# Theoretical Investigation of Responsivity/NEP Trade-off in NIR Graphene/Semiconductor Schottky Photodetectors Operating at Room Temperature

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## Abstract

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## 1. Introduction

_{2}Si) and platinum silicide (PtSi) Schottky PDs have been extensively investigated for the realization of infrared CCD image sensors. Pd

_{2}Si/Si Schottky PDs were developed for satellite applications showing the ability to detect a spectrum ranging from 1 to 2.5 μm when cooled to a temperature of 120 K [4,5]. On the other hand, PtSi/Si Schottky PDs were developed for operation at longer wavelengths ranging from 3 to 5 μm [6,7], although they require a lower temperature of 80 K. A focal plane array (FPA) constituted by an array of $512\times 512$ PtSi/Si pixels was realized, demonstrating the first spectacular convergence between Si photonics and electronics [8]. Unfortunately, these devices can only work at cryogenic temperature. Indeed, the low Schottky barrier height (SBH) required to achieve an acceptable efficiency (0.21 eV for PtSi [7] and 0.34 eV for Pd

_{2}Si/Si [4]) is comes at the cost of PD noise (dark current), which must be reduced by lowering the working temperature. PD noise affects the noise equivalent power (NEP), that is, the minimum detectable optical power, which has a huge impact on both the device sensitivity and the bit error rate (BER) of a communication link. Higher Schottky barriers make it possible to achieve low noise, but they unfortunately also lead to low efficiencies. This efficiency–noise trade-off is a peculiar characteristic of the Schottky PDs based on the IPE.

## 2. Theoretical Background

## 3. Theoretical Results and Discussion

_{0.3}Ga

_{0.7}As and p-GaAs can be optimized only in a narrow window of the NIR spectrum, whereas n-Si can be optimized in a broader range, including at 1.55 μm where only a small reverse voltage ${V}_{R}=0.66$ V for maximizing the $R/NEP$ ratio is required. Indeed, at a reverse voltage of $0.66$ V the ${{\Phi}}_{B0}=0.73$ eV of the graphene/n-Si junction can be reduced to its optimum value of ${{\Phi}}_{B}^{*}(1.55\mu \phantom{\rule{3.33333pt}{0ex}}$m) = 0.71 eV. In contrast, p-GaAs requires a higher reverse voltage of 12 V to maximize $R/NEP$. Finally, n-Ge stands out among the analyzed semiconductors in view of the possibility to be employed over a region of the NIR spectrum above 2 μm. The range of wavelengths where $R/NEP$ can be optimized for various semiconductors, by applying a reverse bias up to 20 V, is summarized in Table 3.

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Conflicts of Interest

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**Figure 1.**(

**a**) Behavior of $g\left({{\Phi}}_{B}\right)$ at 300 K for three wavelengths: 1.3 μm, 1.55 μm, and 2 μm; (

**b**) optimized responsivity R (blue solid line) and optimized Schottky barrier height (SBH) ${{\Phi}}_{B}^{*}$ (red dashed line) as a function of the wavelengths.

**Figure 2.**Band diagrams of (

**a**) graphene/n-semiconductor and (

**b**) graphene/p-semiconductor junctions at the thermal equilibrium and when a reverse bias ${V}_{R}$ is applied. At the thermal equilibrium, graphene has an initial carrier density $n({V}_{R}=0)$. After a reverse bias this charge density becomes $n\left({V}_{R}\right)$. ${E}_{0}$ represents the vacuum energy level while ${E}_{F}^{0}$ is the Dirac point. ${{\Phi}}_{\mathrm{gr}}^{0}$, ${\chi}_{\mathrm{sm}}$, ${E}_{g}$, ${E}_{C}$, and ${E}_{V}$ are respectively the intrinsic graphene work function, electron affinity, conduction band, bandgap, and valence band. ${E}_{F}^{\mathrm{sm}}$ is the Fermi energy level in the semiconductor and $q{{\Phi}}_{B0}$ the Schottky barrier at zero bias. The values of the Schottky barrier $q{{\Phi}}_{B}$ depend on the graphene Fermi energy level ${E}_{F}$ that shifts when a voltage is applied.

**Figure 3.**(

**a**) Intersection between the curve ${{\Phi}}_{B}^{*}\left(\lambda \right)$ at 300 K and the values of SBH ${{\Phi}}_{B0}$ at the interface between graphene and several semiconductors in conditions of thermal contact (no voltage applied to the junction); (

**b**) reverse voltage ${V}_{R}$ to apply to the graphene/semiconductor junction as function of the wavelength for maximizing the signal-to-noise ratio ($SNR$) (${{\Phi}}_{B}={{\Phi}}_{B}^{*}$) for various semiconductors. The values of ${{\Phi}}_{B}0={{\Phi}}_{B}({V}_{R}=0)$ were calculated through Equations (15)–(18) by considering an initial graphene p-doping of ${n}_{0}={10}^{12}$ cm${}^{-2}$ and a doping of $N={10}^{16}$ cm${}^{-3}$ for all the semiconductors reported in Table 2.

