rapid multiscale simulation of nanoscale mosfets
TRANSCRIPT
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
MOS-AK Silicon Valley 2020
MultiscaleSimulation
Billions of transistors
Devices
FEMQuantum effects
Circuit simulations
Motivation
Alexander Kloes 1
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
Motivation
Is there a way to combine a compact model with quantum-based TCAD simulations?
What are the advantages?
Alexander Kloes 5
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
cNEGF Simulation Approach - Simplifications
Alexander Kloes 10
Approximation vs. energy§ Reducing number of NEGF
calculations
§ 12 energy levels
§ 2 parts
- tunneling current- thermionic emission current
§ Linear interpolation
MOS-AK Silicon Valley 2020
cNEGF Simulation Approach - Simplifications
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
MOS-AK Silicon Valley 2020
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)
MOS-AK Silicon Valley 2020
cNEGF-MOS Tool
Alexander Kloes 13
Tool on nanoHUB.org
MOS-AK Silicon Valley 2020
cNEGF-MOS Tool
Alexander Kloes 14
Tool on nanoHUB.org
MOS-AK Silicon Valley 2020
cNEGF-MOS Tool
Alexander Kloes 15
Tool on nanoHUB.org
MOS-AK Silicon Valley 2020
cNEGF-MOS Tool
Alexander Kloes 16
Tool on nanoHUB.org
MOS-AK Silicon Valley 2020
cNEGF-MOS Tool
Alexander Kloes 17
Tool on nanoHUB.org
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
Verification
Alexander Kloes 19
Transfer characteristics§ Lch= 6 nm, Tch = 2 nm
§ T= 300 K
§ Ballistic current
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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
MOS-AK Silicon Valley 2020
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