**6. Leveraging bandstructure engineering for better detectors: artificial materials**

Advances in fabrication capabilities at atomic levels, using techniques such as molecular beam epitaxy (MBE), atomic layer deposition (ALD), high precision sputtering and chemical vapor deposition (CVD), and colloidal chemical deposition has brought to us the marvels of building novel materials from ground up; materials such that nature does not build on its own. The use of such materials have proliferated many fields of applied sciences and engineering and new applications come up every few years. In the context of Electrical Engineering, such high precision artificially created nanostructured materials include superlattices, which are candidates for the "next transistor" material. One such example are high mobility GaAs| AlGaAs quantum wells which have been candidates for such devices [19] for a long time, and high electron-mobility transistors (HEMT) [20] built from such quantum wells have proven useful in many applications in telecommunications and low power amplifiers. These composite material stacks are of particular interest due to the tunability of their physical behavior through material design, therefore there is growing interest in such stacks for detector designs. A lot of the recent efforts in exploration of such novel materials have been in lower dimensional materials. Of course, physically every piece of a material has all 3 dimensions; the dimensionality in this context means the physical behavior demonstrated by this material can be captured using condensed matter theories of materials at lower dimensionality. We now briefly discuss the physics that is demonstrated by lower dimensional materials, and discuss the possibilities in sensing applications that have been developed or proposed using such materials.

#### **6.1 Energy levels and 0-D material**

First pedagogical problem presented in almost all quantum mechanics text is solving the Schrodinger Equation for a particle in an infinite potential well (i.e. particles cannot leak out from the well) and the resulting quantization of allowed "sharp" energy states which a particle may possess [21]. An immediate extension of this problem in the context of an atom led to the accurate prediction of ionized Hydrogen spectra by Niels Bohr and observation of electron diffraction in Stern-Gerlach experiments, which sealed the deal for quantum mechanics, so to say. The story is more complex in condensed matter where interactions of many electrons in close consort lead to a continuum of allowed states with some gaps in between them. In mid 1980s advances in semiconductor processing allowed fabrication of

**Figure 2.**

*(a) A quantum dot is made of a semiconducting material with dimensions typically less than 100 nm. (b) The energy spectra of a quantum dot showing a series of thin narrow bands. (c) The two bands of interest: valence and conduction bands participate in photodetection action where incident light promotes electrons from valence to conduction band, from where it can be detected in an external circuitry.*

ultra-small dots of particles (**Figure 2a**.) which resemble the pedagogical problem described earlier. The allowed particle states are similarly confined to discrete or very small bands of allowed energies, which are determined primarily by the material type and size of the dots. From the point of view of energy-eigenstates, this is analogous to the particle in a well, only this time it can be physically fabricated with high accuracy and control, hence the name "Quantum Dots" for this kind of a material. It is also immediately obvious why we can call such materials artificial we can physically select the energy eigenstates rather than depend purely on the intrinsic configuration of the atoms in the material. **Figure 2b** shows an illustrative example of such a material's energy spectra. Ability to tune the eigenstates in quantum dots allows us to build photon detectors of specific wavelength, since the de-Broglie relation links the wavelength to the corresponding energy: *<sup>E</sup>* <sup>¼</sup> *<sup>ℏ</sup><sup>c</sup> <sup>λ</sup>* where symbols have usual meaning. As an example, the mid-wave infrared (MWIR) corresponds to around 0.25–0.35 eV of energy gaps between conduction and valence bands. Photodetection action then utilizes the light-matter interaction (**Figure 2c**), where incident photon kicks a "bound" electron from valence band to the conduction band which can then be detected -in an external electron counting circuitry.

#### **6.2 From 0-D to 3-D**

It is possible to build from bottom-up a picture of evolution of bands and density of states as a function of dimensionality, an illustrative example shown in **Figure 3** (see [21] for a textbook level exposition). Starting from the Gedanken two energy level "simple" model, we obtain a collection of the full 3-D bands. The 0-D can be thought of as a collection of two such bands generally falling on top of each other. However Pauli's Exclusion principle of Fermions do not allow each of these levels to fully overlap, which provides a finite spread of these levels (sub-bands) which are smeared together into a continuum within the bandwidth due to Heisenberg's Uncertainty principle. These two quantum mechanical principles give rise to all bandstructure phenomena in materials.

A 1-D material can be thought of as a collection of multiple 0-D materials, which leads to stacking of multiple thin bands near each other (sub-bands) which merge

*Physics of Nanostructure Design for Infrared Detectors DOI: http://dx.doi.org/10.5772/intechopen.101196*

**Figure 3.** *Evolution of density of states spectra from 0-D sharp bands to 3-D bulk materials.*

into a continuous density of states/bands with an energy dependence of *D*∝1*=* ffiffiffi *E* <sup>p</sup> , this being the density of states of a nanowire. Similarly stacking multiple nanowires together gives us sub-bands that yield into a constant density of states of 2-D materials, prime examples being graphene, MoS2, black phosphorus etc. Stacking of these 2-D materials then yields the familiar world of 3-D or "bulk" materials with density of states *D*∝√*E*.

The advantage of low dimensional materials lie in the density of states and bandstructure that can give rise to unique electrical properties that can be advantageous in building high quality detector. We next discuss some of the engineering opportunities and challenges faced by photodetector materials of low dimensionality.
