1. Introduction

The lowest frequency limit of a THz laser based on intersubband transitions is still an open question. Quantum Cascade Lasers (QCLs) have been recently demonstrated at 2.1THz (8.6meV), and, by applying a strong external magnetic field, at 1.35THz (5.6meV) [1–5]. At these frequencies, typical intersubband linewidths are ~ 1meV, and start to be comparable with the transition energy. Although in this regime an important role might be played by inversionless Bloch gain, all the same the achievement of population inversion is hampered by the difficulty of obtaining selective electronic injection into the upper laser state [6]. This task is made more demanding by the existence of the in-plane energy continuum characteristic of 2-D subbands, enabling elastic scattering directly into the lower laser level. Irrespective of the specific diffusion mechanism, the scattering rate to the lower subband increases for decreasing transition energies [7].

From a technological and commercial perspective, the realisation of semiconductor lasers operating in the low-end of the far-infrared or Terahertz (THz) frequency spectrum is also highly desirable. In fact the penetration depth of THz radiation through many materials of ordinary use, such as plastic and cloth, substantially increases at lower frequencies. This is crucial for the exploitation of THz QC lasers in application such as security screening, requiring the ability to efficiently detect and visualise concealed explosives and weapons [8,9]. Finally QCLs are also the most promising high power solid state THz sources to be used in combination with present day heterodyne receivers for sub-millimeter astronomy [10].

In this work we demonstrate electrically pumped intersubband lasers with a photon energy of 8.3meV (f = 2THz, λ = 150μm), the lowest of any QC laser reported to date without applying an external magnetic field. Recently, QCLs emitting at 2.1 THz (λ = 141μm) have been reported based on a GaAs/AlGaAs heterostructure with 15% Al concentration. The active region relies on optical phonon-depopulation and the optical confinement is obtained via a 10 μm thick double-metal waveguide. Threshold voltages and current densities of ~ 10V and 560A/cm² have been reported at 4K, with a maximum output power in excess of 1mW [3]. In this work, the QCL active region consists of a GaAs/AlGaAs heterostructure with 10% Al concentration, and is based on a bound to continuum design, where the lower laser level is depopulated via elastic scattering processes. This results into a voltage drop per period of only 22meV, enabling operation at threshold voltages just under 3V. Lasing takes place on the second (possibly third, see the next Section) order mode of a double-metallic, 200μm thick waveguide. At T = 4K, we obtain a maximum peak power of 50mW, and of 17mW in continuous wave (CW), with threshold current densities of 115A/cm². For the two operating regimes maximum temperatures are 77K and 47K respectively.

2. Active region and waveguide design.

The band diagram of one period of the active region (AR) is displayed in Fig. 1. The design was derived from a recently demonstrated QCL emitting at 2.9THz [11]. The upper laser level consists of a single isolated subband, whilst the bottom state lies at the top of a group of closely space subbands spanning an energy range of 14meV. This scheme ensures an efficient electronic injection into the upper state via resonant tunnelling with, at the same time, a fast depopulation of the lower state via elastic scattering. The laser transition, corresponding to an energy of 8.5meV, is between states 2 and 1, with a computed oscillation strength of 12. The latter decreases steadily from 2 to virtually zero, for transitions from state 2 to the remaining subbands forming the superlattice miniband [11]. Carrier injection into the upper state occurs via resonant tunnelling from state g, across a 5nm thick Al_0.1Ga_0.9As barrier. At anticrossing the computed energy splitting is ΔS = 1.6 meV. The 3^d and 4^th wells before the injection barrier are doped at a level of 1.3×10¹⁶cm^-3, giving an average doping density in the AR of 2.6×10¹⁵ cm^-3.

From a study made on the previously demonstrated 2.9THz laser, we found that reducing the splitting and/or the doping density in the active region limited the level of current flowing through the device before the formation of the miniband and the subsequent injection in the upper laser state: this immediately reflected into a reduction of the threshold current density (J_TH) (see also the following Section) [13]. On the other hand we also found that increasing one or both of these parameters resulted into an increase of the maximum current across the structure (J_MAX). For a given J_TH, J_MAX should ideally be the largest possible in order to maximise the output power and the operating temperature, therefore determining the optimum Δ_S and doping density is ultimately the product of a compromise. The values chosen here (Δ_S = 1.6meV and 2.6 ×10¹⁵ cm^-3 average doping) are close to those delivering the best performance for the 2.9 THz QCL (1.8meV and 2.8×10¹⁵cm^-3) [11,13].

