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Nominal device characteristics Variations in device characteristics .variation distributions on model parameters
.model model parameters
Variation Block
“The EDA industry needs to deliver a new generation of chip-design tools to ease variability problems.” “We need to develop tools to relieve designers from concerns about these variabilities.” “We need to apply very powerful statistical techniques to guide device sizing.”
A=N() (also used in implicit definitions)
Uniform distribution:
B=U()
Cumulative distribution function:
C=CDF(x1,y1,.....xn,yn)
2005 Synopsys, Inc. (9)
0. 99 0. 9 99 91 6 0. 99 93 2 0. 99 94 8 0. 99 96 0. 4 99 98 0. 99 9 1. 96 00 0 1. 12 00 0 1. 28 00 04 1. 4 00 06 1. 00 0 1. 76 00 09 2
Variations on model parameters
Variations on model parameters Element Variation
2005 Synopsys, Inc. (8)
Advances In HSPICE
Independent Random Variables
Normal distribution:
Other parameters are made available on demand. These parameters only supported if specified in model
Advances In HSPICE
2005 Synopsys, Inc. (13)
Variations on Element Parameters
Example 2:
a = N() b = N() c = 'a+2*sgn(b)‘
2005 Synopsys, Inc. (10)
Advances In HSPICE
Syntax for Describing Variation
Basic construct for describing variation:
2005 Synopsys, Inc. (6)
Variation Block: Options and Common Parameters
Options
options regarding use of Variation Block ignore_variation_block ignore_local_variations ignore_global_variations options for dependent analyses
2005 Synopsys, Inc. (5)
Advances In HSPICE
Variation Block General Syntax
.variation options define parameters common to all sub-blocks .global_variation define random variables define variations of model parameters .end_global_variation .local_variation define random variables define variations of model parameters .element_variation define variations of element parameters .end_element_variation .end_local_variation .end_variation Advances In HSPICE
Monte Carlo analysis is cornerstone of a tool suite which addresses these needs.
2005 Synopsys, Inc. (2)
Advances Inቤተ መጻሕፍቲ ባይዱHSPICE
Variations of Device Characteristics on Silicon
Global variations
lot wafer chip site on same wafer
Local variations
same chip devices < 1mm apart
2005 Synopsys, Inc. (3)
Advances In HSPICE
Expressing Variability
Common parameters:
to define parameters which can be used in global
and local variation sub-blocks
(but not in other parts of models or netlist) Advances In HSPICE
Rules:
If expression does not contain reference to random variable, then Normal Distribution assumed with zero mean and sigma of the expression (implicit definition) All definitions are 1 sigma Advances In HSPICE
2005 Synopsys, Inc. (4)
Advances In HSPICE
Variation Block
Introduced in HSPICE 2005.09 with DCmatch analysis Contains definitions for global and local variations Emphasis on variations in materials and manufacturing Variation definitions used for Monte Carlo and DCmatch
2005 Synopsys, Inc. (7)
Sub-Blocks
Global Variations: Random variables
independent transformed
Local Variations: Random variables
independent transformed
Advances In HSPICE
Dependent Random Variables
Arbitrary distributions from the basic distributions Example 1:
var = U() Y = ’0.5 * (D+E) + (E-D) * var ‘ creates a uniform distribution from D to E
.element_variation R R = 10 .end_element_variation
2005 Synopsys, Inc. (14)
Advances In HSPICE
Applying Variation to Groups of Elements Extended syntax for defining condition:
Syntax for defining variations on element parameters:
elementType elementPar=‘Expression for Sigma’
Application: For elements without models To define local temperature Example:
2005 Synopsys, Inc. (16)
Advances In HSPICE
