Physics of Nanostructure Design for Infrared Detectors

*Nibir Kumar Dhar, Samiran Ganguly and Srini Krishnamurthy*

## **Abstract**

Infrared detectors and focal plane array technologies are becoming ubiquitous in military, but are limited in the commercial sectors. The widespread commercial use of this technology is lacking because of the high cost and large size, weight and power. Most of these detectors require cryogenic cooling to minimize thermally generated dark currents, causing the size, weight, power and cost to increase significantly. Approaches using very thin detector design can minimize thermally generated dark current, but at a cost of lower absorption efficiency. There are emerging technologies in nanostructured material designs such as metasurfaces that can allow for increased photon absorption in a thin detector architecture. Ultra-thin and low-dimensional absorber materials may also provide unique engineering opportunities in detector design. This chapter discusses the physics and opportunities to increase the operating temperature using such techniques.

**Keywords:** infrared detectors, nanostructure, metasurfaces, plasmonics, detector noise, dark current, absorption, thin absorber, photon trap

#### **1. Introduction**

Infrared (IR) detectors and focal plane array technologies (FPA) have proven to be at the heart of many defense and commercial applications. Most of these detectors require cryogenic cooling to minimize thermally generated dark current, causing the size, weight, power and cost (SWaP-C) to increase significantly. The objective of this chapter is to discuss physics and development of new approaches in nanostructure engineering of light matter interaction to enhance photon field absorption in very thin infrared absorbing layers, thereby significantly reduce thermally generated noise, thus paving a path to higher operating temperature and eliminating bulky and costly cryogenic coolers. Breakthroughs are necessary in materials design to considerably reduce the detector noise caused by the surface leakage and dark current to enable high operating temperature. The device architecture must be commensurate with improved quantum efficiency and increased lifetime, ideally being only background shot noise limited. This however cannot be accomplished by merely improving the material quality alone. Achieving extremely low dark currents at higher temperature using nanostructured thin absorption layers will lead to practical infrared detector technology that can have wide spread applications.

Since the early 50s, there has been considerable progress towards the materials development and device design innovations. In particular, significant advances have been made during the past couple of decades in the bandgap engineering of various compound semiconductors that has led to new and emerging detector architectures. Advances in optoelectronics related materials science, such as metamaterials, nanostructures and 2D material designs have opened doors for new approaches to apply device design methodologies, which are expected to offer enhanced performance at higher operating temperature and lower cost products in a wide range of applications.

This chapter discusses advancements in the detector technologies and presents physics of emerging device architectures. The chapter introduces the basics of infrared detection physics and various detector figure of merit (FOM). Advances in pixel scaling, junction formation, materials growth, bandstructure design and processing technologies have matured substantially to make an impact towards higher operating temperature detectors [1]. The concepts presented here are informational in nature for students interested in infrared detector technology. The central ideas discussed are the opportunities to use thin detector designs to reduce thermally generated dark current and increasing radiation absorption techniques. Thus achieving lower SWaP-C.

#### **2. Detector characterization parameters**

IR detectors can be categorized as being either a quantum or thermal device. In a quantum detector, electromagnetic radiation absorbed in a semiconductor material generates electron-hole pairs, which are sensed by an electronic readout circuit (ROIC). In a thermal detector, on the other hand, the incident IR photons are absorbed by a thermally isolated detector element, resulting in an increase in the temperature of the element. The temperature is sensed by monitoring an electrical parameter such as resistivity or capacitance. In this chapter we are primarily concerned with quantum detectors.

