3.1.

Exploiting new materials and strain engineering

Typical type II quantum well of the active region in an ICL is composed of two InAs layers to confine electrons and one GaInSb layer for confinement of holes, all usually surrounded by AlSb barrier. Such structures are called “W-shaped” as the potential profile resembles the “W” letter. The use of a double InAs layer for confinement of electrons increases the oscillator strength of the optical transitions, when compared to a single sequence of just InAs and GaInSb. The respective band diagrams of an exemplary structure and its fundamental confined states are shown in Fig. 1 compared to a type II structure with a single InAs layer to visualize the wave functions’ overlap enhancement.

Figure 1.

Band diagrams and the fundamental states wave functions in typical InAs/GaInSb QWs of type II (left) and W-shaped (right) designs.

As the entire system is nominally strained (independently of the used substrate, which is GaSb or InAs) on one hand, and on the other to obtain enough gain for lasing relatively large transition intensity (absorption) is needed, the layer thicknesses are usually very thin (in the range of 1-4 nm) and the In content in the GaInSb layer is kept below 40% (to do not exceed about 2% of the compressive strain). Figure 2 shows the dependence of the fundamental type II transition energy and the related squared overlap integral of the electron and hole wave functions versus the thickness of the InAs layer of a “W” quantum well (as this is the most efficient tuning parameter).

Figure 2.

InAs layers’ thickness dependence of the transition energy (wavelength) – left, and squared wave functions’ overlap – right.

It can be seen, that nominally these type II structure can cover the spectral range of emission from below 2.5 to about 10 µm at least, and that using W-design allows pushing the active transition further to the infrared while increasing the transition oscillator strength significantly. However, when going beyond 6 µm the squared overlap gets below 0.2, which is already very low with respect to build enough gain and reach the lasing thresholds. Therefore, this is one of the main active region parameters requiring improvements.

In spite of the abovementioned successful development of ICLs utilizing such QWs, their apparently reached limitations, and hence, one of the routes to further exploit this kind of interband cascaded scheme is to modify the active material and use the strain engineering as an additional tool. We have proposed¹⁰ to use GaAsSb material for confinement of holes, which makes the QW layer tensely-strained, in contrast to GaInSb, where the amount of strain can be regulated by the composition. The tensile strain causes a reversed order of the valence band edges (the light band edge at k = 0 goes above the one for heavy holes), which in the quantum well where different effective masses are involved yet plus the states intermixing that the character of the QW ground state for holes can be continuously tuned from fully heavy hole (HH) to fully light hole (LH) character. Figure 3 shows schematically how the confinement potential changes in function of the arsenic content in the GaAsSb layers.

Figure 3.

Band edge diagrams for three As contents in W-design InAs/GaAsSb/InAs QWs.

This has important consequences to all the optical properties, including also the wavelength tunability as well as the wave functions’ overlaps. The latter are, in general, increased due to mainly the contribution of the light hole sates to the lowest valence band confined state, i.e. a decreased effective mass translating into broader wave function extension and hence better overlap with the electron wave function. Figure 4 shows examples of the squared wave functions moduli for InAs/GaAsSb/InAs of two different compositions.

Figure 4.

Squared moduli of the wave functions for InAs/GaAsSb/InAs QWs of two different compositions.

Figure 5 shows the spectral tunability of the optical transitions for the two lowest valence band states, which is at least as good as for GaInSb-containing QWs but with significantly larger oscillator strengths - the squared overlap integrals can be larger from about 20% at shorter wavelengths to even a factor 3-5 at longer wavelengths of the MIR.¹⁰ It is seen in Fig. 5 that for the particular example the ground state character switches from heavy into light hole for about 16% of arsenic. The bottom part of the figure plots the value of the strain in the given range of As contents in order to show that up to about 20% of arsenic they are well below 2%, i.e. realizable from the practical, epitaxial growth point of view.

Figure 5.

Transition energies (wavelengths) in function of the As content for InAs/GaAsSb/InAs QW; the amount of strain is shown at the bottom.

3.2.

Tailoring the valence band mixing for polarization independence

The valence band states intermixing effects are even more important for the dispersion relations beyond k = 0, which contribute significantly to total absorption and hence the laser gain function in the conditions of high carrier concentrations as in operational devices. Therefore, in order to account for the mixing effects properly the respective contributions must be integrated over k. On the other hand, the optical transitions selection rules are polarization dependent and for the edge emitting devices the states mixing affects the ratio between the TE and TM linear polarizations – increasing the LH contribution makes the transition more TM polarized, which for typical compressive strain structures are dominated by heavy holes and hence the gain is also predominantly TE polarized. Using tensely-strained material of GaAsSb allows tailoring this dependence. To calculate the gain spectra the transitions rates are integrated k_|| for all the interband transitions, where the transitions rates are weighted by the corresponding population factor [f_n^c(k_||)-f_m^v(k_||)], where f_n^c(k_||) and f_m^v(k_||) are the Fermi distribution functions for electrons and holes, respectively, at given temperature. To include the spectral broadening in each transition caused by all sources of the electron scattering, we convolve the expression for the optical gain with Lorentzian line shape function over all the transition energies. Eventually, the optical gain is calculated for different carrier injection densities to simulate the experimental conditions. More details can be found in Ref. 26.