**Figure 4.**(

**a**) The optimized $R/NEP$ and (

**b**) the optimized $NEP$ of the Schottky graphene-based PDs for various semiconductors as function of the wavelength range individuated in Table 3. All figures were obtained at room temperature and by considering a graphene circular area in touch with the semiconductor with radius of 500 μm and a load resistance of 10 M$\mathsf{\Omega}$. The arrows indicate the validity regions of the proposed optimization procedure.

**Table 1.**Values of the Schottky barrier ${{\Phi}}_{B}^{*}$ optimizing the responsivity (R)/noise equivalent power ($NEP$) ratio at the three wavelengths of interest: 1.3 μm, 1.55 μm, and 2 μm at $T=300$ K. The corresponding efficiency ${\eta}_{\mathrm{int}}^{\mathrm{SLG}}$ and responsivity R, calculated respectively through Equations (2), (3) and (14), are also shown. SLG is the acronym of single layer graphene.

$\mathit{\lambda}$ (μm) | ${\mathsf{\Phi}}_{\mathit{B}}^{*}$ (eV) | ${\mathit{\eta}}_{\mathsf{int}}^{\mathsf{SLG}}$ | R (A/W) |
---|---|---|---|

1.3 | 0.86 | 0.10 | 0.10 |

1.55 | 0.7 | 0.11 | 0.14 |

2 | 0.52 | 0.14 | 0.23 |

**Table 2.**Bandgap ${E}_{g}$ and electron affinity ${\chi}_{\mathrm{sm}}$ of various semiconductors together with values of SBH when the Schottky junction is formed, calculated thanks to Equations (15)–(17) by taking into account an initial extrinsic p-doping ${n}_{0}={10}^{12}$ cm${}^{-2}$ of the single-layer graphene (SLG) and the thermal equilibrium contact with the substrate. For the calculations we considered low-doped semiconductors (i.e., $N={10}^{16}$ cm${}^{-3}$).

$\mathit{Semiconductor}$ | ${\mathit{E}}_{\mathit{g}}$ (eV) | ${\mathit{\chi}}_{\mathbf{sm}}$ (eV) | ${\mathsf{\Phi}}_{\mathsf{B}0}^{\left(\mathsf{n}\right)}$ (eV) | ${\mathsf{\Phi}}_{\mathsf{B}0}^{\left(\mathsf{p}\right)}$ (eV) |
---|---|---|---|---|

$Si$ | 1.12 | 4.00 | 0.73 | 0.39 |

$GaAs$ | 1.43 | 4.07 | 0.66 | 0.77 |

$A{l}_{0.3}G{a}_{0.7}As$ | 1.77 | 3.77 | 0.96 | 0.84 |

$Ge$ | 0.66 | 4.13 | 0.60 | − |

**Table 3.**Range of wavelengths in which the $R/NEP$ ratio of the Schottky photodetectors (PDs) can be maximized by applying a reverse bias up to 20 V.

$\mathit{Semiconductor}$ | ${\mathit{\lambda}}_{\mathbf{min}}$ (nm) | ${\mathit{\lambda}}_{\mathbf{max}}$ (nm) |
---|---|---|

$n-Si$ | 1541 | 2099 |

$p-GaAs$ | 1459 | 1582 |

$n-GaAs$ | 1692 | 2417 |

$p-A{l}_{0.3}G{a}_{0.7}As$ | 1346 | 1447 |

$n-A{l}_{0.3}G{a}_{0.7}As$ | 1197 | 1508 |

$n-Ge$ | 1852 | 2843 |

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**MDPI and ACS Style**

Crisci, T.; Moretti, L.; Casalino, M. Theoretical Investigation of Responsivity/NEP Trade-off in NIR Graphene/Semiconductor Schottky Photodetectors Operating at Room Temperature. *Appl. Sci.* **2021**, *11*, 3398.
https://doi.org/10.3390/app11083398

**AMA Style**

Crisci T, Moretti L, Casalino M. Theoretical Investigation of Responsivity/NEP Trade-off in NIR Graphene/Semiconductor Schottky Photodetectors Operating at Room Temperature. *Applied Sciences*. 2021; 11(8):3398.
https://doi.org/10.3390/app11083398

**Chicago/Turabian Style**

Crisci, Teresa, Luigi Moretti, and Maurizio Casalino. 2021. "Theoretical Investigation of Responsivity/NEP Trade-off in NIR Graphene/Semiconductor Schottky Photodetectors Operating at Room Temperature" *Applied Sciences* 11, no. 8: 3398.
https://doi.org/10.3390/app11083398