Due to the various mechanisms used by detectors to convert optical to electrical signals, several FOM are used to characterize their performance. The output of the detector consists of its response signal to the incident radiation and random noise fluctuations. One such FOM is the Responsivity (*R*) of the detector, defined as the ratio of the root mean squared (RMS) value of the signal voltage (*Vs*) or output current to the RMS input radiation power (*ϕ*) incident on the detector. The responsivity is given as:

$$R\_v(\lambda, f) = \frac{V\_s}{\phi(\lambda)}; R\_i(\lambda, f) = \frac{I\_s}{\phi(\lambda)}\tag{1}$$

The spectral current responsivity can also be written in terms of quantum efficiency as:

$$R\_i(\lambda, f) = \frac{\lambda \eta}{hc} q \text{g} \tag{2}$$

Where, *λ* is the photon wavelength, *η* is the quantum efficiency (QE) (more on QE in Section 4), *h* is the Plank's constant, *c* is the speed of light, *q* is the electronic charge and *g* is the gain. For photovoltaic (p/n junction) detectors *g* = 1.

The responsivity is usually a function of the bias voltage, the operating electrical frequency, and the wavelength. An important parameter typically used in infrared

detectors is the Noise Equivalent Power (NEP). It is the minimum incident radiant power on the detector required to produce a SNR of unity. Therefore, it can be expressed as:

$$\text{NEP} = \frac{V\_n}{R\_v} = \frac{I\_n}{R\_i} \tag{3}$$

NEP is usually measured for a fixed reference bandwidth. The NEP is typically proportional to the square root of the detector signal, which is proportional to the detector area of optical collection *Ad*. An important factor in detector operation is the detectivity *D*, which is the reciprocal of NEP. It is the signal-to-noise ratio. There are multiple approaches to characterize this FOM, a useful one is the specific or normalized detectivity, *D*\* given by:

$$D^\* = D\left(\sqrt{\delta fAd}\right) = \frac{\sqrt{\delta fAd}}{\text{NEP}}\tag{4}$$

Or

$$D^\* = \frac{I\_{signal}}{I\_{noise}} \frac{\sqrt{\delta \hat{f} A d}}{P\_{opt}} \tag{5}$$

Where, *Isignal* ¼ *Ilit* � *Idark* and *Ilit* is the photocurrent, *δf* is the bandwidth of the measurement, *Ad* is the detector optical area, *Popt* is the optical power (*ϕλ*) incident on the detector, and *Inoise* is the RMS noise current. This noise current depends on the dark current *Idark* and its exact formulation depends on the type of noise dominant in the detector. These noises are primarily of the following four kinds:


It is clear from the above discussion that the performance of the detector is heavily impacted by the dark current. Lower is the dark current, higher is the relative signal and lower is the noise. *Therefore, dark current reduction without sacrificing photogeneration is the central goal of detector design and engineering*.

#### **3. Dark current vs. temperature**

The ultimate in detector performance is achieved when the noise generated by the background (scene) flux is greater than any thermally generated noise within the detector (for more information see Ref. [2]). Such condition is termed as background Limited Performance or BLIP. It can be seen that the bigger component of noise inherent in the detector is the dark current. It is the output current when no background flux is incident on the detector and depends strongly on the detector temperature. The dark current increases with temperature since the carrier thermal energy KT increases with temperature. When the carrier thermal energy is equal to or greater than the bandgap (*Eg*) energy, more thermally generated carriers are promoted to the conduction band giving rise to dark current. It is this reason; quantum detectors need to be cooled to a temperature that minimizes the dark current. However, this requires cooling to cryogenic temperature where large coolers are used. This is an inherent problem because it increases the size, weight, power and cost.

The dark current with respect to temperature can be defined as an Arrhenius equation [3]:

$$I\_{dark}(T) = A\_{\epsilon} I\_0 \mathbf{T} \exp\left(\frac{-E\_a}{K\_B T}\right) \tag{6}$$

Where *Ae* is the electronic area of the detector, *J*<sup>0</sup> is a constant that depends on the detector absorber materials properties, *KB* is the Boltzmann constant,*T* is the detector temperature and *Ea* is the activation energy to promote a carrier into the conduction band. This equation clearly illustrates how dark current increases with temperature. The BLIP condition is achieved at a temperature (*T*BLIP) where photocurrent becomes equal to the dark current.

