fourth generation mosfet model and its vhdl-ams … · may 7th, 2004 mos-ak group spring'04,...
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MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Fabien Prégaldiny and Christophe Lallement
ERM-PHASE, Parc d’innovation, BP 10413, 67412 Illkirch cedex, France
Fourth generation MOSFET Fourth generation MOSFET model and itsmodel and its
VHDLVHDL--AMS implementationAMS implementation
2MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
OutlineOutline
Introduction
The 4th generation of MOSFET models
New quantum surface potential model
Model implementation in VHDL-AMS
Results and comparison with experiments
Conclusion
3MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
OutlineOutline
Introduction
The 4th generation of MOSFET models
New quantum surface potential model
Model implementation in VHDL-AMS
Results and comparison with experiments
Conclusion
4MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
IntroductionIntroduction
Scaling of CMOS technologyThinner gate oxide tox
Greater substrate doping level Na
Increasing importance of quantum mechanical effects (QME) and polydepletion effect (PDE)
Increase of model complexity and number of parameters (e.g. BSIM 3, BSIM 4)
Development of a new physics-based modelAnalytical surface-potential-based modelQME included in a fully transparent wayStraightforward use of a charge sheet model
5MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
OutlineOutline
Introduction
The 4th generation of MOSFET models
New quantum surface potential model
Model implementation in VHDL-AMS
Results and comparison with experiments
Conclusion
6MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
History of compact modelsHistory of compact models
10µm 1µm 0.1µm
Lg < 0.5 µmLg > 2 µm Entry into thesubmicronic era
7MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Major compact modelsMajor compact models
BSIM 3v3, BSIM 4: threshold-voltage-based modelsRegional approximations
Smoothing functions used as a model (e.g. drain current)
Increasing complexity, dramatic number of parameters
EKV 3.0: charge linearization modelBulk used as a reference: symmetric model structure
Alternative to surface-potential-based models
MM 11, SP: surface-potential-based modelsModels close to physics
Explicit formulation of the surface potential
Symmetric model structure (idem EKV)
3rdge
nera
tion
4thge
nera
tion
8MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
SurfaceSurface--potentialpotential--based model based model
Why φs-based models ?Starting point is Brews’s model which is totallysymmetric and satisfies all benchmark tests
No discrepancies between I-V and C-V models
Single equation for the whole operation range
Major drawback: time consuming!!
Solution: explicit approximation [1-2]
φ = ( , )s gb chf V Vsuch as [1] R. van Langevelde and F. M. Klaassen, Solid-State Electronics, vol. 44, pp. 409-418, 2000.
[2] T. L. Chen and G. Gildenblat, Solid-State Electronics, vol. 45, pp. 335-339, 2001.
9MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
OutlineOutline
Introduction
The 4th generation of MOSFET models
New quantum surface potential model
Model implementation in VHDL-AMS
Results and comparison with experiments
Conclusion
10MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Quantum mechanical effectsQuantum mechanical effects
High channel doping and ultra-thin gate oxides result in a very high normal field at the Si -SiO2 interface, which in turns leads to:
Significant bending of the energy bands
Narrow potential well at the interface
Quantization of the carriers motion in the ⊥direction to the interface
Splitting of the conduction (valence) band into discrete subbands
Displacement of the inversion (accumulation) layer carrier distribution from the interface
11MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Quantum mechanical effectsQuantum mechanical effects
Energy band diagram (in transversal direction) of an n-MOSFET
12MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Resulting effectsResulting effects
QM & PD effects change the relationship between charges and applied voltages
Increased surface potential φs
Reduced inversion charge Qinv
Increased threshold voltage Vth
Reduced drain current Id...
C-V characteristics are particularly affected
Analog and RF design require a consistent modeling of all electrical characteristics
13MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
QME modeling QME modeling –– inversioninversion
Approximation of the variational approach
Concept of moderate inversion approximation [3]
where nall is the equivalent carrier density
ε′ ⋅ ⋅ ⋅ ⋅
1/32
2
( , )12( , )3
all g chg ch
si
n V Vm qb V V
( )2( , ) ⋅′ ′= ⋅ − −oxall g ch g to ch
Cn V V V V Vq
[3] F. Prégaldiny, C. Lallement, R. van Langevelde and D.Mathiot, Solid-State Electronics, vol. 48, pp. 427-435, 2004.
and an hyperbolic smoothing function′gV
14MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
QME modeling QME modeling –– inversioninversion
This provides an explicit relationship betweenthe quantum increment of the surface potentialand the gate and source/drain voltages.
Quantum shift of the conduction band, i.e. pseudobandgap widening
In terms of surface potential we get
∝ 2( , ) ( , )w g ch g chE V V b V V
( , ) ( , ) /δφ =s g ch w g chV V E V V q
15MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Model validation Model validation –– inversioninversion
Comparison between the quantum and classical models
16MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
QME modeling QME modeling –– accumulationaccumulation
Structure of the valence band more complexHow to achieve a simple, analytical and efficient model?
Triangular potential well approximationWe should take into account several energy levels...
Problem: how then to define a pseudo bandgap wideningas in inversion?
Choice of a semi-empirical approachDefinition of an equivalent density of majority carriers [4]:
[4] F. Prégaldiny, C. Lallement and D. Mathiot, Solid-State Electronics, vol. 48, pp. 781-787, 2004.