 

Fig. 1. Band diagram of 1 period of the active region under an electric field of 1.5 kV/cm. In red are the moduli squared wavefunctions of the upper (2) and lower (1) laser state. The green shaded areas represent the superlattice minibands. Highlighted are also the lower and upper miniband ground states g and 3 (thick green lines). Injection into state 2 occurs via resonant tunnelling from level g across a 5nm thick Al_0.1Ga_0.9As injection barrier. Starting from this barrier, from left to right, the layer sequence in nm is: 5/12.6/4.4/12.0/3.2/12.4/3.0/13.2/2.4/14.4/2.4/14.4/1.0/11.8/1.0/14.4, with the barriers in bold. The underlined layers are n-doped at levels of 1.3 × 10¹⁶ cm^-3.

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Minimizing intersubband absorption of the emitted light is another important aspect of THz QCL AR design. Here, we avoided absorption from subbands g and 2 into the upper superlattice miniband by having ΔE₂₃ = 16meV, i.e. twice the transition energy ΔE₁₂. Similarly, we could have ruled out absorption within the lower miniband by designing the latter with a width smaller than ΔE₁₂. Instead, in order to guarantee a relatively large phase-space of final states for scattering from state 1, we have preferred to maintain a 14meV wide miniband, consisting of 8 subbands separated by an energy difference larger than the typical line broadening (~ 1meV). This should help an efficient depopulation of the lower laser level. Resonant cross absorption was minimised by spatially chirping the wavefunctions in the miniband, which reduces substantially the dipole matrix elements between pairs of states separated by the laser transition energy.

Compared to the previous 2.9THz laser, the concentration of Al in the barriers was decreased from 15% to 10%. This was made to allow the use of slightly thicker barriers, rendering the structure less sensitive to fluctuations in the growth rate. In addition, lowering the Al concentration is expected to reduce interface roughness scattering [12]. Although the influence of this scattering mechanism on THz QCL’s performance must still be clearly demonstrated, however recent experimental studies carried out on these lasers under strong magnetic fields, suggest that the reduction of interface roughness scattering results into an increase of the upper state lifetime, improving population inversion [4].

The structure was grown with a Molecular Beam Epitaxy reactor (Veeco ModGen II) on a 3’’ SI GaAs substrate. 110 repeat periods of the AR presented in Fig. 1 were sandwiched between a 70nm thick, 5.0×10¹⁸ cm^-3 n-doped top contact, and a 600nm thick bottom contact layer, doped at a level of 1.0×10¹⁸ cm^-3. The latter was grown on top of a 300nm, undoped Al_0.5Ga_0.5As etch stop layer [14]. Samples were processed into 250μm wide ridge cavities by wet chemical etching the active region down to the top of the lower n+ contact layer. Top Pd/Ge (25/75nm) and bottom AuGeNi (120nm) ohmic contacts were formed by thermal evaporation and rapid thermal annealing. Substrates were mechanically thinned to 200μm, and finally non-annealed Ti/Au (20/150nm) metallization layers were deposited over top and bottom contacts, and on the back of the substrate.

 

Fig. 2. (a) 1-D mode intensity profile of the first, second and third order mode for the present 200μm-thick waveguide at f = 2THz (λ = 150 μm). The computed waveguide losses and overlap factor with the active region are respectively of 1.15 cm^-1 , 0.045; 2.8 cm^-1 , 0.145; 2.5 cm^-1, 0.13. (b) Figure of merit χ = Γ/α_w for the first three modes as a function of frequency. The waveguide thickness is 200 μm (c) Figure of merit χ = Γ/α_w for the 2^nd order mode at f = 2THz as a function of waveguide thickness.

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Waveguiding in THz QCLs relies on surface plasmon modes formed at the interface between metal and semiconductor. These couple naturally to the TM polarised intersubband photons, and the large and negative metal dielectric constant enables extremely strong optical confinements [1,2,14]. In Fig. 2(a) the one dimensional mode profiles for the waveguide used in this work are displayed at f = 2THz (λ = 150μm), for a total wafer thickness of 200μm. At such long wavelengths the plasmon mode underneath the top contact merges with the surface plasmon bound at the bottom of the SI GaAs substrate, effectively giving rise to a double-metallic confinement [4]. At sufficiently high frequency, lasing in this type of waveguide takes place on the fundamental TM mode. As the frequency decreases and approaches the plasma frequency in the AR, the magnitude of the refractive index is reduced, resulting into a rapid fall of Γ, the mode overlap with the AR. Although reducing the AR doping weakens this effect, eventually lasing on higher order modes becomes more advantageous. This is shown in Fig. 2(b) where we report, for the first three order modes, the figure of merit χ = Γ/α_w vs frequency, where α_w are the computed waveguide losses [15]. At 2THz, compared to the first order (Γ = 0.045, α_w = 1.15cm^-1), 2^nd (Γ = 0.145, α_w = 2.8cm^-1) and 3^d (Γ = 0.13, α_w = 2.5cm^-1) order modes yield a ~ 30% higher figure of merit, essentially due to the higher Γ. Given the uncertainty in the calculation of the waveguide loses and also considering that for these devices the mirror losses are to a large extent unknown, it is impossible to establish whether lasing takes place on the 2^nd or 3^d order mode. Instead, as shown in Fig. 2(c), when the waveguide thickness approaches 100μm, the 2^nd order mode definitely takes over the 3^d. Indeed for the former, decreasing the wafer thickness increases both Γ and α_w, maintaining the figure of merit approximately constant. Therefore thinning of the substrate should result into a lowering of the laser threshold, since the mirror losses are expected to decrease [14].

