of Figure 2) and so we associate the slow timescale with thermalisation and subsequent sweepout of injected holes from confined states. While the type-II timescales are much longer (τ_s ∼ 100 − 300 ps) in comparison to type-I (τ_s ∼ 30 ps − 70 ps) they are shorter than expected for type-II structures [8]. We note that the pump / probe wavelength is shorter than the spontaneous emission peak at low injection and thus we are probing on the high energy side of the inhomogeneous distribution where states have a reduced confinement and thus lower thermalisation time. The proximity of the WL may also reduce the hole confinement and corresponding thermalisation time [15].

 

Fig. 2 Experimental pump-induced gain dynamics and fitting (black) for different RB voltages 0–3 V. Inset: the parameter τ_s and its fitting (black line) to τ_s = τ_s,0exp(−V/V₀) as a function of voltage V with τ_s,0 ≈ 300 ps and V₀ = 3 V.

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To explore the fast range, the gain and phase dynamics over the first 20 ps are shown on Figure 3. In the FB absorption regime (1.5 V, 6 mA), there is conventional behaviour i.e. the pump pulse adds carriers at t=0, there is a sub ps spike due to two photon absorption (TPA) / four wave mixing (FWM), and subsequently a gain increase and phase reduction due to injection of carriers is apparent which slowly returns to the unpumped level. In the RB regime, following the sub ps TPA/FWM spike at t=0, we see a new timescale (3–5 ps) in the gain dynamics that is present for RB voltages from 0–3 V where the timescale does not noticeably change over this voltage range. In the corresponding phase dynamics, this timescale is also present but is much weaker in comparison to the main signal (the main signal being due to direct injection of carriers which also occurs in the FB case)..

 

Fig. 3 Gain (left) and phase (right) dynamics at 1020 nm for a variety of bias levels. Individual time traces have been vertically offset for clarity.

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3. Rate equation model

The fast 3–5 ps timescale involves a sharp gain dropout that cannot be approximated with a simple function and so, to reproduce this behaviour we consider a rate equation model of type-II QDs, originally proposed in [18]. Due to the unconfined nature of the electrons in the QD, the dynamics (and thus the model) is dominated by hole dynamics and involves equations for hole densities in the dot n_d, the 2D WL n_2d, and the GaAs barrier n. These are given by

 

Fig. 4 (left) Schematic of hole processes considered in the model: (1) Single photon absorption (2) Two photon absorption into barrier (3) Capture from barrier to 2D gas (4) Capture from 2D gas to dot (5) Escape from dot to 2D gas (right) Calculated hole dynamics for n_d (0) = 0.5 and n(0) varying from top to bottom as 1, 0.75, 0.5, 0.25, 0.125. Inset: FB case for n_d (0) = 1.0 and n(0) = 0.5.

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Following [18] we assume τ = 10 ns and choose τ_GaAs = 100 ps to reflect the additional possibility of carrier sweepout due to RB. Since we are focusing on the fast dynamics, we neglect any RB dependence of these times as they are too long to influence the fast dynamics. The ps range of the fast recovery defines the range of the capture and escape processes with τ_cap < τ_esc. We set τ_relax = 1 ps, τ_cap = 1 ps and τ_esc = 3 ps.

To account for the influence of RB on the fast dynamics, we note that the main effect of increasing RB will be increasing the sweepout of photogenerated carriers [17]. This effect will be much stronger for holes in the barrier (n) than QD holes (n_d) and so we mimic the effect of RB by reducing the initial value of n while the initial value of n_d constant. We thus neglect the impact that RB has on τ_GaAs as we are interested only in the fast timescales over a small voltage range.

The calculated hole dynamics is shown on Figure 4 (right) and features a very similar timescale as in the experimentally observed gain dynamics on Figure 3 (left). The initial fast drop in n_d relates to the capture and escape times (τ_cap, τ_esc), and its subsequent rise is dependent on photogenerated holes in the barrier being captured to the QD. Larger initial values of n lead to much stronger increases in n_d as expected. As is the case in the experiment when RB is changed, there is no significant change in the fast time scale as the initial value of n varies. The slow timescale of the calculated dynamics is 350 ps for each case. Its relationship with τ_GaAs is explained in Ref. [16] for type-I devices, where a proportionality factor involving τ_cap and τ_esc is derived. A similar relationship can be expected here.

The FB behaviour can also be recovered if we recognise that in FB, the initial hole occupancy of the QD will be greater due primarily to current flowing in the device and consequently there will be increased Pauli blocking of the capture of holes injected in barrier states. This case is represented in the inset of Figure 4 (obtained by initialising n_d to 1.0) and shows that there is no longer a clear 3–5 ps timescale due to this blocking.

While the model provides a mechanism for the 3–5 ps timescale, there are some features of the experimental data that remain unexplained. It is not clear why the 0.3 mA FB gain dynamics looks very similar to transparency while the phase dynamics exhibits a large change. Also, for RB voltages of −1 V and −2 V, after the TPA/FWM spike, the gain reduces below the pre-pump level for a short period. Finally, the fact that the 3–5 ps timescale is almost absent in the phase should be addressed.

These points can be explored if we consider the fast dynamics at an OPO wavelength of 1050 nm (Figure 5). At this wavelength, we no longer have the anomalous transparency-like gain dynamics at 0.3 mA FB. Also, in the gain dynamics, the amplitude of the 3–5 ps component is much weaker than it is at 1020 nm. In the FB phase dynamics, we have conventional behaviour but surprisingly in RB, the 3–5 ps timescale dominates (as it does for the RB gain dynamics at 1020 nm).

 

Fig. 5 Gain (left) and phase (right) dynamics at 1050 nm for a variety of bias levels. Individual time traces have been vertically offset for clarity.

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One possible explanation for the differences between 1020 nm and 1050 nm relates to the 20 nm bandwidth of the OPO pulse. As a result, the pulse may contain spectral components that experience different gain/phase conditions which will average out on detection. This effect was seen in the RB refractive index dynamics for type-I QDs where positive index changes for some spectral components cancelled with negative index changes for other components and resulted in a low to zero average phase change for the pulse [19].

Such cancelling, together with the strong bias dependence of the wavelength of type-II emitters (Figure 1) may account for the low to zero gain change measured at 0.3 mA FB and the reduction below pre-pump levels for RB levels of 1 V and 2 V. This behaviour would be consistent with an absorption spectrum that was changing dynamically with carrier level so that, when measuring close to peak absorption, a shift in the peak would increase the absorption for some wavelengths but decrease for others and thus cancel on average.

This explanation could account for the difference in behaviour when moving to 1050 nm. If we have moved away from peak absorption then different spectral components of the pulse would no longer experience opposite gain changes and cancel. In the case of the phase, we can also have cancelling but it is expected to occur at a different wavelength (here it is 1050 nm) which depends on the energy of the transitions contributing to the phase change. A much more detailed modelling effort is required to investigate the interplay of these effects further.

4. Conclusions

In conclusion, detailed measurements of the ultrafast dynamics of type-II QD based SOAs in FB and RB absorption regimes are presented. A strong 3–5 ps timescale has been identified which is reproduced using a rate equation model and thereby associated with hole recapture by the QD following higher order absorption of part of the pump pulse into barrier layers. Additional cancelling effects are identified in the gain and phase dynamics that are attributed to the strong carrier dependence of emission frequency that is characteristic of type-II structures. These dynamical features are unique to type-II based structures and may provide opportunities for improved ultrafast photonic devices such as monolithic mode locked lasers and semiconductor saturable absorber mirrors.