TSUPREM-4 Models TSUPREM-4 User’s Manual

lus-

in

seant

m-

rium

to

Equation 2-76

where is the concentration of dopant atoms in transient dopant-defect cters andDDC.T.0 , DDC.T.E , DDC.F.0 , DDC.F.E , DDCF.D.N, DDCF.N.N,DDCF.I.N , DDCR.N.N, andDDCR.I.N are parameters on theIMPURITYstatement.

This equation models dopant-defect clusters withDDCF.D.N dopant atoms percluster,DDCF.I.N interstitials required to form a cluster,DDCR.I.N interstitialatoms required to dissolve a cluster, and interstitialsthe cluster.DDC.F.0 andDDC.F.E control the amount of clustering whileDDC.T.0 andDDC.T.E control the rate of clustering and declustering. Becau

is subtracted from the total concentration before computing , the dopin transient clusters is inactive and immobile.

The net capture rate of interstitials by clusters is given by

Equation 2-77

whereIFRACM is a parameter on theIMPURITY statement (see“Point DefectDiffusion Equations” on page 2-32). Ideally,IFRACM should be equal to

, but it is available as a separate paraeter for flexibility in modeling.

The dopant-defect clustering model is enabled by specifyingACT.FULL on theMETHOD statement.

Segregation of Impurities

The segregation of impurities at material interfaces is treated as a nonequilibprocess byTSUPREM-4.

Segregation Flux At an interface between materials and , the impurity flux from materialmaterial (normal to the interface) is given by

Equation 2-78

where

• and are the concentrations in materials and , respectively

• is the interface transport coefficient

• is the equilibrium interface segregation coefficient

KddF DDC.F.0 exp DDC.F.EkT

-----------------------– ⋅=

Cdd

DDCF.I.N DDCR.I.N–

Cdd Ca

Rdd IFRACMCdd∂

t∂------------=

DDCF.I.N DDCR.I.N–( ) DDCF.D.N⁄

i j J ij

J hCi

m----- Cj–

=

Ci Cj i j

h

m

2-26 Confidential and Proprietary S4 1999.2

Draft 6/22/99

TSUPREM-4 User’s Manual Diffusion

cesrfaces

l

ili-

f

erials,

eri-

This expression represents the impurity flux in the diffusion equation at interfabetween different materials and between the ambient gas and the exposed suof the simulation structure.

The segregation is based on the chemical impurity concentrations when theACT.EQUI model is used and the active concentrations whenACT.TRAN isused. (When , the chemical concentrations are used in allcases.) For materials using the polycrystalline model, segregation at materiainterfaces is based on the concentration in the grain interior.

TransportCoefficient

The transport coefficient is given by

Equation 2-79

SegregationCoefficient

The segregation coefficient defines the ratio in equilibrium, when theinterface impurity flux vanishes. The segregation coefficient is given by

Equation 2-80

The coefficientsTRANS.0, TRANS.E, SEG.0, andSEG.E for each impurityand pair of materials are defined on the coefficient statements for impurities(“ IMPURITY” on page 3-225,“ANTIMONY” on page 3-269,“ARSENIC” onpage 3-275,“BORON” on page 3-281, and“PHOSPHORUS” on page 3-287).For an interface between materials and , material is specified by theMATERIAL parameter and material is specified with the/MATERIA parameter.

Moving-BoundaryFlux

There is an additional flux at oxidizing interfaces due to the consumption of scon containing impurities. The flux is from the silicon into the oxide and is ofmagnitude , where is the impurity concentration on the silicon side othe interface and is the velocity of the interface.

Interface TrapModel

Assuming that there are trap sites at the interface between two adjacent matthe dopant diffusing through the interface can be trapped into the trap site[11].The model is activated by specifying theITRAP parameter on theMETHOD state-ment.

Equation 2-81

whereσ is the areal density of occupied trap sites andl is the length along theboundary and,Fi andFj are the dopant flux to the interface trap sites from matals i andj, respectively.

V.COMPAT 6.4≤

h TRANS.0 expTRANS.E–

kT----------------------------

⋅=

Ci Cj⁄

m SEG.0 expSEG.E–kT

--------------------- ⋅=

i j ij

vCSi CSiv

σ∂t∂

------l∂

∂D

σ∂l∂

------ – Fi F j+ +=

S4 1999.2 Confidential and Proprietary 2-27

Draft 6/22/99

Appendix A: Default Coefficients TSUPREM-4 User’s Manual

Segregation and Transport Coefficients

Table A-6 Pair Kinetics Parameters (all impurities; CM.SEC units) (7)

DIPAIR.0 3.65e-4 00

DIPAIR.E 1.58

DVPAIR.0 3.65e-4

DVPAIR.E 1.58

R.I.S 10000

E.I.S 000

R.V.S 10000

E.V.S 000

R.IP.V 10000

E.IP.V 000

R.VP.I 10000

E.VP.I 000

Table A-7 Segregation Coefficients

Boron Phosphorus Arsenic Antimony

Silicon/oxideSEG.0 1.126e3 [8] 30.0 [9] (8) 30.0 [9]0 30.0 [9]SEG.E 0.91 000 0.00 0.0 0.0

Polysilicon/oxide (9)SEG.0 1.126e3 30.00 30.0 0 30.0 0

SEG.E 0.91 00 0.0 0.0 0.0

Silicon/TiSi 2

SEG.0 0.3 000 1.0 0.8 0 0.8

SEG.E 0000.0 0.0 0.0 0.0

Polysilicon/TiSi 2

SEG.0 0.3 000 1.0 0.8 0.8

SEG.E 000.00 0.0 0 .0 0.0

Silicon/WSi 2 [4]- [7]

SEG.0 1.0 000 5.0 10.0 0 10.0

SEG.E 0000.0 0.0 0.0 0..0

Polysilicon/WSi 2

SEG.0 1.0 000 5.0 10.0 0 10.0

SEG.E 0000.0 0.0 0.0 00

Other Impurities and Pairs of MaterialsSEG.0 1.0 000 1.0 0 1.0 0 1.0 0

SEG.E 000000 00 00 00

Table A-8 Fluorine Segregation Coefficients

Silcon/Oxide Polysilicon/Oxide

SEG.0 5.62e-8 5.62e-8

SEG.E 0.0 0.0

A-4 Confidential and Proprietary S4 1999.2

Draft 6/22/99

TSUPREM-4 User’s Manual Default Coefficient Values

Table A-9 Interface Transport Coefficients

Boron Phosphorus Arsenic Antimony

Silicon/ambient [10] (10)TRANS.0 1.674e7 9.0e5 9.0e5 1.5e3

TRANS.E 2.481 1.99 1.99 1.04

Oxide/ambient (11)TRANS.0 1.647e7 9.0e5 9.0e5 1.5e3

TRANS.E 2.481 1.99 1.99 1.04

Polysilicon/ambient (11)TRANS.0 1.674e7 9.0e5 9.0e5 1.5e3

TRANS.E 2.481 1.99 1.99 1.04

Polysilicon/silicon (12)TRANS.0 100. 000 100. 00 100. 000 100. 000

TRANS.E 0.0 0.0 0.00 0.0

Silicon/TiSi 2

TRANS.0 1.0e6 1.0e6 1.0e6 1.0e6

TRANS.E 2.0 2.0 2.0 2.0

Polysilicon/TiSi 2

TRANS.0 1.0e6 1.0e6 1.0e6 1.0e6

TRANS.E 2.0 2.0 2.0 2.0

Silicon/WSi 2 [4]-[7]

TRANS.0 2.0e-2 3.0e-3 3.0e-3 3.0e-3

TRANS.E 0.0 0.0 0.0 0.0

Polysilicon/WSi 2

TRANS.0 2.0e-2 3.0e-3 3.0e-3 3.0e-3

TRANS.E 2.0 2.0 2.0 2.0

Table A-10 Interface Transport Coefficients (All Impurities)

Silicon/Oxide, and Polysilicon/Oxide

TRANS.0 0.1

TRANS.E 0.0

All Materials with Nitride and Oxynitride

TRANS.0 0.0

TRANS.E 0.0

Table A-11 Interface Trap Impurities ( CM.SEC units)

Boron (13) Phosphorus (14) Arsenic (15)

Oxide/Silicon, and Oxide/PolysiliconTRANS.0 0.166 7.15 0.231

TRANS.E 0.486 1.75 0.766

SEG.0

SEG.E /SEG.E - SEG.E(Table A-5)