3. Experimental results and discussion.

For the electrical and optical characterisation, devices were indium soldered to copper holders and mounted on the cold finger of a continuous flow liquid helium cryostat. In Fig. 3, voltage-current density (V-J) and peak output power-current density (P-J) curves are shown for a 3.16mm long device, with high reflectivity back-facet coating (SiO/Ti/Au).

 

Fig. 3. V/J and P/J curves for a 3.16mm long device, with high reflectivity back-facet coating (SiO/Ti/Au). The V/J curve was collected in a three-terminal configuration. The laser was operated in pulsed mode with 250ns long pulses at a repetition rate of 80kHz. An additional 7Hz, 50% duty cycle slow modulation was superimposed to match the detector response time. Insets. Laser spectra recorded with a Fourier Transform Infrared Spectrometer with a resolution of 7.5 GHz (0.25 cm^-1). The device was driven in continuous wave at T = 4K.

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The laser was operated in pulsed mode with 250 ns long pulses at a repetition rate of 80 kHz. In order to match the detector response time, the pulse train was gated with a 7Hz, 50% duty cycle slow modulation.

Electrical measurements were performed in a three-terminal configuration by using the two bottom contacts on the sides of the ridge. In this way the voltage drop across the n+ channel underneath the AR is removed. The light output was measured under vacuum thanks to a broad area thermopile detector mounted on the cryostat window and positioned at a distance of ~ 1mm from the laser facet. The right hand power scale in Fig. 3 results from calibrations performed with an absolute THz power meter (Thomas Keating Instruments THz Power Meter).

 

Fig. 4. Low bias electroluminescence spectra collected with a Fourier Transform Infrared Spectrometer at T = 4K. The device was driven in pulsed mode with a 290 Hz repetition rate and 20% duty cycle. Inset. V/J curve. The coloured circles indicate the voltage and current density at which each spectrum was recorded.

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At 4K the threshold current density is 114A/cm², with a maximum collected peak power of 50mW at J = 160A/cm². Lasing takes place up to a maximum temperature of 77K. At threshold, we observe a marked decrease of the differential resistance, which is normally a sign of (i) a good injection efficiency in the upper state, and (ii) a high upper to lower state lifetime ratio [16]. Assuming a unit injection efficiency, from the computed total losses, and from the ratio of the differential resistance above and below threshold (= 0.5) we estimate a slope efficiency dP/dI at threshold of 180mW/A. From Fig. 3, we obtain dP/dI = 200mW/A at T = 4K. Considering the uncertainty in the computed α_w and mirror losses the agreement is excellent. However we must consider that the latter were derived from the Fresnel reflectivity using the computed effective index. It is known that this approach can lead to an overestimation of the mirror losses when the waveguide thickness approaches the wavelength in the material, thus increasing the computed slope efficiency [17].

In Fig. 3 the sudden power drop at high currents corresponds to an abrupt increase of the operating voltage, marking the end of resonant injection into the upper state. This occurs at approximately 2.3V, i.e. at an electric field F = 1.65kV/cm, in good agreement with the computed value at which states g and 2 anticross, (F ~ 1.75kV/cm).

The emission frequency (Inset of Fig. 3) is centered at ~ 2THz, corresponding to a transition energy of 8.3meV [18]. We observe no significant shift with voltage. Form band diagram calculations, computed transition energies are between 7.8 and 8.9meV (1.9–2.15 THz) at electric fields in the range 1.2–1.65kV/cm. These were derived from the measured voltages between threshold and power saturation in the 4K J/V curve of Fig. 3, assuming a uniform electric field distribution along the AR. Although the latter is probably a good approximation at intermediate voltages, however our data suggest a different picture in the low voltage region.

In Fig. 4 spontaneous emission is clearly observable down to bias voltages as low as 0.5 V, always centred at the measured laser transition energy E₂₁ = 8.3meV [19]. With such a high number of closely spaced subbands, calculating the actual low-bias potential profile is an extremely challenging task, and goes beyond the scope of this paper. In fact, relying on simple Schrödinger-Poisson calculations, we found that in this voltage range Coulomb effects are crucial in determining the band diagram and level alignment. Therefore a precise knowledge of the carrier distribution, which can only be computed within a fully self-consistent transport model, is mandatory [20].

