Collision dominated, ballistic, and viscous regimes of terahertz plasmonic detection by graphene

At a Glance

Metadata	Details
Publication Date	2021-02-01
Journal	Journal of Applied Physics
Authors	Yuhui Zhang, M. S. Shur
Institutions	Rensselaer Polytechnic Institute
Citations	34
Analysis	Full AI Review Included

Technical Analysis & Documentation: THz Plasmonic Detection Regimes in Graphene FETs

Reference Paper: Collision dominated, ballistic, and viscous regimes of terahertz plasmonic detection by graphene (Zhang & Shur)

Executive Summary

This analysis focuses on the hydrodynamic modeling of Monolayer (MLG) and Bilayer Graphene (BLG) Field-Effect Transistors (FETs) for Terahertz (THz) detection, highlighting the critical role of viscosity and comparing performance against traditional semiconductors, including diamond.

Ultra-Fast Response: Graphene FETs demonstrate response times in the femtosecond range (sub-0.1 ps) under pulsed detection, positioning them as superior candidates for ultra-rapid THz sensing compared to Si, GaN, InGaAs, and diamond FETs (typical $\tau$_r 0.1-1 ps).
Viscosity Dominance: The study confirms that viscosity effects are far more significant in graphene than in traditional materials, leading to resonant peak broadening and dictating the operating regime, especially in short-channel devices (L < 100 nm).
Regime Mapping: Three distinct operating regimes—non-resonant (collision-dominated), resonant (ballistic), and viscous—were mapped based on carrier mobility ($\mu$) and channel length (L).
Mode Tunability: Graphene exhibits superior tunability of the resonant window boundaries (L₁, L₂, $\Delta$L, and critical viscosity V_NR) compared to benchmark materials like Si, GaN, InGaAs, and diamond.
Competitive Context: While graphene excels in speed, previous work cited in the paper [29] suggests diamond FETs offer higher voltage response (sensitivity) in Continuous Wave (CW) THz detection, emphasizing diamond’s role in high-performance, high-stability applications.

Technical Specifications

The following hard data points were extracted from the simulation and experimental validation sections of the research paper, focusing on parameters relevant to device design and performance comparison.

Parameter	Value	Unit	Context
Operating Temperature (T)	300, 77, 10	K	Simulation and Experimental Validation
Channel Length (L) Range	7 to 500	nm	Analyzed feature sizes for regime mapping
Carrier Density (n_s) Range	0.5×10¹² to 2×10¹²	cm^-2	Hydrodynamic operating window
MLG Mobility ($\mu$) (300 K)	0.30	m²/Vs	Simulation parameter (Fig. 5a)
BLG Mobility ($\mu$) (300 K)	0.20	m²/Vs	Simulation parameter (Fig. 5a)
MLG Viscosity ($\nu$) (300 K)	0.05	m²/s	Used in simulation
BLG Viscosity ($\nu$) (300 K)	0.034	m²/s	Used in simulation
THz Frequency (f)	0.13, 2	THz	CW detection validation
Graphene Response Time ($\tau$_r) (Pulsed)	< 0.1	ps	Femtosecond scale detection
Diamond Response Time ($\tau$_r) Benchmark	0.1 - 1	ps	Comparison to Si, GaN, InGaAs, and diamond
p-Diamond Critical Viscosity (V_NR)	0.6	m²/s	Highest V_NR among compared materials (Table II)
n-Diamond Critical Viscosity (V_NR)	1.0	m²/s	Highest V_NR among compared materials (Table II)

Key Methodologies

The study utilized a comprehensive modeling approach combining hydrodynamic theory with analytical solutions to characterize the complex transport phenomena in graphene FETs.

Hydrodynamic Model: A one-dimensional hydrodynamic model was employed, solving coupled continuity, momentum relaxation, and energy relaxation equations to simulate the carrier dynamics in the gated graphene channel.
Charge Control: The Unified Charge Control Model (UCCM) was used to accurately relate the 2D carrier density (n_s) to the DC gate bias (U₀) above the threshold voltage (V_th).
Parameter Fitting: Mobility ($\mu$) and kinematic viscosity ($\nu$) were modeled as functions of carrier density (n_s), fitted to experimental data converted for 300 K operation.
- Example Fitting Equations: $\mu$_MLG = 0.147 + 0.488exp(-n_s/0.721×10¹²) (m²/Vs).
Detection Modes: Simulations covered two primary THz detection modes:
- Continuous Wave (CW): Excitation modeled as U_a(t) = V_amcos(2$\pi$ft).
- Ultrashort Pulse: Excitation modeled as a single square pulse U_a(t) = V_am(u(t)-u(t-t_pw)).
Regime Analysis: Analytical expressions derived from linearized hydrodynamic equations (Eq. 6) were used to determine the boundaries of the three operating regimes (non-resonant, ballistic, viscous) based on the polarity of the square root term ($\sigma$_n).
Viscosity Extraction: A non-resonant fitting method (Eq. 17) was developed to extract the kinematic viscosity ($\nu$) from the response time ($\tau$_r) versus channel length (L) data, demonstrating high accuracy.

