Physics at the Nanoscale and applica1ons. Phelma / Grenoble INP and Ins1tut Néel / CNRS

Transcription

1 Physics at the Nanoscale and applica1ons Phelma / Grenoble INP and Ins1tut Néel / CNRS

2 Physics at the Nanoscale I Basics of quantum mechanics II Sta1s1cal Physics III Forces at the nanoscale IV Electron tunneling and applica1ons V Quantum electronic transport

3 Scope Density of States Tunnel Current Scanning Tunneling Microscopy and uses in Nanoscience Single Electron Devices M.F. Crommie, C.P. Lutz and D.M. Eigler, Science (1993)

4 Electron Tunneling Coun1ng available energy states Total number of states available N(E) Harmonic Oscillator ½ 3/2 5/2 with spin without spin Energy [hbar.ω] dn/de 0 ½ 3/2 5/2 In average dn/de=1/hbar.ω Energy [hbar.ω] Harmonic Oscillator ( ) E n =!ω n +1/2 dn/de 0 Hydrogen atom Level degeneracy = 2n 2 E n = 13.6eV Energy n 2 E 1 E 2 E 3

5 Electrons in a solid Fermi level T Energy

6 Density of states and Fermi level Energy Fermi energy Temperature Fermi level Energy up to which all states are filled (at T=0).

7 Quantum tunneling Energy Posi9on

8 Graphene Electron Tunneling Density of States examples Semiconductor S. Mar1n et al., Phys. Rev. B 2015 Ge(001) Kubby et al., PRB (1987) Al-Pb tunnel junc1on at 1.6K Superconductor Nobel prize 1973

9 Electron Tunneling The Tunnel effect again Conductor 1 Conductor 2 Conductor 1 Conductor 2 Thin insulator = tunnel barrier I = e P L R exp( d /d 0 ) I = 0 Conductor 1 Conductor 2 Conductor 1 Conductor 2 Situa1on 3 Situa1on 4 Situa1on 1 Situa1on 2 I = 4e P L R I = 3e P L R

10 Energy Electron Tunneling Fermi Golden Rule Filled electronic states Insulator Filled electronic states Tunneling possible? Yes Net current? I = 0 Number of occupied states in 1 Number of occupied states in 2

11 Energy Electron Tunneling Fermi Golden Rule -V ev Filled electronic states Number of occupied states in 1 Insulator Filled electronic states ev I e! P L R Number of occupied states in 2 Tunneling possible? Net current? At T=0 Yes [ ] ρ L (E ev )ρ R (E) f L (E ev ) f R (E) I e! P L R E F +ev E F ρ L (E ev )ρ R (E)dE de

12 Electron Tunneling Tunneling Spectroscopy 3.5k B T V Energy ev Filled electronic states Number of occupied states in 1 Insulator Filled states ev Number of occupied states in 2 Tunneling possible? Net current (At T=0)? I e!p L R If ρ L constant Only at high enough bias E F +ev E F ρ L (E ev )ρ R (E)dE di dv ρ R (E + ev)

13 Superconductor Electron Tunneling Tunneling Spectroscopy Planar Al-Pb tunnel junc1on at 1.6K Nobel prize 1973 Superconduc1ng density of states (theory) o Vacuum PtIr - Al junc1on. Scanning Tunneling Spectroscopy experiment at 80 mk o Local DOS Low Temperatures can be crucial for good spectroscopies

14 Electron Tunneling The inven1on of STM Nobel Prize 1986

15 A benchmark in surface science : the 7x7 surface reconstruc1on of silicon (111) A few years later Omicron and Specs websites

16 Instrumental aspects of STM Mechanical vibra1on isola1on Piezoelectric components for coarse and fine displacement

17 Electron Tunneling The issue with mechanical vibra1ons Experimental STM current fluctua9ons in and out of contact (PtIr 9p on graphene). Ques9on: es1mate the amplitude of mechanical vibra1ons in the setup

18 x M = difference between 1p and base posi1ons: Electron Tunneling Vibra1on isola1on x M t ( ) = x M0 sin( ωt + ϕ #) base x( t) = x 0 sin( ωt + ϕ) T S = x M0 x 0 = $ & % $ $ 1 ω ' & & ) % % ω # 0 ( ω # ' ) ( ω ' ) ( 2 $ ω ' + & ) % Q # # ( ω 0 2 Driven harmonic oscillator. x ( S t) = x S0 sin( ωt) T = x 0 x S0 = # ω & 1+ % ( $ Qω 0 ' 2 # # 1 ω 2 & & # % ( ω & + % $ $ ω 0 ' ( % ( ' $ Qω 0 ' 2 2 Incoming vibra1ons / mechanical damping. Prac1cal limita1on: f 0 > 2 Hz

