RELEVANCE OF DEVICE MODELING AND NUMERICAL SIMULATION FOR :

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RELEVANCE OF DEVICE MODELING AND NUMERICAL
SIMULATION FOR

• INTERCONNECT SIMULATION
• ELECTROMAGNETIC WAVE EFFECTS ON MICROWAVE
  TRANSISTORS
• FROM THE ANALYSIS OF SOME RELEVANT LITERATURE
• ADVANCED DEVICE MODELING (HIGHER ORDER MOMENT
  EQUATIONS) AND NUMERICAL METHODS (HIGH
  RESOLUTION CONSERVATIVE SCHEMES) REQUIRED !

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MODELS INCORPORTATED IN COMMERCIAL SIMULATORS

• ISE
• DRIFT-DIFFUSION
• ENERGY TRANSPORT
• SIMPLIFIED HYDRODYNAMICAL
• THERMAL
• PARAMETERS PHENOMENOLOGICALLY ADJUSTED
• LACKING
• PHYSICS BASED MODELS
• ELECTROMAGNETIC INTERACTIONS
• INTERCONNECTS

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MODELLING AND SIMULATING INTERCONNECTS

• ON CHIP INTERCONNECTS ARE A LIMITING FACTOR TO
  THE OVERALL PERFORMANCE OF CIRCUITS. ON CHIP
  WIRING DELAYS ARE A SIGNIFICANT PORTION OF THE
  TOTAL CHIP DELAY TIME.
• METAL-INSULATOR-SEMICONDUCTOR INTERCONNECTS ARE
  OF PARAMOUNT INTEREST
• ELECTROMAGNETIC FIELD COUPLING WITH DEVICE CHARGE
  CARRIERES TRANSPORT IS REQUIRED FOR ACCURATE
  DESCRIPTION
• G.WANG, R.W.DUTTON, C.S..RAFFERTY, DEVICE LEVEL
  SIMULATION OF WAVE PROPAGATION ALONG
  METAL-INSULATOR SEMICONDUCTOR INTERCONNECTS, IEEE
  TRANS ON MICROWAVE THEORY AND TECHNIQUES, VOL.50,
  (2002), pp.1127-1137.

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MAIN RESULTS

• DETERMINATION OF THE SLOW SPEED FOR THE
  FUNDAMENTAL TM MODE
• AT VARIANCE WITH THE USUAL TREATMENT WHERE THE
  SEMICONDUCTOR IS TREATED AS A MEDIUM WITH UNIFORM
  CONDUCTIVITY, THE DEVICE DESCRIPTION ENABLES TO
  I
• ANALYZE THE HIGHER MODES GENERATION THROUGH THE
  NON LINEAR BEHAVIOUR OF THE SEMICONDUCTOR
• TREAT BOTH SMALL SIGNAL AND LARGE SIGNAL CASES

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FUNDAMENTAL MODE PROPAGATION Ex AND Ez
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FUNDAMENTAL MODE PROPAGATION ELECTRON AND HOLE
CONCENTRATIONS
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SECOND HARMONIC Ex AND n
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HIERARCHY OF MOMENT EQUATIONS

• THE NON STATIONARY DRIFT DIFFUSION EQUATIONS ARE
  THE FIRST TERM IN THE HIERARCHY OF MOMENT
  EQUATIONS (1) AND (3)

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RELATIVE MAGNITUDES OF THE RELAXATION TIMES

• IN THE HIERARCHY OF THE MOMENT EQUATIONS THE
  RELAXATION TIMES FOR MOMENTUM, ENERGY, ENERGY
  FLUX, FLUX OF ENERGY FLUX, ETC. APPEAR
• IT IS POSSIBLE TO LIMIT TO THE DRIFT-DIFFUSION
  EQUATIONS ONLY IF THE OTHER RELAXATION TIMES
  COULD BE CONSIDERED NEGLIGIBLE
• HOWEVER
• MONTE CARLO SIMULATIONS (MUSCATO) SHOW THAT THE
  RELAXATION TIME FOR ENERGY IS LARGER THAN THE
  OTHERS AND THE MOMENTUM AND ENERGY FLUX
  RELAXATION TIMES ARE COMPARABLE !

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EXTENDED MODELS

• INCORPORATE BALANCE EQUATIONS FOR MOMENTUM,
  ENERGY AND ENERGY FLUX
• THE RELAXATION TIMES FOR MOMENTUM AND ENERGY FLUX
  ARE OF THE SAME ORDER OF MAGNITUDE
• THE ONSAGER RECIPROCITY THEOREM OF IRREVERSIBLE
  STATISTICAL PHYSICS MANDATES THAT AT LEAST THE
  ENERGY FLUX BALANCE EQUATIONS MUST BE INCLUDED
  (MUSCATO, 1998)
• THE PARAMETERS APPEARING IN THE PDE MUST BE
  OBTAINED FROM THE PHYSICAL MODEL, EITHER THROUGH
  MONTE CARLO DATA FITTING OR BY ASYMPTOTIC
  SOLUTIONS OF THE BOLTZMANN EQUATION.

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ELECTROMAGNETIC WAVE EFFETCS ON MICROWAVE
TRANSISTORS

• WHEN SEMICONDUCTOR DEVICES ARE OPERATED AT
  SUFFICIENTLY HIGH FREQUENCY THE QUASI STATIC
  (POISSON BASED) SEMICONDUCTOR DEVICE MODELS FAIL
  TO REPRESENT ACCURATELY THE COUPLING OF THE
  ELECTROMAGNETIC WAVE PROPAGATING IN THE DEVICE
  WITH THE CARRIERS.
• THE FULL MAXWELL EQUATIONS MUST BE COUPLED TO THE
  DEVICE EQUATIONS (MOMENTS EQUATIONS)
• ALSUNAIDI, IMTIAZ, EL-GHALAZY, ELECTROMAGNETIC
  WAVE EFFECTS ON MICROWAVE TRANSISTORS USING A
  FULL WAVE TIME DOMAIN MODEL, IEEE TRANS ON
  MICROWAVE THEORY AND TECHNIQUES, 44, (1996),
  799-899

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DEVICE MODEL USED BY ALSUNAIDI ET AL.
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SOME RESULTS
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LIMITATIONS

• ELECTROMAGNETIC PROPAGATION THROUGH THE DEVICE
• THE RELAXATION TIMES OF THE ENERGY FLUX ARE OF
  THE SAME ORDER AS THOSE FOR MOMENTUM.
• THEREFORE THE ENERGY FLUX MOMENT EQUATION SHOULD
  BE CONSIDERED
• THE DEVICE MODEL, AS IN THE PREVIOUS CASE, DOES
  NOT OBEY THE ONSAGER RECIPROCITY THEOREM.TO
  RESTORE THE ONSAGER RECIPROCITY THEOREM AT LEAST
  THE ENERGY FLUX BALANCE EQUATION MUST BE INCLUDED
• NECESSITY OF EXTENDED MODELS (HIGHER ORDER
  MOMENTS).

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EXTENDED HYDRODYNAMICAL MODELS
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APPLICATION OF THE METHOD
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TEST 1D DIODE N N N
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TEST FOR THE EXTENDED MODEL WITH 1D
STRUCTURESMUSCATO ROMANO, 2001
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TEST OF THE EXTENDED (MEP-CLOSURE) MODELS ON A 2D
BIPOLAR TRANSISTOR
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ENERGY BAND AND HOT ELECTRONS
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MOMENTUM PRODUCTION (y-COMPONENT)
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