Rapid Multiscale Simulation of Nanoscale MOSFETs

MOS-AK Silicon Valley 2020

Rapid Multiscale Simulation of Nanoscale MOSFETs:

Is an Interplay Between Compact Models and NEGF Possible?

Alexander Kloes

NanoP - THM University of Applied Sciences, Giessen, Germany

MOS-AK, Dec. 11., 2020


MultiscaleSimulation

Billions of transistors

Devices

FEMQuantum effects

Circuit simulations

Motivation

Alexander Kloes 1


Motivation – TCAD Simulation

Alexander Kloes 2

TCAD Simulation§ FEM simulation

- 2D / 3D- Mesh- fundamental physics

§ Advantages

- close to device structure- including quantum effects

§ Disadvantage

- time consuming- single device


Motivation – Circuit Simulation

Alexander Kloes 3

Circuit design§ Many transistors

§ SPICE-like simulators

§ Compact models

- less degree of freedom

- without iterations

- very fast

§ Iteration on circuit level


Motivation

Alexander Kloes 4

TCADSPICE

Extraction of compact model

parameters

Feedback circuit FOM to technology

variation

Combination SPICE - TCAD§ Compact models are used as

„unidirectional“ bridge

between TCAD and SPICE

§ Example:

Design Technology

Co-Optimization

(DTCO)

…but:§ very time consuming

§ no concurrent simulation


Motivation

Is there a way to combine a compact model with quantum-based TCAD simulations?

What are the advantages?

Alexander Kloes 5


cNEGF Simulation Approach – Simulation Flow

Alexander Kloes 6

Focus on ultra-scaled MOSFETs§ Lch= 6 nm to 30 nm

§ Ballistic current

- Mean free path comparable to device length

§ Source-to-Drain tunneling

- increased leakage current- worse subthreshold slope- scaling limitation

§ Quantum-based simulation approach:

non-equilibrium Green’s function

(NEGF) formalism


cNEGF Simulation Approach – Simulation Flow

Alexander Kloes 7

2D Electrostatics(analytical compact model)

Device current

1D NEGF(requires matrix inversion)

§ Below VT: [1]Laplace eqn solved by conformal mapping

§ Above VT: Extension by pinning the surface potential(1D solution of Poisson eqn)

NEGF approach from literature [2]

Not self consistent!

Accuracy to be verified!

[1] M. Graef, T. Holtij, F. Hain, A. Kloes, and B. Iniguez, “Improved analytical potential modeling in Double-Gate Tunnel-FETs,” Mixed Design of Integrated Circuits Systems (MIXDES), vol. 21, pp. 49–53, 2014

[2] S. Datta, “Nanoscale Device Modeling: the Green’s Function Method.” Superlattices and Microstructures, vol. 28, no. 4, 2000


cNEGF Simulation Approach - Limitations

Alexander Kloes 8

Material§ Undoped silicon channel

§ S/D n-type silicon

Aspect ratio§ 2D potential model

requires Lch > 2x TchLch = 10 nmVds=0.4 Vtch=2 nm

§Channel surface


cNEGF Simulation Approach - Simplifications

Alexander Kloes 9

Slicing of the conduction band§ 2D potential

§ 1D slices (source-to-drain)

- Channel to insulator interface- Channel center

§ Integrate vs. parabolically shaped

approximation of current density

Accuracy

Simulation speed



Alexander Kloes 10

Approximation vs. energy§ Reducing number of NEGF

calculations

§ 12 energy levels

§ 2 parts

- tunneling current- thermionic emission current

§ Linear interpolation



Alexander Kloes 11

Backscattering§ Ballistic current:

ultra-short channel devices

§ Quasi-ballistic current: Lch ≈ λ

§ Including scattering in NEGF: too complex

§ Option: Calculation of transmission and

reflection within distance l [3]

