Chapter Objective: learn the general techniques that are essential for SPM. Chapter.1: Tips STM tips: requirements Geometry: Need for atomically-sharp apex for atomic resolution on a flat surface, rest of the tip can be blunt. An artefact: tip imaging Sample with needle-like structures: a Al O 3 surface imaged by AFM. Strong relief: need for a small angle, otherwise the surface is not faithfully imaged. The latter point is also true for AFM and related techniques. The blunt tip is imaged by the sharp sample needle-like structures. Effect recognized by observation of numerous identical structures. Different brightness due to different heights of the needles.
STM tips: materials Criteria: Surface quality, low oxydability, Ease of preparation, Rigidity. STM tips: etching techniques Material-dependent, W is easy. The reactants flow governs the locality of the etch. Materials: W: easy to etch, rigid. Pt: very low oxydability, but soft. Au: very low oxydability but very soft. Pt 90 Ir 10 : good rigidity/oxydability compromise. 1 µm 100 µm Tip can be simply cut from a wire. Electrochemistry-based recipies are more reliable. The excess etching time after the drop of the lower part has a strong influence on the final tip geometry: Long over-etch = blunt tip. STM tips: final preparation Used in some specific cases. Objectives: Improve tip geometry, remove oxide: - by thermal treatment: at 1000 C : WO 3 + W -> 3 WO volatile - by field evaporation (atom migration) Attach some atoms of another element (Si, Cu): - by controlled collision Chapter.: Basics of piezo-electricity
The piezo-electric effect Discovered by Pierre and Jacques Curie (1880). Expansion/contraction electrical potential difference Needs to be an electrically insulating material. If z and - z are equivalent axes, no piezo-electric response. Only some anisotropic crystals are piezo-electric: quartz, Rochette salt KNaC 4 H 4 O 6-4H O, PZT ceramics The piezo-electric coefficients Standard notations: x 1 y # x& z (poling axis) 3 % ( % x ( # d 11 d 1 d 31 &# E x & % y( % (% ( In the linear response regime: = d 1 d d 3 % y ( E y % z $ d 13 d 3 d (% 33 ' $ E ( z ' % ( $ z ' If voltage applied along the poling axis, only d 3 are effectively used: x x = d 31 E z most used mode, d 31 = 10-3 to 10 Å/V z z = d 33 E By symmetry, usually d z 3 = d 31 The PZT materials (1) Ceramic, solid solutions of PbZrO 3 and PbTiO 3. Pb-Zr-Ti = PZT. Ferro-electric with T Curie about 50 C, to be used well below. Polarization process (60 kv/cm, 1h) necessary, aligns dipoles along poling axis (z). Before poling During poling After 3 cubic tetragonal T > T Curie dimensionless number related to the effectiveness of electrical to mechanical energy conversion. The PZT materials () Piezo-electric coefficients depend strongly on composition and temperature. d 31 = 1-3 Å/V d 33 = -6 Å/V O Pb Ti, Zr T < T Curie
The tripod Chapter.3: Piezo-electric actuators L Used by Binnig et al. Difficult to mount, not very rigid. But easy to operate and to calibrate at the metrological level (with capacitive sensors). L A bar for every direction: L = Ld 31 E z = d 31 e V e 3: poling axis 1: movement axis V Length L = cm, thickness e =.5 mm, V = 50 V (E el = 10 5 V/ m), d 31 =.5 Å/V δl max = 5000 Å, sensitivity = 0 Å/V The piezo-electric tube The piezo-electric tube Inner and outer faces are metallized to form two electrodes. Radial poling, radial electric field : axis 3 = radial direction. Used to generate a movement in the tube axis direction.. L = Ld 31 E z = d 31 L e V Direction of poling and of electric field V Z Example: Length L = cm, wall thickness e = 0.5 mm, V max = 50 V (E el = 5.10 5 V/m), d 31 =.5 Å/V. δl max = 5000 Å =.5 µm, sensitivity = 100 Å/V Similar sensitivity but natural rigidity of the tubular geometry. On drawing, deformation is much exaggerated.
The scanner tube The scanner tube Tube with again radial poling. Four quadrant electrodes on the outer face: + V x,y and V x,y applied on two opposite electrodes. Again, a voltage V z can be applied on the (single) internal electrode. L X = π d 31 De V -V X V X Same parameters + Diameter D = 1 cm. δx max = 50000 Å = 5 µm, sensitivity = 00 Å/V V X V Z -V X -V Y V Y Bow: displacement not purely lateral. Voltage V z applied to inner electrode: Z movement capability added. Three movements can be done simultaneously. Compact and quite sensitive : broadly used. The benders Similar effect as the scanner tube but in a single plate geometry. The shear piezos The labels 4, 5 and 6 in piezo-electric coefficients describe rotations. +V 0 +V Poling in the up direction Here, E is applied along direction 1, perpendicular to poling. The corresponding strain coefficient d 15 is as high as 11 Å/V. Low stiffness, force and resonant frequency. A scanner built with 4 benders polarized in two halves: no angle with interest for laser beam reflection in AFM. Base X = d 15 V L = 1 mm, V max = 50 V (E el =.5 10 5 V/m), d 15 = 10 Å/V δx max = 50 Å. High forces, used in coarse positioning. V
Fragility (it s a ceramic!) Chapter.4: Limitations of piezo-electric actuators No pulling force without preload. Mounting rules: Ball tips or flexures to decouple lateral forces Ball tips or flexures to decouple bending forces. No lateral force or torque. www.physikinstrumente.com/ tutorial/index.html Bolting of both ends is not recommended. Hysteresis and creep The scan Hysteresis for various peak voltages. 60 µm 60.6 µm 61. µm 61.8 µm 0.1 1 10 100 Creep after a 60 µm displacement www.physikinstrumente.com/tutorial/index.htmlwww.physikinstrumente.com/tutorial/index.html L t (s) [ ( )] ΔL = ΔL t=0.1 1+ γlog t 0.1 Tip is moved to start position, scanned over the surface, and moved back to start position. Start of the image and so on Trace: tip is scanned, topography is recorded. Retrace: tip is scanned back. Fast scan direction Slow scan direction
Exemple of hysteresis effect Closed loop operation Difference between trace and retrace images: the image is traced in the hypothesis of a displacement at constant speed, which is not the case. Capacitive position sensor trace retrace Closed loop operation: position is measured and corrected. Available in various commercial AFMs. Other limitations High voltage amplifiers noise: about 1 mv over 0 to 5 khz. Induced mechanical noise = about 0.1 Å! (sensitivity 100 Å/V) Mechanical resonances: Elongation : Flexion : f elongation = c 4L f flexion = 0.56 D + d c = 3 km/s, L = 1 cm, d = D = 3 mm f elongation = 10 5 Hz ; f flexion = 10 4 Hz 8 c 4L Chapter.5: Coarse positioning how to make approach of a sample towards a tip (from mmm scale down to nm) Aging: re-calibration needed.
The inertial motor Example of commercial inertial motors Wagon on two rods, non-sliding condition : From Attocube company: T <f N T = ma : tangential part N : normal part of the contact force If a > fn m the wagon slides. One step = about 10-50 nm. C. Renner et al., Rev. Sci. Instrum. 61, 965 (1990). The Pan motor Based on shear piezos. Walker (inchworm) regime: Leg by leg movement: 3 stick more than 1. Retraction of the 4 legs together. Can also be operated in the inertial regime (4 legs pulsed together). S. Pan et al, Rev. Sci. Instrum. 70, 1459 (1999). Stepper motors walker mode Present in most commercial AFMs, accuracy down to 30 nm. The electromagnet 1 is turned on, aligning the nearest rotor teeths with the stator teeths. At this point, the rotor are slightly offset from electromagnet teeths. The electromagnet is turned on, Here 5 teeths on rotor, on stator period corresponding to 4 teeths, rotation of 360 /(5x4)=3.6 per cycle. Works usually only in ambiant conditions (grease needed).
Chapter.6: Design rules and examples O. Züger, H. P. Ott, and U. Dürig, Rev. Sci. Instrum. 63, 5634 (199). Vibration isolation x M = difference between tip and base positions: x M t Driven harmonic oscillator, ω 0, Q. Driven harmonic oscillator, ω 0, Q. base x( t) = x 0 sin( ωt + ϕ) x S ( t) = x S0 sin( ωt) T S = x M0 x 0 = T = x 0 x S0 = ( ) = x M0 sin( ωt + ϕ #) Incoming vibrations / mechanical damping. Practical limitation: f 0 > Hz $ & % ω # ' ) ( ω 0 $ $ 1 ω ' ' & ) & % % ω # 0 ( ) ( $ ω ' + & ) % Q # # ( ω 0 # ω & 1+ % ( $ Qω 0 ' # # 1 ω & & # % ( ω & + % $ $ ω 0 ' ( % ( ' $ Qω 0 ' Need for a double stage isolation With positioning motors Very low temperature (60 mk) AFM-STM with Attocube motors F. Dahlem, T. Quaglio, H. Courtois (008). With a 100 nm vibration source at 1 khz, a 10-5 transfer amplitude gives here a 1 pm vibration on the microscope. 10-3 gives 100 pm = 1 Å.
The beetle geometry Veeco microscope (at CIME) Well adapted to ultrahigh vacuum (UHV) systems. Excellent access to sample and tip. Coarse approach based on the displacement of the 3 feet along a ramp. J. Frohn et al., Rev. Sci. Instrum. 60, 100 (1989). Piezo tube for tip scanning Stepper motors for sample coarse positioning. STM electronics Tunnel current Chapter.7: SPM electronics V bias Current preamp. tip sample Z piezo Set point error signal e(t) = 0 at equilibrium feedback loop PID regulation Z position High Voltage amplifier XY piezo Scan drive Here, the sample is scanned. It could be the tip, no difference.
The tunnel current measurement C wire I t R C stray V S = R I t Bandwidth = 1/RC stray = 10 8.10-1 =10-4 s Op-amp noise = current noise + voltage noise/wire-ground impedance i OA = i noise + C wire ωv noise Thermal noise of the resistance R : - + P noise = 4k B TΔf i Johnson = 4k BTΔf R R = 100 MΩ usually 1 na -> 0.1 V about 5 nv/hz 1/ 0.3pA in [0;3kHz] signal set-point - error e(t) The PID regulation P I D K I K P e( t) e( t)dτ de( t) K D dt Σ$ correction signal P, I and D signals generated analogically with op-amps or digitally. Ziegel-Nichols coefficients setup procedure: increase K P until oscillations appear, reduce K P to 0.45 of this critical value, set K I to 0.85 the oscillation period. K D little useful. J. Ziegel, N. Nichols, Trans. ASME 64, 759 (194). SPM electronics Probe data information Probe signal processing tip sample Z piezo XY piezo Set point Scan drive error signal e(t) = 0 at PID regulation equilibrium Chapter 3 feedback loop Z position High Voltage amplifier Imaging with a STM Objective: to learn the different STM imaging techniques. Here, the sample is scanned. It could be the tip, no difference.
Important parameters Chapter 3 Imaging with a STM 3.1: Imaging principle and techniques Voltage bias determines the energy range of probed electronic states V tip - V sample > 0 : e- from sample to tip, occupied states are imaged. V tip - V sample < 0 : e- from tip to sample, empty states are imaged. Scanning frequency: below the resonance frequency of tubes, below the bandwidth of the tunnel current regulation if active. Tunnel resistance R t determines the tip-sample distance. Usually, the current is the parameter: R t = V I t = 5 MΩ to 5GΩ Constant current imaging Tunnel current regulation is active and effective at every time. I t = Cst During the x,y scan, the regulation output V z is : - amplified and sent to the piezo - measured. V z (x,y) scaled by the Z-piezo sensitivity gives the topography information. Constant height imaging Tunnel current regulation is inactive (or active with a long time constant so that mean slope is followed). During scan, the regulation output V z is close to constant, the tunnel current I t is measured. I t gives the topography information. Possible only on atomically-flat surfaces, highly-sensitive but non-linear information. Much less used. V z I t time V z I t time
The corrugation Corrugation d is by definition: Chapter 3 Imaging with a STM 3.: The spatial resolution the topography variation amplitude as measured by the microscope. It is a fraction of Angtröm on an atomically flat surface, and can be larger on rougher surfaces. Depends on every experimental conditions. Can be decreased by a blunt tip, an inefficient regulation : not an intrinsic quantity. Spatial resolution Trying to model the atomic resolution Binnig (1978); hypothesis of a continuous media. ( ) = I 0 exp' α Δx I Δx % & The tunnel current is concentrated on a scale: R α << R R ( * where α = mw ) R = 10 nm, α = 1 Å -1 : current flows on a scale x = 1 nm. Spatial resolution is not limited by the tip radius. x Tip radius R Model of a continuous media surface: homogenous electron gas. Calculated corrugation d theo : Δd theo h, = exp π & R + d) /. ' ( αa * - + 0 1, if a >> π α and d >> /. - α 1 0 Stoll (1984) For a metal : a =.5 to 3 Å, k = 1 Å -1, h = 3 Å. Tip: R = d = 3 Å calculated d theo = 0.01 Å: too small compared to experiment! This model fails to describe the atomic resolution: the hypothesis of a continuous media is incorrect. d a d h
The origin of atomic resolution Dangling states: anisotropic d z localized states close to the Fermi level. e - orbitals overlap is strongly modulated during scan. Contrast depends strongly on the nature of the atoms at the tip apex: Better resolution on Si after a controlled collision. Chapter 3 Imaging with a STM 3.3: The STM benchmark Si 7x7 Complete description implies including the tip-surface interaction. Si (111) 7x7 Si (111) 7x7 : the model Si (111) annealed at 1000 C, slow cooling-down. Single vacancies or adsorbates are visible: true atomic resolution. 7x7 reconstruction minimizes nb of pending bonds : 49->19 Miller index refer to the number (= 7) of atomic cells involved. In STM, the adatoms only are visible, a well as the corner vacancies. Omicron website: http://www.omicron.de/results
Surface dynamics studies Real-time dynamics of Pb atoms on Si J.-M. Rofriguez-Campos et al, Phys. Rev. Lett. 76, 799 (1996), Institut Néel, Grenoble.