Circuit Model of Cantilevered Carbon Nanotube CNT

1
Circuit Model of Cantilevered Carbon Nanotube
(CNT)

• Ethan N. Phung

University of Massachusetts Lowell Department of
Electrical and Computer Engineering Center for
Advanced Computation and Telecommunications
2
Outline

• Background
• Objectives
• Problem Statement
• Mechanical Model of Vibrating Carbon Nanotube
• Circuit Model of the System
• System of First-Order Differential Equations
• Results
• Summary and Future Work
• Acknowledgment

3
Background

• A recent study1 demonstrated the application of
  a carbon nanotube (CNT) as Frequency Modulated
  (FM) signal receiver/detector.

- A single CNT was shown to function as an
antenna, a tuner, an amplifier, and a
demodulator, simultaneously.

• Due to its high electrical conductivity and the
  sharpness of its tip, CNT can function as a good
  electron field-emitter.

1K. Jensen, J. Weldon, H. Garcia, and A. Zettl.
Nano Lett., 2008, 8 (1), p 374
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Objectives

• Derive an electrical circuit model of the
  cantilevered CNT vibrations subject to
  electromagnetic (EM) force.
• Analyze and validate the circuit model as a
  receiver/detector.

5
Problem statement

• Analyze the CNT performance as a receiver using
  an electrical circuit model

Ts

• Mechanical vibrations of CNT induced by external
  EM wave

H(?)
L length of the CNT ? rotational
angle A projected cross sectional area
of CNT H(?) H0L?2/2
separation Ts FM modulated signal
A
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Model Parameters

• Due to field emission of CNT, the effective
  capacitance C is

2. Under ?ltlt0 assumption, the time-varying
potential is
v(t)
Where, the total charge Q(t)Q0q(t) .
3. The total force acting on the CNT is F(t) F0
f(t), where,
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Mechanical Model of Vibrating CNT

• The mechanical vibration of CNT under EM wave
  excitation can be described as a damped
  oscillator. Therefore, the equation of
  conservation of angular momentum governing this
  system is

where j Moment of inertia r Frictional
coefficient k Stiffness Ts External
applied source
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Circuit Model of the System

• The circuit model above is obtained based on the
  two equations below

-
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Circuit Parameters and Variables
Electric charge q(t)
Induced Current
Load Resistor RLoad
Resistor 1/r
Resistor R
Inductor 1/k
Capacitor
Capacitor j
Voltage ?
Induced Voltage
External Current Source
Turn ratio
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Simplification

Define,

then,
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First-Order Differential Equations
Let Then, final three first-order differential
equations are

Associated initial conditions at t0
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Modulated Signal

where, ?S ltlt ?C
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Solution

• The solution of y1, y2 ,y3 red, green, and
  blue, respectively.

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Input and Output Comparison

• The output signal (BLUE) is the envelope of the
  input signal.

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Conclusion

• Based on the experimental result, the circuit of
  the system is functioning as an amplitude
  demodulator. The charge q(t) is extracting the
  input signal by creating its envelope waveform.
• Micro power electronic devices.

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Acknowledgment

• This work was carried out at Center for Advanced
  Computation and Telecommunications (CACT) at the
  University of Massachusetts Lowell, and fully
  supported by NSF-REU grant No. 0649235. I would
  like to extent my gratitude to Professor Charles
  Thompson and Professor Kavitha Chandra for their
  help and advising throughout this work.