MBE growth of THz quantum cascade lasers

Chapter 28

MBE growth of THz quantum cascade lasers Z.R. Wasilewski* National Research Council of Canada, Ottawa, Ontario, Canada *Present Address: Department of Electrical and Computer Engineering, Waterloo Institute of Nanotechnology, University of Waterloo, Waterloo, Ontario, Canada

Chapter Outline 28.1 Introduction 28.2 Quantum cascade lasers e from mid-infrared to THZ 28.2.1 The timeline 28.2.2 THz QCLs e the resonator designs 28.2.3 THz QCLs e the active region design 28.2.4 Theoretical modelling and simulation 28.3 MBE as a unique device optimisation tool 28.4 THZ quantum cascade lasers e MBE growth challenges 28.4.1 MBE system description 28.4.2 Structural parameters 28.4.2.1 Flux drift

631 632 632 633 633 634 636 639 639 640 640

28.1 INTRODUCTION The terahertz (THz) frequency region of electromagnetic radiation, also referred to as far-infrared, is located between infrared and microwave spectral regions and is often defined as frequency range between 300 GHz and 10 THz (wavelength range between 1000 and 30 mm) [1]. Until relatively recently, applications of THz radiation had been limited primarily to astronomy and analytical sciences. In these fields, THz has in fact been the spectroscopy region of choice, owing to very strong characteristic molecular rotational and vibrational absorptions lines in this region. It has also been used extensively in solid-state physics because of the match with phonon frequencies and shallow impurity transitions. Bulky and expensive sources of THz radiation were among the prime reasons for THz band not finding widespread applications, remaining the most underdeveloped spectral region of the electromagnetic radiation. Nevertheless, as a result of numerous innovations in high-tech industry as well as increased security, safety and environmental concerns, the last decade witnessed growing interest in new applications of THz technology.

Molecular Beam Epitaxy. http://dx.doi.org/10.1016/B978-0-12-387839-7.00028-2 Copyright Ó 2013 Elsevier Inc. All rights reserved.

28.4.2.2 28.4.2.3 28.4.2.4 28.4.2.5

Random flux instabilities Flux transients Flux uniformity Substrate rotation-induced layer nonuniformity 28.4.3 Doping issues 28.4.4 Surface morphology 28.4.5 Interfacial roughness (IR) scattering 28.5 Future prospects Acknowledgements References

641 644 645 646 648 649 650 652 653 653

These include, but are not limited to, safety and security; environmental monitoring; search and rescue; biological, medical and pharmaceutical sciences; quality control and information and communications technology (ICT). Availability of bright and compact photon sources is the key to widespread adoption of THz technology in these and other emerging applications. Arguably, the most promising devices likely to meet such requirements are quantum cascade lasers (QCLs). Although QCLs are already well established in the 4.5e12-mm spectral region, where continuous wave (cw) devices operating at room temperature are commercially available, THz QCLs capable of operation without cryogenic cooling have not been demonstrated yet and are at the focal point of research programmes in many laboratories around the world. Two key reasons are responsible for such slow progress. The first one is related to the optical losses in the laser cavity, which are much greater at these long wavelengths. The second, even greater challenge, is related to the difficulties in generating sufficient population inversion between electronic levels with very small energy spacing necessary to

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generate light in this spectral region. This is well illustrated by comparing photon energy Zu to the lattice thermal energy kBT for these devices. As of the time of writing this book, the highest operating temperature, Tmax, for THz QCL was 199.5 K [2], with lasing at 3.2 THz. For this laser the photon energy Zu exceeds the lattice thermal energy kBT by 28%. For comparison, if standard telecom laser operating at 1.55 mm was to match this figure of merit it would have to lase at temperatures in excess of 11,000
C e over twice the surface temperature of the Sun. In the strictly QCL category the number is not as shocking but still impressive. The present-day best QCLs operating at 5 mm are lasing up to about 400 K. If they were to match this number, they would have to operate up to 2600
C, way above the melting point of their components. Even though the achieved operating temperatures of THz QCLs have already surpassed “reasonable” expectations, there are no obvious barriers which would prevent these devices from operating even at room temperature [3]. However, further progress in this area will demand the very best of all “creation” stages: (i) modelling/design, (ii) epitaxial growth and (iii) device fabrication. This chapter has been divided into several sections. Section 28.2 gives a highly condensed introduction to quantum cascade lasers with the main focus on devices working in the THz spectral region. Section 28.3 discusses unique to MBE optimisation strategy e particularly useful for complex devices such as QCLs e which stems from the predictable and reproducible molecular flux profiles across stationary and rotating substrates. Section 28.4 provides a detailed analysis of the factors which need to be addressed during MBE growth when striving for the highest-performance devices, in particular THz QCLs where at the present stage high growth precision is of great importance for design optimisation. Finally, Section 28.5 discusses the new THz QCL design approaches and promising materials which may offer some advantages over the presently dominant GaAs/AlGaAs material system, particularly for high-temperature operation.

28.2 QUANTUM CASCADE LASERS e FROM MID-INFRARED TO THZ 28.2.1 The timeline Of all semiconductor devices, QCLs provide some of the best illustrations of the power of electronic structure engineering offered by the advanced epitaxial technologies such as MBE. The first proposal of superlattice-based unipolar laser has been put forward in 1971 by Kazarinov and Suris [4], just a year after Esaki and Tsu in their seminal work [5] showed that periodic potential e which should form in the conduction band of hypothetical at that

Molecular Beam Epitaxy

time epitaxial heterostructure superlattice e will lead to strong modification of the vertical electronic transport through such structure, with well-defined negative differential resistance (NDR) regions. The promise of a source of coherent radiation based on the sequential tunnelling in multiple quantum wells immediately generated great interest in many laboratories around the world. Nevertheless, it took over two decades of intense research before the practical implementation of QCL was demonstrated in 1994 at Bell Labs by Faist et al. [6]. This historical breakthrough device, lasing at 4.26 mm and made of AlInAs/InGaAs materials system lattice matched to InP substrates, was developed thanks to the joint effort of Federico Capasso’s device group and pioneering MBE group led by Alfred Cho. Clearly, the rather long path from the concept to demonstrator reflects the timelines for perfecting the art of molecular beam epitaxy for these demanding structures and advancing the understanding of the complex dynamics of electronic transport through them. In fact, as revolutionary as it was for its times, the original proposal by Kazarinov and Suris had two major flaws: (i) the undoped active region and (ii) operating point in the NDR region of the voltageecurrent characteristic [7]. Each of these design issues practically excludes proper operation of the device under bias due to (i) injection induced space-charge effects destroying uniform bias across all the QCL stack modules and/or (ii) formation of high-electric field domains typical of NDR region in multiple quantum well systems [8e13]. The electron injection-related problems have been effectively circumvented by including in each composite module of the laser stack a doped region serving as a local source of electrons. Thus, in the scale of the whole multimodule active region, the charge neutrality is ensured, since the negative charge of the cascading electrons is balanced in each module by stationary positive charge of the ionised donors. Providing individual doped regions for each module of the laser stack is in fact the only common improvement to all the practical QCL implementations over the original proposal by Kazarinov and Suris. Addressing the second issue (ii) basically translates into optimising the injection and extraction of electrons into and from the upper and lower lasing states, respectively, while maximising the optical transition oscillator strength and avoiding the NDR effects. This process, which reduces to skilful engineering of the conduction band profile along the active region stack, set in turn by the material compositional profile, is still at the heart of the ongoing research. Since the Bell Labs’ first QCL demonstration of 1994, numerous working active region designs using several different material systems have been proposed and laser action has been demonstrated in a very broad spectral region from 2.6 mm [14] to 250 mm or 1.2 THz [15]. It is interesting to note that the first

Chapter | 28

MBE growth of THz quantum cascade lasers

intersubband emission excited by sequential resonant tunnelling was reported for 2.2 THz photons [16], yet the first THz QCL was demonstrated only in 2002 [17], thirteen years after this spontaneous emission report and eight years after the demonstration of the first mid-infrared QCL. This illustrates very well the scale of the earliermentioned challenges which had to be addressed in order to obtain the light amplification in QCL devices at THz spectral region.

28.2.2 THz QCLs e the resonator designs The long delay from demonstrating the mid-infrared QCL to reporting the first THz QCL has been to a large extent due to the resonator design challenges. While not much modification was needed to adapt conventional telecom laser dielectric waveguides to the mid-infrared QCLs, new waveguiding schemes had to be introduced for THz region, where very long wavelength of photons would require prohibitively thick dielectric claddings and result in poor overlap of the optical mode with the gain media. Therefore, commonly used in microwave engineering double plasmon confinement in metaledielectricemetal transmission lines, the so-called “plasmon waveguides”  capable of confining TM polarised modes in resonators with subwavelength vertical dimension  have been adapted for these devices. Two distinct types of such waveguides are commonly used. The first one, called semi-insulating surface plasmon (SISP), was introduced with the first THz laser (4.4 THz) by Ko¨hler as a result of collaborative effort between Alessandro Tredicucci’s group at Scuola Normale Superiore in Pisa, Italy, and Cavendish Laboratory, Cambridge University, UK [17]. Instead of double metal cladding, it uses metallisation only on the top of the laser mesa, replacing the metal layer below the active region with heavily doped GaAs layer [17], typically about 800 nm thick, all grown on semi-insulating GaAs substrate. Introduction of the semiinsulating substrate considerably reduced the free-carrier absorption losses compared to the earlier versions which used Nþ substrates [18,19] and was one of the key design improvements behind the successful demonstration of the lasing action in THz region. The second type of waveguide is the true metalemetal design (MM), first implemented by Williams et al. [20] for 3 THz QCL within collaborative effort between Qing Hu’s MIT group and John Reno’s MBE lab at Sandia National Laboratories. Compared to the MM design the SISP waveguide has two key advantages: the processing is much simpler and the extraction of the light from the cavity is considerably easier, resulting in much higher output powers and better beam geometry for SISP lasers. Indeed, record output power levels of up to 250 mW

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pulsed, and 130 mW c.w. [21] have been demonstrated in THz QCLs with SISP waveguides. On the other hand, the subwavelength confinement of light in the vertical direction in MM waveguide, which is responsible for the high impedance mismatch between the cavity mode and free-space mode (reflectivity between 0.7 and 0.9 [22]), results also in a very high mode confinement factor (nearly 100% overlap with the active gain region). Because of that MM devices have lower lasing threshold currents, Ithr, higher dynamic range and higher maximum operating temperatures, Tmax, the latter additionally helped by much better heat extraction for this design [23,24]. The above-mentioned very inefficient coupling of terahertz radiation between subwavelength metalemetal waveguides and free space can be corrected in several ways, improving the beam geometry at the same time, e.g. by using distributed feedback grating resonant with the third-order Bragg condition [25], via integration with horn antennae [26] or by engineering the dispersion of surface plasmon polaritons through texturing metallised semiconductor surface with subwavelength structures of various geometries [27,28]. Good beam geometry has also been demonstrated, along with often desirable surface emission, through patterning a photonic crystal on the top MM THz laser metallisation [29] for electrically pumped device.

