Scanning Tunneling Microscopy (STM) (II)

Transcription

1 Sanning Tunneling Mirosopy (STM) (II) Instrumentation: The following figure shows essential elements of STM. A probe tip, usually made of W or Pt-Ir alloy, is attahed to a piezo drive, whih onsists of three mutually perpendiular piezoeletri transduers: piezo, y piezo, and z piezo. Upon applying a voltage, a piezoeletri transduer epands or ontrats. One ontrols -y piezo to san in y plane and uses oarse positioner and z piezo to bring the tip and the sample within a few angstroms. The eletron funtions in the tip overlap eletron funtions in the sample surfae. A bias voltage, applied between the tip and the sample, auses an eletrial urrent to flow. Suh a urrent is a quantum-mehanial phenomenon, tunneling. The tunneling urrent is amplified by the urrent amplifier to beome a voltage, whih is ompared with a referene value. The differene is then amplified to drive the z peizo. The phase of the amplifier is hosen to provide negative feedba: If the tunneling urrent is larger than the referene value, then the voltage applied to the z piezo tends to withdraw the tip from the sample surfae, and vie versa. Therefore, an equilibrium z position is established through the feedba loop. As the tip sans over the y plane, a two-dimensional array of equilibrium z positions, representing a ontour plot of the equal tunneling-urrent surfae, is obtained and stored. Figure. Shemati diagram of the sanning tunneling mirosope EE6 Winter 7

2 The ontour plot is displayed on a omputer sreen, either as a line-san image or as a gray-sale image (olor-sale). The line-sale image is a sequene of urves, eah of whih represents a ontour along the diretion with onstant y. The gray-sale image is similar to a bla-andwhite television piture. The bright spots represent high z values (protrusions), and the dar spots represent low z values. The following figures are line san image and olor-sale image of graphite surfae. Now we shall loo into a little bit more details on individual omponent of the STM and we start with the Piezoeletri Sanner. Piezoeletri effet was disovered by Pierre Curie in about 88. Quartz rystal: (Si positive, O negative) The pressure put on the rystal auses a displaement of the harge inside the rystal. Opposite harge are olleted at the opposite sides of the rystal. By stressing the quartz plate an eletrial harge is generated. EE6 Winter 7

3 STM use inverse piezoeletri effet, i.e., by applying voltage on the material and the material deforms. The piezoeletri materials used in STM are various inds of lead zironate (PbZrO3) or lead titanate eramis (PbTiO3) sine these would have a larger piezoeletri oeffiient (unit: Å/V) and other advantages. V L S L Definition: E =, strain tensor: S =, piezoeletri C: C = = L L E V Priniple of piezo element. The applied voltage maes the element longer or shorter m,i.e.,a fration of one mirometer to atomi resolution Priniples of the tube sanner: The ombination of three piezo elements maes it possible to move the STM tip in the -, Y-, and Z-diretions. Tripod Sanner In most modern sanning probe mirosopes, one uses a tube geometry. Tube Sanner Figure Defletion of a tube sanner. (A) Opposite and equal voltages are applied to the y eletrodes of a tube sanner. The, z eletrodes are grounded. A positive stress (pressure) is generated in the upper quadrant, and a negative stress (tension) is generated in the lower quadrant. (B) At equilibrium, a distribution of stress and strain is established suh that the total torque at eah ross setion is zero. This ondition determines the defletion of the tube sanner in the y diretion. Using elementary geometry, you will get: dvl y = πdh dy dl and a piezo onstant for tube sanner is K tube = = dv π Dh EE6 Winter 7 3

4 Vibration Isolation Effetive vibration isolation is one of the ritial elements in ahieving atomi resolution by STM. The typial resolution in the z-diretion (normal to sample surfae) is about.nm. Therefore, the disturbane from eternal vibration must be redued to less than.nm. This is done by introdution of Vibration Isolation System in STM. Muh of the physis of vibration isolation an be illustrated as single-stage suspension-spring isolation system in the following figure and understood easily. Fig. A vibrating system with one degree of freedom and its transfer funtion. (a) The vibrating system. A mass M is onneted to the frame through a spring and a visous damper. Regarding STM, the frame represents the floor, and the mass represents the STM. (b) The transfer funtion, whih is the ratio of the vibration amplitude of the mass to that of the frame at different frequenies. The restoring fore of the spring ating on the mass is: f=-(-), is the stiffness of the spring A visous (damping) fore is ating between the frame and the mass: ' ' ' f = ( ) Newton s law: '' ' ' '' F = M ( ) ( ) = M M M M ' ' γ = γ '' ' = '' here, is natural irular frequeny = πf = M ' M EE6 Winter 7 4

