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ATOMIC FORCE MICROSCOPY Lecture II S. Papernov Principles of SPM Instrumenta7on

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Atomic force microscopy lecture by Semyon Papernov, scientist at Laboratory for Laser Energetics

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  • ATOMIC FORCE MICROSCOPY

    Lecture II

    S. Papernov

    Principles of SPM Instrumenta7on

  • I. Introduc7on The purpose of the Scanning Probe Microscope is obtaining high-resolu7on 3 dimensional maps of a surface through sensing of the interac7on force between the probe and sample

    The dierence between SPM and a conven7onal probe-based prolometer is in that the SPM is capable of controlling 7p-sample interac7on with high precision. This is accomplished through electronic feedback loop mechanism, which protects the 7p and sample by maintaining forces between them at a specied level.

  • II. SPM Fundamentals 1. Control mechanisms The rst SPMs were Scanning Tunneling Microscopes ( STMs ), which use tunneling current to monitor 7p-sample separa7on. This separa7on is typically maintained at several atomic diameters, or about 1nm. As 7p-sample separa7on changes due to feature height ( or depth ), the tunneling current density j changes according to exponen9al rela7onship:

    ( )skVs

    kej 020

    22exp

    4

    =

    !( 1 )

    where s is the eec7ve tunnel distance, k0 the inverse decay length of the wave func7on density outside the surface, V the applied voltage. That provides excep7onal precision in controlling 7ps height above the surface, since slight distance varia7on causes drama7c dierences in tunneling current. This monitoring mechanism remains the most sensi7ve used in SPM, achieving greater resolu7on than any other method.

  • The other approach oering good sensi7vity and widely used in Atomic Force Microscopes ( AFMs ) is based on the op7cal lever

    Laser beam movement is monitored over two axes: ver7cally and horizontally. Tips upward and downward movement shiQs the beam between upper and lower photodiode parts, crea7ng dieren7al signal which can be converted into height informa7on. Lateral movements of the beam are also monitored through dieren7al signal from leQ and right por7ons of the photodiode which corresponds to the twis7ng of the can7lever due to fric7onal phenomena on the surface.

  • 2. Feedback loop gains The feedback system must be op7mized for each new sample. This is accomplished by adjus7ng various gains in the SPMs feedback circuit. The analogy with hot air balloon:

    a) Propor9onal gain If al7tude > setpoint value, turn burners o. If al7tude < setpoint value, re burners.

  • Example: Propor7onal gain = 1, the balloon is 25 meters too low, use 10 l/sec rate. The balloon is 50 meters too low, use 20 l/sec rate. Propor7onal gain = 2, the balloon is 25 meters too low, use 20 l/sec rate.

    Although this sort of feedback gain works well for linear models, for nonlinear models there remains always some residual error. b) Integral gain Integral gain is used to correct the cumula7ve error between a system and its target state. In the case of the balloon, if running average error during some 7me interval puts the balloon below the setpoint al7tude, the burners are red. If the average error puts the balloon above the setpoint, the burners are turned o.

  • The eect of integral gain feedback is to reduce total error by addressing error over longer period of 7me and smooth out short-term, uctua7ng eects of propor7onal gain. The integral gain is highly sensi7ve, and if set too high, there is a tendency to overshoot the setpoint. Therefore, it must be used carefully.

    c) Feedback gains in SPM In the case of probe 7p, the objec7ve is quite similar: the operator assigns a setpoint value corresponding to a certain amount of 7p-sample force, then adjusts gains to track the surface as closely as possible while maintaining the setpoint. Instead of burners, however, the Z axis piezo crystal uses voltage to control the 9p-sample separa9on.

  • d) Setpoint

    In scanning probe microscopy, setpoint refers to how large is a 7p-sample interac7on force to be maintained.