Tuning all the described parameters for the strain-controlled type II QW structures allows finding conditions where the TE and TM gain functions become equal, in some range of wavelengths at least. Figure 6 shows an example of the derived gain functions for W-design InAs(2.8 nm)/GaAs_0.12Sb_0.88(7 nm)/InAs(2.8 nm) QW. It is seen that gain in both polarizations is equal in the 3 µm range. This result paves the way towards polarization independent emitters or amplifiers in the MIR.

Figure 6.

Transition energies (wavelengths) in function of the As content for InAs/GaAsSb/InAs QW; the amount of strain is shown at the bottom.²⁶

3.3.

Enhanced electric field sensitivity for passive mode-locking

In order to realize a passively-mode locked device the absorbing medium dynamics should be much faster than the gain medium dynamics, i.e. τ_a<<τ_g. One can consider using electric field as a tool to affect oscillator strength of the active optical transition, which is inversely proportional to its lifetime. However, to make such an approach efficient, high sensitivity of the tailored quantum structure to external bias is required. As the strain-engineered “W” structures involve more light-hole-like valence band states, their wave function is more extended in the real space in the z direction, and hence greater layers thicknesses can be taken into account. This then turns into higher sensitivity to external electric field. Figure 7 shows the calculated electric field dependence of the relative oscillator strength (with respect to case of zero electric field) and the related transition energy (emission wavelength) for W-design type II QW made of InAs(6 nm)/GaAs_0.2Sb_0.8(7nm)/InAs(3.6 nm). It is worth underlining, that the used QW layer thicknesses are indeed larger than those for InAs/GaInSb structures, and that the two InAs wells confining electrons are of different thicknesses. The latter is due to the electric field effect which in one of its directions makes this partly asymmetric system even more asymmetric (lower oscillator strength) and in the opposite symmetrize the structure and enhances the transitions oscillator strength (shorter lifetimes as required in the saturable absorber section). For the discussed case, a change of the oscillator strength by a factor of 5 could be obtained in the fields’ range of -100 to +100 kV/cm, which is promising from the point of view of the mode-locked operation. This is especially as it concerns the possible emission wavelengths of about 4 µm, i.e. in target range of many gas sensing applications. However, similar data can also be obtained in other ranges of MIR from about 2.5 to 6 µm at least.²⁷

Figure 7.

Electric field dependence of the fundamental transition oscillator strength (calculated with respect to the case without electric field) and transition energy (emission wavelength) for W-design InAs(6 nm)/GaAs_0.2Sb_0.8(7nm)/InAs(3.6 nm) QW.²⁷

3.4.

Strain-free active region

As the involvement of compressively and tensely strained materials is possible in these MIR emitting type II structures, one can combine both into one system and aim at a fully strain-free system. This would be crucial for growth technology and easier multilayer device fabrication, but it also opens up new possibilities of the band structure and optical properties engineering, as the layers’ critical thickness is not a limiting factor anymore.

In addition, when quaternary materials are included, the energy gaps can be tuned independently, which connected with varying the layers’ thicknesses give basically a full freedom in the emission wavelength coverage for such QWs. As the two kinds of substrates used, InAs and GaSb, differ slightly in their lattice constants, the unstrained system must be different in both cases. For holes’ confinement material it means a different composition of GaInAsSb layer, whereas for electrons’ QW it can be or pure InAs (for the InAs substrate) or InAs_0.91Sb_0.09 (lattice-matched to GaSb).

Figure 8 shows the results of calculations for numerous type II quantum wells and their various parameters, however all for compositions lattice-matched to InAs or GaSb. It proves, on one hand, that indeed the unstrained QWs can be designed for any wavelength of the 3-10 µm range, and beyond, but on the other hand, that the transitions oscillator strength (expressed via the squared wave functions’ overlap integrals) are significant in all cases, i.e. suitable for the use in the active region of ICLs.

Figure 8.

Optical transition energy (and the related emission wavelength) as well as the squared overlap integrals for various In(As,Sb)/(Ga,In)(As,Sb)/In(As,Sb) with different layers’ thicknesses and compositions assuring the lattice matching to an InAs or GaSb substrate.