11.2.1 Growth Rate Calibration

The operation of a THz QCL is strongly dependent on the repeatable production of the correct thicknesses of wells and barriers throughout the growth of the active region stack. Figure 11.3 shows the theoretical emission frequency (photon transition energy) as a function of global active region thickness for two different active region designs, a 2.7 THz bound‐to‐continuum design [10] and a 3 THz bound‐to‐continuum with phonon extraction/injection design [12]. Each simulation point (open circles) represents a self‐consistent calculation for commensurate percentage changes in global well and barrier thickness for the two designs. The alignment condition was taken as the field at which anti‐crossing between the upper and injector states occurs, as this resonance characterises a maximum in device conduction. Both designs show that the thickness of each active region should be within ±1% of the design to achieve emission within ±0.05 THz (approx. ±0.25 meV). As the composition of most THz QCL designs comprises >95% GaAs, this is the dominant growth rate to calibrate and monitor. Analysis of the first THz QCL design [18] indicated that the growth rate calibration of the barrier composition alloy, AlAs, affects the optical transition energy less, with a 5–10% calibration window. For barrier layers containing low percentage alloy compositions this is not surprising, however, due to the tunnelling transport nature of the carrier injector scheme in this type of device, this value will be tighter to achieve optimal laser performance [21].

Looking in closer detail at the simulated theoretical variation in design lasing frequency as a function of active region period thickness for the two designs, there are a number of similarities but also differences. Firstly, there is a trend, with active regions thicker than the nominal design to red shift. However, for active regions thinner than the nominal design, the bound‐to‐continuum blue shifts whereas the bound‐to‐continuum with phonon extraction appears to plateau. For the bound‐to‐continuum design there is an approximate linear variation over a 10% change of active region thickness, such that the frequency of the design can be tuned over ∼440 GHz, shifting by ∼44 GHz per percentage change in layer thickness. For the bound‐to‐continuum with phonon extraction design, this linear blue shift is only observed when increasing the layers above their nominal design, again producing ∼40 GHz per percentage change in active region thickness.

Also plotted in Figure 11.3 are twelve and six QCL wafer growths of the two active region designs, respectively (black squares), performed on a Veeco modGenII MBE chamber that includes a set of deliberate variations in global thickness to verify the simulations. The period length of each QCL wafer was determined by high‐resolution X‐ray diffraction, fitting the spacing of the satellite peaks around the [004] lattice reflection with an accuracy of 0.5% [22]. Each wafer was processed into 250 µm wide by 3 mm long ridges using a single plasmon waveguide architecture from the centre location of the grown wafer. The frequency plotted for each wafer is the centre frequency at maximum laser power, measured using a Fourier transform infrared spectrometer with 7.5 GHz resolution. This is when the structure is fully aligned and maximum current is being passed (J_max). Clearly, there is very good agreement between the data from the wafers and the simulations for both the THz QCL designs [23]. A similar tuning trend has also been observed in Ref. [24] for the 2.7 THz bound‐to‐continuum design, demonstrating a 160 GHz reduction in frequency for a +4% increase in Ga growth rate. A similar 110 GHz decrease in frequency shift was observed for a 3% thickness increase for a 2.0 THz bound‐to‐continuum active region design, showing the robustness of this active region design [25].

We have seen the effect systematic scaling of the active region has on the emission frequency of a 2.7 THz bound‐to‐continuum design. This leads us to question what effect this engineering will have on the electrical properties of the laser. Simulations of the electrical properties were modelled [11], suggesting that a thicker structure should have lower alignment fields and a smaller splitting between the injector and upper states. The reduction in both alignment field and magnitude of the anti‐crossing with increased thickness should be observed as a decrease in bias at J_max. The anti‐crossing between the injector and the upper state is related to J_max, because the bottleneck for electron transport is the thickest barrier, known as the injection barrier.

Figure 11.4 shows the experimental results for a series of QCL device growths to test this prediction. A reference wafer (V433) was grown to the published design [10], except that there were only 45 repeats of the active region. Two further wafers were grown with all the wells and barriers 5% thinner (V431) and 5% thicker (V434); the wafer designs were the same as the reference in all other respects. From the electrical data in Figure 11.4(a) we can see that the experimental results are in good agreement with the predictions from the simulations. The thicker structure (V434) reaches maximum power at a lower field and has a lower current at maximum power. We see that the opposite is true for the thinner structure (V431), which has a higher J_max and higher bias at maximum power than the reference (V433). The period lengths for the wafers were obtained by X‐ray diffraction, with this trend being clearly shown in Figure 11.4(c). The frequencies of each design also agree with the simulation data presented in Figure 11.3(a), showing that these devices cover an ∼300 GHz range. Clearly the performance of the laser structures has been affected dramatically by varying the global thicknesses of the layers, suggesting that optimal laser performance is achieved only around the nominal design, reinforcing the stringent growth accuracy required for each layer thickness.