## **4. Fundamental photon detector action: absorption, generation, detection**

Photodetectors can be built in a variety of device configurations [4]. The major ones include a light dependent conductor (photoconductor), light dependent diode (photodiode, avalanche photo-diode), photovoltaic (such as solar cell), or thermal detector/bolometer (Seebeck effect detectors). At the most fundamental level, all these devices depend on the excitation of matter particles by transferring incident photon energy into the absorber material. In the case of a thermal detector, the excited matter particles are phonons and electrons, in the case of a photovoltaic or photoconductive detector, it is an electron-hole pair also called excitons, and in certain cases it is plasmons acting as an intermediary between the electrons and photons.

It is obvious that the photodetector action depends on the transduction efficiency of the absorbed photons (light) into a detector particle species, primarily an electron (matter) and its subsequent electrical readout. This efficiency is called the internal quantum efficiency (IQE). In most high-quality detectors, this approaches unity, though it is possible to obtain higher than one IQE if the material bandstructure can be engineered to emit more than one electron per absorbed photon, which typically needs special quantum engineered bandstructures, since the electron relaxation post-generation must be "direct" or radiative. External quantum efficiency (EQE) captures the effect of light absorption within this approach, i.e. EQE ¼ Absorption � IQE.

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

EQE is a function dependent principally on three factors: photon wavelength, detector temperature, and absorption efficiency. We illustrate this using an example as follows. In Ref. [5] we developed a quantum mechanical model of IQE in polycrystalline PbSe mid-wave IR detectors. This formulation is developed on the lines of the Shockley-Quiesser approach [6]. In this approach the photons of energies larger than the material bandgap first thermalizes to the band edge and then creates a photo-generated carrier. We modeled the absorption efficiency using the classic Moss model [7] which considers non-uniformity of photon absorption in film thickness direction, *x*, film reflectivity *r*, and effective absorption coefficient *α*, and is given by:

$$\kappa(\mathbf{x}) = \frac{(\mathbf{1} - r)(\mathbf{1} - e^{\mathbf{x}\mathbf{c}})}{\mathbf{1} - r e^{\mathbf{c}\mathbf{x}}} \tag{7}$$

The IQE is given by excitation of matter particle modes. In the same example the carrier generation is given as:

$$\eta\_{IQE}(\lambda, T) = \frac{E\_{\rm g}(T) \int\_{0}^{\infty} D(E, \lambda) N(E, \lambda) \zeta(E, T) dE}{\int\_{0}^{\infty} ED(E, \lambda) N(E, \lambda) dE} \tag{8}$$

Where *Eg* is the bandgap (a function of detector temperature, *T*), *D*, *N* are photon density of states and occupancy function, which itself is a function of phonon spectra (and hence a function of wavelength *λ*), and a band edge disorder function *ζ* which accounts for Urbach tails [8] into the bandgap (again dependent on *T*). The overall EQE is then given by:

$$
\eta\_{\rm EQE}(\lambda, T, \mathfrak{x}) = \eta\_{\rm IQE}(\lambda, T)\kappa(\mathfrak{x}) \tag{9}
$$

It can be seen from Eq. (7), that for thin films the absorption efficiency can be quite small; in fact. as *x* ! 0, *κ* ! 0. This is evident in many thin film "2D materials" where quantum efficiency can be quite poor, and as an illustration, in a single layer graphene, the absorption coefficient is below 3%. In Section 5 below we give a brief description of how thin absorber layers can be used to increase the detector operating temperature.

EQE allows us to calculate the rate of photo-generated carriers. The generation rate can be numerically calculated by:

$$G(T) = \int\_{0}^{t} \int\_{0}^{\infty} \eta\_{EQE}(\lambda, T, \varkappa) n\_{opt}(\lambda, T) d\lambda d\varkappa \tag{10}$$

Where, *nopt*ð Þ *λ*, *T* , the photon density can be calculated from Planck's distribution function for a black body source or some other appropriate distribution function for an artificial or structured light source. The generated carrier density is given by Δ*n* ¼ *G T*ð Þ*Aoptτ* where *Aopt* is the optical area, i.e. the area open to photon collection and generation, and *τ* is the carrier lifetime. Specific detector design converts this generated carrier density into an equivalent photoresistance, photocurrent, or photovoltage which depends on the modality and details of the specific design of the detector. It can be seen that the carrier lifetime plays a critical role; long lived the carrier, better is the signature of photogeneration.