=
−= ⋅∑
2
1
( )( )
ig fbox
acc gi i
V VCp Vq a
17MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
QME modeling QME modeling –– accumulationaccumulation
Quantum shift of the valence band, i.e. pseudobandgap widening
In the same way than in inversion we get
′ ∝ 2 3 where( ) ( ) w g eff gE V F V
δφ′ ′=( ) ( ) /s g w gV E V q
∝ ( )eff acc gF p V
[ ]φ φ δφ= ±qm at a given bias ( , , ) gb db sbs ss V V V
Finally, in both inversion and accumulation regions,the surface potential is defined as:
18MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Full model validationFull model validation
Surface potential computed as a function of gate voltageSymbols represent results obtained by a self-consistent resolution of the Schrödinger and Poisson equations.
19MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Charge sheet Charge sheet modelmodel
for where , g, s, d or b
for
∂+ = ∂= = ∂− ≠ ∂
i
jij
i
j
Q i jV
C i jQ i jV
Definitions of the charges:
Evaluating the transcapacitances:
b ox sQ Cγ φ= − ⋅ ⋅
( )g inv bQ Q Q= − +
( )inv ox gb fb s p bQ C V V Qφ φ= − ⋅ − − − −
20MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Comp. with SComp. with S--P simulationsP simulations
Gate transcapacitance as a function of gate voltage
21MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
OutlineOutline
Introduction
The 4th generation of MOSFET models
New quantum surface potential model
Model implementation in VHDL-AMS
Results and comparison with experiments
Conclusion
22MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
VHDLVHDL--AMS code: the AMS code: the functionsfunctions-- Functions declarationPACKAGE fab_functions IS
... ... ...pure function phis2_qm(Cox,Vg,Vch,...,phit:real) return real;... ... ...
END;
List of all the functions
-- Functions definitions
PACKAGE BODY fab_functions IS
-- Classical description of the surface potentialpure function phis2(Vg,Vch,Vfb,…,phit:real) return real is
variable ret :real;begin
ret := ...;return ret;
end phis2;
-- Quantum description of the surface potentialpure function phis2_qm(Cox,Vg,Vch,...,phit:real) return real is
variable ret :real;begin
ret := ...;return ret;
end phis2_qm;
END fab_functions;
Definition of each function
23MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
VHDLVHDL--AMS code: the AMS code: the entityentity
library ieee;use ieee.electrical_systems.all;
ENTITY mosfet IS
generic (W :real :=1.0e-6; -- Gate widthL :real :=1.0e-6; -- Gate lengthNa :real :=5.0e23; -- Substrate dopingNp :real :=1.0e26; -- Polysilicon dopingtox :real :=3.0e-9; -- Oxide thicknessMu0 :real :=0.050; -- Low-field mobilityVfb :real :=-1.0; -- Flatband voltageTheta1 :real :=0.20; -- Mobility parameter 1Theta2 :real :=0.30); -- Mobility parameter 2
port (terminal G,D,S,B:electrical);
END ENTITY mosfet;
24MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
VHDLVHDL--AMS code: the AMS code: the architecturearchitecture
use ieee.math_real.all;use user_fp.fab_functions.all;
ARCHITECTURE quantum OF mosfet IS
constant T :real := 300.0;constant q :real := 1.602e-19;...quantity Qg_qm :real;quantity Qb_qm :real;...quantity Vdb across D to B;quantity Vsb across S to B;quantity Vgb across G to B;quantity Ids_qm through D to S;...
BEGIN-- Gate charge density
Qg_qm == Cox*(Vgb-Vfb-phis2_qm(Cox,Vgb,Vsb,...,phit));
-- Bulk charge densityQb_qm == Cox*gamma*(phis2_qm(Cox,Vgb,Vsb,...,phit))**0.5;
-- Inversion charge density / Drift current / Diffusion current / Transcapacitances / etc....
END ARCHITECTURE quantum;
25MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Simulation resultsSimulation results
26MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
OutlineOutline
Introduction
The 4th generation of MOSFET models
New quantum surface potential model
Model implementation in VHDL-AMS
Results and comparison with experiments
Conclusion
27MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Comparison with experimentsComparison with experiments
Drain current of an n-channel MOSFETExperimental data from an advanced Philips’ CMOS technology
28MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Comparison with experimentsComparison with experiments
Normalized gate transcapacitance vs gate voltage Experimental data from a 0.18 µm CMOS technology (Philips)
29MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Comparison with experimentsComparison with experiments
Cdg+Csg transcapacitance of an n-channel MOSFETExperimental data from a 0.18 µm CMOS technology (Motorola)
Noempirical
parameter
30MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
ConclusionConclusion
An analytical and quantum surface-potential-based MOSFET model has been presented
The new model describes accurately all the fundamental electrical characteristics of MOSFET, and that from accumulation to strong inversion
The quantum model requires no additional parameter in comparison with the classical model
Implementing the model in competitive HDLs such as VHDL-AMS and Verilog-AMS is straightforward
Comparisons with numerical simulations and experimental data show excellent results
31MOS-AK Group Spring'04, Stuttgart – F. PrégaldinyMay 7th, 2004
Thank you !