**3. Graphene-HgCdTe detector modeling effort**

#### **3.1 Modeling approach**

The modeling effort was individually built upon various elements that combine to form a comprehensive model for this detector material technology. The overall goal of this modeling approach was to determine through simulations an accurate determination of electrical detector device behavior, including I-V characteristics, noise, responsivity, and other performance metrics. In addition, the directivity D\* and noise equivalent temperature difference (NETD) may be derived from basic material parameters and device design and operating specifications to allow and guide further design optimizations.

The modeling effort, depicted schematically in **Figure 4**, entailed modular construction of the complete detector simulation platform from the individual models as data were made available from experiments and device characterizations. These have involved specific material modeling of the HgCdTe, graphene, and HgCdTegraphene interface.

#### **3.2 Modeled performance parameters in HgCdTe**

This graphene-HgCdTe MWIR detector fundamentally functions as a photo-controlled current source rather than a light/heat-dependent resistance, characteristic of the typical operating mode for bolometers. **Figure 5** compares the theoretical dark current and photocurrent, film resistance, and detectivity (D\*) performance parameters in the HgCdTe for a conventional photoconductive detector (**Figure 5**(**a**)) with that for this type of HgCdTe-based MWIR detector (**Figure 5**(**b**)). It is here noted that D\* does not change appreciably because ultimately the material properties are

*Doping and Transfer of High Mobility Graphene Bilayers for Room Temperature Mid-Wave… DOI: http://dx.doi.org/10.5772/intechopen.101851*

**Figure 4.** *Flowchart diagram illustrating the modeling approach and relationship between the different models utilized.*

the same; altering the area of the current collection does not significantly change this fundamental property. The current and resistance, however, are each significantly lower for this latter detector design in view (**Figure 5**(**b**)). The incorporation of high mobility graphene in this detector can further enable higher responsivity and greater D\*.

#### **3.3 Graphene-HgCdTe interface band structure models**

**Figure 6** shows the *E-k* dispersion relation and density of states (DOS) determined for the HgCdTe/graphene interface. The contribution of individual atoms to the DOS is likewise computed. The carbon contributes maximally to the conduction band, while HgCdTe species contribute to the valence band.

Bandgap engineering of the HgCdTe detector material is additionally possible through adaptive control of the epitaxial growth process parameters. This provides the capability to optimize the performance to achieve desired spectral range and operating temperature specifications for the development of graphene-enhanced MWIR detectors and FPAs.

The work function of Hg0.73Cd0.27Te, ΦMCT, is determined (5.52 eV) based on the following relation:

$$
\boldsymbol{\Phi}\_{\text{MCT}} = \boldsymbol{\varkappa} \boldsymbol{\Phi}\_{\text{CdTe}} + \left(\mathbf{1} - \boldsymbol{\varkappa}\right) \boldsymbol{\Phi}\_{\text{HgTe}} \tag{1}
$$

where *x* is the CdTe concentration in Hg1−*x*CdxTe, and ΦCdTe and ΦHgTe, the work functions of CdTe and HgTe, are 4.5 eV and 5.9 eV, respectively. As shown in

**Figure 5.**

*Modeled dark current and photocurrent, film resistance, and detectivity (D\*) (from top to bottom) in HgCdTe for (a) conventional photoconductive detector design, and (b) design of this HgCdTe MWIR photoconductive detector.*

**Figure 6.** *E-k dispersion relation and density of states for HgCdTe/graphene interface.*

*Doping and Transfer of High Mobility Graphene Bilayers for Room Temperature Mid-Wave… DOI: http://dx.doi.org/10.5772/intechopen.101851*

**Figure 7.** *Band diagram for graphene/HgCdTe/Si detector heterostructure.*

**Figure 7**, Hg0.7Cd0.3Te produces a built-in Vbi potential with *p*-doped graphene of ~0.6 eV. (With *n*-doped graphene having a work function 4.25, Vbi becomes as high as 1.27 eV.) Given its intermediate work function between that of HgCdTe (5.5 eV) and *n*-doped Si (4.1 eV), the use of the CdTe buffer layer facilitates band matching of the HgCdTe/CdTe/Si layers.
