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Si/SiGe Material System

The work presented in this thesis contributes towards the development of a terahertz Si/SiGe quantum cascade laser. The effort is one of many within the larger framework of the quest for the first silicon laser, but is driven by specific terahertz applications (discussed in Section~\ref{sec:applications}) as well as the more general benefits that silicon possesses.

Motivation

Albeit an optically pumped device, the furore surrounding the advent of the silicon Raman laser1 highlighted the widespread interest in a silicon laser. In what some have described as the “holy grail” of optoelectronics, the realisation of an electrically pumped silicon based laser promises great value for the semiconductor industry. With the potential displacement of current technology and opening of new opportunities in near-field communications, such technology would be of great financial worth. Despite the difficulties of the requirement to work in the complex valence band with mixed hole states and the highly strained growth, discussed in Chapter~\ref{chp:heterostructure}, silicon has a number of technical benefits over the III-Vs.

CMOS Compatibility

With more than a 98 % share of the semiconductor market2 and mature Complimentary Metal Oxide Semiconductor (CMOS) process technology, silicon based integrated circuits are unrivalled in terms of production cost, volume and yield. Whilst it can be argued that silicon heterostructure devices are not strictly CMOS compatible, the industry has been proven to modify CMOS specifications when the need arises. For example, the formation of the BiCMOS process when the SiGe HBT went into manufacture3 and the introduction of SiGe channels in strained silicon transistors4. With CMOS compatibility comes the possibility of monolithic integration of the laser with other CMOS/BiCMOS devices and the realisation of a complete “system-on-chip”. Not only would this provide an extra economic benefit in terms of manufacture costs, but also significantly improve performance by eliminating some of the data transfer bottlenecks present in hybrid circuit interconnects.

Lifetimes & Phonon Scattering

Residing in different groups of the periodic table, III-V alloys are polar materials. This is a major difficulty in the realisation of a room temperature terahertz QCL as well as preventing operation within the Reststrahlen band around 8-12 THz5. With radiative transitions below the phonon energy, Polar Optical (PO) phonon scattering needs to be addressed. Whilst the process can be controlled somewhat by band structure engineering, such phonon scattering is strongly temperature dependent. This severely reduces the upper state lifetime, impeding the maintenance of population inversion and preventing lasing at high temperature6. As a non-polar alloy, SiGe suffers no such limitations. With negligible PO phonon scattering, the work in Chapter~\ref{chp:lifetimes} records lifetimes that are near invariant up to room temperature and of the same order as those achieved at low temperatures in GaAs .

Thermal Conductivity

The ability to dissipate heat through the substrate is a significant factor in the performance of devices at elevated temperatures. The fact that substrate thinning is required in many III-V QCLs is testament to this. Silicon has a thermal conductivity around three times that of a typical GaAs substrate7 - a further factor contributing to improved temperature performance. The degraded thermal performance of SiGe should be mentioned, and is discussed in Section~\ref{sec:virtual_substrate}.

Optical Transparency

Silicon is one of the most transparent semiconductors in the far-infrared, with an absorption coefficient more than an order of magnitude smaller than that of GaAs\cite{absorption_silicon, absorption_gaas}. With reduced optical losses, lasing in a silicon heterostructure device would be aided by a reduction in the required gain and threshold current.

Buried Waveguides

Silicon processing provides proven wafer-scale technologies for the formation of buried waveguides unavailable in the III-V material system. The advantage of this is largely in circumventing some of the difficulties in producing good quality double-metal waveguides, thus expediting the fabrication process. An investigation of buried silicides for waveguiding is given in Chapter~\ref{chp:electroluminescence}.

Si/SiGe Cascades
\label{sec:sige_cascades}

Silicon germanium devices have received increased attention since the first superlattice growth in 19758. In particular, this enabled the realisation of the MODFET (MOdulation Doped Field Effect Transistor) in 19839, the highly successful HBT (Heterojunction Bipolar Transistor)10 that went into manufacture in 1998 and the strained-silicon MOSFET (Metal Oxide Semiconductor Field Effect Transistor) which is now present in many modern microprocessors. Such advances contributed to the interest in the possibility of a SiGe QCL, with the first formulation made by Soref et al. in 1998\cite{si_qcl_formulated1, si_qcl_formulated2}. The description was fairly broad but delivered ideas for possible band structures and growth considerations. The first Si/SiGe quantum cascade emitter (QCE) followed two years later, demonstrated by Dehlinger et al. in 200011. As already mentioned, it is a requirement that devices are engineered for valence band (hole) operation, discussed further in Chapter~\ref{chp:heterostructure}. Figure~\ref{fig:bands_sige_first} shows the design of the device. Each period consists of five SiGe wells with a Ge fraction of 21-32 %, making a mini-superlattice type cascade with a vertical radiative transition for improved oscillator strength. Grown pseudomorphically on a silicon substrate with 100 nm silicon spacers every fourth period, the structure was not strain compensated, resulting in just 12 periods making up the entire stack. The device produced picowatt intersubband emission around 10 μm, and was an important step in proof-of-concept for Si/SiGe quantum cascade devices.

