Electron Mean Free Path and Electrical Resistivity of Epitaxial W(001)

Pengyuan Zheng

Ph.D. Candidate

Department of Materials Science and Engineering

Rensselaer Polytechnic Institute, Troy, NY, USA

2014 Rensselaer Nanotechnology Center Research SymposiumWednesday, Oct 29, 2014

Advisor: Daniel GallSponsors: Semiconductor Research Corporation and National Science Foundation

Overview• Technical Background

• Classical framework

• Scientific motivation

• Experiment set up

• Key findings

• Conclusion

Interconnect Bottleneck

2

http://download.intel.com/newsroom/kits/22nm/pdfs/22nm-Details_Presentation.pdfhttp://download.intel.com/newsroom/kits/14nm/pdfs/Intel_14nm_New_uArch.pdfITRS Report 2007

Figure data source : ITRS 2013

14 15 16 17 18 19 20 21 22 23 24 25 26 27 28

104

105

Metal 1 half pitchR

C d

elay

(p

s)

1mm long Metal 1 wire

Corresponding Intermediate Wire

Year

0

5

10

15

20

25

30

35

wid

th (

nm

)

50x larger

Metal layer 1 width120 nm 95 nm 68 nm 52 nm 40 nm 26 nm

S. M. Rossnagel and T. S. Kuan, J. Vac. Sci. Technol. B 22, 240 2004.

~10 nm: = ~ 7 o

o - Bulk Resistivityρ(uΩ

-cm

)

Film thickness (nm)

Larger Cu Interconnect Resistance Longer RC delay

3

Causes for Resistivity Increase

(1) More Surface scattering

(2) More Grain boundary scattering

(3) Narrower line:

Roughness effects

Schematic from Schindler

When Line width or Grain Size < Electron mean Free Path

Classical Monte-CarloKuan (2000)

Solution & Challenge • Metal with very short λ negligible size effect at reduced

dimension on ρ .

4

• Limited knowledge on λ

- Nobel metal Cu 39 nm , Ag 53 nm, Au 38nm

- Metal with complicated Fermi surface such as W 2-54 nm

• λAl 15 nm but ρAl > ρCu until d < 10nm due to larger ρbulk

Surface scattering Grain boudnary scattering

W. Zhang at,. al.

Determine through Surface Scattering

i

x

f

x vv

specular scattering if:

(Fuch Sondheimer Model)

- film resistivity

ο - bulk resistivity

- electron mean free path

d - film thickness

K.Fuchs, Proc. Cambridge Philos. Soc. 34, 100 (1938) E.H.Sondheimer, Adv. Phys. 1, 1 (1952)

p: specularity parameter

p = 1 -> 100% specular scattering

p = 0 -> completely diffuse scattering

1

2

21

2

2121

531 1

)1)(()1)(1(2)

11(

4

31/

dt

epp

eppeepp

ttk kt

ktktkt

o

i

y

f

y vv

p1 and p2 to count scattering at unlike surfaces:

J. S. Chawla, et,. al. Phys. Rev. B, 84, 235423 (2011)

p1

p2

diffuse speculare-y

x

𝑣𝑥𝑖

𝑣𝑦𝑓

𝑣𝑥𝑓

5

approximation for d ≥

p

d1

8

31

, where k = /d.

• Metal with small ρxλ .

6

Goal

• Metal more specular surface scattering.

7

MgO(001)

5-400 nm W(001)

Microstructures of Cu Films

56 57 58 59 60

5 nm

10.7 nm

20.2 nm

48.2 nm

10x

Inte

nsi

ty (

arb

. u

nit

s)

2

75x

4x

d = 400 nm

W 002

10 100-1.5%

-1.0%

-0.5%

0.0%

0.5%

1.0%

nm

d (nm)

28.8 29.0 29.2 29.4

(a)

In

tensi

ty (

arb. unit

s)

=0.27°

Single Crystal W deposited• (001)W║(001)MgO and [010]W║ [110] MgO

X Ray Diffraction (XRD)

Rocking Curve

0.310 0.315 0.320 0.336 0.337

0.71

0.72

0.73

0.940

0.945

0.950

kn

m-1

knm

-1

d

W 103

MgO 113

Pole figure Reciprocal space map

d = 400 nm d = 400 nm d = 400 nm

Residual Stress

8

0.5 1.0 1.5 2.0 2.5

108

1018

°°° °°

5.0 0.1 nm

10.7 0.1 nm

20.2 0.1 nm

d = 48.2 0.1 nm

Inte

nsi

ty (

arb.

unit

s)

(a)

Thickness and Roughness Measurement• X-Ray Reflectivity (XRR)

• Films’ thicknesses agree with expectation.

• Surface roughness increase due to kinetic roughening

• Surface roughness small - negligible contribution to ρ.

0 10 20 30 40 50

0.5

0.6

0.7

0.8

0.9

1.0

1.1

(b)

rms

rou

gh

nes

s <

r> (

nm

)

d (nm)

9

Resistivity vs W(001) Thickness • No increase of ρ upon air

exposure.

• W-vacuum and W-liquid N2 interfaces exhibit completely diffuse scattering.

• λ293k = 38±1 nm

• λ77k = 365±10 nm

• ρ*λ is independent of T.

3/2

2

3/12 )3( effne

neff = 16 x 1021 cm-3 0.25 carriers/atom

Agree with the total uncompensated carriers from de Hass-van Alphen effect.D.M. Sparlin and J.A. Marcus, Phys. Rev. 144, 484 (1966).

Why Diffuse Surface Scattering on W?

W.F. Egelhoff, Jr., Surf. Sci. Reports 6, 253 (1987)

• Narrowing of the d-band of a transition metal at the surface Electron transfer to/away from surface

• Net positive charge at surface perturbs surface potential

diffuse scattering

10

ConclusionGoal 1

λ293k ,w = 38±1 nm ~ λ293k ,Cu

Ρbulk,w* λ293k ,w > Ρbulk,Cu* λ293k ,Cu

0.25 carrier/atom < 1 carrier/atom

Metal or alloy with carrier/atom >> 1

Goal 2

Diffuse Surface Scattering on W

Smooth Surface Potential

11

Acknowledgements

SRC Industrial Liaisons:Intel Corporation - Florian Gstrein, Jasmeet Chawla, Michael Haverty,

Christopher GeorgeGlobalfoundries - Derya Deniz, Xunyuan Zhang

Applied Materials - He Ren

SponsorsNaitonal Science FundationSemiconductor Research Corporation

Lab Officer:Ray Dove, Rob Planty, Don VanSteele

Group Members:Brian Ozsdolay, Tianji Zhou,Karthik Balasubramanian

Advisor:Daniel Gall

12

Q&A

Thank you for your attention !

13