Comparison among modeling approaches for gate current

computation in advanced gate stacksARCES: N.Barin, C.Fiegna, E.Sangiorgi

BU: P.A.Childs

FMNT-CNRS: D.Brunel , C.Busseret, A.Poncet

PISA: A.Campera, G.Fiori, G.Iannaccone

POLIMI: R.Gusmeroli, C. Monzio Compagnoni, A.L.Lacaita, A.S.Spinelli

TUW: M.Karner, H.Kosina, E.Langer

UDINE: F.Driussi, P.Palestri, L.Selmi

WUT: B.Majkusiak, J.Walczak

Aim of Task 3 of SINANO Work-Package 4Study of the performance and reliability of conventional (SiO2) and

high-k thin insulator gate stacks for sub-50nm MOSFETs)

• To support the understanding of device reliability issues and potential limitations of device performance related to the gate stack architecture of future CMOS technologies.

The activities foreseen in this context are:• simulation of C/V and I/V for different gate stack and device

architectures; • investigation of the effects of high-K materials and of the related

defects, traps, charges, etc.. on the low-field mobility and carrier transport properties of the inversion channel.

Two main phases :• comparison of gate leakage currents in advanced device

architectures; • assessment of modeling requirements for ultra-thin oxide and

high-k, metal gate stacks.

OUTLINE

• Modeling approaches• Template devices• Results

– C/V– I/V– Microscopic quantities

• Comparison with experiments• Conclusions

Simulation Framework

• Solution of the Schrödinger equation in the poly-Si/dielectric/Si stack

EyV

dy

d

m )(

2 2

22poly

Diel.

Si

• Boundary conditions ?

+Poisson Equation

Boundary Conditions

Closed

In principle: no current !

Define quantum boxes

=0 at both sides of a box

Ig: semiclassical approach

Boundary Conditions

Open: resonance peakInject plane waves and compute transmission/reflection

Ei

Boundary Conditions

Open: perfectly-matched-layer

Absorbing boundaries

Complex eigenvalues

Boundary Conditions

Periodical The Schrödinger equation is solved two times,applying Dirichlet and then Neumann conditions on both sides.

This is like simulating an infinite periodical structure, but only over one half period

T-prob. from the contact to the semiclassical turning point

Approaches followed by the partners

Model 1Model 2Model 3Model 4Model 5Model 6Model 7

Different definitions of the quantum boxes in closed-boundaries

OUTLINE

• Modeling approaches• Template devices• Results

– C/V– I/V– Microscopic quantities

• Comparison with experiments• Conclusions

Template Devices

• Device A: pure SiO2 (tOX=1nm) NPOLY=1020cm-3 (n-type)

NSUB=1018cm-3 (p-type)

• Device B: pure SiO2 (tOX=3nm) NPOLY=51019cm-3 (n-type) NSUB=31017cm-3 (p-type)

• Device HK: 4nm HfO2+ 1nm ITL NPOLY=1020cm-3 (n-type) NSUB=31017cm-3 (p-type)

• Device A and B are from: C. A. Richter, IEEE EDL, vol.22, p.35, 2001.

Simulation Parameters

Same parameters in all modeling approaches

OUTLINE

• Modeling approaches• Template devices• Results

– C/V– I/V– Microscopic quantities

• Comparison with experiments• Conclusions

Results: C/V curves

•Good overall agreement•Small problems in accumulation and at beginning of inversion (different models for poly-quantization)

HK

Internal quantities affecting C/V

Cond.Band in accumulation Subbands in inversion

Results: I/V

HK Errors within a factor of 10

Much larger in accumulation (not shown)

Internal quantities affecting IG

HK

Escape-time

Internal quantities affecting IG

Tunneling probability

HK

OUTLINE

• Modeling approaches• Template devices• Results

– C/V– I/V– Microscopic quantities

• Comparison with experiments• Conclusions

Comparison with experimentsData from N.Yang et al., IEEE T-ED, vol.46, p.1464, 1999.Same physical parameters as in the template devices.

NPOLY=1020cm-3

NSUB=51017cm-3

(from C/V)

Conclusions• Unprecedented comparison effort carried out by seven

academic groups• Good agreement between results obtained using very

different models (open/closed boundaries)• Approaches based on closed boundaries, coupled with

the evaluation of the semiclassical escape-time provide a good trade-off between efficiency and precision

• Results submitted to IEEE T-ED, 2nd review step: mandatory revisions

• Comparison of Trap-Assisted-Tunneling