Quantum confinement§ Adaption of the flat band voltage

§ Empirical fitting of 2D DOS

§ Limitation: 2 nm < tch < 5 nm

[3] M. S. Lundstrom, “Elementary scattering theory of the Si MOSFET,” IEEE Electron Device Letters, vol. 18, no. 7, pp. 361–363, 1997


cNEGF-MOS Tool

Alexander Kloes 12

Tool on nanoHUB.org [4]: https://nanohub.org/tools/cnegfmos/

[4] Fabian Hosenfeld, Alexander Kloes (2020), "Compact NEGF-Based Solver for Double-Gate MOSFETs," https://nanohub.org/resources/cnegfmos. (DOI: 10.21981/DDVA-0459)

http://nanohub.org/tools/cnegfmos


cNEGF-MOS Tool

Alexander Kloes 13

Tool on nanoHUB.org


cNEGF-MOS Tool

Alexander Kloes 14

Tool on nanoHUB.org


cNEGF-MOS Tool

Alexander Kloes 15

Tool on nanoHUB.org


cNEGF-MOS Tool

Alexander Kloes 16

Tool on nanoHUB.org


cNEGF-MOS Tool

Alexander Kloes 17

Tool on nanoHUB.org


Verification

Alexander Kloes 18

§ Reference TCAD: NanoMOS [5]

§ Lch = 6…30 nm

§ Tch = 2 nm

§ tin = 1 nm (high-k: 25)

§ Aluminum gate

§ S/D doping: 2 x 1020 cm-3

[5] Z. Ren, S. Goasguen, A. Matsudaira, S. S. Ahmed, K. Cantley, Y. Liu, Y. Gao, X. Wang, and M. Lundstrom, “NanoMOS,” 2016. https://nanohub.org/resources/nanomos


Verification

Alexander Kloes 19

Transfer characteristics§ Lch= 6 nm, Tch = 2 nm

§ T= 300 K

§ Ballistic current


Verification

Alexander Kloes 20

Temperature§ Emission current

- repressed at lower temperatures

- @300 K -> 60 mV/dec- @75 K -> 15 mV/dec

§ Lch = 6 nm

- slope is much worse- tunneling dominates

§ Lch = 10 nm

- almost ideal slope- emission current dominates

for low and high T


Verification

Alexander Kloes 21

Output characteristics§ Lch = 30 nm, Tch= 2 nm

§ ballistic vs. non-ballistic

§ backscattering reduces the

current

§ fitting:

µ = 1400 cm2/Vs

solid lines: ballisticdashed lines: non-ballistic


Verification

Alexander Kloes 22

Insight to current transport§ Lch = 6 nm, Tch= 2 nm

§ Vds = 0.5 V

§ T = 300 K

§ Plotting separately:

- tunneling current- thermionic emission


Conclusions

Alexander Kloes 23

Experimental interplay:

§ Non-iterative (though not fully analytical)

§ Demonstrates a way to accelerate quantum simulations by 100x

Interplay of compact models with numerical simulators maybe a pathway to efficient multiscale simulations

Compact

Model

Quantum

FEM


Acknowledgements

Alexander Kloes 24

Fabian Hosenfeld

(Phd student 2014-2017)

This project was supported by:

• German Federal Ministry of Education and Research, contract No. 03FH001I3

F O R S C H U N G A N F A C H H O C H S C H U L E N

[6] F. Hosenfeld, F. Horst, B. Iniguez, F. Lime, A. Kloes, A quantum wave based compact modeling approach for the current in ultra-short DG MOSFETs suitable for rapid multiscale simulations, Solid-State Electronics, Vol. 137, pp. 70-79, 2017

[7] F. Hosenfeld, F. Horst, M. Graef, A. Farokhnejad, F. Hain, G. V. Luong, Q.T. Zhao, B. Iniguez, A. Kloes, Rapid NEGF-based calculation of ballistic current in ultra-short DG MOFSETs for circuit simulation, International Journal of Microelectronics and Computer Science, Vol. 7, No. 2, pp. 65-72, 2016

[8] F. Hosenfeld, NEGF based analytical modeling of advanced MOSFETs, PhD thesis, Universitat Rovira i Virgili, Spain, 2017

https://doi.org/10.1016/j.sse.2017.08.006

https://ijmcs.dmcs.pl/documents/10630/212938/IJMCS_2_2016_5.pdf

http://hdl.handle.net/10803/462901

Rapid Multiscale Simulation of Nanoscale MOSFETs

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