19 Need for a double stage mechanical isolation Exercice: a 1 µm rms vibra1on source at 500 Hz perturbs the STM from the outside. Es1mate the transfer amplitude for one or two isola1on stages, and the resul1ng rela1ve 1p-sample distance vibra1on amplitude. (Answer : 300 pm and 1 pm respec1vely)

20 Lead Zirconate Titanates (PZT) 3 T Curie = C, to be used well below. polariza1on process (6 kv/mm, 1h) aligns dipoles along z. Depolariza1on possible if E > 1 kv/mm. T > T Curie - d 31 = 1-3 Å/V d 33 = 2-6 Å/V Before poling During poling Aver O Pb Ti, Zr T < T Curie

21 Piezo-electric scanner tubes L = Ld 31 E z = d 31 L t V X = 0.9d 31 L 2 D t V

22 Experimentalists considera9ons High voltage amplifiers noise? : about 1 mv over 0 to 5 khz. Mechanical resonances? : Elonga1on : f elongation = c 4L Flexion : f flexion = 0.56 D2 + d 2 8 c 4L 2 Temperature dependence of d 13 : a factor 5 to 10 smaller at low temperatures Exercice : propose a tube design that allows a horizontal scan range of 2 µm using a ±100V source at low temperature and has a maximum (f elonga1on, f flexion ). Es1mate the noise in posi1on at room temperature due to the amplifiers. (c = 5000 m/s at low temperature, depolariza1on field 1 kv/mm, d 31 = 1.5 Å/V at room temperature)

23 Contribu1ons of STM to solid state physics Carbon nanotubes : LDOS vs. structure Manipula1ng single atoms and molecules

24 Carbon nanotubes (n,m) defines the tube geometry. n = m : armchair m = 0 : zig-zag n m : chiral Theore1cal predic1on for a chiral nanotube: n - m = 3k : metallic n m 3k : semiconductor

25 CNT imaging chiral CNTs on a Au surface. armchair zig-zag Wildoer et al, Nature (1998)

26 CNT spectroscopy Metallic and semiconduc1ng tubes iden1fied. semiconduc1ng Sta1s1cs agrees with 1/3 of chiral ones being metallic. Energy gap in SC tubes: E gap = 2γa 3d metallic

27 Cu{ng a nanotube Voltage pulse (5 V) in the STM mode. L. C. Venema et al., Appl. Phys. Le. (1997).

28 Atom manipula1on D.M. Eigler and E.K. Schweizer, Nature 344, 524 (1990)

29 Atom manipula1on Clean Ni surface with Xe atoms : UHV necessary Low temperature (4 K) to freeze atom diffusion. Tunnel image at 10 mv/1 na, Atom manipula1on by increasing current up to 16 na.

30 The making of

31 The quantum mirage H.C. Manoharan, C.P. Lutz and D.M. Eigler, Nature 403, 512 (2000)

32 Electron Tunneling Single Electron Devices: Charging Energy Adding an electron to a bulk conductor: E > E F Neglected here repulsive Coulombian interac1on between electrons. Any closed conductor has a charging energy E c = e2 C Promo9ng 1 e - adding 1 e -

33 Electron Tunneling Single Electron devices: Coulomb Blockade Coulomb diamonds in a ver1cal island structure (Delv 98) Coulomb Blockade only effec9ve if k B T < E c

34 Electron Tunneling Single Electron devices: experimental realiza1ons Horizontal 2DEG SET (Stanford) Ver1cal 2DEG SET (Delv & Tokyo) Electromigra1on single gold nanopar1cle SET (Cornell) Shadow evapora1on metallic SET (Helsinki) What is the experimental temperature required for observing Coulomb Blockade in each of the above systems?

35 Electron Tunneling Single Electron devices: be er transistors? Drawbacks: o State of the art nanofab required. Mass produc1on impossible at present. o (Very) Low temperatures necessary o Resis1ve (R > h/2e 2 = 12.9 kω). Advantages: o conductance changes over a very narrow gate voltage range huge swing. o Can be fast (>GHz). o Func1onali1es beyond classical electronics

36 Conclusions o Single Electron Tunneling: a tool for spectroscopy o STM sensi1ve to both topography and density of states. Extremely fine and constraining measurements : z 1pm, usually high vacuum, some1mes low temperatures, mechanical mobility, A door to the nanoworld : local DOS, local manipula1on o Single Electron Devices: from basic physics to new promising logic devices.