Schemes for Single Electron Transistor Based on Double Quantum Dot Islands Utilizing a Graphene Nanoscroll, Carbon Nanotube and Fullerene

At a Glance

Metadata	Details
Publication Date	2022-01-04
Journal	Molecules
Authors	Vahideh Khademhosseini, Daryoosh Dideban, Mohammad Taghi Ahmadi, Hadi Heidari
Institutions	University of Kashan, University of Glasgow
Citations	4
Analysis	Full AI Review Included

6CCVD Technical Analysis & Quantum Electronics Material Platform Solutions

Reference: Khademhosseini et al. Schemes for Single Electron Transistor Based on Double Quantum Dot Islands Utilizing a Graphene Nanoscroll, Carbon Nanotube and Fullerene. Molecules 2022, 27, 301.

Executive Summary

This study investigates the performance enhancement of Single Electron Transistors (SETs) by utilizing double quantum dot (DQD) islands constructed from advanced carbon allotropes: Graphene Nanoscrolls (GNS), Carbon Nanotubes (CNT), and Fullerene ($\text{C}_{60}$). The findings critically inform the material requirements for next-generation nanoscale and quantum electronics.

Core Achievement: Successful modeling and comparison of $\text{GNS-CNT}$ SET and $\text{GNS-C}_{60}$ SET structures using Schrödinger’s equation and the Landauer formalism.
Performance Superiority: The $\text{GNS-CNT}$ SET demonstrated superior electronic properties, exhibiting lower Coulomb Blockade (CB) ranges and significantly higher current levels (up to 0.22 µA at 300 K) compared to the $\text{GNS-C}_{60}$ SET.
Dimensional Optimization: SET performance is optimized by maximizing island size (e.g., 5 nm $\text{L}_{GNS}$, 84 nm spiral length, lowest number of turns), which results in thinner tunnel barriers and faster electron transfer speeds.
Operating Conditions: Device functionality was confirmed at 300 K (room temperature), demonstrating potential for practical commercial applications, although performance is heavily temperature-dependent.
Critical Implication for Diamond: The necessity for a stable, ultra-pure carbon platform for integrating complex DQD structures underscores the need for high-quality, MPCVD single-crystal diamond (SCD) substrates capable of supporting nanoscale fabrication and high-speed operation.
6CCVD Value Proposition: 6CCVD provides the necessary foundation—epitaxial SCD and customized Polycrystalline Diamond (PCD) wafers with industry-leading surface finishing ($\text{Ra} < 1$ nm) and integrated metalization for realizing high-performance quantum and SET devices.

Technical Specifications

Key operational parameters and simulated results extracted from the study for the DQD SET structures.

Parameter	Value	Unit	Context
Operating Temperature (T) Range	100 to 300	K	Higher T reduces Coulomb Blockade (CB) range and increases current.
Max Current ($\text{I}_{\text{ds, max}}$)	~0.22	µA	Achieved by $\text{GNS-CNT}$ SET at $\text{T}=300$ K, $\text{V}{\text{g}}=3$ mV, $\text{V}{\text{ds}}=5$ mV.
Max Current Ratio ($\text{GNS-CNT}$ / $\text{GNS-C}_{60}$)	~2.0:1	Ratio	$\text{GNS-CNT}$ current is approximately double that of $\text{GNS-C}_{60}$ at 300 K.
Optimal GNS Length ($\text{L}_{1}$)	5	nm	Highest current obtained due to thinner effective tunnel barriers.
Optimal GNS Spiral Length ($\text{L}’$)	84	nm	Highest current due to thinner tunnel barrier thickness.
Optimal GNS Turns (Lowest Tested)	20	Turns	Yields largest island size and lowest zero-current region.
CNT/Fullerene Length Range ($\text{L}{2}$/$\text{L}{3}$)	0.4 to 2	nm	Shorter lengths resulted in increased current.
Total Coulomb Diamond Area ($\text{GNS-CNT}$)	0.366	$\text{V}^{2}$	Lower area signifies higher conductance and smaller zero-conductance region.
Total Coulomb Diamond Area ($\text{GNS-C}_{60}$)	1.372	$\text{V}^{2}$	Larger area signifies lower conductance.
Gate Voltage ($\text{V}_{\text{g}}$) Range Tested	1 to 3	mV	Increasing $\text{V}_{\text{g}}$ shifts energy levels, increasing tunneling speed and current.