5 γ: damping onstant: M = γ Assume a sinusoidal vibration: t i e t ) ( = at the steady state, the motion of the mass should also be sinusoidal: t i e t ) ( = Substitute these two into previous equation, we obtain γ γ i i = The ratio of the amplitudes is the transfer funtion or the response funtion of the vibration isolation system: 4 ) ( 4 ) ( γ γ = In the engineering literature, the deibel (db) unit is frequently used: ) ( log Z = (db) () ~ figure shown in previous page. An effiient vibration isolation means a small (). Two-stage suspension spring vibration isolation system: Fig. A two-stage suspension-spring vibration isolation system. Two masses are hung from the frame via two springs and tow damping mehanisms. The ratio between the vibration amplitudes of the frame and of the seond mass (the transfer funtion) is alulated. The effiieny of its vibration isolation is muh better than the single-stage system. For two masses: M ' ' ' '' ) ( ') ( = ) ( ') ( ' '' = M For a sinusoidal eternal eitation, = t i e = = =,, ] [ A v v v v is = ] [ i M M A and transfer funtion : Z Z log EE6 Winter 7 5

6 Staed plate-elastomer system Fig. Staed plate system and its transfer funtion. (a) A fivefold staed-plate vibration system, with four sets of viton piees between metal plates. (b) Transfer funtion for 3, 5, and 7 fold staed-plate vibration system. Easysan STM uses suh approah. The STM is plaed on a soft rubber mattress, whih in turn lies on a two-ilogram heavy granite piee whose base is made of foam material. The rubber mattress damps the high frequeny vibrations, while the base damps the low frequeny vibrations. Coarse Positioner Coarse positioner is another important element, whih moves the relative position of the tip versus the sample in steps eeeding the range of the piezodrive. Fig. The piezoeletri stepper the louse. It onsists of a piezoeletri plate (PP), standing on three metal feet (MF), separated by high dieletri-onstant insulators (I) from three metal ground plates (GP). The feet an be lamped eletrostatially to the ground plate by applying a voltage V F. By alternatively ativating the lamping voltage and the voltage on the piezo plate, the louse rawls lie a reature with three legs. EE6 Winter 7 6

7 The above piezoeletri stepper is somewhat ompliated devie. In many surfae-siene eperiments, the atual loation on the sample surfae does not matter. A one-dimensional stepper is suffiient. In its simplest form, a fine-pith lead srew an mae ontrolled steps of a few mirometers. One typial design is shown as Single-tube STM in the following: Fig. Single-tube STM. The tube piezo sanner is adhered inside a sturdy metal ylinder, whih sits on three srews on the base plates. The two front srews mae the oarse approahing. The rear srew maes fine approahing by using the two front srew as the pivot ais. The rear srew is atuated by a stepping motor for automati approahing. The entire unit is rigid enough that a mediore vibration isolation devie an provide atomi resolution. In our STM used for LAB, we have so-alled Inertial Coarse Positioner. Bendable tile is a piezo rystal, by using a saw tooth voltage (rises slowly, drops quily), the sample holder is moving ahead. EE6 Winter 7 7

8 Eletronis and Control Fig. A shemati of the feedba loop in an STM. The tunneling urrent, after the urrent amplifier and the logarithmi amplifier, is ompared with a predetermined voltage, whih represents the urrent setpoint. The error signal is proessed by the feedba eletronis, whih typially ontains an amplifier and an integration iruit. The output of the feedba eletronis is applied to the z piezo, to eep the error between the atual tunneling urrent and the referene urrent very small. The voltage applied to the z piezo is reorded as the topographi image. Tunneling urrent ourring in STM is very small, typially from.na to na. Suh small urrent has to be amplified by Current amplifier: Vout = I inrfb The minus sign indiate that the phase is reversed. Typially the feedba resistane is MΩ in STM. Estimate: If you have one na of input urrent, what is the output? I in _ R FB V out Logarithmi amplifier: s Sine the tunneling urrent: I T e, logarithmi amplifier is to mae the entire eletroni response linear with respet to tunneling gas s. ev ev Diode I-V: I = I (ep( ) ) I ep( ) T T By using an input resistor, the logarithmi amplifier aepts voltage input: I in R IN _ Diode V out T Vout = onst. ln I IN e So for every deade of input, the output hanges about 6mV. After that, the V L is ompared to referene V P, the differene is sent to feedba eletronis, and amplified to beome a voltage and ontrol z-piezo. EE6 Winter 7 8

