Elementary Process of Electromigration at Metallic Nanojunctions in the Ballistic Regime

Transcription

1 Elementary Process of Electromigration at Metallic Nanojunctions in the Ballistic Regime Kaz Hirakawa Institute of Industrial Science, University of Tokyo CREST, JST collaborators: Akinori Umeno, Kenji Yoshida, and Shuichi Sakata

2 Outline 1. Introduction Electromigration (EM) Commonly believed mechanisms for EM 2. Feedback-controlled electrical break junction Experimental Critical voltage for atom removal events -- EM spectroscopy 3. Elementary process of EM What is the crucial parameter in the ballistic regime? Critical current density 4. Summary

3 Electromigration (EM) Failure of VLSI interconnects Blow-outs of fuses and filaments IBM J. Res. Dev. Cover of July 1995 issue C. -K Hu et al., APL 81, 1782 (2002). typical J max = a few MA/cm 2 Limits the reliability of metal wires, filaments, and VLSI interconnects

4 Formation of Atomic Scale Nanogap Electrodes Fabricating Nanogap Electrodes 300 nm I Electromigration moleucles SiO 2 p-si Nano-fuse electrical stress ~ 1 nm Molecular junction H. K. Park, P. L. McEuen et al., Nature 407, 57 (2000). Not always end up with nanogaps. Understanding of the physics of EM is very important! H. K. Park et al., APL, 75, 301 (1999).

5 1 Joule heating Critical Power Dissipation P* = IV = V 2 /R τ exp Mechanism of Electromigration Rise in temperature Enhances mobility of atoms ( ) n E k T j a B 2 Electron wind force Atoms are pushed by momentum transfer from electrons Mean Time to Failure (MTTF) of wires voids hillocks H. B. Huntington et al., J. Phys. Chem. Solids 20, 76 (1961) A. Scorzoni et al. Mat. Sci. Rep. 7, 143 (1991) / C. Durkan et al. Ultramicroscopy 82, 125 (2000) Purpose of this study To clarify the elementary process of EM in the atomic scale nanojunctions Diffusive regime OK Atomic scale nanojunction?? Novel analysis tool: EM Spectroscopy Ballistic regime Are Junction the conventional voltage is mechanisms the crucial parameter still valid in an atomic-scale? e - I Critical Current Density j* ~ a few MA/cm 2

6 Double-layer resist EB lithography Sample Preparation lower sensitivity e-beam PMMA PMMA 100 nm higher sensitivity PM(MA-AA) substrate SiO 2 /Si SEM image of the samples Shadow Evaporation PMMA SiO 2 Si sub PMMA SiO 2 Si sub PMMA SiO 2 Si sub -11 tilt (1 st layer) +11 tilt ( 2 nd layer) 0 ( 3 rd layer)

7 Feedback-Controlled Electrical Break Junction I A V LPF R S V J, G J 4.2 K 200 nm G J (2e 2 /h) G J V C phase I T = 4.2 K V J 100 s Time (s) V J (V) Feedback control of EM Sharp decreases in G J (sign of EM) reduce V Peak V J = V C (critical voltage) D. R. Strachan et al. Appl. Phys. Lett. 86, (2005)

8 Semi-classical and Ballistic Regimes in EM 1 V C 2 / R J = P* = const. P* = critical power V C (V) 0.5 II Deviation from P* = const. line I 0.01 R J (h/2e 2 ) nanojunction (= G J -1 ) Joule heating dominant for G J > 50 G 0 (Phase I) Deviation from the P* = const. line for G J < 50 G 0 (Phase II)

9 Atomic-scale EM in Phase II (G J < 50G 0 ) 40 G J phase II G J < 50G 0 region EM spectrum for G J (2e 2 /h) 30 V C V J (V) Counts Time (s) V J 100 s V C (V) G J shows step-wise drops by ~ G 0 The junction is in the ballistic regime (QPC) One-by-one removal of atoms from the junction Histogram of Vc EM Spectroscopy (spectroscopy of atom removal events)

10 Counts EM-Spectroscopy for Nanojunction - Elementary Process of EM - V C = E b /e nanojunction e Vc (V) ev C Atom removal events most frequently occur V J = 0.4 V E b EM in the ballistic regime is induced by kinetic energy transfer from a single electron to a single atom. Surface diffusion potential:e b S. Günther et al. Surf. Rev. Lett. (1997) For gold E b = eV STS measurement Conventional picture A single electron e-wind Electron wind force モデル kicks out a single atom A. Umeno & K. Hirakawa, APL 94, (2009).

11 Critical Voltages for EM 40 V J = 320 mv below V c G (2e 2 /h) 35 V J = 460 mv above V c Time (s) 100 s EM does not develop unless V J exceeds the critical voltage V c (= E b /e).

12 Critical Voltage in the Ballistic Regime Counts (arb. units) T = 300 K 150 K 77 K ev C (ev) ev e*vc EM (ev) K Temperature (K) Almost no temperature dependence was observed in the EM spectrum.

13 Technological Implication of EM Spectra surface diffusion potential activation energy of MTTF nanojunction wire Counts ev nanojunction region -e ev J 10 diffusion potential Vc (V) τ E a exp ( E k T ) a = 0.42eV B The EM spectrum has a peak at the activation energy for the mean time to failure (MTTF) of metallic wires. E a can be determined from EM spectra.

14 Stability and Critical Current Density (V C ~ 0.3 V for Ni) Ni nanogap electrode J is of the order of A/cm 2! K. Yoshida, A. Umeno, S. Sakata, and K. Hirakawa, submitted. When V J < V C, a 3-atom Ni junction is very stable. The current density is of the order of cm 2, which is 4 orders of magnitude larger than the critical current density known for EM.

15 Summary We have investigated the elementary process of EM in the ballistic regime by introducing a novel spectroscopic approach ( EM spectroscopy ) EM is induced by kinetic energy transfer from a single electron to a single atom. The crucial parameter is the junction voltage, not the current density! V C ~ E d /e Metal junctions are stable even when j ~ A/cm 2, as long as V J < V C. Scientific/technological implications Reliability of VLSI interconnections nanojunction region -e ev J diffusion potential