Key Methodologies

The study relied primarily on quantum mechanical modeling and simulation techniques to derive and compare the electronic behavior of the proposed DQD SET structures.

Device Structure Design:
- Double quantum dot islands ($\text{GNS-CNT}$ and $\text{GNS-C}_{60}$) were designed and visualized using Atomistix ToolKit (ATK) software.
- Both islands were configured to contain equal numbers of carbon atoms (96 carbon atoms) for comparative analysis.
Electronic Simulation and Modeling:
- DFT/LDA Method: Density Functional Theory (DFT) utilizing the Local Density Approximation (LDA) was selected for simulating the charge stability diagrams.
- Schrödinger’s Equation: The SET structure was divided into five distinct regions (two potential wells representing the islands and three tunnel junctions). Schrödinger’s equation was solved for each region to determine the electron wave function.
- Transmission Coefficient Calculation: Boundary conditions were applied to the wave functions to calculate the electron transmission coefficient ($\text{T}{\text{GNS}}(\text{E})$, $\text{T}{\text{CNT}}(\text{E})$, $\text{T}{\text{C}60}(\text{E})$) for the individual islands, which were then combined for the total DQD transmission ($\text{T}{1}(\text{E})$ or $\text{T}_{2}(\text{E})$).
Current (I-V) Derivation:
- Landauer Formalism: The drain-source current ($\text{I}_{\text{ds}}$) was modeled based on the Landauer formalism, integrating the total transmission coefficient $\text{T}(\text{E})$ and the Fermi probability function $\text{F}(\text{E})$.
- Parameter Variation: MATLAB was used to implement the analytical models and investigate the impacts of crucial engineering parameters, including GNS dimensions (length, turns, spiral length), CNT/Fullerene length, temperature, and applied gate voltage ($\text{V}_{\text{g}}$), on the resultant current and Coulomb blockade range.

6CCVD Solutions & Capabilities

The successful integration and commercialization of high-performance nanoscale devices like the DQD SET requires a foundation of materials engineering excellence. While the research focuses on $\text{sp}^{2}$ carbon allotropes, the stable, high-performance substrate for integration, especially for SETs involving quantum phenomena (like leveraging Nitrogen-Vacancy centers), must be high-quality diamond. 6CCVD specializes in providing the MPCVD diamond platforms essential for replicating and advancing this cutting-edge research.

Applicable Materials for Advanced Carbon Nano-Integration

To support the integration of carbon nanomaterials (GNS, CNT) or to create diamond-based quantum dots (e.g., using bulk or shallow NV centers), 6CCVD recommends the following materials:

6CCVD Material	Grade / Feature	Application Relevance to SET Research
Optical Grade Single Crystal Diamond (SCD)	Ultra-low N content (Type IIa)	Ideal base platform for growing, transferring, or positioning carbon nanostructures; crucial for quantum computing/sensing where low defects are paramount.
Boron-Doped Diamond (BDD)	Heavy Doping Capability	Used for highly conductive electrodes, gates, or source/drain contacts required in SET structures, leveraging diamond’s thermal and chemical stability.
High-Purity Polycrystalline Diamond (PCD)	Wafers up to 125 mm	Cost-effective substrate for larger-scale electronic integration and sensor arrays utilizing SET principles (e.g., gas molecule detection, memory).

