Quantum Transport Simulation in DG MOSFETs using a Tight Binding Greens function Formalism

1
Quantum Transport Simulation in DG MOSFETs using
a Tight Binding Greens function Formalism
M. Bescond, J-L. Autran, M. Lannoo
4th European Workshop on Ultimate Integration of
Silicon, March 20 and 21, 2003
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Outline

• Overview of the problem
• Device considered
• Theory Tight Binding Greens function formalism
• Results and discussion
• Conclusion

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Overview of the problem

• Device dimensions scale into the nanometer
  regime.
• The Greens function formalism represents a basic
  method to describe the quantum behavior of the
  transistors capacity to describe interactions
  and semi-infinite contact (source, drain).
• However, most of the studies consider this
  formalism in the EMA, whose validity in the
  nanometer scale is debatable

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Device considered

• Single Atomic conduction channel DG MOSFET.
• Mixed-mode approach
• The axis source-channel-drain is represented by
  an atomic linear chain treated in tight binding
  (1).
• The other parts of the system are classically
  treated from a dielectric point of view.
• (1) M. Bescond, M. Lannoo, D. Goguenheim, J-L.
  Autran, Journal of Non-Cristalline Solids (2003)
  in press.

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Device considered

• Band profile versus position
• Hypothesis
• Source and drain are considered as metallic
  reservoirs.
• We consider a negative Schottky barrier of 0.11
  eV.

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Tight binding Greens function formalism

• Retarded Greens function (2) S. Datta,
  Superlatt. Microstruct., 28, 253 (2000).
• One defines and
• Electron density can be computed as
• f Fermi-Dirac distribution

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Tight binding Greens function formalism

• The current
• The device is virtually cleaved into two regions
  
• The transmitted current I through the plane
  separating the two parts is

, where Q is the charge density of the system.
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Tight binding Greens function formalism

• In the tight binding set, hamiltonian operator
  has the following form
• The associated retarded Greens function of the
  uncoupled system is
• The final expression of the current is

Include the self energies of the semi-infinite
source and drain.
? Coupling matrix
-2?in g-g
?(I-gVgV))-1
Tr1 trace restricted to part 1
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Results and Discussion
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Results and discussion

• IDS versus VG at two different temperatures
• Tunneling current affects
• - the magnitude of the current in the
  subthreshold region,
• - the quantitative shape of the curve.

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Results and discussion

• IDS (VG) for several values of the channel length
  

• For a 20 nm device, the curve has a nearly
  perfect slope of 60 mV/decade.

• In smaller devices, the increase of the
  subthreshold current is due to electron tunneling
  through the bump of the electric potential
  profile.

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Results and discussion

• IDS vs VDS. Dashed line represents the current
  obtained with a quantum of conductance G0 2e²/h
  (3).
• In thin channels, the conductance is quantified
  in units of G0.
• Saturation shows up only when the electron
  potential energy maximum in the channel is
  suppressed by positive gate voltage, and is due
  to the exhaustion of source electrons.

Reflections due to the drop voltage
(3) R. Landauer, J. Phys. Condens. Matter, 1,
8099 (1989).
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Results and discussion

• Transmission coefficient for VG 0.7 V

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Conclusion

• Single conduction channel MOSFET device using
  tight binding Greens function formalism has been
  simulated.
•  Tunneling transistor  tunneling effect
  changes the overall shape of the current
  characteristics the subthreshold curve is no
  longer exponential.
• Even in the strong-tunneling regime the
  transistor is still responsive to gate voltage.
• Because of the decrease of the transverse number,
  the resonant level energies of the channel have
  to be determined with a high precision.

Next step include the 3D silicon atomic
structure.