Discussion

As follows from the above results, the GLIPs under consideration can have high responsivity and detectivity in near and far IR spectral ranges. The GLIPs with Д ~ 0.1 eV can operate also in the terahertz range fuo ~ 0.025 - 0.05 eV{h(o/2n ~ 6 - 12 THz), exhibiting reasonable values of the responsivity and detectivity.

In Section 50.4, we have omitted the analysis of the responsivity spectral behavior in the range of very low photon energies, because the interband absorption in this range can be complicated by the smearing of the carrier spectrum, fluctuations of the potential profile (existence of the electron-hole puddles), and formation of a narrow energy gap (due to specific doping or substrate properties) [34-39]—factors which are not described by Eqs. (50.2) and (50.3) and, hence, are beyond our device model.

The barrier height for the thermalized electrons in the GLIPs with doped GLs is equal to ⁼ A^fdoped) + £gl- This height determines both the tunneling and thermionic dark currents. Comparing the dark currents in a GLIP with the acceptor doped GLs and with that in a GLIP with undoped GLs but with a higher barrier (A(^und°P^ed) = Atherm > A^(doped)), one can find that these currents are equal to each other or, at least, of the same order of magnitude. In contrast, taking into account that the barrier heights for the electrons photoexcited in the doped and undoped GLs are equal to A^(doped) - h(o/2 and д(ипс1орес1) - hco/2, respectively, we conclude that the escape rate of the photoexcited electrons and, hence, the GLIP responsivity in the former case is larger than that in the latter case (because A(^d°P^ed) c A^(undoped)). Thus, the GL doping by acceptors offers better GLIP performance in comparison with the GLIPs without doping of the GLs but at an elevated barrier height (larger difference in the GL and barrier material affinities).

Calculating both the photocurrent and the dark current in the GLIPs with the doped barriers, we have disregarded the effect of the donor and acceptor spatial fluctuation in the device plane. These fluctuations can lead to pronounced fluctuation of the electric field Eqi and, consequently, the tunneling current created by the photoexcited and thermalized electrons (see, for example, Refs. [40, 41]). As for the photocurrent and, hence, the GLIP responsivity the fluctuations in question promote an increase in these quantities. This implies that the values of the GLIP responsivity can somewhat exceed those obtained above. Since, considering, the detectivity focused on the GLIPs with undoped barrier layers, the problem of doping fluctuation is out of the scope of this work.

Since the photoexcited and injected electrons acquire kinetic energy propagating across the device under the electric field, they can be hot. If the electron energy relaxation length L_f = v_dr_f, where u_d and r_f are the electron drift velocity and the energy relaxation time, respectively, exceeds the heterostructure period d, the electron effective temperature T_eff is mainly determined by the applied bias voltage V [42]. An increase in Pleads to an increase of ^eff and to a drop of the capture efficiency p [30] (see also references therein). Since the responsivity R_a °c 1/p [see Eqs. (50.6) and (50.7)], the electron heating promotes higher values of the responsivity. As demonstrated by the particle Monte Carlo modeling of the electron capture into quantum wells (QWs) in heterostructures (albeit made of the standard material) with doped barriers [43], the doping affecting the potential profile in the barrier layers can result in a somewhat steeper drop of the capture efficiency with increasing voltage. The hot propagating electrons can provide a heating of the carriers localized in the GLs enhancing the electron thermionic escape. Apart from this, some fraction of the energy of the absorbed photons goes to the carrier heating [21]. This can lead to a decrease in the GLIP detectivity. However, one might expect that at a small capture efficiency and not too high radiation intensities, the negative impact of the heating is not too strong. The electric field across the GLs, modifying the wave functions of the photoexcited and thermalized electrons and, hence, the try-to-escape time, can lead to an increase in both the photocurrent and the dark current. This promotes higher values of the GLIP responsivity, but can add complexity to the voltage dependences of the GLIP detectivity. The consideration of the latter, as well as more rigorous treatment of the thermo-assisted tunneling, requires a generalization of the GLIP model that is beyond the scope of this work.

Generally, the selection of materials for the GLIPs from a wide variety of them is a matter of using of a proper band alignment (see, for example, Refs. [14, 44]). Several already fabricated and experimentally studied devices using the vdW heterostructures with the GLs, which can serve as the reference points for the GLIP realization, were reported recently [45-49]. The GLIPs with relatively low barriers able to operate in the THz range can be based on the Oxide family materials with the electron affinity close to that in GLs (for example, Ru0₂ and Ti0₂ [50]).

The comparison of the GLIP characteristics with the characteristics of photodetectors, using similar operation principles, namely with intersubband quantum well infrared photodetectors (QWIPs) [25, 29] shows the following advantages of the former:

• (i) A higher responsivity due to both higher probability of the electron photoexcitation associated with the use of the interband transitions in the GLs and the intraband (intersubband) transitions in the QWs;
• (ii) A higher detectivity associated with higher responsivity and weaker dark current (due to a larger activation energy);
• (iii) Sensitivity to normally incident radiation (because of the use of the interband transition), so there is no need in special coupling structures;
• (iv) No need in the GL doping, although such a doping, as shown above, pro videsan opportunity to vary the GLIP characteristics, in particular, enhancing the GLIP performance;
• (v) Possibility of the GLIP operation in the range hco^ 0.025 - 0.05 eV (co/2n ^ 6-12 THz), where using more conventional materials (e.g., III-V compounds) is hindered by optical phonon absorption;
• (vi) Additional optimization is possible by changing the applied bias. As seen from Eqs. (50.4) and (50.5), such an optimization could be reached in the voltage range on the order of V ~ 8л

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