9 Maing STM tips: Materials: W, Pt-Ir, et. Proedures: ) Eletrohemial tip ething: For W: Cathode: 6H O6e - =3H (g)6oh -. Anode: W(s)8OH - =WO 4 4H O6e -. Ething ours at the air-eletrolyte (NaOH) interfae. The ething taes a few minutes. When the ne of the wire near the interfae beomes thin enough, it ruptures, maing two tips at the same time. EE6 Winter 7 9

10 To eth Pt-Ir tips, a solution ontaining 3 M NaCN and M NaOH is used. A irular Ni foil is used as the athode. The tips (for eample W) generated by eletrohemial ething are seldomly appliable immediately as the tip surfaes is overed with oide, ontaminations as well as organi moleules, et. Proedure : Annealing the tip. The purpose of the tip annealing is to remove the ontamination and oides without ause tip blunting. The removal of tungsten oide is based on the following mehanism: On tungsten surfaes, the stable oide is WO3. At high temperature, the following reation taes plae: WO 3 W=3WO (g). Several methods for annealing are shown here. EE6 Winter 7

11 Proedure 3: Field evaporation and ontrolled deposition: By ontrolling the field intensity at the tip ape, the most protruding W atoms are stripped off, leaving a well-defined tip ape. (see figure, with one atom, tree atoms and 7 atoms. Some people do annealing and filed deposition at the same time: EE6 Winter 7

12 Atomi metalli ion emission: Binh and Garia reported in 99 that at temperatures around one third of the bul melting temperature (for W: 34 C), by applying an even higher eletri field to the tip, the metal ions move to the protrusions and emit from the ends. These tips may ontain multi mini-tips at the tip end, and you now this is fine for STM measurements to resolve atomi resolution. In situ tip treatments: The tips treated by the above proedures may still not resolve atomi images of your sample. Now you may try a ouple of method during the measurements. ) High field treatment: Atomi resolution is supposed to be obtained at a smaller gap voltage, but is not obtained, try to inrease the gap voltage to inrease the field at the tip for some time and redue the gap voltage ba to the original again. EE6 Winter 7

13 ) Controlled ollision: EE6 Winter 7 3

14 Resolution of STM: Topographi images in onstant urrent mode In order to now the orrugation Z, we start with the tunneling urrent, whih is a funtion of r =(,y) and Z I=I ( r, Z) () If Z is perpendiular to a nearly perfet surfae, the tunneling urrent an be deomposed into a onstant (that is, independent of r ), and a small variable omponent that represents the features of the surfae: I ( r, Z)= I (Z) I( r,z) () In the above figure, Z( r )=Z Z( r ) (3) Substitute (3) into (): I= I (Z ) (di (Z)/dZ) Z( r ) I( r,z) (4) Due to the smallness of I, the variation of this term is negleted. The topographi image is then defined by the ondition of onstant urrent: Z( r I( ) ) = (5) di ( Z) ( ) dz Remember, we have obtained the tunneling urrent: I evρ s (,E F )e -Z (6) ρ s : loal density of states. In priniple, if you substitute Eq(6) into Eq(5), you will have the orrugations of your sample (image), however, the determination of the density of states is nontrivial. EE6 Winter 7 4

15 In a model proposed by Tersoff and Hamann in 985 where they assume that only s-wave solution matters (s-wave-tip model) as shown in the following: For simple metal surfae with fundamental periodiity a, y Z (/)ep[-( -)Z] (7) a Here Z is the distane from the top-layer of the sample surfae to the enter of urvature of the tip. K is the deay onstant, with a typial value of the wor funtion, ø=4ev, a plot of Eq(7) for different struture periodiities is shown: EE6 Winter 7 5

16 As an eample, for Al() surfae, Z 3.e -.56Z (8) The units are in Å. At a distane of 3 Å, Z.3 Å, Suh resolution has been muh better than those methods that we were taling about earlier. Nevertheless, STM eperiments have routinely demonstrated orrugation amplitudes more than one order of magnitude greater than this Fermilevel LDOS s-wave orrugation, i.e. the real resolution is around. Å, why? Beause the s-wave-tip model is too simple. The atomi orrugation Z depends on the spatial distribution and on the type of tip and sample surfae states. Therefore, the determination of eletroni state on the tip ape and the sample is important to obtain reasonable atomi orrugation. On the tip: Eletroni density of states at the Fermi level for ommon tip materials an be summarized in this table: And there are other types of states ontributes to the tip density of states: EE6 Winter 7 6

17 On the sample surfae side, different surfae eletroni state will result in different atomi orrugation, for eample: Here: β=γ-, and γ is determined from a mathematial identity: I (π/γ)e -γz On the whole, the determination of an aurate atomi resolution depends on different tip-sample system and spatial distribution. This is not a trivia, fortunately the resultant resolution for STM is more than enough for us to study and haraterize nanostrutures. EE6 Winter 7 7

18 Classial images and eplanations: ) Graphite (See Figure) Graphite is built up by layers with a honeyomb arrangement of arbon atoms being strongly ovalently bonded to eah other. The nearest-neighbor distane is.4å. The lattie onstants: A=.456Å, C=6.67Å. The honeyomb layers are staggered and held together by van der Waals fore. It sounds lie now we are going to see the arbon heagons of the topmost lattie plane. Unfortunately it is not the ase. You will only be able to se every other arbon atom. Tae a top view of the graphite. Beause the lattie planes are shifted relative to eah other, only half of the atoms have a diret neighbor in the seond lattie plane (A atoms). The other half of the atoms (B atoms) is loated above the enter (hollow site) of the sifold arbon ring in the seond layer. Now you see not all the atoms in the surfae layer are the same. What we disussed previously is now important: the tunneling urrent depends on the loal density of states. The B-sites ehibits a higher LDOS than the A-sites as A-site atoms have etra bonds to the arbon atoms in the seond layers. Therefore, A-site atoms are epeted to be seen as protrusions in STM image (See figure below). Question: What is the distane between the nearest atoms in an STM image of graphite? EE6 Winter 7 8

19 ) Si() (7 7) surfae. EE6 Winter 7 9

20 The first suess of STM was the real-spae imaging of the Si()-7 7 struture. It taes a long time for people to understand the 7 7 struture. First, we would lie to disuss the Wood notation. In other words, what does 7 7 mean? Wood suggests that it should use a simple notation to represent the surfae atom arrangement. The atom arrangement on the surfae of any solid is normally different with that inside the rystal. We an hoose unit ell vetors say b and b based on its -D Bravais lattie, we also now an idealize substrate rystal has its own unit ell vetor a and a. The notation is developed in suh a way that ) the angle between b and b is the same as the angle between a and a of the (hl) surfae of substrate A, and ) b=ma, b=na, then we say the surfae struture is: A(hl)-(m n) The simplest ideal surfaes are alled singular surfaes. They have the strutures that would form if a perfet bul rystal ould be ut to epose the atoms of an {hl} plane at the surfae without allowing them to adjust to their new environment by relaing from their bul positions. Beause their atoms have the same arrangement as bul planes, singular surfaes are also alled surfaes. 77 On a nasent leaved Si() surfae, one unit ell ( ) has only atom. The reonstruted surfae (7 7) is onstituted of 49 Si surfae atoms (disovered by low-energy eletron diffration (LEED)). But the detailed arrangement of these 49 atoms, i.e., reonstrution, is very ompliated, atually involves the seond and the third Si layers underneath the surfae layer of 49 atoms. EE6 Winter 7

21 In fat, the struture is not stable at all and the atoms reonstruted to form a pattern struture as shown in the following figure. The silion atoms labeled A move up from the seond layer to the first layer. The eletrons at the Si atoms labeled B transfer to the A atoms, to mae these dangling bonds fully oupied. On the other hand, the dangling bonds at the B atoms beome empty states. To resolve this surfae, a voltage-dependent imaging method an be used. (What inds of images at different voltages are left for you as an imagination problem) Here, however, we want to eplain a little bit on the Si() pattern that we shown in the leture notes STM-. Beause the bonds between the dimer Si atoms are oupied and the dangling bonds at the top-surfae Si atoms (atually the seond layer) are unoupied, the STM image at positive bias and negative bias should be different. By applying a positive voltage with respetive the Si substrate, the eletrons will tunnel from oupied states of Si dimers. Note: two -Si atom dimmer shows one bright spot. At a negative bias with respetive to the Si substrate, the eletrons will tunnel to the unoupied dangling bond of the Si atoms on the surfae. Eah dangling Si atom ontributes one bright spot in the image. Metastable Si()- ( ) struture is not stable, by heating it in ultra-high vauum to above 4ºC, it is reonstruted to a stable struture, i.e., 7 7 pattern. Taayanagi et al. proposed the DAS model as shown in the previous figure, whih turns out to agree well with eperiments. As you an see, the surfae (one unit ell) onsists 9 dimers, adatoms, and a staing fault layer. By taing images at different biases, the surfae information an be resolved. For eample, the bright dots in eah unit ell are representing the adatoms. EE6 Winter 7