Fourth generation MOSFET model and its VHDL-AMS implementation

Transcription

1 Fourth generation MOSFET model and its VHDL-AMS implementation Fabien Prégaldiny and Christophe Lallement ERM-PHASE, Parc d innovation, BP 10413, Illkirch cedex, France

2 Outline Introduction The 4 th generation of MOSFET models New quantum surface potential model Model implementation in VHDL-AMS Results and comparison with experiments Conclusion 2

3 Outline Introduction The 4 th generation of MOSFET models New quantum surface potential model Model implementation in VHDL-AMS Results and comparison with experiments Conclusion 3

4 Introduction Scaling of CMOS technology Thinner gate oxide t ox Greater substrate doping level N a 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 model Analytical surface-potential-based model QME included in a fully transparent way Straightforward use of a charge sheet model 4

5 Outline Introduction The 4 th generation of MOSFET models New quantum surface potential model Model implementation in VHDL-AMS Results and comparison with experiments Conclusion 5

6 History of compact models L g > 2 µm Entry into the submicronic era L g < 0.5 µm 10µm 1µm 0.1µm 6

7 Major compact models 3 rd generation 4 th generation BSIM 3v3, BSIM 4: threshold-voltage-based models Regional approximations Smoothing functions used as a model (e.g. drain current) Increasing complexity, dramatic number of parameters EKV 3.0: charge linearization model Bulk used as a reference: symmetric model structure Alternative to surface-potential-based models MM 11, SP: surface-potential-based models Models close to physics Explicit formulation of the surface potential Symmetric model structure (idem EKV) 7

8 Surface-potential potential-based model Why φ s -based models? Starting point is Brews s model which is totally symmetric 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] such as φ = fv (, V ) s gb ch [1] R. van Langevelde and F. M. Klaassen, Solid- State Electronics, vol. 44, pp , [2] T. L. Chen and G. Gildenblat, Solid-State Electronics, vol. 45, pp ,

9 Outline Introduction The 4 th generation of MOSFET models New quantum surface potential model Model implementation in VHDL-AMS Results and comparison with experiments Conclusion 9

10 Quantum mechanical effects High channel doping and ultra-thin gate oxides result in a very high normal field at the Si -SiO 2 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 10

11 Quantum mechanical effects Energy band diagram (in transversal direction) of an n-mosfet 11

12 Resulting effects QM & PD effects change the relationship between charges and applied voltages Increased surface potential φ s Reduced inversion charge Q inv Increased threshold voltage V th Reduced drain current I d... C-V characteristics are particularly affected Analog and RF design require a consistent modeling of all electrical characteristics 12

13 QME modeling inversion Approximation of the variational approach Concept of moderate inversion approximation [3] bv (, V ) g ch 12 m q 2 εsi ( V, V ) 3 where n all is the equivalent carrier density 2 n all g ch 2 Cox n ( V, V ) = V V V q ( ) all g ch g to ch and V g an hyperbolic smoothing function 1/3 [3] F. Prégaldiny, C. Lallement, R. van Langevelde and D. Mathiot, Solid-State Electronics, vol. 48, pp ,

14 QME modeling inversion Quantum shift of the conduction band, i.e. pseudo bandgap widening E ( V, V ) bv (, V ) w g ch g ch In terms of surface potential we get δφ ( V, V ) = E ( V, V )/ q s g ch w g ch 2 This provides an explicit relationship between the quantum increment of the surface potential and the gate and source/drain voltages. 14

15 Model validation inversion Comparison between the quantum and classical models 15

16 QME modeling accumulation Structure of the valence band more complex How to achieve a simple, analytical and efficient model? Triangular potential well approximation We should take into account several energy levels... Problem: how then to define a pseudo bandgap widening as in inversion? Choice of a semi-empirical approach Definition of an equivalent density of majority carriers [4]: p acc ( V ) g C = 2 ox q 1 i = ( V V ) g a i fb i [4] F. Prégaldiny, C. Lallement and D. Mathiot, Solid-State Electronics, vol. 48, pp ,

17 QME modeling accumulation Quantum shift of the valence band, i.e. pseudo bandgap widening 23 E ( V ) F ( V ) where w g eff g Feff pacc( Vg ) In the same way than in inversion we get δφ ( V ) = E ( V )/ q s g w g Finally, in both inversion and accumulation regions, the surface potential is defined as: φ = φ ± δφ s [ qm] s s at a given bias ( V, V, V ) gb db sb 17

18 Full model validation Surface potential computed as a function of gate voltage Symbols represent results obtained by a self-consistent resolution of the Schrödinger and Poisson equations. 18

19 Charge sheet model Definitions of the charges: Q = γ C φ b ox s ( ) Q = Q + Q g inv b ( φ φ ) Q = C V V Q inv ox gb fb s p b Evaluating the transcapacitances: C ij Q + i for i = j Vj = where i, j = Q i for i j Vj g, s, d or b 19

20 Comp. with S-P S P simulations Gate transcapacitance as a function of gate voltage 20

21 Outline Introduction The 4 th generation of MOSFET models New quantum surface potential model Model implementation in VHDL-AMS Results and comparison with experiments Conclusion 21

22 VHDL-AMS code: the functions -- Functions declaration PACKAGE 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 potential pure function phis2(vg,vch,vfb,,phit:real) return real is variable ret :real; begin ret :=...; return ret; end phis2; -- Quantum description of the surface potential pure function phis2_qm(cox,vg,vch,...,phit:real) return real is variable ret :real; begin ret :=...; return ret; end phis2_qm; Definition of each function END fab_functions; 22

23 VHDL-AMS code: the entity library ieee; use ieee.electrical_systems.all; ENTITY mosfet IS generic (W :real :=1.0e-6; -- Gate width L :real :=1.0e-6; -- Gate length Na :real :=5.0e23; -- Substrate doping Np :real :=1.0e26; -- Polysilicon doping tox :real :=3.0e-9; -- Oxide thickness Mu0 :real :=0.050; -- Low-field mobility Vfb :real :=-1.0; -- Flatband voltage Theta1 :real :=0.20; -- Mobility parameter 1 Theta2 :real :=0.30); -- Mobility parameter 2 port (terminal G,D,S,B:electrical); END ENTITY mosfet; 23

24 VHDL-AMS code: the architecture 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 density Qb_qm == Cox*gamma*(phis2_qm(Cox,Vgb,Vsb,...,phit))**0.5; -- Inversion charge density / Drift current / Diffusion current / Transcapacitances / etc.... END ARCHITECTURE quantum; 24

25 Simulation results 25

26 Outline Introduction The 4 th generation of MOSFET models New quantum surface potential model Model implementation in VHDL-AMS Results and comparison with experiments Conclusion 26

27 Comparison with experiments Drain current of an n-channel MOSFET Experimental data from an advanced Philips CMOS technology 27

28 Comparison with experiments Normalized gate transcapacitance vs gate voltage Experimental data from a 0.18 µm CMOS technology (Philips) 28

29 Comparison with experiments No empirical parameter C dg +C sg transcapacitance of an n-channel MOSFET Experimental data from a 0.18 µm CMOS technology (Motorola) 29

30 Conclusion 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 30

31 Thank you! 31