OAI-PMH como alternativa para la recolección de los datos

In QCLs, transitions between subbands are used as opposed to transitions between the conduction band and valence band. This allows for low energy transitions and hence low frequency laser emission.

The building block of the QCL is the QW. Semiconductor QWs are one dimensional potential wells of finite depth with wave functions that penetrate into the surrounding barriers. For multiple quantum wells, if the barrier thickness is sufficiently reduced, the tails of QW wave functions can reach across and experience the potential confinement of adjacent QWs. In the most basic case of two identical QWs with a thick barrier, the wave functions are the same in each QW and the wells are not coupled. As the thickness of the barrier between the two QWs is reduced, the wave functions become degenerate in energy with an energy gap between them. This can be extended to multiple QWs. The wave functions can be delocalised over many QWs with a small emery gap between each, forming a broad energy continuum called a miniband. This is important for QCL design.

The idea behind QCL operation, was originally proposed by R.F. Kazarinov and R.A. Suris in 1971 [50]. This was the use of a staircase of QWs for light amplification. The staircase is created by applying an electric field to a multiple QW structure. Electrons can cascade down the QWs with a photon emitted at each step. Unfortunately, lasing was not observed experimentally from this design. This was due to non-uniform uniform electric field formation and the emission of longitudinal optical-phonons (LO-phonons).

A benefit of using intersubband transitions in a laser is that that the active region can be easily cascaded. Carriers travel from period to period as they cascade through the structure. The cascade has two significant advantages. A single carrier has the potential to emit a number of photons equivalent to the number of periods in the cascade, increasing the devices efficiency. Also, less population inversion is required per period for a cascade, since the gain is occurring over a larger area. This gives a lower threshold current for the device.

Despite the many challenges, the use of a biased superlattice for light amplification has gone on to be the foundation of the QCL. Lasing in QCLs has been achieved by using multiple coupled QWs to form a miniband in each period of the active region as opposed to the single QW that was used in each period of the early biased superlattices intended for light emission. This is the reason behind the complex designs seen in QCL structures.

The QCL period can be split into the following regions, an active region, where light is emitted by an optical transition between subband energy levels and a

injector/extractor region which is responsible for quickly extracting the electrons from the lowest lasing level in the active region and injecting them into the top of the next active region. These regions are illustrated in figure 2-2. It is important that that correct electric field is applied to a QCL structure to give the band-alignment required in the regions for radiative transitions in the active region.

Figure 2-2 - Simplified schematic diagram of regions in a QCL structure period. The energy levels indicated all lie within the conduction band. Adapted from [51]

Intersubband emission was first observed in 1988 in the terahertz spectrum from a GaAs/AlGaAs superlattice grown by organometallic chemical vapour deposition [52]. Due to the many challenges present in fabrication a functioning QCL, it was not until 1994 that lasing was observed in a quantum cascade structure, at Bell Labs at a frequency of 75 THz [53] by Faist et al. This was achieved in a AlInAs-GaInAs superlattice grown by MBE. The active region in this design utilised fast optical phonon (LO-phonon) scattering to quickly remove carriers from the lowest lasing level. In 1997, a new bound-to-continuum (BTC) QCL active region design was presented [54]. In this structure, the laser transition is between two minibands and the rapid carrier scattering within a superlattice is utilised to give population inversion.

Figure 2-3 - Schematic diagram of the relevant levels and injection efficiencies in a cascade laser. Adapted from [55]

For a QCL, gain, , is proportional to the population inversion, , that exists between the upper radiative state, and the lower radiative state, . If, as is shown in figure 2-3, a fraction of the current flow is injected into the upper state of the active region and a fraction into the lower state, the gain can be described by equation 2-1 [56], where are the total lifetimes, the intersubband scattering time between the and states and the transition cross section.

( (

) ) 2-1

It can be seen from equation 2-1 that the gain of the laser is strongly dependant on the efficiency of the injector region and the ratio of the lifetimes. If the injector region is efficient, a large fraction of the carriers is injected into the upper state, creating a large population inversion. Also, if the carriers have a long lifetime before being non-radiatively scattered between the upper and lower states, and a short lifetime before being removed from the lower state, a large population is created. A QCL design must aim to maximise - and minimise

reasonable gain. Since the injection efficiencies and lower state lifetimes are difficult to both predict and measure [55], equation 2-1 is not ideal for predicting device gain, however it is useful in explaining the different strategies employed in QCL design.

The two QCL designs which have come to be accepted as the most successful in the THz regime GaAs QCLs [10] are the bound-to-continuum and the phonon depopulation design. Bound-to-continuum designs use radiative transitions between an isolated state and a miniband. The miniband both quickly depopulates the lower laser level by electron-electron scattering and then acts as an injector into the single bound state. The efficiency of the injection into the upper radiative subband is intended to be maximised by this design [56]. In the phonon depopulation design fast electron–optical-phonon scattering is utilised to depopulate the lower laser level [14,57].

An example of the simulated bandstructure in a bound-to-continuum Si/Si0.15Ge0.85

QCL design is given in figure 2-4 for the L-valley (conduction band minima at the L- symmetry point of the Brillouin zone [192]). The design has been calculated by Dinh

et al [60] using a density matrix method which includes coherent transport and

Figure 2-4 – Example of bound-to-continuum Ge/Si0.15Ge0.85 QCL design adapted

from [59]. The simulated conduction band profile and electron wavefunctions are shown for two periods of the structure. The design has a repeating period of 6 QW’s,

with thicknesses (in nm) from the left of the figure of

5.0/1.2/14.3/1.3/12.9/1.6/7.9/1.8/7.1/2.5/7.8/4.3 where the italic font represents Si0.15Ge0.85 barriers, the standard font Ge QW’s and the underlined sections regions

doped at 8 x 1018 cm-2. The wave functions in bold lines are the upper laser states and the wavefunctions in dotted lines the lower laser states.

The lasing transition in figure 2-4 is between the two states in the widest quantum well, the main QW, with a frequency of 4 THz. The barrier to the left of the main QW is known as the injection barrier, since it is the main factor in determining the injection efficiency into the upper radiative subband in the main QW. A miniband is formed by the wave functions from the QWs between the main QWs. Due to the lattice mismatch of Si and Ge, a structure of this kind must be grown on a virtual substrate (discussed in section 2.5).