28.2.3 THz QCLs e the active region design Most of the active region designs used for THz QCLs are in fact modifications e albeit not trivial by far e of designs first proposed and demonstrated for QCLs operating in mid-infrared spectral region. Table 28.1 lists the schemes employed thus far, quoting the first mid-infrared and THz implementations. Besides the original papers quoted, excellent comparative reviews have been written on both mid-infrared QCLs [30,31] and THz QCLs [1,32,33], while in-depth discussions can be found in several doctoral dissertations (e.g. Williams, 2003 [34], Callebaut, 2006 [35], Kumar, 2007 [7]). With exception of the longest wavelength THz laser e BC design at 1.2 THz by Walther et al. [15], and recent SAI-design at 1.8 THz by Kumar et al. [36], the best high-temperature performance in THz frequencies has been demonstrated by RP-type QCLs [37], in particular the RP design based on 3-well module, first proposed by Luo et al. [38]. This includes three consecutive reports of the record-high operating temperatures for QCLs in the THz range e Tmax: 178 K in 2008 [23], 186 K in 2009 [39] and 199.5 K in 2012 [2]. Despite this seemingly slow progress in improving Tmax, the current understanding of the processes behind operation of these lasers offers rather optimistic prognosis regarding reaching the temperatures achievable with standard thermoelectric coolers without introducing yet another revolutionary

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TABLE 28.1 THz QCL laser designs Type

First mid-infrared QCL

Chirped Superlattice CS

Tredicucci et al., 1998 [123] Ko¨hler et al., 2002 [17]

Optical transition between the superlattice (SL) mini-bands which form at operating bias. Depopulation via fast relaxation in the lower SL. No direct use of LO phonon.

Bound to Continuum BC

Faist at al., 2001 [124]

Scalari at al., 2003 [125]

Similar to Chirped SL, but the upper lasing state is localised in the gap between mini-bands. No direct use of LO phonon.

Resonant Phonon RP

Faist et al., 1994 [6]

Williams et al., 2003 [37]

Resonant tunnelling injection into upper lasing level and depopulation of the lower lasing level via fast scattering by LO phonons. Several distinct variations proposed: 4-well [126], 3-well [38] and 2-well [127].

Two Phonon Resonance TPR

Faist et al., 2002 [30]

Williams et al., 2006 [126] Like resonant phonon, but depopulation of the lower lasing level via emission of two LO phonons.

Scattering Assisted Injection SAI

Yamanishi at al., 2008 [128] Kumar at al., 2011 [36]

PhononePhotonePhonon PpP

design [3]. Also, as will be discussed later in this chapter, several other material systems offering potential advantages over GaAs/AlGaAs for THz QCLs are investigated at present. Coherent THz radiation, besides the direct generation based on optical transitions between suitably engineered electronic levels with the energy spacing equal the energy of the desired photons, can be generated in a process of difference frequency mixing (DFM) of mid-infrared waves using engineered nonlinear susceptibility of asymmetric semiconductor superlattices [40]. Thus, using two mid-infrared QCL lasers with photon energy spacing such that their difference would be equal to the energy of the desired THz radiation, one should be able to generate THz photons at room temperature. The feasibility of this approach was studied using CO2 laser pumps and GaAs/ AlGaAs multiple quantum well structure by Dupont et al., in 2006 [41]. Tunability in broad range from 234 GHz to 4.56 THz with the maximum conversion efficiency of ~160 nW/W2 was reported. More practical implementation had been demonstrated in 2007 by Belkin et al., [42], in a form of a dual wavelength InGaAs/InAlAs: InP QCL with giant second-order nonlinear susceptibility active region (the so-called DFG QCL) producing 60 nW of THz power at 80 K, and an improved design a year later

First THz QCL

Dupont et al., 2012

Operating principle

Resonant injection into a level LOphonon energy above the upper lasing level and subsequent fast LO scattering to the upper lasing level. Injection SAI-type; extraction 2-well RP-type.

producing 300 nW at room temperature. Most recently, Lu et al. [43] demonstrated single-mode THz emission at 4 THz in this type of device with conversion efficiency w10 mW/W2 and maximum room temperature output power of 8.5 mW. This rapid progress and a clear optimisation path promise mW-level room-temperature THz lasers in the near future. One should note that it is too early to say which approach for generation of coherent THz radiation e THz QCL or DFG QCL e will dominate in the future commercial devices. Indeed, THz QCLs operating with thermoelectric coolers may prove to provide more output power, better stability and overall better wallplug efficiency than DFG QCLs operating at room temperature.

28.2.4 Theoretical modelling and simulation Despite nearly two decades since the first demonstration of quantum cascade laser, understanding carrier dynamics in these devices remains a very hot topic. Remarkably, much of the progress in mid-infrared QCLs has been achieved using modelling methods which are surprisingly simple in view of the complexities of the electron dynamics in such devices [30,44]. In fact, despite continuing progress in fully

Chapter | 28

MBE growth of THz quantum cascade lasers

quantum-mechanical modelling using nonequilibrium Green’s function (NEGF) approach [9,45e50], new relatively simple yet very useful models are still being proposed [51e53]. At their core, all but NEGF calculations rely on solving rate equations for steady-state conditions where stationary or quasi-stationary solutions of Schro¨dinger equation in the effective mass approximation are considered rather than travelling pseudo-particle wavepackets. In the simplest implementation of such an approach a system of 1D Schro¨dingerePoisson equations is solved self-consistently in the z-direction as a function of applied bias using conduction band potential of several QCL periods, while standard energy dispersion of free electron with effective mass me ðkÞ is assumed for the motion in (x, y) plane. This produces a series of subbands indexed by quantisation in the z-direction. Typical representation of such a system is shown in Figure 28.2a, where the modulus squared of the eigen wavefunctions for the bottom of each subband (i.e. for kx ¼ ky ¼ 0) is plotted in the z-direction, with the vertical position of each such plot anchored at the bottom of the corresponding subband. Owing to the delocalisation of the electronic wavefunctions over more than one QCL period such a graph is often called “extended wavefunction” representation. With this approach charge transport in the z-direction is effectively “simulated” by considering scattering of electrons between such quasi-stationary states. Thus, the electrons are traversing the structure thanks to the sequence of scattering events (Figure 28.1), where on average such events are moving electrons to the states which are localised progressively closer to the positively charged contact. The respective scattering times needed to solve the rate equation are either (i) explicitly calculated using Fermi’s golden rule approximation with appropriate scattering potential, (ii) taken from literature or (iii) fitted for best agreement with experiments. The ultimate modelling approach operating in this effectively hopping transport picture [54,55] uses Monte-Carlo (MC) method for simulating the “hopping” of electrons within and between the subbands [56e60]. As long as the relevant states do not anticross with other states with a small Rabi frequency, i.e. their minimum energetic separation is larger than homogeneous level broadening, this method provides generally good agreement with measured optical transition energies, current densities and gain dispersion versus temperature or applied electric field [2]. It is interesting to note that for this extended wavefunction representation the wavefunction localisation by dephasing processes is excluded [61]; in other words, the coherent processes which are at the very core of the QCL concept, such as the sequential resonant tunnelling events, are not considered explicitly. Coherent transport and its role in THz QCLs have been a subject of debate for some time, and rather convincing arguments for its paramount place have been presented based on rigorous

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FIGURE 28.1 Schematic illustration of the operating principle for the resonant injection, LO-phonon depopulation (RP-type) THz QCL laser using as an example the design of the ful ¼ 0.475 structure from reference [2]. (Lower panel) high-angle annular dark-field scanning transmission electron microscope image of the actual structure. (Upper panel) Schematic representation of the layers mapped from the selection rectangle in the STEM image below. The layer dimensions are identified above together with the information on the doping level and location of the Sidoped regions. For illustrative purposes, the ladder of electronic levels for the optimum operating bias is overlaid. Using notation from Figure 28.2b, from left to right, the phonon well (with Si-doping) precedes the injection ˚ ), through which electrons tunnel resonantly from the ground barrier (43 A level (gn  1) into the upper lasing level (un) of the n-th module. The upper (un) and lower (ln) lasing levels are hosted in the double well (89 and ˚ ) which, along with the barrier in between (24.6 A ˚ ), is designed in 81.5 A such a way as to separate the upper and lower lasing levels spatially, thus giving the transitions a diagonal character. Electrons are moved from un to ln subband either by nonradiative scatting evens or by photon emission (3.2 THz). Subsequently, electrons tunnel resonantly via extraction barrier ˚ ) into the extraction level en in the n-th phonon well, where via ultra(41 A fast LO-phonon scattering are transferred to the lower injection level gn, from which they tunnel into the next QCL module’s level unþ1, etc (For colour version of this figure, the reader is referred to the online version of this book).

quantum-mechanical considerations [47,62]. Nevertheless, it has been shown [47] that as long as the scattering-induced level broadening is smaller than the distance between the anticrossing levels, the nondiagonal elements of the density matrix (in the extended wavefunction basis) are small and their influence can be approximated by differences in the levels occupancies, which is basically the approach taken within the MC modelling. Another family of simplified

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(a)

Molecular Beam Epitaxy

quite independently of the inelastic scattering events. This dephasing process will result in “dampening” of such charge oscillations and, if strong enough, will cause a net accumulation of charge in front of the barrier and slowdown in electron transport which has to be explicitly included in the rate equation [66].

28.3 MBE AS A UNIQUE DEVICE OPTIMISATION TOOL

(b)

FIGURE 28.2 Two different sets of eigen wavefunctions used in modelling [extended for Monte Carlo calculations e (a) and localised for density matrix (b)] for the electronic structure of QCL device illustrated in Figure 28.1. Modulus square of the wavefunctions for the bottom of each subband (i.e. for kx ¼ ky ¼ 0) is plotted in the z-direction, with the vertical position of each such plot anchored at the bottom of the corresponding subband. See the main text for further discussion (For colour version of this figure, the reader is referred to the online version of this book).

approaches working well with the rate equations is based on the density matrix (DM) theory in tight binding approximation [51,63e68], and also can be derived from the NEGF model via suitable simplifications [47]. Unlike for the extended wavefunction approach, localised states are chosen as the basis (Figure 28.2b), with the simplest approximations using solutions of Schro¨dinger equation for potential which is basically a subsection of one QCL period with the rest of the period(s) replaced on both sides by infinitely thick barriers. Naturally, the thicker the real barriers surrounding such region, the better the approximation. THz QCLs with relatively thick injection and extraction barriers are therefore good candidates for such an approach. The DM-based modelling is particularly suitable for considering resonant tunnelling processes in real quantum systems, where elastic scattering events on interfacial roughness (IR), alloy fluctuations or ionised impurities will cause gradual loss of phase of the tunnelling electron as it “bounces” back and forth with Rabi frequency between the resonant levels on both sides of the barrier,

As always the case for an open and complex quantum systems, each of the above-mentioned modelling methods relies on numerous approximations, necessary to make the computational burden manageable. Thus, ultimately it is up to the experiment to endorse or dismiss validity of the assumptions and simplifications behind them. Even though experiments on a single device can provide a large volume of data to compare with modelling (e.g. temperature dependence of threshold and peak currents, slope efficiency, and light-currentevoltage characteristics), the best verification of a model for quantum cascade laser is done by changing the key structural parameters of the device at the nanoscale and verifying if the model predictions are indeed explaining resulting changes in the device properties. For THz QCLs such “structural” tests are expensive and time consuming, since each THz QCL wafer takes from 12 to 20 h to grow. In principle, one can take advantage of the variation of the growth rates across the substrate, if large enough and accurately known. However, in such a situation all structural parameters, i.e. layer thicknesses and compositions, as well as doping levels, will vary from device to device, making it nearly impossible to establish some systematic path for model development and verification. A different approach is therefore preferable, one taking advantage of unique capabilities of modern MBE systems, that is varying only one structural parameter of the device across the wafer, while preserving high uniformity for the rest. Figure 28.3 shows the result of flux modelling for our e described in the following section e V90 MBE system and standard effusion cell equipped with conical 30-cc crucible. The top panel shows the 3D topographic map of GaAs (or AlAs) layer thickness which would be grown on stationary 30  30 cm “virtual substrate” positioned in the same plane and centred at the same point as the substrate. The lower panel shows the same surface in a semi-transparent mode revealing the relative size and position of 300 substrate, as well as its projection on the topographic surface of the layer thickness. Also shown are relative positions and orientations of the 12 effusion cells present on this system, with the cell used to deposit the investigated layer emphasised here for better visibility. In reality, the wafer surface on which the layer is grown is directed towards the floor of the system, while the

Chapter | 28

MBE growth of THz quantum cascade lasers

FIGURE 28.3 Result of flux modelling for our V90 MBE system and standard effusion cell equipped with conical 30-cc crucible. (Upper panel) 3D topographic map of GaAs (or AlAs) layer thickness which would be grown on stationary 30  30 cm “virtual substrate” positioned in the same plane and centred at the same point as the substrate. (Lower panel) The same surface in a semi-transparent mode revealing the relative size and position of 300 substrate, as well as its projection on the topographic surface of the layer thickness (the black oval outline). Also shown are relative positions and orientations of the 12 effusion cells installed on this system, with the cell used to deposit the illustrated here layer emphasised for better visibility (For colour version of this figure, the reader is referred to the online version of this book).

effusion sources are pointing upwards towards the wafer, with the cell extended axis intersecting the substrate centre. It is clear that the thickness of the deposited layer changes strongly across the 300 wafer, in this case nearly by a factor of two along the wafer diameter in the direction towards the effusion source used. Nevertheless, introducing wafer rotation during the growth will result in a very uniform layer, with total thickness variation from the centre to the edge of 300 substrate of less than 0.5%. The origin of this remarkable improvement can be understood by examining the thickness profile shown in the upper panel of the figure.

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The spoon-shaped imprint on the thickness topographic map is actually located above the projection of the extended cone of the crucible onto the substrate surface, i.e. points in this area can see all emitting surfaces of the cell e the melt and the crucible walls [69]. The further away are points on the map from this area, the less of the emitting surfaces will contribute to the flux they receive. The actual flux topography in this “sweet spot” is in fact that of a saddle rather than a spoon, with positive curvature (valley shape) along the flux direction and negative (hill shape) perpendicular to it. This is largely thanks to such topography that e despite the substantial curvatures both ways e very uniform layers can be grown using substrate rotation during deposition process. With changing the molecular beam incidence angle from steep to shallow the positive curvature will keep increasing while the negative one (perpendicular to the beam) is not changing very much. Thus, an optimum angle exists for the cell orientation with respect to the substrate normal e shown to be very close to 45
[69] e where both curvatures compensate each other perfectly during rotation. Moving below this point towards shallower incidence angle will flip thickness profile shape of layers grown with substrate rotation from convex to concave. The property described here of the molecular flux distribution presents a unique tool for covering a large range of chosen structural parameters by stooping rotation for the deposition time of such feature, while the rest of the structure can have very high uniformity by being grown while rotating the substrate. Figure 28.4 shows an example where such grading is applied to Al0.15Ga0.85As barrier. Panels (a) and (b) are showing contours of Al and Ga flux, respectively, normalised to the flux at the substrate centre. The arrows indicate the molecular beam directions relative to the wafer orientation. The resulting Al0.15Ga0.85As thickness contour plot is shown in panel (c), along with the effective thickness gradient direction, while the contour plot for the barrier aluminium content x is shown in panel (d). Here, the substrate orientation is chosen in such a way that cleaving the stripe for processing in the direction perpendicular to the major flat will produce samples with approximately constant aluminium fraction x ¼ 0.15, and fairly broad range of the barrier thicknesses: from about 0.75 to 1.3 of its value for the waver centre for the case considered case. Naturally, care needs to be taken when fixing the orientation of the wafer for the stationary deposition. This can be ensured by using RHEED electron beam and surface reconstruction “fingerprint” for precise and reproducible wafer alignment along the desired azimuth. In the context of THz QCLs this approach has been used to study the effects of doping [70] in a 4-well RP-type QCLS, as well as to investigate the influence of injector barrier thickness [71] and extractor barrier thickness [72] on the laser performance for a 3-well RP-type THz QCL [38]. The results of these studies proved to be of vital

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FIGURE 28.4 Results of modelling of AlGaAs layer thickness grown on stationary substrate in V90 MBE system. Panels (a) and (b) show contours of Al and Ga flux, respectively, normalised to the flux at the substrate centre. The arrows indicate the molecular beam directions relative to the wafer orientation. Panel (c) shows the resulting Al0.15Ga0.85As thickness contour plot together with the effective thickness gradient direction. Panel (d) shows contour plot for the AlGaAs aluminium content x. The substrate orientation is chosen in such a way that cleaving the stripe for processing in the direction perpendicular to the major flat will produce samples with approximately constant aluminium fraction x ¼ 0.15, and a fairly broad range of the barrier thicknesses: from about 0.75 to 1.3 of its value for the waver centre (For colour version of this figure, the reader is referred to the online version of this book).

importance in developing the density matrix model for these devices [51]. Thanks to several simplifications guided by these results, it was possible to propose the model yielding analytical formulae for a number of observables. This model was subsequently used together with an optimisation procedure to further perfect the 3-well RP QCL design, raising the Tmax record at that time from 186 K [39] to 199.5 K [2]. Equally important was the impact of this relatively simple and transparent model on the understanding of the main mechanisms governing the operation of THz QCLs, which stimulated work on other functional design concepts for these devices [73]. The great value of such an analytical model is illustrated in Figure 28.5, where the influence of flux drift during MBE growth on the laser gain is investigated. The three semi-transparent surfaces plotted represent the dependence of the spectral gain for the RP 3-well THz laser on the bias voltage for three different growth rates e optimum, 1.5% below the target and 3% below the target, all at T ¼ 160 K. For illustrative purposes, the plots are truncated at the gain value of 30 cm1, which, for this temperature, approximately equals expected losses in the metalemetal device with copper claddings. The first clear observation, which can be derived from this plot, is

Molecular Beam Epitaxy

(a)

(b)

(c)

(d)

the large width of such gain surface in both photon energy and bias electric field variables. This means that even if each period maximised gain at somewhat different bias and photon energy, there would be plenty of tolerance to get light amplification in the entire stack, as long as one is not striving to maximise Tmax. Thus, with the laser operating at cryogenic temperatures, where the peak gain can be substantially higher than losses, this device appears to be very robust when it comes to fluctuations of structural parameters of the laser from period to period. Second, a rather expected finding, is that proportional shrinking of the layer thicknesses induces shift of the peak gain photon energy and bias voltage towards larger values, while at the same time the gain is progressively reduced in the entire region. This finding suggests that one can vary continuously structural dimensions of THz QCL from period to period and still get lasing action, although the lasing energy is expected to increase with the bias voltage. Indeed, exactly such a behaviour has been reported in devices where the growth rate and consequently layer thicknesses were deliberately changed continuously during the deposition from þ6% to 4% of the nominal value [74]. Such a strategy works when the maximum lasing temperature is

Chapter | 28

MBE growth of THz quantum cascade lasers

(A) (B) (C)

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properties [77]. Even though a vast literature is available for this material system and several conference proceeding papers addressed the topic of growth of THz QCLs [78e80], a comprehensive discussion of MBE-related issues which may influence performance of these devices is lacking. In the following, we attempt to fill this gap, primarily based on the experience accumulated in our MBE laboratory.

28.4.1 MBE system description

FIGURE 28.5 Calculations using the density matrix model [51] for the dependence on the bias voltage of the spectral gain for the RP 3-well THz laser for three different growth rates e optimum (A), 1.5% below the target (B) and 3% below the target (C). The calculations are done for T ¼ 160 K. For illustrative purposes, the plots are truncated at the gain value of 30 cm1, which for this temperature approximately equals expected losses in the metalemetal device with copper claddings (For colour version of this figure, the reader is referred to the online version of this book).

of secondary importance. However, as explained earlier, it is increasing the Tmax for THz QCLs to the thermoelectric cooler’s range which is of paramount importance for bringing these devices into the mainstream of applications. With this in mind, the uniformity of the laser stack is in fact of the highest priority when optimising the device design towards this goal.

28.4 THZ QUANTUM CASCADE LASERS e MBE GROWTH CHALLENGES In this section, we discuss the key issues which should be addressed when optimising molecular beam epitaxial growth of GaAs/AlxGa1xAs-based THz QCLs. The choice of Al content x in the barriers is mainly dictated by the carrier injection scheme employed. As of the time of writing this chapter, the resonant tunnelling electron injection to the upper lasing level together with resonant LO-phonon depopulation of the lower laser level scheme (RP-type) enabled highest operating temperatures. For such a design relatively low barriers are needed, and x ¼ 0.15 has been the choice for nearly all published designs. This material system can be deposited successfully within a fairly wide window of growth parameters, offering some of the highest quality heterostructures available for both photonic and electronic applications. Indeed, AlGaAs is one of the first material systems grown by MBE [75,76], and much has been written over the years on its growth and

Most of the discussion in this section is based on our experience with the MBE system custom built for us by VG Semicon e at that time subsidiary of Thermo Scientific e and delivered in 2002. Despite significant differences compared to their earlier V90 MBE platform, the system is still referred to as V90, primarily because of its single 400 substrate size capability, which places it in between the smaller V80 system, which has single 300 capability, and V100 capable of growth on 3  400 or 1  600 substrate platens. Several such systems have been subsequently manufactured and deployed, before VG Semicon MBE group and related intellectual property were purchased in 2008 from Oxford Instruments by Riber. The system, illustrated in Figure 28.6, is a vertical design, fully automated MBE system with all the operations in the UHV chambers under computer control, including wafer transfer processes. Growth chamber is equipped with twelve 4.500 effusion cell ports. The cell layout, as of the time of writing this chapter, is illustrated in the upper panel of the figure. Veeco Mark V Arsenic valved cracker cell has been used as a source of arsenic dimers (As2); dual filament Veeco 300 g SUMO cells have been used as sources of Ga; Veeco Al cold-lip cells equipped with 30 cc conical crucibles have been used for aluminium evaporation; and a 5cc Veeco dopant source has been used for Si doping. Other sources, not used for the THz QCL growth discussed in this chapter, are Veeco UNI-bulb RF plasma source with custom-made dynamic NþAr mixing delivery system, Veeco 5cc Be source, Veeco 300 g SUMO cell for In, e-Science Titan source for In, Veeco low-temperature SUMO cell for Te and Veeco Corrosive Series Valved Cracker for Sb evaporation. All cells are directed at the substrate centre at close to optimal 45
angle [69] with effusion distance of approximately 25 cm. The system is equipped with 35 keV Staib RHEED gun and kSA 400 RHEED acquisition and analysis system with capability of surface reconstruction monitoring along eight crystallographic azimuths with a rotating substrate. Substrate temperature is monitored simultaneously using ex situ calibrated home-made band-edge spectrometry system and SVT RoboMBE IS4K reflectance-compensated pyrometry system. The latter is also used to monitor the

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FIGURE 28.6 V90 MBE system at the National Research Council, Canada, with the effusion sources layout (For colour version of this figure, the reader is referred to the online version of this book).

layer reflectivity during the growth at 470- and 950-nm wavelengths. The system is also equipped with several residual gas analysers (RGAs), including desorption mass spectrometry (DMS) unit on the bottom monitoring port directed at the substrate.

28.4.2 Structural parameters Perhaps the most obvious requirement for the grown QCL structure is that the basic design parameters, such as thicknesses of AlGaAs barriers and GaAs wells, aluminium composition in the barriers and Si doping levels, are on target: ideally, this would mean target parameters along the structure in the growth direction, laterally across the wafer and from process to process throughout the growth campaign. In the following, we discuss the key limitations

of real-world MBE reactors which should be considered when embarking on a THz QCL growth programme. Increasingly, theoretical modelling, device design, testing, fabrication and growth of the structures are not performed in one location. Many groups nowadays obtain epitaxial structures externally, often from more than one source, trusting that structure parameters adhere to the original design, or e at the very least e the important for processing and modelling parameters are known and correctly quoted. This puts great responsibility on MBE growers, since much effort can go to waste if erroneous information is supplied along with the epitaxial structure.

28.4.2.1 Flux drift Temporal stability of atomic fluxes in MBE is of key importance for the growth of THz QCLs. For typical design

Chapter | 28

MBE growth of THz quantum cascade lasers

where the thickness of the active region is about 10 mm (e.g. ˚ ) it takes over 11 h to grow such a stack 228 repeats  440A ˚ /s. However, for when using GaAs growth rate of 2.3 A a fixed effusion cell temperature, the flux will be decreasing over time as Ga is being used up and the melt level in the crucible drops. The rate of this decline is going to depend on the design of the cell and that of MBE system itself. For the case of V90 MBE system equipped with dual-filament SUMO cells for gallium we are using up on average about 0.37 g of material for Ga evaporation equivalent of 1 mm of GaAs. This number has been derived from the initial charge of Ga in the crucible and by integrating over time the atomic flux leaving the cell until all Ga is consumed. Such data are readily accessible for most MBE systems, using the recordings of cell temperature and flux calibrations: Zt2 MGa ¼ a

FGa ðtÞdt

(28.1)

t1

where MGa stands for the amount of Ga used between time t1 and t2 and FGa ðtÞ is the nominal Ga flux at the substrate centre at the time t. Proportionality factor a can be calculated by integrating over the entire campaign period and replacing MGa with the net amount of Ga used, i.e. the difference between the loaded and remaining charge in the crucible. The flux FðtÞ needed here can be expressed as FðtÞ ¼ AðtÞeBðtÞ=ðTðtÞþ273Þ

(28.2)

where T(t) is Ga cell temperature in
C at the time t, while parameters A and B are obtained through suitable flux calibration procedure, typically using monitoring ion gauge (MIG): g (28.3) FGa ¼ pffiffiffiffiffiffiffiffi jMIG TGa where jMIG stands for MIGpion ffiffiffiffiffiffiffifficurrent, g is a calibration constant and the factor TGa takes into account the temperature dependence of the average speed of Ga atoms traversing the ion gauge. The flux is also directly related to the growth rate through the relationship ℛ GaAs ¼ b FGa  ℛ b GaAs ðTsub Þ

(28.4)

where, with the flux expressed in units of atoms/cm2s, ˚ /s, b ¼ 4.531015 ℛ GaAs stands for GaAs growth rate in A for homoepitaxial GaAs and ℛ b GaAs is the GaAs desorption rate at substrate temperature Tsub. It is therefore important to conduct suitable calibrations at temperatures where this desorption does not introduce a significant error. For GaAs growth temperatures of up to about 630
C the desorption is often assumed to be negligible. However, highly accurate desorption rate measurements,

641

performed in our laboratory using dual-wavelength in situ reflectance of thin GaAs film on AlAs layer, give a value ˚ /s for ℛ b ð630
Þ. This correction results in of 0.016 A GaAs about 0.7% slower GaAs growth rate for a typical target of ˚ /s, which will affect the performance of THz QCL 2.3 A structure, if not factored in properly. Moreover, as an example, if 10-degree temperature gradient exists across the substrate, with the hotter regions, say, at 640
C ˚ (ℛ b GaAs of 0.031 A/s), additional variation of structure parameters across the substrate will result. Overall, we find that up to about 700
C desorption rate of GaAs can be described well as thermally activated: EGaAs =kB T ℛb GaAs ðTÞ ¼ Ce

(28.5)

using C h 3.57  1024 and single activation energy of 4.72 eV, a number close to 4.59 eV derived by Taferner et al. [81] using desorption mass spectrometry. The 2% difference is likely related to the substrate temperature measurement and calibration methodology. Indeed, a comparison of the absolute desorption rates indicates close to thirty-degree difference in temperature calibration between ours and Taferner’s data, with the latter quoting lower temperatures. In our case, the temperature was measured using a combination of pyrometry and a calibrated band-edge absorption spectroscopy in order to eliminate possible problems due to pyrometer access window coating, or scattered light in the reactor. Provided the cell temperatures are logged continuously on a daily basis and the baseline characteristic of the cell was established during previous campaign, eqn (28.1) becomes a powerful tool for forecasting the flux behaviour during the very long THz QCL structure growth, as well as from growth to growth. Figure 28.7 shows an example of calibration curves for one of Ga SUMO cells on our V90 MBE system. The actual experimental data typically show scatter with about 0.2
standard deviation from such fit. Both dependences are plotted as a function of the integrated flux emitted from the cell, the latter for convenience represented as an effective GaAs deposition thickness. Initial charge in the crucible is assumed here to be 175 g of gallium. As seen from the figure, the rate of temperature increase needed to keep the growth rate constant almost triples from the full charge to nearly depleted cell. Nevertheless, the calibration shown in the lower panel allows to compensate the flux decline during long deposition times by ramping Ga cell temperature during the deposition with the rate appropriate to the level of charge in the crucible.

28.4.2.2 Random flux instabilities The discussion so far has been limited to the behaviour of fluxes from gallium cells, where molten Ga typically does not have a tendency to wet PBN crucible walls or react with

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Molecular Beam Epitaxy

˚ /s GaAs growth rate. Second-order polynomial fit to experimental data. (Lower) Incremental FIGURE 28.7 (Upper) Ga cell temperature required for 2 A ˚ /s GaAs growth rate. The horizontal scale is in units of mm of GaAs which would have been grown increase of Ga cell temperature required to sustain 2 A with this cell if the shutter was opened all the time, given the thermal history of the cell and of its calibration (For colour version of this figure, the reader is referred to the online version of this book).

them. However, the situation is not as controllable for aluminium cells, where liquid aluminium readily wets the crucible and in the long term reacts with it, forming polycrystalline aluminium nitride coating. At the same time, boron is leeched out into Al melt, which with time may lead to crystalline aluminium boride-floating precipitates, which will have a tendency to destabilise Al flux [82]. We found partial relief from the problem by first precoating the crucible with small aluminium charge, annealing it at above 1400
C in its MBE port for one day longer than needed to evaporate all aluminium, prior to loading proper Al charge for the campaign. This process has a tendency to form uniform aluminium nitride coating of the crucible interior, permitting the cell to reach stable operating conditions sooner and reducing considerably instabilities related to boride precipitates. As a bonus, very good outgassing is done to the cell shutter and its port. Nevertheless, since Al cells are operating with cooler lip area, in order to prevent aluminium from running up and out of the cell, molten

aluminium accumulates tend to form at the top portion of the crucible. These formations have a tendency to alter the flux. Moreover, they can evolve over time, depending on the cell thermal history, causing flux instabilities. On the other hand, once the cell reaches the steady-state condition it can be very stable, since the highly emitting area for Al cells includes also the wetted with aluminium walls, unlike for Ga cell where it is limited to the melt surface. Thus, once the flux of Al stabilises, the cell temperature does not need to be incremented during deposition period. Nevertheless, a small redistribution of Al in the crucible during the growth, and related flux changes, cannot be entirely avoided with the present Al cell designs. To get a measure of flux stability, as a matter of principle, before the growth and after we always perform a flux-checking routine for all group III cells using retractable monitoring ion gauge. Typically, for the case of aluminium, better than 0.5% stability is measured for the 15e17-h period needed for the growth of THz QCL. Occasionally though, deviations of up

Chapter | 28

MBE growth of THz quantum cascade lasers

to about 2% were recorded. For the case of resonant injection THz QCLs, where AlGaAs barriers have 15% Al compositions, such 2% instability is difficult to diagnose with postgrowth characterisation such as XRD. Indeed, a 2% increase in aluminium flux will increase the individual module thickness by less than 0.1% or about 0.1 monolayer (ML). Nevertheless, this Al flux drift will result in 2.7-meV increase in the barrier height. The aluminium migration problem is well illustrated with a rather extreme case recorded in our laboratory when testing suitability for this material of SUMO-type cold-lip, 180-cc narrow nozzle crucible/cell design (Figure 28.8). The upper panel of the figure shows the recording of the flux arriving at the substrate over the monitoring period of about 1 h 20 min, while the lower panel shows the cell thermocouple readings over the same time period. The shaded area on the left side of the graphs shows the cell behaviour with PID temperature stabilisation locked to the bottom thermocouple. Clearly, adequate temperature control has been achieved keeping the cell at 1260  0.1
C. Nevertheless, the flux is very unstable showing 15% deeps with an approximately 150 s cycle. The origin of this behaviour is easier to

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understand when examining the cell behaviour above the 4000-s mark, where PID stabilisation is replaced with a constant power mode. As expected, when the shutter is closed the heat losses are smaller and the cell is heating up with constant power delivery, while the opposite is happening when the shutter is opened. Very revealing, however, are the temperature spikes with the same cycle duration as the flux instability. The second, narrower shaded area on the graphs isolates one period of such instability. It can be seen that a rapid increase of the flux is correlated with the drop in the temperature of the melt at the bottom of the crucible. As the temperature starts to recover, the flux drops again, and so on. This behaviour is due to the transport of molten aluminium from the bottom to the top of the crucible, where it forms a narrow ring at the base of the much cooler nozzle, effectively shadowing some of the atomic flux from the wafer. As the size of the blob supporting this ring grows, the gravity wins over and the blob of cooler aluminium drops down, lowering temporarily the temperature of the melt at the bottom of the crucible while opening up the nozzle. We should stress at this point that such an extreme behaviour is rare and stable FIGURE 28.8 (Upper) Aluminium flux recorded for cold-lip narrow nozzle Al cell over a period of 5000 s. Shutter was opened five times over this period. (Lower) Recoding of readings for the thermocouple in contact with the bottom of the crucible collected over the same time period. For both panels, the shaded area on the left shows the cell behaviour with PID temperature stabilisation locked to the bottom thermocouple, while the rest of the data were collected with constant power applied to the cell. The narrow shaded area isolates one cycle. See the main text for discussion (For colour version of this figure, the reader is referred to the online version of this book).

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operation of similar Al effusion cells has been reported by many users. Anecdotal evidence points to surface finish and the exact composition of the pyrolytic boron nitride (PBN) e a typical crucible material e as primary factors responsible for the degree of Al creep in any particular case. Nevertheless, as mentioned earlier, for the growth of THz QCL structures we have been relying on the standard cold-lip 30-cc conical cells. Flux instabilities are not limited to Al cells. Sometimes problems develop with other effusion sources and unless diligent ex situ characterisation of each structure is performed, a great deal of time and effort can be wasted on processing and testing of such unscreened failed layers. Thick periodic stacks of QCLs make XRD characterisation an excellent tool to assess adherence of the grown structure to the original design. Figure 28.9 shows XRD Omega/ 2Theta scans of [400] obtained on QCL structure grown with Ga cell which failed soon after. This particular, undiagnosed at the time, problem manifested itself in random discrete shifts in the flux leaving the cell, resulting in parts of QCL stack being grown at different from target growth rates. This resulted in the splitting of superlattice (SL) reflections, particularly well visible for the highest recorded, 4th order reflection, indicating two other periodicities in the stack differing by 3.6% and 1.1% from the design. For reference, the dynamical simulation of the rocking curve for the nominal structure is also shown in this graph and following two graphs. A less extreme case, shown in Figure 28.10, is a progressive increase in FWHM of SL peaks with increasing the reflection order (i.e. angular distance from the main SL Bragg reflection, in our case not well resolved from the GaAs substrate reflection). This growth was performed without the earlier-discussed compensation of Ga flux drift. Such evolution of FWHM can be used to very accurately estimate the stability of the growth rate throughout the entire QCL stack. In this case,

FIGURE 28.9 XRD Omega/2Theta scans of [400] reflection for a THz QCL structures. The bottom curve shows the dynamical simulation using nominal structure parameters, while the upper curve shows the actual experimental data. This growth was done using Ga cell which subsequently failed. The splitting of SL reflections, particularly well visible for the 4th order reflection, indicates two discrete Ga flux shifts from its target value, by 1.1% and 3.6% (For colour version of this figure, the reader is referred to the online version of this book).

Molecular Beam Epitaxy

Ga flux drifted by about 1% over the 15 h used to grow the active region. Figure 28.11 shows the comparison between the dynamical simulation of the nominal QCL structure and the experimental curve measured on the structure where Ga flux drift compensation was performed using calibration like the one shown in Figure 28.12. For this structure, the layer thicknesses were on target to better than 0.1% across the entire 10-mm-thick stack of 228 repeats.

28.4.2.3 Flux transients The change of thermal environment of the cell upon opening the shutter can cause large flux transients which can last up to several minutes. If present, they can significantly degrade the quality of multilayer structures, particularly for the case of QCLs. The exact shape and magnitude of such a transient will depend on the cell design, shutter-cell geometry, shutter material and the shutter opening sequence used during deposition. Although some relief can be obtained by appropriate cell power ramp during shutter opening, it is best to address the problem with cell and/or cell-shutter relative geometry design choices. The discussion of numerous strategies for compensating or eliminating the transients goes beyond the scope of this chapter. In the case of our MBE system,

FIGURE 28.10 (Upper) XRD Omega/2Theta scans of [400] reflection for a THz QCL structures. The bottom curve shows the dynamical simulation using nominal structure parameters, while the upper curve shows the actual experimental data. No compensation of Ga flux drift, related to the change of the melt level during growth, has been applied for this structure. (Lower) Subsection of the same data showing the high-order SL reflection broadening indicative of 1% drift of the size of QCL individual modules along the stack of 253 repeats, attributed to the drift of Ga flux (For colour version of this figure, the reader is referred to the online version of this book).

Chapter | 28

MBE growth of THz quantum cascade lasers

645

the shutter transients for Ga, as monitored with MIG, are below 1%, while about 1% transient is present for Al cell in a form of small flux deep after the shutter opening, which recovers quickly to the initial level. Such small transients are common for hot-lip SUMO cell designs, while the optimum cell orifice-shutter geometry on V90 reduces this effect further. For the case of Al cell the already small transient was further reduced to the abovequoted value by pulling back the cell in the port by about 3 00 /4 , thus increasing the distance to the cell shutter by the same amount. Care should be taken with this approach to ensure that such a pullback will not result in increased penetration of the molecular beam into the growth chamber with the closed shutter [83].

28.4.2.4 Flux uniformity FIGURE 28.11 (Upper) XRD Omega/2Theta scans of [400] reflection for a THz QCL structures. The bottom curve shows the dynamical simulation using nominal structure parameters, while the upper curve shows the actual experimental data. Excellent agreement of the simulation and experimental scan is seen. This QCL’s structural parameters are within 0.1% of the target values. (Lower) Subsection of the same data showing the high-order SL reflections. The absence of detectable broadening for these high-order satellites, along with the excellent S/N, puts the upper limit for the flux drift during the growth of this 228 repeat RP-type THz QCL at less than 0.1% (For colour version of this figure, the reader is referred to the online version of this book).