Variation Block Example
.variation .global_variation NMOS SNPS20N vth0=0.07 u0=10 % PMOS SNPS20P vth0=0.08 u0=8 % .end_global_variation .local_variation nmos snps20N + vth0='1.2e-9/sqrt(get_E(W)*get_E(L)*get_E(M))' + u0='2.3e-6/sqrt(get_E(W)*get_E(L)*get_E(M))' % pmos snps20P + vth0='3.4e-9/sqrt(get_E(W)*get_E(L)*get_E(M))' + u0='4.5e-6/sqrt(get_E(W)*get_E(L)*get_E(M))' % .element_variation R r=10 % .end_element_variation .end_local_variation .end_variation
2005 Synopsys, Inc. (15)
Advances In HSPICE
Supported Elements and Parameters
M R C Q D L I V dtemp dtemp dtemp dtemp dtemp dtemp dtemp dtemp Lval DCval DCval Rval Cval
element_type ( condition_clause ) element_parameter = ‘Expression for Sigma’
Example:
.element_variation R (element_name .end_element_variation 'ra*‘ ) R=20 %
2005 Synopsys, Inc. (11)
Variations on Model Parameters
Syntax for defining variations on model parameters:
modelType modelName modelPar=‘Expression for Sigma’
2005 Synopsys, Inc. (12)
Advances In HSPICE
Supported Model Parameters
BSIM3 (level 49) lint tox BSIM4 (level 54) lint toxm R C dlr cox wint u0 wint toxe dw del vth0 nsub vth0 u0 rsh capsw thick vfb nsub Vfb
Par=‘Expression for Sigma’
abbreviated notation for variation_in_Par=‘Expression for Sigma’ Constructs for expressions:
Constants, parameters or functions Absolute variation or relative ( space % ) Perturb() to reference random variable
Addition to Expression for Sigma:
get_E(*) to reference element parameters (w, l, m) for modeling dependence on device geometry
Example:
nmos nch vth0='1.2e-9/sqrt(get_E(L)*get_E(W)*get_E(M))‘ pmos pch u0='2.3e-6/sqrt(get_E(W)*get_E(L)*get_E(M))' %
Monte Carlo Simulation in HSPICE
Feature upgrade for 2006.03 release
As the semiconductor industry faces the challenges of 90 and 65nm technologies, their leaders realize:
.model model parameters
Variation Block
“The EDA industry needs to deliver a new generation of chip-design tools to ease variability problems.” “We need to develop tools to relieve designers from concerns about these variabilities.” “We need to apply very powerful statistical techniques to guide device sizing.”
A=N() (also used in implicit definitions)
Uniform distribution:
B=U()
Cumulative distribution function:
C=CDF(x1,y1,.....xn,yn)
2005 Synopsys, Inc. (9)
0. 99 0. 9 99 91 6 0. 99 93 2 0. 99 94 8 0. 99 96 0. 4 99 98 0. 99 9 1. 96 00 0 1. 12 00 0 1. 28 00 04 1. 4 00 06 1. 00 0 1. 76 00 09 2
Variations on model parameters
Variations on model parameters Element Variation
2005 Synopsys, Inc. (8)
Advances In HSPICE
Independent Random Variables
Normal distribution:
Other parameters are made available on demand. These parameters only supported if specified in model
Advances In HSPICE
2005 Synopsys, Inc. (13)
Variations on Element Parameters
Example 2:
a = N() b = N() c = 'a+2*sgn(b)‘
2005 Synopsys, Inc. (10)
Advances In HSPICE
Syntax for Describing Variation
Basic construct for describing variation:
2005 Synopsys, Inc. (6)
Variation Block: Options and Common Parameters
Options
options regarding use of Variation Block ignore_variation_block ignore_local_variations ignore_global_variations options for dependent analyses
2005 Synopsys, Inc. (5)
Advances In HSPICE
Variation Block General Syntax
.variation options define parameters common to all sub-blocks .global_variation define random variables define variations of model parameters .end_global_variation .local_variation define random variables define variations of model parameters .element_variation define variations of element parameters .end_element_variation .end_local_variation .end_variation Advances In HSPICE
Monte Carlo analysis is cornerstone of a tool suite which addresses these needs.