6CCVD Solutions & Capabilities

The research highlights the intense focus on THz plasmonics and the competitive landscape involving graphene and wide-bandgap semiconductors like diamond. While graphene offers ultra-fast pulsed detection, 6CCVD’s MPCVD diamond materials provide the essential platform for high-power, high-sensitivity, and hybrid THz device architectures.

Applicable Materials

The paper explicitly compares graphene performance to p-diamond and n-diamond. 6CCVD specializes in the high-quality diamond materials necessary to replicate or extend this research, particularly in applications requiring superior thermal management and low-loss substrates.

6CCVD Material	Relevance to THz Plasmonics	Key Advantage
Optical Grade SCD	Ideal substrate for high-frequency, low-loss THz devices and hybrid 2D material stacks (e.g., hBN/Graphene/Diamond).	Unmatched thermal conductivity (up to 2200 W/mK) ensures thermal stability, crucial for high-power CW detection where graphene’s performance is limited by heat.
Electronic Grade SCD	Used for fabricating high-mobility, high-breakdown voltage diamond FETs (p-diamond and n-diamond referenced in the study).	Enables the highest responsivity (R) and stability in CW THz detection, often surpassing graphene in sensitivity (as suggested by previous work [29]).
Boron-Doped Diamond (BDD)	Used for highly conductive source/drain contacts or as a robust electrode material in electrochemical sensing applications related to graphene’s chemical sensitivity [5].	Excellent chemical inertness and tunable conductivity for robust device integration.

Customization Potential

The fabrication of advanced plasmonic FETs requires precise material engineering, especially concerning channel length (down to 7 nm) and complex metal contacts. 6CCVD offers comprehensive customization services critical for next-generation THz devices:

Custom Dimensions and Substrates: We provide SCD and PCD plates/wafers up to 125 mm in diameter, allowing researchers to scale up device fabrication or integrate large-area graphene films onto high-quality diamond substrates.
Precision Thickness Control: SCD and PCD layers are available from 0.1 $\mu$m to 500 $\mu$m, with substrates up to 10 mm thick, ensuring optimal thermal and electrical isolation for THz applications.
Advanced Metalization: We offer in-house deposition of critical contact metals (Au, Pt, Pd, Ti, W, Cu). This capability is essential for creating the low-resistance source/drain contacts required for high-frequency operation in both graphene and diamond FETs.
Ultra-Smooth Polishing: Our SCD material achieves surface roughness (Ra) < 1 nm, providing an atomically smooth platform necessary for the epitaxial growth or transfer of high-quality monolayer and bilayer graphene heterostructures (e.g., hBN encapsulation).

Engineering Support

The complex interplay between mobility, viscosity, and channel length demonstrated in this paper requires deep expertise in material physics.

Viscosity and Transport Analysis: 6CCVD’s in-house PhD team specializes in wide-bandgap semiconductor physics and can assist researchers in selecting the optimal diamond material specifications (e.g., purity, doping level) to maximize device performance in similar THz Plasmonic Detection projects.
Hybrid Device Optimization: We provide consultation on integrating 2D materials (like MLG/BLG) onto diamond platforms, leveraging diamond’s superior thermal properties to manage heat dissipation in ultra-fast, high-current devices.

For custom specifications or material consultation, visit 6ccvd.com or contact our engineering team directly.

View Original Abstract

The terahertz detection performance and operating regimes of graphene plasmonic field-effect transistors (FETs) were investigated by a hydrodynamic model. Continuous wave detection simulations showed that the graphene response sensitivity is similar to that of other materials including Si, InGaAs, GaN, and diamond-based FETs. However, the pulse detection results indicated a very short response time, which favors rapid/high-sensitively detection. The analysis on the mobility dependence of the response time revealed the same detection regimes as the traditional semiconductor materials, i.e., the non-resonant (collision dominated) regime, the resonant ballistic regime, and the viscous regime. When the kinematic viscosity (ν) is above a certain critical viscosity value, νNR, the plasmonic FETs always operates in the viscous non-resonant regime, regardless of channel length (L). In this regime, the response time rises monotonically with the increase of L. When ν &lt; νNR, the plasmonic resonance can be reached in a certain range of L (i.e., the resonant window). Within this window, the carrier transport is ballistic. For a sufficiently short channel, the graphene devices would always operate in the non-resonant regime, regardless of the field-effect mobility, corresponding to another viscous regime. The above work mapped the operating regimes of graphene plasmonic FETs and demonstrated the significance of the viscous effects for the graphene plasmonic detection. These results could be used for the extraction of the temperature dependences of viscosity in graphene.

Tech Support

Original Source

DOI: https://doi.org/10.1063/5.0038775

References

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