The above-discussed possible sources of deviation from design for the grown structures were focussed on temporal growth rate instabilities. For the successful development of structures which critically rely on accuracy of layer thicknesses and compositions, such as THz QCLs, good knowledge of growth rate uniformity across the substrate is just as important. Although large modern production MBE reactors offer very high layer uniformity, it is not often the case for laboratory MBE systems on which novel structures, such as THz QCLs, are developed. It is not uncommon that layer thicknesses vary by more than 3% FIGURE 28.12 (Upper) Contour plots of thickness maps for GaAs and AlAs grown on stationary 100 mm wafer obtained from XRD mapping of periodic GaAs/AlAs multilayer stack. Contours are spaced by 10% of the centre thickness. AlAs was deposited using cold-lip Al 300 g SUMO cell, while GaAs was deposited with 300-g SUMO cell. No power was applied to the tip filament of the Al cell resulting in a steep temperature gradient along the cell which caused strong collimation of the Al cell. (Lower) Uniformity of GaAs and AlAs layer for the growth on rotating substrate derived from the stationary profiles above (For colour version of this figure, the reader is referred to the online version of this book).

646

from the wafer centre to the edge of 300 substrate, despite the substrate rotation during the growth. Although optimal MBE system geometry has been identified over two decades ago [69], the 45
angle between the cell axis and normal to the wafer indicated there is not easy to implement in small systems without some serious compromises. Also, at any given cellesubstrate geometry lateral layer thickness uniformity will strongly depend on the cell design. Creative solutions, such as tailored “shower-head” nozzles for effusion sources, can in part correct cellesubstrate geometry shortcomings, however, often at the price of cell reliability and/or cost. More common are situations where despite good system geometry layer uniformity is poor because of particular cell/crucible design or a particular thermal profile along the crucible. For the case of V90 system discussed here, the cellesubstrate geometry is very close to optimum. Indeed, for AlAs deposited using coldlip Al cell equipped with standard 30-cc conical PBN crucible the uniformity of layer grown on rotating substrate is better than 0.5% from centre to the edge of 300 substrate. In addition, for e-Science cell equipped with Titan twocomponent graphite crucible (designed for Ga or In), an excellent layer uniformity on rotating substrates of better than 0.2% has been demonstrated for our V90 system. However, surprisingly poor uniformity could be obtained under some circumstances on the same system. Figure 28.12 compares flux distribution on stationary substrate (top panel) and layer uniformity on rotating substrate (bottom panel) for hot-lip Ga SUMO and cold-lip Al SUMO. The latter in fact was the same effusion cell which showed strong flux instability (Figure 28.8) discussed earlier. However, this time only 7 g of Al was loaded into the cell which resulted in very good temporal flux stability. It should be pointed out that overall crucible geometry was practically the same for Ga and Al SUMO cells used here. The thickness maps shown in Figure 28.12 were obtained from just one structure which was grown on 100-mm stationary GaAs substrate and comprised 10 repeats of GaAs/AlAs sequence with nominal thicknesses of individual GaAs and AlAs layers (at the substrate centre) ˚ and 230 A ˚ , respectively. The structure was of 270 A designed to elucidate the reason for a very poor AlGaAs compositional uniformity we were measuring across the layers grown using this particular cell combination. XRD map was performed on 5  5 mm grid across the substrate and the data were analysed to extract thicknesses of GaAs and AlAs layers. Obtained in such a way, GaAs and AlAs stationary thickness profiles were subsequently used to calculate the uniformity of GaAs and AlAs across 300 rotating substrate, shown in the lower panel of the figure. It can be seen that Ga SUMO cell gives adequate uniformity across the 300 substrate, with the layer thickness decreasing by slightly more than 1% from the centre to the wafer edge. Very bad uniformity, however, was revealed for Al SUMO

Molecular Beam Epitaxy

cell with AlAs layer thickness dropping by 11% from the centre to the edge of 300 substrate. The reason behind this poor uniformity is the steep temperature gradient we applied along the cell, with cold-lip narrow nozzle at the top of the cell, resulting in a strong collimation of the molecular beam leaving the cell. This is clear from the contour plot of the stationary thickness map for AlAs layers. The situation is very different for Ga SUMO, where the temperature gradient is opposite, with the cell nozzle being much hotter than Ga melt in order to prevent droplet formation in this region. Thus, the nozzle itself in this case is a significant source of molecular flux by efficiently reemitting all Ga atoms which arrive to this region from the rest of the cell interior. Unfortunately, such a mode of operation is not possible in the case of aluminium. Because of the strong tendency for molten Al to wet PBN, keeping the nozzle hotter than the melt would result in Al running out of the crucible and damaging the cell. Nevertheless, a considerable improvement of Al flux uniformity can be obtained for this cell by careful adjustment of the nozzle temperature relative to the melt, to maximise re-emission from this region, yet avoiding the uncontrolled Al migration out of crucible.

28.4.2.5 Substrate rotation-induced layer nonuniformity Even though, as discussed in Section 28.3 of this chapter, substrate rotation is introduced specifically to achieve high growth rate uniformity across the wafer, it can lead to significant lateral thickness variations in situations where the duration of single revolution of the substrate is comparable to the layer deposition time. This is because at any given time a considerable gradient of molecular fluxes exists over the wafer for every source used. The upper panel in Figure 28.13 shows deviation from the target thickness for a point on the 300 substrate 30 mm away from the wafer centre (inset) as a function of an angle the wafer rotates during the said layer deposition. The calculations were performed for the case of GaAs growth in our V90 MBE reactor. It can be seen that nearly 10% error can result if the substrate rotates by only 180
during the layer deposition time. Over one percent error is still possible for this particular location on the wafer if 4 ½ rotations take place during layer deposition and it takes more than twenty revolutions per deposition time to ensure an error smaller than 0.2% (Figure 28.13, lower panel). Such situations can be readily encountered during QCL growth, where AlGaAs ˚ range. With AlGaAs barrier thicknesses are in the 5e50-A ˚ growth rate of 2.71 A/s the respective deposition times are in the range of 1.8e18.5 s. If one substrate rotation takes several seconds e which is fairly common e considerable errors can occur for thin layers. Moreover, for any chosen point on the substrate this error will vary from repeat to

Chapter | 28

MBE growth of THz quantum cascade lasers

FIGURE 28.13 (Upper) Substrate rotation-induced deviation from a layer target thickness as a function of the angle (in units of rad/2p) wafer rotated during the considered layer deposition. The calculation was done for a point 30 mm off the centre of 300 substrate. The inset shows the relative location of this point to the group III effusion cell used for the growth, at the moment of commencing the layer deposition. (Lower) Maximum thickness error which can be made if the deposition time is not synchronised with rotation vs. number of rotations (N) per layer deposition. For the case considered in the upper panel this would constitute rotation by an angle a ¼ p(2N  1) (For colour version of this figure, the reader is referred to the online version of this book).

repeat of the QCL active region module, effectively introducing disorder in the layer periodicity leading to inhomogeneous gain broadening. Also, the error amplitudes shown in Figure 28.13 depend strongly on the location of the sampled point with respect to the effusion cells used at the time of commencing the deposition. Importantly though, as expected, this error vanishes at the same time on the entire substrate if an exact number of wafer revolutions is performed during the layer deposition. This points to what appears to be an effective way of suppressing such a problem by synchronising the rotation rate with the layer deposition time. For the growth of QCLs this is not an easy task, and typically cannot be achieved equally well for all the layers in the period. It takes final amount of time to change the rotation rate, and this change is typically accomplished when the layer is already growing. Therefore, the time evolution of the rotation rate has to be carefully planned in each particular case. The rotation-

647

induced uniformity problems are not limited to thin layers if more than one group III (or group V) element is used for the layer growth, as is the case for AlGaAs. This is particularly obvious if Ga and Al cells are located opposite to each other on the system. With such configuration at any point of time, considerably higher Al composition will be grown on the wafer side closer to the Al cell than on the side facing Ga cell. This effect cannot be compensated by ensuring the integer number of substrate revolutions during the layer deposition and in general can result in a strong vertical AlGaAs compositional modulation. For scenarios where very slow rotation rate is used the resulting modulation periodicity L equals to ℛ AlGaAs  Tr , where ℛ AlGaAs is the AlGaAs growth rate and Tr is the rotation period [84]. For QCL growth rotation needs to be quite fast to aid synchronisation with deposition time and L is often comparable to one ML, thus no longer representing actual period of compositional modulation. Instead, it should be thought of as an effective layer thickness grown during single substrate rotation period, in general not equal to integer number of MLs. Such a proximity of rotation rate to ML deposition rate can lead to a large variety of compositional profiles across the barriers, depending on the exact growth parameters, and relative locations of Ga and Al cells on the system. Figure 28.14 shows two such examples, each calculated for three different cell configurations. It can be seen that for L ¼ 1.48 ML a rather strong compositional modulation on the atomic scale can result, with Al and Ga located opposite to each other. This may have significant consequences, particularly for very thin barriers. Indeed, ˚ (~1.8 ML) scatter of for a nominal barrier width of 5A effective composition along the QCL stack will approach 0.14e0.16 for the points 30 mm away from the wafer centre. Both the above-discussed rotation-induced problems can be to some degree corrected by synchronising rotation rate with the growth time of one QCL period. This will ensure good periodicity of the structure at every point on the wafer, even though the exact period and its potential profile will vary across the wafer. In addition, both the above-discussed problems vanish at the rotation axis position, that is the wafer centre for the case of growth on single substrate. Thus, assuming that the system is capable of excellent lateral layer uniformity otherwise, one can assess the influence of the rotation-induced nonuniformity and effectiveness of applied synchronisation by comparing devices fabricated from the central part of the wafer with these made from material closer to the wafer edge. In the case of QCLs, one would expect that thickness variations of the layers which might be present away from the wafer centre would lead to the broadening of laser gain at the price of decreasing its maximum value. A similar effect on laser gain would be expected from the compositional striations, since they will lead to variations in the

648

Molecular Beam Epitaxy

FIGURE 28.14 Monolayer to monolayer Al0.15Ga0.85As compositional modulations due to substrate rotation rate not being synchronised with the monolayer (ML) deposition rate. The two left graphic columns represent two different sets of deposition and rotation rates for the growth of AlGaAs, one resulting in larger and the other in smaller than one ML thickness L of the grown barrier, which would be deposited over one rotation period. Each graphic row represents a different scenario for relative Ga and Al cell configuration as indicated in the right graphic column (For colour version of this figure, the reader is referred to the online version of this book).

exact barrier potentials from period to period along the QCL stack. The only way to eliminate both kinds of rotationinduced nonuniformities is restricting structure design in such a way that all ternary and quaternary layers (i.e. AlGaAs barriers for typical THz QCL) have thicknesses equal to the integer number of MLs and one or several full wafer revolutions take place over the ML deposition time. Also, if the GaAs growth rate is chosen equal to the AlGaAs growth rate e possible if two Ga cells are used e an ideal scenario is possible, where the rotation rate is fixed to the ML deposition rate for the growth of entire QCL stack, resulting in a high lateral uniformity of both AlGaAs and GaAs layers in the structure.

