State-of-the-art
In the figure we present a comparison of different THz sources that are available for use. Free electron lasers are the brightest available sources but require a synchrotron & are therefore many millions of € in cost. Compact versions are being researched but these are still far from market and likely to cost several €100k once developed. Gas lasers are available with >100 mW powers but again cost > €100k & are large & impractical being pumped with dangerous class-IV, high-power CO2 lasers. A range of electron tube technologies, such as backward wave oscillators (BWOs) and klystrons operate with impressive powers at room temperature but have limited lifetimes & are still expensive ~€100k when the power supplies are included.
GaAs THz QCLs now span frequencies between 0.8 to 4.8 THz[i],[ii],[iii]with output powers up to 1 W at 3.4 THz & 10 K[iv] & & more recently have managed to get above 200 K for operation although the power output falls off significantly to ≤40 µW at high temperatures due to polar optical phonon scattering & backfilling. There are many approaches which mix photonic sources to provide difference frequencies in the THz. Visible and near infrared lasers have been used to obtain THz output but stable output at a specified frequency has been difficult to achieve due to the ×1000 reduction in wavelength. Recently, 300 K mid-infrared InGaAs QCLs have been mixed to achieve 10 to 120 µW output[v], indeed exploiting the above mentioned nonlinear frequency conversion in asymmetric-coupled quantum wells. Such InGaAs QCL chips have also been bonded onto Si wafers[vi], but this chip-by-chip manipulation technology will always be expensive compared to any Si based solution, the non-linear mixing significantly limits the efficiency (both theoretically and practically) & the difference in thermal expansion coefficients will produce serious reliability issues & require low power operation if the devices are to survive with any useful lifetimes. We therefore see a significant opportunity to develop a room temperature silicon-based THz source.
The 1W GaAs QCL powers are only available at cryogenic temperatures, with the output power significantly reduced when the operating temperature of the laser is increased. 200 K operation has been obtained with ≤40 µW output[vii]. These operating temperatures are still below the limit where Peltier coolers can be used. As the output power decreases significantly at higher temperature, it is clear that polar optical phonon scattering limits the ability to produce a high temperature THz GaAs QCL, due to the huge reduction of non-radiative lifetimes with increasing temperature. The limitation of III-V THz QCLs is then due to intrinsic material properties. Group IV materials, however, are non-polar & therefore produce far weaker decrease in the non-radiative lifetimes as the temperature is increased[viii],[ix],[x] circumventing such issues. Experiments with Si0.4Ge0.6 QWs have demonstrated hole subband lifetime reductions of only a factor of 2 between 4K & 225K. Electron lifetimes in Si QWs have similar long lifetimes of ~30ps at 4K[xi]. In n-type Ge QWs a lifetime ~30ps has been measured at T~100K, also for subband separation just below the Ge-Ge optical phonon energy[xii],[xiii]. Si based QCLs will have a number of other advantages over III-V QCLs. Si has far lower free carrier absorption at THz frequencies than GaAs for a given doping density which should result in lower waveguide losses for identically doped material[xiv],[xv]. The ×3 higher thermal conductivity of Si over GaAs should help reduce the threshold current density (Jth). The combination of all these effects could potentially allow significantly higher operating temperatures than III-V lasers. Moreover, QCLs made of Group IV materials will not have any forbidden reststrahlen band of operation so Si-based QCLs will be able to operate at frequencies where no III-V QCL can operate (the 5 to 12 THz range).
For a Si-like band structure on conventional (001) substrates, the electron m* in the tunnelling direction of the Δ-valleys is ~0.93 m0 making it very difficult to engineer QCL structures[xvi]. As a consequence, all demonstrations of Si-based QC emitters have been using to-date p-type material, exploiting hole-to-hole radiative transitions[xvii],[xviii],[xix],[xx]. While electroluminescence has been demonstrated, the large non-parabolicity and high effective masses (m*>0.3m0) have made it difficult to engineer gain above 10 cm–1(see Fig. 2). As a guideline, the lowest calculated Si/SiGe waveguide losses at 3 THz, requires at least 16 cm–1 of gain from a QC design to produce lasing while metal-metal waveguides which are simpler to fabricate and provide higher operating temperatures through better thermal management requires 20 cm–1, which is therefore a good guide for the gain value required for a QCL.
Plausibility of proposed research and foundational nature.
In this proposal, we propose to use pure Ge QW designs & L-valley electrons for the first experimental demonstration of a n-type Ge/SiGe QCL grown on a Si substrate. Recently, a number of publications have demonstrated intersubband transitions[xxiii]. Their narrow line-shape demonstrates the high degree of control achieved in the deposition process resulting in an excellent crystal & interface quality[xxiv]. This feature, together with the measured long non-radiative relaxation times and the estimated gain in optical pumped n-type asymmetric Ge QWs suggests that these structures are suitable for the development of THz emitters.[xxv] We show below that the low effective mass m* =0.118m0 and the long non-polar lifetimes[xxvi]. In the Ge/SiGe system provide gain close to values demonstrated in GaAs THz QCLs at 4K and potentially allow 300K operation. Furthermore, the cheap & mature available Si process technology will allow at least a ×100 reduction in the cost of THz QCLs compared to GaAs devices. Such devices could be further developed into vertical cavity emitters (i.e. VCSELs – no such III-V THz demonstration to date) using transitions from different valleys for parallel imaging applications or integrated with Si photonics to allow THz bandwidth telecoms. Finally we propose to also investigate optically pumped structures[xxvii],[xxviii],[xxix] to better understand the material gain. Moreover, these structures have the potential for broadband tunability, higher output powers, and higher operating temperatures than THz QCLs.
These promising n-type Ge on Si heterostructureshave been recently made available thanks to the very recent developments in SiGe epitaxy, driven by interest in Ge on Si nanoelectronics and Si photonics with Ge photodetectors[xxx], in particular with the development of high-quality buffer layers[xxxi] and Ge on insulator wafers (GeOI) suitable for low defect density, Ge-rich heterostructures. With the low m*, the n-type Ge on Si heterostructure system is thereforemuch more promising than any previous Group IV system for realising a Si-based QCL, especially as the lower m* results in higher tolerances to heterolayer thickness fluctuations. These new developments and the background physics suggests that Ge QCLs are now a high risk with high reward approach to achieving a cheap and practical THz laser with room temperature operation.
The concept of n-type QCLs using Ge QWs on Si substrates was suggested by Driscoll & Paiella[xxi][xxii]. FLASH consortium comprises one partner with long standing experience in high-quality SiGe heterostructure growth by CVD, & one partner with industrial CVD equipment for SiGe thin film growth. We believe these high quality heterolayers on low defect density buffers with pure Ge QWs will be the key to the demonstration of a n-type Si-based QCL.
We propose to work on the two most successful designs of THz QCLs in the GaAs materials system: bound-to-continuum and phonon depopulation. The m* in the tunnelling direction <001> of these QWs is calculated to be 0.118 m0, which is far closer to the GaAs value of 0.067 m0. The lower m* and greatly reduced non-parabolicity will significantly increase the dipole matrix element and gain for such designs.
These findings provide confidence that n-type Ge QCLs are the best approach to achieving a QCL on a silicon substrate operating at room temperature which would provide a step change in cheap, practical and high power THz sources for a wide range of applications.
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