2005 Synopsys, Inc. (2)
Advances Inቤተ መጻሕፍቲ ባይዱHSPICE
Variations of Device Characteristics on Silicon
Global variations
lot wafer chip site on same wafer
Local variations
same chip devices < 1mm apart
2005 Synopsys, Inc. (3)
Advances In HSPICE
Expressing Variability
Common parameters:
to define parameters which can be used in global
and local variation sub-blocks
(but not in other parts of models or netlist) Advances In HSPICE
Rules:
If expression does not contain reference to random variable, then Normal Distribution assumed with zero mean and sigma of the expression (implicit definition) All definitions are 1 sigma Advances In HSPICE
2005 Synopsys, Inc. (4)
Advances In HSPICE
Variation Block
Introduced in HSPICE 2005.09 with DCmatch analysis Contains definitions for global and local variations Emphasis on variations in materials and manufacturing Variation definitions used for Monte Carlo and DCmatch
2005 Synopsys, Inc. (7)
Sub-Blocks
Global Variations: Random variables
independent transformed
Local Variations: Random variables
independent transformed
Advances In HSPICE
Dependent Random Variables
Arbitrary distributions from the basic distributions Example 1:
var = U() Y = ’0.5 * (D+E) + (E-D) * var ‘ creates a uniform distribution from D to E
.element_variation R R = 10 .end_element_variation
2005 Synopsys, Inc. (14)
Advances In HSPICE
Applying Variation to Groups of Elements Extended syntax for defining condition:
Syntax for defining variations on element parameters:
elementType elementPar=‘Expression for Sigma’
Application: For elements without models To define local temperature Example:
2005 Synopsys, Inc. (16)
Advances In HSPICE
Variation Block Example
.variation .global_variation NMOS SNPS20N vth0=0.07 u0=10 % PMOS SNPS20P vth0=0.08 u0=8 % .end_global_variation .local_variation nmos snps20N + vth0='1.2e-9/sqrt(get_E(W)*get_E(L)*get_E(M))' + u0='2.3e-6/sqrt(get_E(W)*get_E(L)*get_E(M))' % pmos snps20P + vth0='3.4e-9/sqrt(get_E(W)*get_E(L)*get_E(M))' + u0='4.5e-6/sqrt(get_E(W)*get_E(L)*get_E(M))' % .element_variation R r=10 % .end_element_variation .end_local_variation .end_variation
2005 Synopsys, Inc. (15)
Advances In HSPICE
Supported Elements and Parameters
M R C Q D L I V dtemp dtemp dtemp dtemp dtemp dtemp dtemp dtemp Lval DCval DCval Rval Cval
element_type ( condition_clause ) element_parameter = ‘Expression for Sigma’
Example:
.element_variation R (element_name .end_element_variation 'ra*‘ ) R=20 %
2005 Synopsys, Inc. (11)
Variations on Model Parameters
Syntax for defining variations on model parameters:
modelType modelName modelPar=‘Expression for Sigma’
2005 Synopsys, Inc. (12)
Advances In HSPICE
Supported Model Parameters
BSIM3 (level 49) lint tox BSIM4 (level 54) lint toxm R C dlr cox wint u0 wint toxe dw del vth0 nsub vth0 u0 rsh capsw thick vfb nsub Vfb
Par=‘Expression for Sigma’
abbreviated notation for variation_in_Par=‘Expression for Sigma’ Constructs for expressions:
Constants, parameters or functions Absolute variation or relative ( space % ) Perturb() to reference random variable
Addition to Expression for Sigma:
get_E(*) to reference element parameters (w, l, m) for modeling dependence on device geometry
Example:
nmos nch vth0='1.2e-9/sqrt(get_E(L)*get_E(W)*get_E(M))‘ pmos pch u0='2.3e-6/sqrt(get_E(W)*get_E(L)*get_E(M))' %
Monte Carlo Simulation in HSPICE
Feature upgrade for 2006.03 release
As the semiconductor industry faces the challenges of 90 and 65nm technologies, their leaders realize: