Ferroelectric Tunnel Junctions: A Theoretical Approach

Transcription

1 Forschungszentrum Jülich Ferroelectric Tunnel Junctions: A Theoretical Approach H. Kohlstedt, A. Petraru, R. Waser Forschungszentrum Jülich GmbH, Institut für Festkörperforschung and CNI, the Center of Nanoelectronic Systems and Information Technology, Germany N. A. Pertsev A. F. Ioffe Physico-Technical Institute, St. Petersburg, Russia Center of Nanoelectronic Systems Information Technology

2 Electron Tunneling through Insulators E W φ( ) W pot Re ΨB Ψ B = B e ik k real k imaginary t k real Ψ C =CC e ik Re ΨA Ψ A = Ae A ik T t = C ep m φ( ) d h Transmission coefficient

3 Electron tunneling: Current Transport Equation Metal 1 I Metal Fermi distributions of (occupied/unoccupied) states j 1- T j -1 + e Fermi distributions of (occupied/unoccupied) i d) states t j j j = ev = j n 1 j e 4π h 1 current density ( k ) ma : direction [ f ] 1( E) f( E T( E, k ) k dk = de ) 3 π o

4 Tunnel Junctions: A short Survey Me I Me Su I Su Mag I Mag Semic I Me E g I I ΔR/R I H Sommerfeld/Frenkel/Holm Giaever/Josephson Jullieré/Moodera/Parkin/ (Sun/Fert for oides) Esaki

5 Ultra-thin Ferroelectric Films (Recent Results) Minimum predicted/measured thicknesss (nm) Karasawa (PTO) Li et al. (PZT) Marayuma (PZT) Tybell (PZT) Ghosez and Rabe (PTO) Pertsev (PTO) Streiffer (PTO) Junquera and Ghosez (BTO) Streiffer (PTO) one unit cell Ferroelectricity eists down to a few number of unit cells! Electrical l and mechanical (strain) boundary conditions are etremely important!

6 Ferroelectric Tunnel Junction High-Resolution TEM P SrRuO 3 e unit cells PZT A 4 nm SrRuO 3 T Tunneling matri element: 1 = C ep m φ ( ) d h Quantum Mechanical Electron Tunneling Polarization State of PZT

7 Superconducting -, Magnetic-, and Ferroelectric Tunnel Junctions Dielectric Barrier Superconductor Superconductor Magnet Magnet π e A I( ) = T ( E) n ( E e ) n h ( E )[ f ( E e ) f ( E) ]de 1 Metal Metal Ferroelectric tunnel junction: Cooperative phenomenon is in the barrier! Ferroelectric Barrier

8 Ferroelectric Tunnel Junction (preliminary Work) Idea: Resistive switching caused by ferroelectricity! 13, 161 (1971). European Patent: A1, 1994 R. M. Wolf and P. W. M. Blom, Philips Electronics, Eindhoven (NL). Patent drawing Measurement

9 Influence of Ferroelectricity on Electron Tunneling olume effects Interface effects S BaTiO 3 + SrRuO 3 - c c Barrier thickness Lattice parameter: Band structure Effective mass - Polarization charge +/- Screening effects Different structure Potential barrier

10 Strain: olume effects I a. ariation of barrier thickness t = to + d - C t -t C oltage b. Shift of the conduction and valence band edges t m T C E Ez dz C h = ep 4π k k + k = z m k z = h E = E + κ S C C 3 ( E E ) C z κ 3 Deformation Potential: Brooks 1955, Herring 1956, Kane 197 c. Change of the electron effective mass h m =, = a Δ E k C m = m a: lattice parameter, Tight binding appro. m + S S = m m + S d t

11 Strain: olume effects II T i i b bilit i WKB i ti ( b d d l) Transmission probability in WKB approimation (one-band model) dz E E m C T t z c = 4 ep π Influence of nonzero piezoelectric constant d h C z c p π ± ± = ) ( ep ) ( d t d m h m E T z π ) ( 3 p ) ( t S m he z 3/ 3/ ± ± z c z c E e d d E E d d E κ κ

12 Strain: olume effects III: I- curves A/cm ) Curren nt density ( 3 Symmetric I c + c -3 (a) d conducta ance, G/G Normalize c + c (b) oltage () oltage () Parameter: d = 5pm/ Barrier height:.5 e Thickness t = 3 nm Center of Nanoelectronic Systems for Information Technology

13 Symmetric I- curve Macroscopic Interface Effect I (non-perfect Screening) Screening at top and bottom equivalent + - M. Dawber et al., J. Condens. Matter, 15, 393 (3) P s + - = = E el Electrode E dep Ferroelectric (a) E el Electrode Same symmetry as in case of strain induced effects t/ t 3

14 Macroscopic Interface Effect II (non-perfect Screening) Screening at top and bottom not equivalent E nf nf Δt - + P s E dep dep Asymmetric I- curce t ( 3 ) 1 = + Edep t Δt ( ) 3 1 = Edep ( t Δt)

15 Symmetric and asymmetric Barrier Structures Symmetric barrier structure φ 1 φ t t` I φ 1 φ φ 1 φ Electrode Ferroelectric Electrode Symmetric I- Asymmetric barrier structure φ a = ( φ 1 + φ ) / φ = ( φ 1 + φ) / b variable fied φ I φ 1 φ Asymmetric I-

16 Etremely Asymmetric (e) Φ.8 a Φ Φ 1 a = Φ 1 b b Φ 1 Y m J (A A/cm ) dj/du (Ω ( -1 cm -1 ) (A) U () U () Reduced Asymmetry Crossing point CP: ΔR - c Symmetric e) Φ ( (e) Φ Φ (e).8 b Φ 1 a Φ Φ 1 a Y m Φ (A) b a.8 Φ 1 Φ a. Φ 1. Y m Φ (A) polarisation state "a".8 b polarisation state "b" Φ 1 a Φ.6.4 a. Φ 1 Y m Φ 1 b b b /cm ) J (A/ J (A A/cm ) J (A A/cm ) U () CP U () (A) U () -.5 (Ω -1 cm -1 ) dj/du ( dj/d du (Ω -1 cm -1 ) dj/du (Ω -1 cm -1 ) U () U () U ()

17 Recent Work on Ferroelectric Tunnel Junctions Nanoscale polarization manipulation and conductance switching in ultrathin films of a ferroelectric copolymer Hongwei Qu,et al., APL 8 43 (3). out-of plane E H. Kohlstedt, N. A. Pertsev, and R. Waser, in Ferroelectric Thin Films X, MRS Symposia Proceedings, 688, 161 (). t J. Rodríguez Contreras, et al., Appl. Phys. Lett. 83, 4595 (3). GaN: an eample! Resonant Electron Tunneling in GaN/Ga 1- Al N strained structures with spontanous polarization and piezoeffect, Phys. Of the Solid State: 43, 59 (1).

18 Outlook Eperimental realization of an FTJ Superconductor/ Superconductor/ New device structures Magnet Magnet Ferroelectric Barrier (IETS)- Inelastic electron tunneling spectrocopy to study: (1) Domain structures in nm thin ferroelectric materials or () Phonon spectra in ultrathin ferroelectric barriers

19 Acknowledgement The work was supported by the HGF-Strategiefonds Piccolo and the lk olkswagen-foundation--project t Nano-sized ferroelectric hybrids under contract number I/ DFG Project: Displacive and Conductive Phenomena in Ferroelectric Thin Films: Scaling effects and switching properties. Center of Nanoelectronic Systems for Information Technology