**7. Engineering opportunities and challenges of low dimensionality materials**

The current efforts towards building high quality photodetectors are thinned absorbers as discussed before. Lowering the bulk dimensions, particularly the depth, reduce dark current and hence noise. This trend then naturally leads to the exploration of low dimensionality of the material for better detectivity. It should be noted that quantum dots as controlled 0-D materials are popular in photovoltaics and some recent works in IR detectors as well, primarily because of precision in control of detection spectra. Quantum dots are also popular in quantum photonics as coherent photon sources and single spin state storage, and also as detectors of high-frequency shot noise by exploiting transport characteristics in such systems which make them particularly sensitive as detectors. We briefly discuss some of the transport signatures of interest that emerge from low dimensionality.

#### **7.1 Sub-bands and conductance quantum**

Confinement in dimensions quantize the corresponding momenta, i.e. the number of "wave modes" of the electrons, similar to confinement of EM waves in waveguides. This can be seen in the intermediate dimension pictures and their corresponding density of states show in **Figure 3**. As discussed before, a 1-D to 2-D transition shows the signatures of multiple "1-D" density of states pieces coming together to form the 2-D density of states. This can have profound effect on the transport signatures. These discrete transverse modes are activated as a Fermi level crosses through them on the application of an external voltage and the famous "staircase" transmission structure was observed [22] by von Klitzing as integer quantum Hall effect, giving rise to the notion of conductance quantum for each ballistic transmission mode. These signatures can determine the overall current voltage characteristics of a detector structure, which should be considered when a detector structure is designed. These include negative differential resistance or NDR effect, as seen in resonant tunneling diodes. It should be noted that there are further signatures of fractional quantum Hall effects which again arise in ultraclean superlattices at cryogenic temperatures due to topological nature of such Hamiltonians. These states, in particular 2/5 fraction are of great interest for topological quantum computing [23]. It remains to be seen how these two fields can intersect technologically in a meaningful way.

#### **7.2 Contacts**

Contacts play a critical role in replenishing and diminishing the carriers in the detector material. This action depends on the relative band alignments between the detector material and the contact. For a low resistance "Ohmic" contact, the corresponding carrier band should be close to each other, since any mismatch leads to resistance as the carriers have to jump "up" or "down", resulting in a change in the momentum and energy, which gives rise to resistance from a mesoscopic point of view [24]. A mismatched contact is called a Schottky contact and works through thermionic emission over the barrier or through a tunneling mechanism. Choice of the contact material plays a critical role in building a high-quality detector, see [25] for a detailed exposition. A low dimensionality material may show narrow bandwidths and low density of states, which do not necessarily make good contacts with bulk wiring leads in a circuit. Choice of a well-matched contact material requires considerable effort. As an example, in quantum dot detectors, the contact is not made directly from the wire lead to the dots themselves, rather they live in a matrix of PMMA and graphite complexes [26]. Recent developments include use of graphene sheets and ribbons to form conformal contacts with the dots and then to a metallic lead. In fact, graphene itself required considerable efforts to find an appropriate contact metal [27]. The central engineering challenge therefore is to build contacts of appropriate quality; in a bipolar structure it may mean building good contacts for both electrons and holes, while in a unipolar, the ideal contact might be an Ohmic one with the transporting carrier, say electron and a blocking Schottky contact with the holes.

#### **7.3 Low density of states**

Low dimensional materials often end up showing very low density of states, resulting in low currents even in the case of ultra-low scattering or near ballistic transport. An equivalent analogy of such a case is two cities being connected by a narrow rural one lane road as compared to a four-lane divided highway. The carrying capacity of the former is a bottleneck in transport. This can lead to high shot noise in the material, though cutting down dimensionality may reduce flicker noise due to cutting down of number of possible paths for a carrier to take from one terminal to the other, if the sample is clean. Additionally, 2-D materials may show Anderson localization effect which shows up as an extra resistance in the case of disordered materials, which can then increase and even exceed the flicker noise

seen in bulk samples. It must be noted that while this low current is a critical issue in logic circuits, this is much less of an issue in detectors, and in fact an advantage of low dimension materials by cutting the dark current significantly. However increased noise in disordered materials dictates fabricating high-quality material samples for detector applications.

### **7.4 Blockaded transport**

0 and 1-D materials may show a behavior called the blockaded transport regime. In this regime, due to ultra-low density of states in the material, presence of one electron in the channel "charges up" the channel so much that it prevents another one to enter due to Coulombic repulsion [28]. This is also called the Coulomb blockade. A similar phenomenon can be seen in spin-polarized transport as well, where certain spins are not allowed to go in and out of the channel [29]. Blockaded transport may raise interesting applications for detection since it allows electrical spectroscopy and is a popular method for doing so in STM experiments and molecular electronics [30], though a controlled mechanism for the process will need to be demonstrated before any such application is realized in sensing domain.

## **7.5 Quantum capacitance**

Another consequence of low density of states is the appearance of quantum capacitance in the transport behavior in the material. Quantum capacitance is given as *Cq* <sup>¼</sup> *<sup>q</sup>*<sup>2</sup>*<sup>D</sup>* [31]. It can be seen that as the density of states *<sup>D</sup>* goes down, the capacitance goes down. This capacitance then effects the electrostatics and transient behavior of the detector material with consequences for detector design and operation. As per basic circuit laws, series capacitances add up as harmonic sum, which is dominated by the smallest capacitance in the system. For large bulk systems, *Cq* is substantial and can be ignored in device capacitance considerations, however in nanowires or nanosheets it starts to play a substantial role. Central consequence of this phenomena is diminished control over the detector electrostatics, particularly if the detector is working in photoFET mode. Therefore, it is critical to design a detector keeping in consideration of quantum capacitance in low dimensions.
