Thermal Conductivity of Semiconductor Materials in SOI Devices, Slides of Computer Science

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Thermal Effects in Nanoscale

Devices. What Do We Know So Far

Some Basic Definitions

Heat transfer: the movement of energy due to a temperature difference and

according to the following three mechanisms:

• Conduction – heat transfer by diffusion in a stationary medium due to a

temperature gradient. The medium can be a solid or a liquid.

• Convection – heat transfer between either a hot surface and a cold moving

fluid or a hot moving fluid and a cold surface. Convection occurs in fluids

(liquids and gases).

• Radiation – heat transfer via electromagnetic waves between two surfaces

with different temperatures.

Specific Thermal Energy vs. Temperature

Derivation of the Heat Diffusion Equation

Thermal Conductivity for Various States of

Matter

Thermal Conductivity of Important Materials

for IC Fabrication

• Si 143 W/m/K
• SiO 2 1.28 W/m/K
• HfO 2 23 W/m/K
• AlN 285 W/m/K
• Diamond 2000-2500 W/m/K
• Polysilicon 125 W/m/K
• Al 250 W/m/K
• Gold (Au) 310 W/m/K
• Silver (Ag) 429 W/m/K
• Copper (Cu) 401 W/m/K

Existing Modeling Packages

• THERMAL3D (Local Modeling)
• GIGA3D (Global Modeling)

Phonons Treatment in Small Structures

-

-

-

Silicon layer thickness (m)

Molecular Dynamics

Phonon Boltzmann Transport Equation

Fourier Law

Superlattice^ Classical SOI Structures

Nanotubes

-

-

-

Silicon layer thickness (m)

Molecular Dynamics

Phonon Boltzmann Transport Equation

Fourier Law

Superlattice^ Classical SOI Structures

Nanotubes

 -Phonon mean free path (  =300nm)

 - phonon mean free length (  =1-2nm)

Energy Transfer Between the Electron Bath

and the Phonon Bath

High Electric Field

Optical Phonon Emission

Acoustic Phonon Emission

Heat Conduction in Semiconductor

 ~ 0.1ps  ~ 0.1ps

 ~ 10ps

 ~ 10ps

Hot Electron Transport

ASU Approach to Thermal Modeling

k+q k k+q k k k+q k k+q ,q , q , q ,q q k+q k k k+q ,q ,q k

(k) r (13a)

( ) (13b)

e r k e a e a

p r e a p p

e v E f W W W W t

g v q g W W t t

     

  

 ^ ^ ^ ^  ^  ^ ^ 

 ^    

 ^ ^  ^  ^  

 ^    

J. Lai and A. Majumdar, “Concurent

thermal and electrical modeling of

submicrometer silicon devices”, J.

Appl. Phys. , Vol. 79, 7353 (1996).

 

3 *^2

LO B e L d LO A LO LO e LO e LO LO A

A LO A B e L A A A LO LO A e L

T nk T T nm v T T C C a t

T T T nk T T C k T C b t

  

 

 ^  ^ ^  

 ^  ^ ^  

Flow-Chart of the Simulator

Average and smooth: electron density, drift velocity and electron energy at each mesh point

end of MCPS phase?

Acoustic and Optical Phonon Energy Balance Equations Solver

end of simulation?

end

no

yes

Define device structure

Generate phonon temperature dependent scattering tables

Initial potential, fields, positions and velocities of carriers

t = 0

t = t +  t

Transport Kernel (MC phase)

Field Kernel (Poisson Solver)

t = n  t? yes

Average and smooth: electron density, drift velocity and electron energy at each mesh point

end of MCPS phase?

end of MCPS phase?

Acoustic and Optical Phonon Energy Balance Equations Solver

end of simulation?

end of simulation?

end

no

yes

Define device structure

Generate phonon temperature dependent scattering tables

Initial potential, fields, positions and velocities of carriers

t = 0

t = t +  t

Transport Kernel (MC phase)

Field Kernel (Poisson Solver)

t = n  t?

Define device structure

Generate phonon temperature dependent scattering tables

Initial potential, fields, positions and velocities of carriers

t = 0

t = t +  t

Transport Kernel (MC phase)

Field Kernel (Poisson Solver)

t = nt = n  t?t? yes

Exchange of Variables

Ensemble Monte Carlo Device Simulator

Phonon Energy Balance Equations Solver

TA TLO

n vd Te

Find electron position in a grid :(i,j)

Find: TL(i,j)=TA(i,j) and TLO(i,j)

Select the scattering table with “coordinates”: ( TL(i,j)=TLO(i,j) )

Generate a random number and choose the scattering mechanism for a given electron energy

0 0 25 50 7575

(^105)

0.

1

1.

x 10^25

Electron Density (m-3) Si/SiO2 interface source channel drain

Si/BOX interface

y (nm) (^) x (nm)^610 25 50

(^011)

0.

0.

0.

0.

0.

0.

0.

Energy (eV)

source channel drain y (nm) x (nm)

Thermal Boundary Conditions

 Shown below is basic configuration of n -chan

mode p -channel SOI devices:

2. SOI Device Description and Mode

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - P

Ba

VS

Source - P

Ba

VS

n -channel

BOX(SiO 2 )

Dirichlet boundary

condition: Tbox=300K

Dirichlet boundary

condition: Tgate=300K

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

 Shown below is basic configuration of n -chan

mode p -channel SOI devices:

2. SOI Device Description and Mode

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - P

Ba

VS

Source - P

Ba

VS

n -channel

 Shown below is basic configuration of n -chan

mode p -channel SOI devices:

2. SOI Device Description and Mode

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - P

Ba

VS

Source - P

Ba

VS

n -channel

BOX(SiO

Dirichlet boundary

condition: Tbox=300K

Dirichlet boundary

condition: Tgate=300K

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

Why substrate is not modeled?

1. Thermal Boundary Conditions

Why Substrate is NOT Modeled? Shown below is basic configuration of n -chann

mode p -channel SOI devices:

2. SOI Device Description and Model

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - P+

Back

VS

Source - P+

Back

VS

 For the n-channel devices, there are three mod

 Thick-film (Partially-depleted) PD-SOI devic

n -channel

BOX(SiO 2 )

Dirichlet boundary condition: Tsubstrate=300K

Dirichlet boundary condition: Tgate=300K

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

 Shown below is basic configuration of n -chann mode p -channel SOI devices:

2. SOI Device Description and Model

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - N+^ P Drain - N+

Si0 2

Gate

Back gate (substrate)

VG VS

VG

VD

tox

tSi

tox

Buried Si0 2

Source - P+

Back

VS

Source - P+

Back

VS

 For the n-channel devices, there are three mod

 Thick-film (Partially-depleted) PD-SOI devic

n -channel

BOX(SiO 2 )

Dirichlet boundary condition: Tsubstrate=300K

Dirichlet boundary condition: Tgate=300K

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

Neumman boundary condition

The presence of the bottom silicon substrate does not affect either the electrical or the thermal characteristics of the structure being considered.

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