Customization Potential for Nanoscale Devices

The construction of nanoscale transistors and quantum dots demands extreme precision in material dimensions, surface finish, and contact engineering. 6CCVD provides end-to-end customization capabilities that directly meet these requirements:

Ultra-Low Roughness Polishing: Achieving $\text{Ra} < 1$ nm on SCD surfaces and $\text{Ra} < 5$ nm on inch-size PCD is crucial for maintaining the electronic integrity of the $\text{GNS/CNT}$ islands and ensuring consistent tunneling junctions.
Custom Wafer Dimensions: We provide custom plates and wafers up to 125 mm (PCD) and custom SCD thicknesses (0.1 µm to 500 µm) to suit various research scales, from fundamental modeling to pilot fabrication runs.
Advanced Metalization Services: SET operation requires precise source/drain/gate contacts. 6CCVD offers in-house deposition of thin films, including Ti, Pt, Au, Pd, W, and Cu, allowing researchers to implement customized contact schemes (e.g., $\text{Ti/Pt/Au}$ stacks) directly onto their diamond substrates.
Precision Manufacturing: Using high-precision laser cutting, 6CCVD can deliver custom-shaped diamond pieces necessary for device geometry constraints or specific micro-electro-mechanical system (MEMS) integrations.

Engineering Support

6CCVD’s in-house team of material scientists and technical engineers, many holding PhDs in related fields, offers comprehensive support for projects involving nanoscale carbon electronics. We assist researchers and engineers with:

Material Selection: Guidance on choosing the optimal diamond grade (SCD, BDD, or PCD) to minimize defects and maximize carrier mobility for projects related to Single Electron Transistors, Quantum Dots, and High-Speed Memory/Sensing applications.
Interface Optimization: Consulting on appropriate metalization schemes and polishing protocols to ensure low-resistance, stable contacts necessary for high-speed electron tunneling devices operating at or near room temperature (300 K).
Custom Growth Parameters: Tailoring MPCVD growth recipes to control impurity levels, necessary for precise creation of conductive (BDD) or isolating (SCD) device regions.

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

View Original Abstract

The single electron transistor (SET) is a nanoscale switching device with a simple equivalent circuit. It can work very fast as it is based on the tunneling of single electrons. Its nanostructure contains a quantum dot island whose material impacts on the device operation. Carbon allotropes such as fullerene (C60), carbon nanotubes (CNTs) and graphene nanoscrolls (GNSs) can be utilized as the quantum dot island in SETs. In this study, multiple quantum dot islands such as GNS-CNT and GNS-C60 are utilized in SET devices. The currents of two counterpart devices are modeled and analyzed. The impacts of important parameters such as temperature and applied gate voltage on the current of two SETs are investigated using proposed mathematical models. Moreover, the impacts of CNT length, fullerene diameter, GNS length, and GNS spiral length and number of turns on the SET’s current are explored. Additionally, the Coulomb blockade ranges (CB) of the two SETs are compared. The results reveal that the GNS-CNT SET has a lower Coulomb blockade range and a higher current than the GNS-C60 SET. Their charge stability diagrams indicate that the GNS-CNT SET has smaller Coulomb diamond areas, zero-current regions, and zero-conductance regions than the GNS-C60 SET.

Tech Support

Original Source

DOI: https://doi.org/10.3390/molecules27010301

References

2017 - Single Electron Transistor with Single Aromatic Ring Molecule Covalently Connected to Graphene Nanogaps [Crossref]
2020 - Room temperature single electron transistor based on a size-selected aluminium cluster [Crossref]
1987 - Observation of single-electron charging effects in small tunnel junctions [Crossref]
2000 - Nano mechanical oscillations in a single-C60 transistor [Crossref]
2017 - Single-electron tunneling through an individual arsenic dopant in silicon [Crossref]
1986 - Coulomb blockade of single-electron tunneling, and coherent oscillations in small tunnel junctions [Crossref]
2002 - Coulomb blockade and the Kondo effect in single-atom transistors [Crossref]
2003 - Coulomb blockade, single-electron transistors and circuits in silicon [Crossref]
2020 - Single-electron current gain in a quantum dot with three leads [Crossref]
2021 - Carbon single-electron point source controlled by Coulomb blockade [Crossref]