 

Fig. 5. CW output power vs current density characteristics as a function of the heat sink temperature. Inset. Threshold current density vs heat sink temperature in CW and pulsed mode for the same device of Fig. 3, and for the 2.9THz QCL of Ref. [11]. The solid lines are guides the eye.

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Despite this fact, it is difficult to explain the observation of a constant transition energy of 8.3meV, down to operating voltages where, assuming a uniform field distribution, the energy drop per period would be of merely 4.5meV (V_bias = 0.5V). In this case resonant electronic injection in the upper state could not occur, and even supposing that the latter is thermally populated by electrons from the hot tail of the distribution, a pronounced Stark-shift of the transition would be expected [21]. For this reason we believe that a more realistic picture is that at low biases, AR periods where states g and 2 are aligned, as in Fig. 1, coexist with periods experiencing a lower electric field, where transport is dominated by electrons flowing between states belonging to adjacent superlattice minibands (see below). The fact that the formation of such electric field domains does not result into visible sawtooth-like features in the V/J curves, is attributed to the high number of strongly coupled subbands, giving rise to multiple, closely spaced resonances that smear out pronounced conductance peaks.

In Fig. 5 we report the L/I characteristics in CW for the same device of Fig. 3. Lasing takes place up to a temperature of 47K, with an output power of 17mW at T = 4K (this value was corrected by the 0.75 transmission coefficient of the cryostat window). In the inset the pulsed mode and CW threshold current densities are plotted as a function of heat sink temperature. Also shown for comparison are the same curves for a 3mm-long, 200μm-wide, back facet coated 2.9THz QCL [11]. In pulsed mode, it is clear that the higher maximum operating temperature of the latter stems from its wider current dynamic range. We also observe that in pulsed mode operation the threshold current density of the 2.0THz laser displays a less pronounced T-dependence [22]. Considering that the present device has smaller transition energy (8.3 vs.12meV) and miniband width (14 vs.16meV), this is attributed to a lower activation energy for the emission of optical phonons from the upper laser state [11].

As mentioned in Section 1, reducing the level of current at low bias is crucial to obtain low-threshold operation. Ideally, one would like a current to start flowing across the structure only once states g and 2 are aligned in all the AR periods, with electronic injection in the upper state solely controlled by the splitting between these two states. This would translate into a differential resistance monotonically decreasing towards zero, starting from a very high value.

 

Fig. 6. Top. J/V curves at T = 4K of the present AR (red) and of the 2.9THz AR of Ref. [11] (blue). Devices were processed in rectangular 250×185 μm² mesa structures. Bottom. Differential resistivity derived from the J/V curves. The drawings represent schematically two AR periods separated by the injection barrier, with the black arrow indicating the main current path. The shaded regions highlight the different transport regimes: (i) at low bias electrons transport between neighbouring minibands; (ii) at intermediate biases carriers are injected in the upper state via resonant tunnelling; (iii) at high voltages the structure breaks.

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In Fig. 6 we display the differential resistance of the present structure (red curve), processed in a rectangular 250×185 μm² mesa in order to eliminate optical feedback. As can be seen, the observed behaviour is not ideal. In the low voltage region (beige shaded) below the local maximum at V = 1.1V (J = 70A/cm²), part of the periods have not yet reached alignment and transport is mainly from neighbouring minibands. The initial increase in differential resistance with bias reflects the progressive closing of this current path until, eventually, at 1.1V, in most of the periods electrons are injected in the upper state via resonant tunnelling from level g. Beyond this point (green shaded) the differential resistance decreases, reaching a minimum at J ~ 106A/cm². In the case of a uniform electric field, this should correspond to states 2 and g reaching anticrossing in all the AR periods. Finally, after passing the anticrossing point, the differential resistance increases again, leading to miniband breaking (blue shaded region). For comparison, in Fig. 6 we also show the differential resistivity of the 2.9 THz laser of Ref. [11]. In this case we observe a more pronounced peak-to-valley ratio, which is partly attributed to the higher splitting at resonance between states g and 2 (1.8meV, compared to 1.6meV for the present structure; see also Section 2), but also to a reduced leakage current.

4. Conclusions

We have reported the operation of a GaAs/Al_0.1Ga_0.9As QCL emitting at 2.0THz, i.e. 150μm, the longest wavelength reported to date without the addition of an external magnetic field. Maximum operating temperatures of 77K and 47K are reported in pulsed and CW mode respectively, with output powers in the tens of mW range.

Future work will focus on improving the performance of the present device. In particular we aim at extending its current dynamic range by improving electronic injection at resonance as well as reducing the miniband-to-miniband current present at low biases.