RATIO.0 0 0 0

RATIO.E 0 0 0

/SEG.0 SEG.0 (Table A-5)÷

S4 1999.2 Confidential and Proprietary A-5

Draft 6/22/99

Appendix A: Default Coefficients TSUPREM-4 User’s Manual

Polysilicon Grain Segregation

Clustering and Solid Solubility

/TRANS.0 0.0166 0.715 0.0231 [12]/TRANS.E 0.486 1.75 0.766 [12]/SEG.0 5.96E3

/SEG.E /RATIO.E - Q.MAX.E -0.285

/RATIO.0 0.178 4.00E-3 6.29E-5

/RATIO.E -0.086 -0.37 -0.738

Q.INI.0 0 0 0

Q.INI.E 0 0 0

Q.MAX.0 2.0E14 [12] 6.8E14 [11] 2.0E14 [12]Q.MAX.E 0 0 0

Table A-12 Parameters for Polysilicon Grain Interior/Boundary Segregation (16)

Boron Phosphorus Arsenic Antimony

Q.SITES 2.5e15 2.5e15 2.5e15 2.5e15

CG.MAX 5.0e22 5.0e22 5.0e22 5.0e22

GSEG.0 12.0 0 1.25 0.6 1.0

GSEG.E 0.0 0.443 0.414 0 .0

GSEG.INI 1.0 0 1.0 1.0 1.0

VELIF.0 1.0e7 1.0e7 1.0e7 1.0e7

VELIF.E 3.0 3.0 3.0 3.0

Polysilicon diffusivity enhancement factors (17)FGB 2.64 95.1 0 0110. 0000 41.8 0

Table A-13 Coefficients for Clustering in Silicon (18)

Arsenic

CTN.0 0 1.03103e-17 [1]CTN.E -0.4 (19)00000

CTN.F 4.0 0000 00000

Table A-11 Interface Trap Impurities ( CM.SEC units)

Boron (13) Phosphorus (14) Arsenic (15)

/RATIO.0 Q.MAX.0 Css×÷

Table A-14 Solid Solubility in Silicon

Temperature (˚C) Boron Phosphorus Antimony

650 1.70e19 [13] 1.20e20 [14] 1.70e19 [14]700 1.70e19 1.20e20 1.70e19

800 4.40e19 2.90e20 2.30e19

900 9.50e19 6.00e20 3.10e19

1000 1.70e20 1.00e21 4.00e19

1100 2.20e20 1.20e21 4.90e19

1200 2.20e20 1.25e21 5.90e19

1300 1.40e20 1.10e21 6.80e19

A-6 Confidential and Proprietary S4 1999.2

Draft 6/22/99

TSUPREM-4 User’s Manual Default Coefficient Values

Point Defect Parameters

1350 1.40e20 1.10e21 6.80e19

Table A-15 Transient activation parameters (Extended Defects AAM)

Boron Phosphorus Arsenic Antimony

T.ACT.0 8.0e-16 8.0e-16 8.0e-16 8.0e-16

T.ACT.E -4.2 -4.2 -4.2 -4.2

ACT.MIN 1.0 2.0 1.0 1.0

CL.INI.A true true true true

Table A-16 Dopant-defect clustering model ( ACT.FULL)

All Impurities

DDC.T.0 0

DDC.T.E 0

DDC.F.0 0

DDC.F.E 0

DDCF.N.N 0

DDCF.I.N 0

DDCF.D.N 0

DDCR.N.N 0

DDCR.I.N 0

IFRACM 0

DDCS.0 0

DDCS.E 0

IFRACS 0

Table A-14 Solid Solubility in Silicon

Temperature (˚C) Boron Phosphorus Antimony

Table A-17 Point Defect Parameters in Silicon ( CM.SEC units) [15]

Vacancy Interstitial

D.0 3.65e-4 3.65e-4

D.E 1.58 1.58

DC.0 1.0 1.0

DC.E 0 0

KB.0 (20)00000 1.0e-21

KB.E -1.0 (21)KIV.0 (22)KIV.E 0

KIV.NORM true

CEQUIL.0 1.25e29 1.25e29

CEQUIL.E 3.26 3.26

VMOLE 0.0 0 5.0e22

DNEG.0 32.47 0 0.00

DNEG.E 0.62 0 .00

S4 1999.2 Confidential and Proprietary A-7

Draft 6/22/99