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

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

Part I: Introduction

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

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 200 400 600 800 1000 1200 1400 20 40 60 80 100 120 Technology Node Resistance (Ohm-mm) 1 2 3 4 5 6 7 8 20 40 60 80 100 120 Technology Node Capacitance (mF/mm) Parasitics Dominate! Gate Capacitance Total Parasitic This reduction due to quantum effects cannot be neglected. Part 1: Introduction

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

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

Part II: Simulation Approach

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

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

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

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 !

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

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 !

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

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

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

Calculated bandstructure

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

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)

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

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

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

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

Questions?