28.4.3 Doping issues Quantum cascade lasers are unipolar devices. In order to avoid injection-induced space-charge effects destroying uniform bias across all the QCL stack modules, each period of QCL is individually doped. With that the charge remains balanced across the structure, with positively charged ionised doping centres, typically Si, ensuring compensation of the charge of flowing electrons for every QCL stack period. In order to improve the lifetime of electrons on the upper lasing level, which helps population inversion, these dopants are typically placed away from the wells responsible for radiative transitions to minimise ionised impurity scattering. Although some overdoping of

each period may help population inversion by increasing the current at optimum alignment and therefore injection into the upper lasing level, it could also increase the cavity losses through increased free-carrier absorption. One should point out that free-carrier absorption in quantum wells is not a simple problem, since the 2D confinement splits the 3D continuum into subbands, and in the first order the only allowed interactions between the electrons and photons are via direct intersubband transitions. Photon polarisation for these transitions is such that its electric field is perpendicular to the quantum well, and, thus, does not couple directly to the free motion of electrons in this plane [85]. Nevertheless, it has been recently shown [86] that infrared absorption evolves smoothly from resonant intersubband transitions in MQW (i.e. thick barriers between wells), to Drude-like absorption in superlattice in the limit of infinite number of wells with vanishing barriers. Thus, in the context of QCL stack using the Drude-like absorption model is to some degree justified [87], especially with structures with superlattice injector regions. Some groups estimate the loss in the THz active region by calculating the off-resonant intersubband transition, an operation which requires a phenomenological broadening [88,89]. When the photon energy is far from any vertical (in k-space) resonant intersubband transition, one needs to consider the oblique in k-space inter- and intrasubband transitions mediated by scattering processes (i.e. interface roughness, impurities, LO phonon, etc.) [85]. Notwithstanding recent theoretical considerations free-carrier absorption in THz lasers may be a factor

Chapter | 28

MBE growth of THz quantum cascade lasers

counterbalancing increased population inversion with increased doping, thus leading to the maximum of the net gain in the cavity as a function of doping level. Some evidence of this effect has been indicated [70] in the study of the influence of doping on the performance of a 4-well resonant LO-phonon-type THz QCL laser [90], where an existence of a maximum for Tmax has been reported at 2D doping level of about 3.6  1010 cm2 per module, for the investigated doping range of 3.2e4.8  1010 cm2. A complementary study done later on a very similar structure [91] reported Tmax to be largely insensitive to the doping level. This study focussed on a lower doping range of 0.43  1010e1.5  1010 cm2, providing nevertheless some overlap with the previous work [70] by including one device with doping of 3.9  1010 cm2. Clearly, more work is needed to positively resolve the issue of existence of the net gain maximum with increasing doping density in the active region of QCL. Significantly, the best hightemperature laser performances have been reported using three-well resonant LO-phonon-type QCL design with the doping level in a rather narrow range of ~2.2e3.0  1010 cm2 per module (~5.0e6.8  1015 cm3 average 3D doping) [2,23,24,39], while the most recent report [2] with highest Tmax ~ 200 K used the doping level of 3.0  1010 cm2 (6.8  1015 cm3 3D). It is prudent therefore to establish beforehand the background doping level for layers grown in the MBE system which will be used for growing THz QCL, preferably using similar growth conditions. Indeed, background doping levels in the 1015 cm3 range are not unusual for “general purpose” MBE systems. In our case, we typically grow 10 mm of undoped GaAs material for Hall measurements using the cell and growth rate intended for QCL, as well as the same substrate temperature. We also keep the Al and Si sources at temperatures which will be used for the QCL growth, to account for any possible outgassing from these ports or cell shutters. Importantly, we also use the same arsenic flux to account for possible As-assisted transport of Si atoms to the growing layer, which may happen despite the closed shutter [83]. Typically, our backgrounds are below ~1  1014 cm3 as judged by fully depleted test sample and low-temperature mobility of test GaAs/ AlGaAs 2DEGs at ~4  106 cm2/Vs. However, we had a case of unidentified p-type contamination at the level of ~2  1015 cm3, traced to the Ga source used. Another doping effect often considered is Si segregation, which will lead to smearing of the Si doping profile in the growth direction. However, even though some Si from the phonon well will segregate into AlGaAs barrier region and beyond, the band bending which would result from charge separation will be negligible at this low doping level. Also, the segregation length, even at the highest growth temperature used for QCLs of 630
C [92], is expected to be too small to

649

enhance substantially the ionised impurity scattering rate in the photon wells. Nevertheless, care needs to be taken while growing the QCL active region on the highly Si-doped GaAs contact layer to minimise potentially significant Si segregation from this layer into the first QCL module, which can alter its properties considerably.

28.4.4 Surface morphology Quantum cascade lasers rely on vertical transport and therefore are quite sensitive to the presence of point defects, which often propagate through the entire structure introducing parallel conductance paths or even shorting the device entirely. Although large-production MBE reactors typically produce layers with point defect densities below 10 defects/cm2 per mm of grown material, numbers above 50 are more common for laboratory MBE systems [93,94]. Since THz QCL structures are typically thicker than 10 mm, point defect densities higher than 500 cm2 may result. Moreover, the presence of conduction singularities in vertical transport through periodic GaAs/AlGaAs stacks has been reported, with such current shunts often not co-located with detectable morphological abnormalities [95]. In general, three paths to point defect generation should be considered: (1) imperfections in epiready surface preparation; (2) particulate contamination during wafer handling; and (3) point defect generation during the epitaxial process. Point defect surface density traceable to channels 1 and 2 does not depend on the thickness of the layer or the particular structure grown. Point defects generated along the channels 3, often referred to as oval defects, are typically related to Ga or In effusion cells or to particulate generation during shutter opening, and their density scales with the thickness of corresponding material deposited, or with the number of shutter actions during recipe execution. Typically, resolution of the problem is very system dependent. Nevertheless, even for very thick structures such as QCLs, requiring well over a thousand shutter actions, very good surface morphology is achievable in laboratory setting. In Figure 28.15 (right), we show the point defect map obtained using KLA Tencor Surfscan 6200 instrument for a 3-inch wafer with 12 mm-thick mid-infrared GaAs/ AlGaAs QCL structure grown in our V90 MBE reactor. The average point defect density for this wafer is 3.2/cm2 and the majority of defects are of the type showed on the Nomarski image on the right. This type of surface defect has been found to co-locate with outcrops of threading dislocations lying on the <111> planes inclined to (001) surface at 55
angle [96]. The average amplitude of the ˚ , while the lateral extent wavy texture is about 50 A of these defects varies. We note that the surface density of these defects is very small, while the density of

650

Molecular Beam Epitaxy

FIGURE 28.15 Surface morphology of 12-mm-thick mid-infrared GaAs/AlGaAs QCL structure grown in our V90 MBE reactor on a 3-inch substrate. The average point defect density for this wafers is 3.2/ cm2 and majority of defects are of the type shown on the Nomarski image on the right. This trilobite-shape morphological instability is attributed to local perturbation of the epitaxial growth due to the decorated with contamination dislocation outcrop (For colour version of this figure, the reader is referred to the online version of this book).

dislocations, or etch pit density (EPD) in the substrate, is about 5  104/cm2; thus, only a very small fraction of these dislocations give rise to such defects. It is plausible therefore that this morphological abnormality is caused not so much by the dislocation but by some contamination molecule or molecular cluster which is pinned to a dislocation outcrop and floats on the surface during the growth of the structure [95].

28.4.5 Interfacial roughness (IR) scattering One of the widely discussed issues in the context of THz QCLs performance is the role of interfacial roughness. It is widely recognised that atomically abrupt interfaces between two materials (e.g. GaAs and AlGaAs), and thus perfectly flat barriers, are unlikely to be formed at typical growth conditions used for the growth of structures such as QCLs. When switching material systems while depositing wells and barriers the starting surface for the next layer is typically composed of partly completed atomic planes at two or more levels, and thus characterised by irregular islands and/or atomic steps. In addition, depending on the material systems and their exact order, some exchange of atoms between the barrier and well materials will take place as a result of segregation during the overgrowth, and this can be nonuniform over the interface surface [97]. Depending on the growth condition, the resulting interface roughness (IR) can vary greatly, both in typical feature lateral size and in their height distribution, which makes quantitative theoretical analysis difficult. Nevertheless, it is generally accepted that for majority of realistic scenarios IR can be treated as a perturbation to the Hamiltonian taking a form of a static potential localised at interfaces of the structure considered. An equivalent approach is to consider fluctuations in the quantum-well width due to IR and its influence on the energy levels [98]. It is commonly assumed that the IR, essentially standing for the spatial distribution of the local interface displacement h(r), is adequately described by the Gaussian autocorrelation function [99]:

Z

hðr  r1 ÞhðrÞdr ¼ D2h er1 =L 2

2

(28.6)

where r is a vector in the (x, y) plane of the interface, Dh represents the average interface displacement and L is of an order of its spatial variation. The presence of IR perturbation gives raise to elastic scattering, leading to dephasing and related broadening during tunnelling and optical transitions. Assuming no IR correlation from interface to interface, the resulting broadening of the transition between two states represented by the envelope functions, jm(z) and jn(z), can be written as [100e102] Zs1 m;n

pffiffiffiffiffiffi 2 2p pmc 2 2 X 2 ¼ D L dU ðzi Þ½j2n ðzi Þ  j2m ðzi Þ2 3 Z2 h i (28.7)

where dUðzi Þ is the band offset at the i-th interface. There is general consensus regarding the strong influence IR scattering has on the performance of mid-infrared QCLs. This has been considered to be mostly detrimental with main research focus on minimisation of IR scattering [102,103]. Nevertheless, it has recently been argued that IR can benefit QCL performance, if used deliberately to increase the scattering rate off the lower lasing level, thus aiding the population inversion [104]. This can be achieved by tuning with growth temperature the IR correlation length L into resonance (Lq z 1) with the exchange wave vector q ¼ kllkinj (L*q z 1) for the elastic intersubband scattering from the lower lasing level ll to the injector inj. For the case of THz QCLs, the role of IR is less clear with some persisting controversies. Wide wells and small dUðzi Þ due to the low barriers both tend to de-emphasise the role IR. Such a conclusion seems to be supported by fully quantum mechanical NEGF calculation by Nelander and Wacker [105] where the IR scattering in THz QCLs is shown to be negligible. However, an opposite conclusion has been reached in the earlier paper by Kubis, Yeh and Vogl [106], also based on NEGF calculations, where the authors claim that the gain in GaAs/Al0.15Ga0.85 A THz

Chapter | 28

MBE growth of THz quantum cascade lasers

QCLs can be suppressed with IR scattering by a factor of ˚ for mean interface roughness Dh 10, using a value of 10 A ˚ and 80 A for correlation length L, numbers which give them best agreement with the experimental IeV dependence. A comprehensive analysis of the influence of different scattering mechanisms on the spectral gain in resonant phonon depopulation (RP) and bound-tocontinuum (BC) THz lasers, done by Jirauschek and Lugli [60] using the Monte Carlo method, also showed strong sensitivity of the gain to IR, with particularly large effect for BC design. However, for these MC calculations as well

651

as in the theoretical modelling of the spectral gain in the three-well RP QCL which demonstrated Tmax ¼ 199.5 K [2] performed by the same group (Ma´tya´s and Jirauschek), ˚ along with correlation a much smaller value of Dh of 1.2A ˚ length L of 100 A was used, giving good agreement with experimental data. This small value of Dh may appear ˚ ) to be the strange, since one would expect 1 ML (2.83 A minimum step height. This apparent difficulty may be resolved by examining 2D model of interface formation in AlAs/GaAs (Figure 28.16a) and Al0.15Ga0.85As (Figure 28.16b). Lower graphs of both panels show initial FIGURE 28.16 The two graphic panels illustrate schematically the qualitative difference between interface morphologies for (a) GaAs on AlAs interface and (b) GaAs on Al0.15Ga0.85As, assuming two identical starting surface morphologies: rough (left) and smooth (right). The lower graphics of each (a) and (b) panel show the surface morphology before the overgrowth with GaAs, and the upper graphics show the interfacial morphology after the overgrowth with GaAs. Gray and white rectangles represent Al and Ga atoms, respectively (group III sublattice is considered only). The same Al atom distribution is used for both “rough” and “smooth” AlGaAs surfaces in panel (b), with the smoothing effect achieved by redistribution of Ga atoms only.

(a)

(b)

652

surfaces of AlAs and AlGaAs, respectively, before overgrowth with GaAs, for two different surface roughness scenarios, and the upper graphs show the interface structure after the overgrowth. While no change in fDh ; Lg takes place after overgrowing AlAs, there is little resemblance of the interface morphology in the AlGaAs/GaAs system to the original AlGaAs surface morphology. Significantly, the final interface in this case is remarkably similar between the rough and smooth starting AlGaAs surface (actually identical for the chosen random Al distribution). It is clear that regardless of the original surface feature length, the correlation length L (after overgrowth with GaAs) is equal to the average distance ˚ between the Al atoms on the surface (of an order of 10 A for this composition), while Dh may be considered here as being close in value to the average distance between Al ˚ . Even atoms in the vertical planes e again about 10 A ˚ ˚ though such a choice of {10 A, 10 A} for fDh ; Lg is very ˚ , 100 A ˚ } values used in the different from the {1.2 A above-quoted MC simulations [2,60], the product Dh  L ˚ 2 vs. 120 A ˚ 2 e and it is the is actually similar e 100 A product which enters the scattering time (Eqn (28.1)). Seeing that Gaussian autocorrelation function is probably not the best choice for the “discrete” roughness of the interfaces in Figure 28.16b, the performance of such a rather crude atomistic consideration appears to be surprisingly good. The model illustrated by Figure 28.16 highlights another important feature of GaAs/ Al0.15Ga0.85As THz QCL material system: the final IR is expected to be very similar in reasonably broad growth parameter space, which includes choice of growth temperature and III/V ratio, both altering group III surface diffusion length and thus the smoothness of the AlGaAs surface before overgrowth with GaAs. Indeed, the same argument will hold for the AlGaAs on GaAs interface. Although in our laboratory we have not conducted rigorous experiments to verify that, anecdotal evidence seems to confirm such a conclusion.

28.5 FUTURE PROSPECTS There is solid ground for optimism when it comes to the prospects of bringing operating temperatures for THz QCLs into the thermoelectric cooler’s range, that is above ~240 K, while staying within the constraints of the wellestablished GaAs/AlGaAs material system. Current understanding of the key roadblocks opens up paths for further optimisation of the RP direct resonant injection schemes relying on diagonal lasing transition [3]. At the same time, new designs are explored such as two-phonon resonance (TPR) depopulation [107], scattering-assisted (SA) electron injection [36] or phononephotonephonon (PpP) variety of SA approach [73], all offering distinct advantages for high-temperature operation. Other

Molecular Beam Epitaxy

materials for THz QCLs are also being investigated. Since the ladder of electronic levels setting the scaffolding for the QCL operation is primarily defined by the confining potential in the z-direction, i.e. the exact shape of quantum wells and separating them barriers, one is not limited to any particular material system when designing such a structure. The dominant presence of GaAs/AlGaAs in the THz QCLs design has been primarily dictated by the maturity of this material system, excellent lattice matching of wells and barriers in entire compositional range and relatively shallow wells needed to form suitable level structure for generating photons in the THz region. Nevertheless, moving to another material system may offer a significant advantage for THz QCLs, justifying the extra effort necessary for material growth and design optimisation. For instance, improvements in performance are expected in material systems offering larger optical phonon energy ELO, such as wide-bandgap semiconductor compounds. Even though optical phonons are used in QCLs in the RP design for fast depopulation of the lower lasing state, they play progressively more detrimental role as the device temperature is increased and are thought to be the prime reason for fast gain drop-off in GaAseAlGaAs THz lasers with increasing temperature [1,3,32,51]. This is primarily due to ultra-fast electroneLO phonon scattering of thermally excited electrons between the upper un and lower ln lasing levels (see Figure 28.2b), the process which has activation energy of ELO  Zuul . LO phonon energies are much larger for the wide-bandgap semiconductor systems such as GaN/ AlGaN and ZnO/MgZnO than they are for GaAs/AlGaAs materials, with ZuLO value in the well material of 91.2, 72.0 and 36.25 meV, respectively. It has been shown with Monte Carlo simulations that while the temperature increase from 10 to 300 K would decrease population inversion in GaAs/AlGaAs by a factor of 4.48, a decrease by only 1.5 and 1.25 is expected for MgZnO and AlGaN 2 THz devices, respectively [108e110]. Even though such findings provide a strong argument for the possibility of demonstrating THz laser based on wide-bandgap semiconductors operating without the need for cryogenic cooling, significant material quality obstacles have to be addressed first. Nevertheless, recent demonstrations of intersubband optical absorption in nitride-based semiconductor quantum wells [111,112] as well as sequential tunnelling electronic transport though QCL-like devices based on this material system [113] give ground to cautious optimism in this area. Also, in the long term, some breakthroughs may come from nonpolar material systems such as SieGe/Si, where the issue of the LOphonon-assisted thermally activated depopulation of the upper laser level does not exist. Even though the progress appears to be relatively slow in this area, THz EL sequential tunnelling devices have already been

Chapter | 28

MBE growth of THz quantum cascade lasers

653

demonstrated [114e116] placing this material system at the present time ahead of the above-discussed widebandgap compounds. Perhaps the greatest promise for the short-term alternatives to GaAs/AlGaAs for THz QCLs offer materials with lower electron effective mass me . Indeed, THz lasers have already been demonstrated in In0.53Ga0.47 AsIn0.52Al0.48As/InP [117] and InGaAsGaAsSb/InP [118e120] material systems. The key benefit of lower effective mass stems from the increased oscillator strength and decreased electroneoptical phonon coupling, both resulting in higher gain for QCL devices. The expected proportionality of the optical gain to ðm Þ3=2 [121] has been confirmed recently in an experiment comparing the optical characteristics of quantum cascade electroluminescent (EL) devices, all emitting at 10 mm but based on three different material systems: GaInAseAlInAs/InP, GaAseAl0.45Ga0.55As/GaAs and InAseAlSb/InAs [122]. Remarkably, not only was the ðm Þ3=2 dependence confirmed with InAseAlSb devices showing EL by a factor of five larger than GaAseAlGaAs counterparts in the entire current range, but also the EL spectral shape for all three material types was nearly identical with about 10 meV FWHM at 77 K. This finding may indicate that InAseAlSb could well be a very suitable material system for THz QCLs in spite of the very high barriers, highly strained interfaces and lower than GaAs LO-phonon energy.

[11] [12]

ACKNOWLEDGEMENTS

[27]

I would like to express my gratitude to all my colleagues at the Institute for Microstructural Sciences, National Research Council of Canada, who were involved in characterisation and processing of the wafers and devices in our THz project as well as in the maintenance of our MBE laboratory. I would like to extend my particular thanks to Emmanuel Dupont for careful reading and “troubleshooting” of this manuscript and numerous stimulating discussions.

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Chapter | 28

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