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

Executive Summary

This analysis investigates the Terahertz (THz) detection performance and operating regimes of Monolayer (MLG) and Bilayer Graphene (BLG) Field-Effect Transistors (FETs) using a hydrodynamic model, focusing on the critical role of electron fluid viscosity.

Ultra-Fast Pulse Detection: Graphene FETs exhibit extremely short response times (t_r), making them highly suitable as femtosecond pulse detectors. Their t_r (0.02-0.3 ps) is significantly faster than that of traditional Si, GaN, InGaAs, or diamond FETs (0.1-1 ps).
Dominant Viscosity Effects: The high kinematic viscosity (v) in graphene electron fluid is a major factor limiting sensitivity in Continuous Wave (CW) detection and dictating the response time in pulse detection, especially in short-channel devices.
Regime Mapping: The operating space is comprehensively mapped into three regimes based on mobility (µ) and channel length (L): non-resonant (collision-dominated), resonant (ballistic), and viscous.
Viscous Non-Resonant Regime: A critical viscosity (V_NR) exists. If the device viscosity exceeds V_NR, the plasmonic FET operates in a fully non-resonant, viscous regime, regardless of channel length.
Mode Tunability: Graphene offers superior mode tunability compared to other materials, allowing the resonant window (L₁ to L₂) to be adjusted over a large dynamic range by changing mobility (µ) and viscosity (v).
Viscosity Extraction Method: A new analytical expression for response time in the non-resonant regime was developed, providing a high-accuracy method for extracting the kinematic viscosity of graphene electron fluid.

Technical Specifications

The following parameters were extracted from the simulation and analytical results for MLG and BLG plasmonic FETs, primarily at T = 300 K and U₀ = 2 V.

Parameter	Value Range / Specific Value	Unit	Context
Operating Temperature (T)	77, 300	K	Primary simulation temperatures.
MLG Mobility (µ)	0.1 to 0.5	m²/Vs	Typical range used in simulations.
BLG Mobility (µ)	0.1 to 0.5	m²/Vs	Typical range used in simulations.
MLG Kinematic Viscosity (v)	0.05	m²/s	Used at T = 300 K.
BLG Kinematic Viscosity (v)	0.034 to 0.8	m²/s	Varies with carrier density n_s and temperature.
Channel Length (L)	7 to 500	nm	Range studied for regime mapping.
Plasma Velocity (s) - MLG	4.54 x 10⁶	m/s	U₀ = 2 V (Table II).
Plasma Velocity (s) - BLG	3.13 x 10⁶	m/s	U₀ = 2 V (Table II).
Graphene Response Time (t_r)	0.02 to 0.3	ps	Pulse detection mode (L=130 nm).
Traditional FET Response Time	0.1 to 1	ps	Si, GaN, InGaAs, Diamond comparison.
Critical Viscosity (V_NR) - BLG	0.392	m²/s	Boundary for resonant operation (U₀ = 2 V).
Lower Resonant Boundary (L₂)	~πv/4s	nm	Minimum channel length required for resonance.
Normalized CW Response (R)	10^-3 to 1	V/W	Amplitude range for MLG/BLG CW detection.

Key Methodologies

The study relied on a combination of numerical simulations and analytical theory based on the hydrodynamic model of the 2D electron fluid in graphene FETs.

Hydrodynamic Modeling: A one-dimensional hydrodynamic model was implemented, solving the coupled governing equations: continuity equation, momentum relaxation equation, and energy relaxation equation.
Parameterization and Fitting: Mobility (µ) and kinematic viscosity (v) were modeled as functions of 2D carrier density (n_s) by fitting experimental data, ensuring the parameters fell within a typical range (0.1-0.5 m²/Vs for µ).
CW Detection Simulation: Continuous Wave (CW) THz excitation (V_amcos(ωt)) was simulated using the traditional open-drain boundary condition (zero current at the drain) to calculate the DC source-to-drain voltage response (dU).
Pulse Detection Simulation: Ultrashort pulse detection was simulated using a single square pulse input (width t_pw) to analyze the temporal voltage response and determine the response time (t_r).
Analytical Regime Definition: Linearized analytical solutions of the hydrodynamic equations were used to define the boundaries of the three operating regimes (non-resonant, ballistic, viscous) based on the square root term (f(L, τ, s, n)) in the expression for the plasmonic oscillation frequency (σ_n).
Viscosity Extraction Method: A non-resonant viscosity extraction method was developed by fitting the simulated response time (t_r) versus channel length (L) data to a high-order polynomial expression derived from the non-resonant analytical solution (Eq. 17).

Commercial Applications

The findings regarding ultra-fast response and material characterization are relevant for several high-tech applications:

Ultra-Fast THz Communications: Graphene FETs, due to their sub-picosecond response times, are ideal candidates for high-speed THz receivers necessary for future 6G and beyond wireless communication systems.
Femtosecond Transient Event Sensing: The ability to detect femtosecond pulses makes these devices critical for time-resolved spectroscopy, pump-probe experiments, and monitoring ultra-fast physical phenomena.
THz Security and Imaging: Graphene detectors can be integrated into high-resolution, real-time THz imaging systems used for non-destructive testing, quality control, and concealed weapon detection.
Fundamental Material Science: The developed viscosity extraction technique provides a crucial tool for characterizing the electron fluid properties in 2D materials, aiding in the design and optimization of advanced electronic components.
Reconfigurable Electronics: Graphene’s high tunability allows for dynamic switching between resonant and non-resonant detection modes via gate bias, enabling the development of reconfigurable THz front-ends.

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

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