**1. Introduction**

Thus far, the profusion of terahertz wave applications, including high-speed communications, industrial quality control, non-destructive cross-sectional imaging, gas and pollution sensing, biochemical label-free sensing, pharmacology, and security screening, has been demonstrated [1–3]. Moreover, the development of terahertz quantum cascade lasers (THz-QCLs) based on semiconductor quantum structures affords an attractive THz radiation source with coherent and compact wave features [4]. The basic radiation mechanism in this type of laser is intersubband transitions relying on quantum transport between discrete subbands. This method prevents the semiconductor bandgap limit at significantly low THz photon energies. The subbands can be freely tailored via engineering the thickness of quantum layers; therefore, the THz radiation frequency coverage is broad. However, THz-QCLs always suffer from temperature-triggered lasing quenching; consequently, the maximum operating temperature (*T*max) is still limited to below room temperature and thus requires additional cooling. Notably, despite stable progress since the first reported THz-QCL operating at 50 K (4.4 THz, pulsed mode) [5],*T*max has been stalled since 2012 (199.5 K) [6]. A recent breakthrough, achieving 250 K operation [7], indeed soothes the uncertainties regarding whether a 300-K-operation is prevented by any physical limit. The result has since spurred further efforts to achieve room-temperature operation.

With regard to the high-temperature THz-QCLs designs, different theoretical models, including density matrix formalism [8–10], non-equilibrium Green's function (NEGF) [11–13], and Monte Carlo techniques [14, 15], have been proposed to understand the effects of temperature on quantum transport, that is, the loss of coherence, parasitic tunneling channels, and non-radiative processes with an increase in temperature. Numerous designs have been proposed, for example, by using diagonal radiative transitions [3] to suppress the thermally activated non-radiation channels (that triggers longitudinal optical (LO)-phonon emission instead of photon emission) between the upper and lower laser subbands, by using phonon resonance to depopulate the lower laser subband [6] yielding higher population inversion and partially relaxing the thermal backfilling, or by using clean subband systems [7] to avoid perturbation from high-lying subbands. Most of these designs use the resonant tunneling (RT) injection mechanism to populate the upper laser subband. In fact, the core feature of QCL design is electrons cascading across hundreds of stacked radiation periods. Therefore, a critical innovation in QCL design is the development of an injector region to maintain stable electrical bias in operations, enabling the first successfully operation of QCLs in the mid-infrared range [4].

However, RT injection in THz-QCLs has several drawbacks, which are illustrated in **Figure 1a**. 1) *Resonance alignment between the injector and upper laser subbands.* Electrons always wait for resonance before being injected into the upper laser subband (*i* ! *u*). Ideally, in the coherent transport regime, the upper laser subband *u* holds as many carriers as the injector subband *i*, which is half of the total available electrons (that means a maximum of 50% share in the upper laser subband). In reality, with a thick injector barrier and the presence of multiple scattering channels, the population inversion generally falls below 50% at low temperatures. 2) *Thermal backfilling*. Moreover, as the injector subband *i* is already mostly populated, thermal backfilling to the lower laser subband *l* cannot be neglected at high temperatures [16, 17]. This process

**Figure 1.**

*Illustration of resonant tunneling (RT) injection (a) and phonon assisted injection (direct-phonon injection) (b).*

### *High-Lying Confined Subbands in Terahertz Quantum Cascade Lasers DOI: http://dx.doi.org/10.5772/intechopen.105479*

introduces twice the adverse impacts, reducing the population inversion by decreasing the injected population and refilling the lower laser subband *l* simultaneously. Given that the population inversion is defined as the difference between the upper and lower laser subband populations, the inversion will undergo significant degradation. 3) *Selective injection issue*. Owing to the small subband energy separation, THz-QCLs face difficulty in selectively injecting electrons into the upper laser subband, while avoiding incorrect injection into the lower laser subband. To enhance this selectivity, the injector barrier (**Figure 1a**) should be chosen meticulously, on one hand, the barrier needs to be sufficiently thick to suppress incorrect injection and reduce the negative differential resistance (NDR) during parasitic alignment bias (i.e. the injector subband *i* and lower laser subband *l* will first align (*i*\$*l*) before reaching the operational bias). However, on the other hand, this barrier must also be sufficiently thin to increase the dynamic range of the laser current density. It is important to note that, owing to the close energy spacing between subbands *u* and *l*, the subband alignments *i*\$*u* and *i*\$*l* occur with similar electric fields. The constraint on the injector barrier worsens when the device lasing frequency approaches small. All the aforementioned RT-QCL issues result in significant challenges in terms of maintaining the population inversion when the operating temperature approaches 300 K, thus impelling designers to develop novel approaches to overcome the bottlenecks associated with RT injection.

An indirect injection scheme (scattering-assited (SA) injection), by designing the injector subband *i* to lie one LO-phonon energy above the upper laser subband *u* (**Figure 1b**), has also been reported [16, 18–20]. SA injection can be traced back as early as 2001 by Scamarcio *et al*. [21], where the method was successfully employed in midinfrared QCLs [17] to inject electrons into the upper laser subband by resonantly emitting phonons from the injector subband (*i* ! *u*). In this case, by combining a diagonal radiative transition, the parasitic off-resonant tunneling from the injector subband *i* to the lower laser subband *l* also can be suppressed. Therefore, this scheme may offer a venue for realizing higher population inversion, even at 300 K. Previous reports [16, 17, 19, 21] provide comprehensive discussions on how SA-QCL designs address the shortcomings of RT-QCLs. However, only three-well [22], four-well [16], and five-well [19] SA-QCL designs have been studied. Moreover, in high-temperature THz-QCLs designs, it is found that a higher *T*max also results from a shorter period length by decreasing the number of desired subbands (seven-well [23], four-well [24], three-well [6], and two-well [25]). In this work, we attempt to study the SA injection in THz-QCL designs based on a short period length that contains only two wells. The result demonstrates a strong deviation between the optical gain and population inversion. In other words, although high population inversion can remain in such designs, when the lasing frequency exceeds 3 THz, the peak gain is considerably small even at low temperatures. This phenomenon is ascribed to the emergence of specific parasitic absorption, which can closely overlap with the optical gain. However, this limitation can be avoided in low-frequency lasing. This implies that specific strategies are required to alleviate the shortcomings of different lasing frequencies when introducing short-period SA injection designs; here in the final part of this work, we also study the feasibility in using step well quantum structures to suppress the absorption effects on the gain.