#### **5. Approach to increase the detector operating temperature**

As discussed above the photon detector action involves electron-hole pair creation when photons impinge on the absorber layer. Typically, the absorber layer

thickness *x* requires to be in the order of the wavelength of interest. For example, a 10 μm radiation detection would require at least a 10 μm thick absorber layer. The photons interact in the absorber volume of *Aex*, where *Ae* is the electronic area of the detector. Typically, the detector's electronic and optical areas (*Aopt*) are same as shown in **Figure 1a**, and usually denoted as *Ad* . As shown in **Figure 1b**, the detector absorber layer can be thinned substantially to reduce the absorber volume and thus dark current by using a metastructured stack with optical collection area *Aopt*.

The dark current, which strongly depends on temperature is also proportional to this volume. The total noise current generated in this volume for a noise bandwidth of *δf* and a gain of *g* is given as [9]:

$$I\_n^2 = 2(G+R)A\_c \kappa \delta f q^2 g^2 \tag{11}$$

Where, *G* and *R* are the generation and recombination rates and other parameters are defined previously. At equilibrium, *G* ¼ *R*, and denoted as 2*G*.

The *D*\* from Eq. (4) can now be calculated using Eqs. (2) and (3) and yields:

$$D^\* = \frac{\eta \lambda}{2hc(\varkappa G)^{\frac{1}{2}}} \left(\frac{A\_{opt}}{A\_{\epsilon}}\right)^{1/2} \tag{12}$$

In Eq. (12) we can see that thickness *x* is in the denominator. Reducing *x* will increase *D*\*, which is what we would want. Another key observation is the ratio of optical collection area to the absorber electronic area. Increasing this ratio also help increase the *D*\* and thus SNR. However, this can only be true if the quantum efficiency with respect to absorption efficiency *k x*ð Þ is maintained, see Eq. (9). Thinner *x* comes at a penalty of lower photon absorption. Therefore, the approach is to reduce the volume by reducing the thickness (*x*) while maintaining sufficient photon absorption. This can be achieved by the use of a secondary matter particle that is not affected by the thickness and in the contrary prefers a thinned absorber: plasmons. Plasmons [10–12] are collective electromagnetic excitation of the electrons in a material that like to live near the "skin" of the material, characterized by the skin depth *δ*. The excitation of plasmons by the incident photon then couples with excitonic modes (collectively called polaritons) which can translate into increased electrical response of the material through increased carrier generation that can be detected as increased photocurrent. This approach also yields interesting quantum phenomena such as topologically protected optical behavior, which is not

#### **Figure 1.**

*Illustration of thick (a) and thin (b) design for increasing the detector operating temperature, where* Aopt *is enhanced absorption using nanostructured materials stack such as metamaterial design.*

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

covered here further. Coupling of photon-plasmon-exciton physics is an exciting field that has led to a whole host of new technologies for detection, including metamaterials [13], negative index materials used in metalenses, and metasurfaces [14–16]. These artificially constructed surfaces (illustrated in **Figure 1b** with area *Aopt*) use carefully designed structure of varying dielectric constants to obtain an artificial composite material that shows behavior not normally seen in any "natural" material. One example of such a material is a matrix of anti-dots, which are voids or physical holes [17, 18] in the detector material that show the physics of absorption enhancement through plasmon polaritons. As shown in **Figure 1b**, the detector absorber volume is reduced considerably and by use of metastructure stack design above one can gain back the photon absorption. More discussions on metastructures is given in Section 9.
