Quantum Device Simulation 30A MOS CV Curve Quantum Currents and - - PowerPoint PPT Presentation

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Quantum Device Simulation 30A MOS CV Curve Quantum Currents and - - PowerPoint PPT Presentation

Nov 21, 2023 159 likes •356 views

Quantum Device Simulation 30A MOS CV Curve Quantum Currents and PHEMTs Introduction Why a Quantum Mechanical based simulator is necessary Introduction to QM issues and theory Implementation and syntax Practicalities of use

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Quantum Device Simulation

30A MOS CV Curve – Quantum Currents – and PHEMTs

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Quantum Device Simulation

Introduction ß Why a Quantum Mechanical based simulator is necessary ß Introduction to QM issues and theory ß Implementation and syntax ß Practicalities of use ß Examples (MOS, PHEMT, Diode)

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Quantum Device Simulation

Introduction (con’t) ß Why Use a QM simulator

ß Reduction in device size => coherence length of electrons ß Thin gate oxides => CV shift ß Channel sheet carrier shift => MOS/HEMT ß Heterojunction tunneling ß Pulse doping ‘smear’

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Quantum Device Simulation

Quantum Issues ß Quantization “carrier confinement”

ß 1D/2D/3D => Quantum Well/Wire/Dot ß Schrodinger's Equation ß Eigen Value Problem

  • + V(y)

+ V(y) z zi

i (y) =

(y) = E Ei

i

z zi

i

(y) (y)

h h2

2

2m 2m*

*

d d2

2

dx dx2

2

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Quantum Device Simulation

Quantum Issues (con’t) ß Results appear as a sequence of

ß Eigen energies => Discrete energies where

electrons may reside

ß Eigen functions => Probability distribution of

electrons along each slice

ß Schrodinger -Poisson => Spacial distribution of electrons to

replace classical one

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Quantum Device Simulation

Quantum Issues (con’t) ß Transport

ß Transmission, Deflection ß Concentration

ß Quantum corrections to standard transport equations ß Provided by Quantum moments equation ß Based on second moments of the Wigner distribution

function

ß Quantum Temperature => Quantum diffusion term ß Bohm Quantum Potential

Uq Uq = - = -

n n2

2

8m 8m*

*

∆ ∆

2 2 Ln

Ln(n) (n)

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Quantum Device Simulation

Implementation and Syntax ß Schrodinger-Poisson Solver

ß models Schrodinger Eigens =15

ß Quantum Moments

ß models quantum ß solve qx.damp=1.0

ß Bohm Quantum Potential

ß BQP

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Quantum Device Simulation

Electrostatic Potential, Classical and Quantum Electron Concentrations

Figure 1.

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Quantum Device Simulation

Eigen Wave Functions and Energy Levels

Figure 2.

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Quantum Device Simulation

MOS 30A Gate – CV Curve

Figure 3.

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Quantum Device Simulation

Figure 4.

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Quantum Device Simulation

Classical and Quantum Electron Concentrations

Figure 5.

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Quantum Device Simulation

HDiode

Figure 6.

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Quantum Device Simulation

Classical and Quantum Electron Concentrations

Figure 7.

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Quantum Device Simulation

Classical and Quantum Currents

Figure 8.

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Quantum Device Simulation

PHEMT – Zero Bias Case

Figure 9.

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Quantum Device Simulation

PHMET

Figure 10.

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Quantum Device Simulation

Model Comparison

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Quantum Device Simulation

Conclusion ß As a device dimenstions shrink, qunatum effects become

more significant

ß Schrodinger-Poisson solve provides calculations of bound

state energies, carrier wave functions and carrier concentrations

ß Quantum effects included in carrier transport by using

quantum moments models