However, this global approach has some merit as a starting methodology to modify a known QCL design in a simple and predictable way to tailor the frequency emission. A similar experimental study was undertaken in Ref. [11] by investigating the effect of globally scaling only the well thicknesses. Scaling by ±5% the wells of the 2.7 THz bound‐to‐continuum design resulted in a commensurate frequency tuning response; a longer structure having larger wells having a lower frequency, achieving again a frequency span of ∼400 GHz. This should not be surprising considering that the majority of the active region thickness in a bound‐to‐continuum design is made up of wells. The effect on transport was as predicted, but not as extreme. Whilst the trend in J_max was consistent, the absolute difference between the three wafers in Figure 11.4(a) was significantly reduced. Again, this should not be too surprising as the absolute barrier thickness of these devices has not changed and one naively expects that the barriers will have more effect on the transport characteristics. The thinner structure still showed very poor lasing performance, however the thicker structure outperformed the original design in both higher light output power, maximum temperature of operation and a lower threshold current.

This methodology was used to produce a series of THz QCL designs between 2.6 and 3.0 THz, operating with the same alignment electric field and matched maximum operating current (i.e. maximum light output); this was done by scaling the wells of the QCL design in Ref. [10] to achieve the desired emission frequency and then modifying the thickness of the barrier layers to harmonise the maximum operating current [11]. Two matched designs were then incorporated into a single broad gain heterogeneous structure [26]. The dual stack heterogeneous QCL wafer demonstrated in a single plasmon waveguide simultaneously two frequency emissions at 2.6 and 2.9 THz and in a metal–metal waveguide continuous lasing over a ∼400 GHz bandwidth [27]. An alternative heterogeneous scheme incorporated 23 laser stacks of the 2.7 THz bound‐to‐continuum QCL that stepwise reduced the Ga growth rate from +6 to −4% of the nominal growth rate for the design. This produced electrically tunable frequency emission over a 330 GHz bandwidth [28].

A similar approach modifying the thickness of the optical transition wells in the short bound‐to‐continuum design with a single quantum well phonon extraction/injection stage [12] achieved QCLs spanning 2.3–3.1 THz, although they operated with different alignment fields and operating current ranges [29]. Three active regions were incorporated into a five‐stack heterogeneous design using a metal–metal waveguide, producing the >1 THz continuous emission from a single device [ 6,30] that is the basis for THz frequency comb lasers [31].

Conventionally, MBE material deposition rates are calibrated in one of two ways, either (i) by ex‐situ measurements of the thickness of calibration layers or (ii) by using in‐situ reflection high‐energy electron diffraction (RHEED) oscillations. To calibrate for the extremely long growth durations needed for THz QCL growth (>12 hours), RHEED is not appropriate as it, (a) cannot measure beyond a few tens of nanometers of layer growth, which can include any initial cell flux transients, and (b) is usually restricted to non‐rotating substrates, so that it may not reflect the true steady‐state growth rates. For THz QCL growth, two calibration approaches have been reported. The first uses the ex‐situ X‐ray diffraction of a simple periodic calibration structure. The respective binary epitaxial layers of the QCL structure are incorporated into a short superlattice (e.g. GaAs/AlAs), which can determine the thicknesses of the individual layers, and hence the respective growth rates. This approach has been used successfully to calibrate both the GaAs/AlGaAs and InGaAs/InAlAs material systems before THz QCL growth [32]. The second calibration approach uses an in‐situ optical measurement, which is desirable as it is a real‐time measurement that is relatively insensitive to any rotation, vibration, wobbling or misalignment of the wafer. Optical thickness measurements [33,34] using a single colour pyrometer (0.94 µm) were used to grow the first THz QCLs and were shown to have a measurement accuracy better than 1% [18]. This has been extended over a wider range of frequencies using pyrometric spectroscopy, which not only facilitates the pre‐growth optical growth rate calibrations, but also allows in‐situ monitoring during the QCL growth [35]. Both growth rate calibration techniques have demonstrated the ±1% accuracy in growth rate needed to ensure optimal growth of the intended design.

11.2.2 Growth Rate Stability

Owing to the extremely long growth durations associated with THz QCL growth, another potential error associated with the epitaxy is any drift from the matrix elements effusion cells (i.e. material depletion and movement). In Section 11.2.1 it was shown that an epitaxial window of ±1% is required to achieve accurate growth of most laser designs. Table 11.1 shows the measured GaAs and AlAs growth rates using single colour optical pyrometry, taken directly before and then after several standard THz QCL growths (∼12–13 µm total thickness), corresponding to an approximate 15‐hour time interval between measurements, for a number of different effusion cells on two different manufacturer's MBE systems. The data is representative of numerous measurements taken from these cells over multiple growth campaigns using a minimum of three optical thickness oscillations for the GaAs and two oscillations for the AlAs calibration layers.

For the five effusion cells used, all the measured growth rate drifts for a standard THz QCL design growth thickness are generally within the 1% margin of accuracy desired. All the effusion cells are standard, commercially available designs for their respective MBE growth systems. The EPI‐Veeco 85 cc dual filament cell includes a low flux transient insert pointing at the centre of the wafer. It is interesting to note that although most measurements show that material depletion dominates (i.e. a negative drift), at the beginning of a growth campaign, material movement for both a fully filled Ga and Al cell can give a positive flux drift. Furthermore, at the end of a growth campaign, cell depletion during growth of a QCL can give rise to downward drifts nearer 2%, especially for the Al cells, which will affect laser performance. For longer growth durations, necessary for thicker active region designs associated with high power lasers or for cells with higher material depletion profiles, an appropriate predetermined temperature ramp can be introduced to compensate for this [35].

11.2.3 Growth Rate Uniformity

Although temporal stability of the matrix element fluxes is a key requirement for the growth of THz QCLs, uniformity of deposition across a growing wafer is equally important. Table 11.2 shows the measured radial uniformity of GaAs and AlAs growth rates using an ex‐situ X‐ray diffraction measurement of a two‐period superlattice structure [36,37], for five different effusion cells on two different manufacturer's MBE systems. The data is representative of numerous measurements taken from these cells over multiple growth campaigns.

For the five effusion cells measured, the radial growth rates show a large variation. For all the Ga cell designs an ∼1% variation is observed within a 2‐inch radius. For the modGENII MBE system, the 400 g SUMO® had a greater variation than the 250 g downward looking (DWL) SUMO®. This is confirmed by the 125 GHz frequency shift in the 2.7 THz bound‐to‐continuum design observed from THz QCL devices processed from the centre of the wafer and the edge grown by the 400 g SUMO Ga cell [23]. Although the VG Semicon VG80H is nominally a 3‐inch growth platform, the above data for the cells used showed that to achieve the required few percent variation window, only 2‐inch substrates could be used for epitaxy of QCLs on this particular system. A greater radial variation was observed for the Al cells, however this is unsurprising due to the tendency of molten Al to wet the pyrolytic boron nitride (PBN) crucible, resulting in a fluctuating, unstable melt front. However, for the current class of GaAs/AlGaAs THz QCLs designs, the flux window for Al is relaxed owing to the low ternary composition in the barriers.

The uniformity of deposition from any effusion cell is dependent not only on the geometry of the MBE system [38], the cell and crucible design [39], but also the evaporation ‘melt’ front of the source material. Consequently, deposition uniformity can vary over the course of an MBE growth campaign, as material depletion alters the area of this evaporating melt front [40]. Using crucible inserts not only reduces flux transients, due to the increased radiation shielding, but allows a constant melt area as seen from the substrate position, even as the melt location recedes [41]. In Ref. [42] the authors show the difference in deposition uniformity when using different effusion sources on a production VG Semicon V90 MBE system. Across a 3‐inch substrate a Ga cell using graphite inserts gave a uniformity <0.2%, whereas a Ga SUMO cell gave <1% variation. In comparison, for Al, a <0.5% variation was seen for a 30 cc conical crucible but this increased to ∼11% for an Al SUMO cell design. However, the SUMO uniformity could be improved by optimising the initial cell fill and the temperature gradient between the cold lip zone and the melt (body), to minimise material creep.

11.2.4 Doping Accuracy

For the epitaxy of III–V semiconductors and particularly the MBE growth of the GaAs and InGaAs material systems, the most common dopants are silicon (n‐type), tin (n), carbon (p‐type) and beryllium (p). Determination of the doping level can be achieved by a variety of methods, however all generally use a set of thick homogeneously doped (volumic doping) epitaxially grown calibration layers. The individual layers are doped in the range spanning 1 × 10¹⁵–5 × 10¹⁸ cm⁻³, with the dopant density measured by either capacitance–voltage (CV) profilometry, secondary ion mass spectrometry (SIMS) or Hall measurements [43]. By far the most reported calibration method for THz QCL growth is ex‐situ Hall measurements [ 18, 32, 35]. At the start of a typical growth campaign, a minimum of six to eight samples are grown to produce a doping calibration curve. Throughout the chamber's growth campaign, additional bulk doped samples are periodically repeated to check the calibration curve's integrity; this is critical for the injection doping levels in the 10¹⁶ cm⁻³ regimes.

Figure 11.5 shows the key laser operating parameters, threshold current density (J_th), maximum current density (J_max) and maximum temperature of operation (T_max) as a function of sheet doping concentration in the active region injector for three different classes of THz QCL design. All designs show similar characteristics; the threshold and maximum lasing currents increase linearly with active region doping and there appears an optimal doping to achieve maximum temperature of operation. These characteristics have also been observed in a 3.45 THz bound‐to‐continuum [45] and a 2.75 THz LO phonon extraction design [46]. Increasing the doping level in the injector has been exploited to produce the highest reported THz output powers [5].

Reference [45] shows that the key influence on this linear increase originates from the increase in losses due to free carrier absorption in the active region. However, Ref. [46] shows that this is not the case for extremely low doped active regions and that waveguide losses become important. Interestingly, the linear relationship between doping and the lasing threshold in all these QCLs designs for any doping level shows that the background impurity level in the MBE system is not yet a limiting factor.