Figure 1: Valence band diagram of the first Si/SiGe quantum cascade11. \label{fig:bands_sige_first}

In general, progress has been made in somewhat sporadic steps, largely attributed to the challenges in band structure engineering. Initially, the majority of work focused on similar heavy-hole intrawell designs, but investigated more explicitly in the context of a QCL\cite{sige_mir_intra1, sige_mir_intra2}. The end of 2002 saw the first Si/SiGe bound-to-continuum QCE12. It too utilised a heavy-hole transition and operated in the mid-infrared at 7 μm. To achieve the desired 100 meV miniband width and strong HH subband coupling (comparable to III-V designs) the structure involved somewhat demanding growth. It included highly strained layers with a well germanium fraction of 80 %, strain-compensated over 30 periods each consisting of 28 layers to yield a 1.2 μm thick active region. The key factor in the design was overcoming the strain accumulation of pseudomorphic growth on silicon that limits superlattice thickness. This was done by growing upon strain relaxed material (Si$_{0.5}$Ge$_{0.5}$ in this case) known as a virtual substrate. Now a standard feature in Si/SiGe cascades, the substrate and other strain related issues are discussed in more detail in Chapter~\ref{chp:heterostructure}.

A particularly noteworthy development was a design unrealised in the III-Vs, specific to Si/SiGe and constituting the first far-infrared QCE. Demonstrated by Friedman et al. in 2001, the structure is the simplest possible, with a period consisting of a single well/barrier pair13. The unique feature is that the radiative transition occurs away from the Brillouin zone centre, at a finite in-plane wavevector. By engineering the LH1 subband to be higher in energy relative to the HH1 subband below it, the selection rules force an anticrossing with the HH2 subband and produces an inverted mass in LH1. Holes tunnel into LH1 at the zone centre where scattering (primarily acoustic phonon, carrier-carrier or alloy) injects the carriers to the local minimum where the radiative transition takes place to HH1. Carriers are then scattered back to the HH1 zone centre where they can continue to resonantly tunnel to the LH1 state of the next period. Figures~\ref{fig:bands_neg_eff_mass} and \ref{fig:bands_neg_eff_mass_disp} show the simplified band diagram and dispersion relation respectively. Maintaining the inverted mass however proves problematic. Whilst such a feature is easily engineered in strained silicon, it is weakened by strain symmetrisation and is almost completely removed with electric field. Furthermore, the design provides no opportunity for carriers to thermalise between transitions. These flaws are unfortunate since quite high gain is possible in this design and the injection barrier thickness conveniently provides a degree of tunability in the upper state lifetime.

Figure 2: The inverted effective mass quantum cascade, constituting the first far-infrared QCE in Si/SiGe13. \label{fig:bands_neg_eff_mass}

Figure 3: In plane dispersion for the inverted effective mass design. Note the LH1 subband minima away from the zone centre13. \label{fig:bands_neg_eff_mass_disp}

Further far-infrared multi quantum well (MQW) emitters were demonstrated by Lynch et al. in 2002. Progress was made from uncoupled well structures14 to coupled wells15. The coupled well band structure was very similar to that of the aforementioned inverted mass design, with each of the 30 periods made up of a single well/barrier pair. Theory correctly predicted edge emission from LH1-HH1 and HH2-HH1 and the first surface-normal emission (without a grating) from the LH1-HH1 transition also. The work was an important first step for the Cambridge group in Si/SiGe quantum cascade research and lead to the more significant interwell emitter in 200316. The structure comprised of 100 periods of well/barrier pairs, engineered for a photon assisted (diagonal) radiative transition between HH1 and LH1 of adjacent wells. Although the interwell design gives a reduction in oscillator strength, the decrease in tunnelling probability improves the chance of population inversion by an increase in the upper state lifetime. The experiment successfully demonstrated electroluminescence from a number of intersubband transitions and forms the starting point for the work presented in this thesis.