0. Effect of Inversion layer Centroid on MOSFET capacitance
EEL 6935 class project
Srivatsan Parthasarathy
SWAMP Group

1. Organization Introduction Simulation Approach Results and Discussion
Scaling Issues in nanometer MOSFETS
Parasitics – the ultimate showstoppers
Project relevance
Simulation Approach
Tools of the trade – what we need
Bandstructure
Self–consistent solution
Computing surface potential
Capacitance
Results and Discussion

2. Part I: Introduction

3. Scaling Issues in nanometer MOSFETS
Phenomenal scaling in last 40 years:
LGATE – from 10 μm to ~30 nm !
Major changes in both technology and materials;
Smart optimizations in device structures
Timely introduction of new processing techniques
New materials (eg. Halo, silicides), but not in channel
Issues with scaling
Parasitics
Lesser control on Short Channel effects
Decreasing ION/IOFF (more leakage with thin oxide)
Industry is looking at new vectors
Strained Si, III-V channel materials, multi-gate architectures
Part 1: Introduction

4. 47% of Channel Resistance
Parasitics
Why does gate capacitance reduce?
Geometric Scaling
To first order, Cox is proportional to scaling factor
Quantum effects
Peak of Inversion Charge is not at Si-SiO2 interface, but instead a few nm inside.
Channel
Resistance
Series
Series Resistance ~
47% of Channel Resistance
at 45 nm
ITRS Roadmap
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Resistance (Ohm-mm) 1 2 3 4 5 6 7 8 20 40 60 80
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Capacitance (mF/mm)
Parasitics
Dominate!
Gate
Capacitance
Total Parasitic
This reduction due to quantum effects cannot be neglected.
Part 1: Introduction

5. Project relevance Very important to quantify capacitance degradation
To build better device models and simulators
To compare how novel channel materials compete with existing technology
Main goal of this project:
To quantify the quantum effects leading to reduction in capacitance using techniques taught in class
Part 1: Introduction

6. What I did in the project
Simulated capacitance degradation for unstrained, planar nMOS
Bandstructure - sp3d5s* TB model with SO coupling
Self-consistent solution of schroedinger-poisson equation
Surface potential calculation
Inversion Capacitance = d(QINV)/d(FS)
The TB Hamiltonian can be used 3-5 materials also, but GaAs or other materials was not simulated ( as initially planned) due to lack of time

7. Part II: Simulation Approach

8. Tools of the Trade What all do we need? Part 2: Approach
Bulk bandstrcture
EMA, k•p, TB … which method to choose?
Trade-offs/Advantages in TB
Bandstrcture for M-O-S structure
Different from bulk bandstructure due to confinement
Self-consistent solution of schroedinger-poisson equations
Computing surface potential
How is FS related to VGATE ?
Part 2: Approach

9. Which method should I follow?
Bandstructure
Many approaches exist in theory
Single/multi-band Effective Mass Approximation (EMA)
Hartree, Hartree-Fock, Local Density Approximation
k•p method - based on the non-degenrate perturbation theory
Empirical and semi-empirical Tight Binding (TB)
sp3s*, sp3d5s* etc.
Density Functional Theory (DFT)
Which method should I follow?
Part 2: Approach

10. Bandstructure (cont.) Tight Binding followed in this project
Main Advantages
Atomistic representation with localized basis set
It is a real space approach
Describes bandstructure over the entire Brillouin zone
Correctly describes band mixinga
Lower computational cost w.r.t other method

11. Simplified LCAO Method
Tight Binding Method
1954
Slater and Koster
Simplified LCAO Method
1983
Vogl et al.
Excited s* orbital
1998
Jancu et al.
Excited d orbitals
2003
NEMO 3D
Purdue
We attempt to solve the one-electron schoredinger equation in terms of a Linear Combination of Atomic Orbitals (LCAO) Y
Cia
f= orbital
Cia= coefficients fia= atomic orbitals (s,p,d)
Caution is needed !

12. Tight Binding Method (cont.)
3 Major assumptions:
“Atom-like” orbitals
Two center integrals
NN interaction
Choice of basis:
Atleast need sp3 for cubic semiconductors
# of neighboring-atom interactions is a choice between computational complexity and accuracy a
(001)
(100)
(010)
(111)
(110)
Type 1
Type 2

13. Tight Binding Method (cont.)
The sp3s* Hamiltonian [Vogl et al. J. Phys. Chem Sol. 44, 365 (1983)]
In order to reproduce both valence and conduction band of covalently bounded semiconductors a s* orbital is introduced to account for high energy orbitals (d, f etc.)
The sp3d5s* Hamiltonian
[Jancu et al. PRB 57 (1998)]
Many more parameters, but works quite well !

14. Tight Binding Method (cont.)
1D chain:
Hamiltonian is tridiagonal
Hamiltonian in spds* basis: a
(001)
(100)
(010)
(111)
(110)
Hl,l+1
Hl,l-1
Hl,l
l+1
l-1 l
H =
Size of each block is 1 x 1
Size of each block is 10 x 10

15. Tight Binding Method (cont.)
Each of the elements in the above matrix is a 5 x 5 block
How to treat SO coupling?

16. Tight Binding Method (cont.)
In sp3d5S* TB, SO interaction of d orbitals is ignored, but SO is present for all other orbitals.
SO interaction happens between orbitals located on the same atom (not neighboring atoms).
Size of each block is 10 x 10  Hamiltonian size is 40 x 40

17. Calculated bandstructure

18. Applying TB to a MOS structure
Application to
finite structure
Bulk Hamiltonian Z
2X2 block
matrix
Type 1
Type 2
MOS Hamiltonian (1D)
NZ X NZ block tridiagonal
NZ Atomic layers X
Size of each block is 10 x 10

19. Applying TB to a MOS structure
Device Hamiltonian Z X
NX Atomic layers
NX X NX block tridiagonal
Block Size = (NZ Nb) X (NZ Nb)
(Nb = 10 for sp3d5)

20. Capacitance Calculation
The schroedinger-poisson equation is solved self-consistently using the method described in the text.
The total carrier concentration n(z) is calculated as a function of distance by summing up the electron concentration in each energy level.
For calculating the capacitance, we need to find surface potential at every gate voltage.
Ronald van Langevelde,"An explicit surface-potential-based MOSFET model for circuit simulation", Solid-State Electronics V44 (2000) P409

21. Simulation results
Characterization of Inversion-Layer Capacitance of Holes in Si MOSFETs, Takagi et al,TED, Vol. 46, no.7, July 1999.

22. Summary
Quantified the effect of inversion layer capacitance with a good TB model for the Hamiltonian
Results agreed with existing published values, so approach seems to be right.
Hamiltonian is not 100% accurate … passivation of surface states at interface, dangling bonds etc.
Simulation was only for a 15 nm “quantum domain”, but still am able to get good results  effectiveness of sp3d5 hamiltonian

23. References and Thanks
Exploring new channel materials for nanoscale CMOS devices: A simulation approach, Anisur Rahman, PhD Thesis, Purdue University, December 2005.
Characterization of Inversion-Layer Capacitance of Holes in Si MOSFETs, Takagi et al,TED, Vol. 46, no.7, July 1999.
Ronald van Langevelde,"An explicit surface-potential-based MOSFET model for circuit simulation", Solid-State Electronics V44 (2000) P409
Dr. Yongke Sun, SWAMP Group, ECE – UF
Guangyu Sun, SWAMP Group, ECE – UF

24. Questions?