    There are two ways of dening setpoint, depending upon the AFM

    opera7on mode: Contact Mode or Tapping Mode. In Contact AFM, setpoint is determined by the amount of the can7lever

    exion as the setpoint increases, the can7lever exes more and 9p-sample forces increase.

    In Tapping Mode, setpoint is determined by the RMS amplitude of the

    oscilla7ng 7p as setpoint decreases, RMS amplitude decreases ( Fig.1 ), but 9p-sample forces increase.

  • 3. Contact AFM operaCng concepts. The AFM system is comprised of two major components:

    a) The scanner b) The AFM detec7on system. The scanner houses the piezoelectric transducer which physically moves the sample in X, Y and Z direc7on, Fig.2.

  • Fig.3

    The detec7on system consists of a laser which generates a beam that is reected o of a exible microfabricated can7lever onto a mirror and nally into a photodetector ( split photodiode ). The circuit generates voltage ranging from +10V to -10V depending on the posi7on of the laser spot on the photodiode. While the sample is scanned under the 7p in X and Y features on the sample surface deect the can7lever, which in turn change the posi7on of the laser spot on the photodiode. This posi7on change is read by the feedback loop which moves the sample in Z to restore the spot to its original posi7on (Fig. 3).

  • The amount of voltage and how frequently it is applied to the Z-axis piezo is controlled by AFM gains. Ques9on: How are gain seMngs used? Answer: Propor9onal gain The computer mul7plies this number 7mes the value read from the comparison circuit every 7me the A/D converter is read. It is a high frequency feedback control. Integral gain - This number is mul7plied 7mes an accumulated average of A/D readings. This is a low frequency feedback control. The displayed image is an average of the correc9ons made to Z in a given display period.

  • 4. Tapping Mode AFM operaCng concepts. An advantage of Tapping Mode AFM is an absence of the fric7onal forces which inuence both, sample and probe. In Tapping Mode the feedback loop keeps a vibra7ng can7lever at a constant amplitude, rather than keeping can7lever at a constant deec7on (contact AFM). The 7p together with can7lever is modulated through mechanical excita7on at its resonance. A laser beam is reected o a can7lever onto a mirror, and then onto a photodetector ( Fig. 4 )

    Fig. 4

  • The laser spot oscillates ver7cally across the photodetector ( photodiode array ) and produces AC signal which aQer ltering is converted to a DC voltage ( RMS Amplitude ). The magnitude of the RMS amplitude is propor7onal to the amount of the can7lever mo7on. The feedback system compares the RMS amplitude to the setpoint voltage. During the engagement process the setpoint is set (automa7cally) smaller than the RMS voltage and the 7p is lowered toward the sample un7l RMS voltage (due to damping eect) reaches the setpoint value.

  • 4.1. Tuning the can7lever drive frequency. The drive frequency plays an important role in the performance of the microscope working in Tapping Mode. Since tapping process involves interac7on with a sample surface, drive frequency appears to be slightly dierent from the free oscilla7on resonance frequency of the can7lever. The can7lever dynamics can be described by the dieren7al equa7on:

    ,tsinF)z(Fkzdtdz

    Qm

    dtzdm 022

    =++

    + ( 2 )

    where m is the eec7ve mass of the can7lever, Q is the quality factor of the free-standing vibra7ng can7lever, F(z) is the force ac7ng between 7p and surface at distance z, F0 and are the amplitude and the frequency of the driving force.

  • Considering F(z) as a small perturba7on one can obtain solu7on of ( 2 ) for the can7lever vibra7on amplitude A :

    ,

    QmF

    aA

    2

    220

    222

    0

    20

    +

    = ( 3 )

    where a is drive amplitude, F = - F/z, 0 =( k/m )1/2

    The Eq.(3) shows, that the new resonance frequency changes to :

    mFk'

    0

    = ( 4 )

    which is equivalent to the change of the spring constant upon z change. Prac7cally it means that working drive frequency have to be slightly oset compare to free oscilla7ng can7lever, see Fig. 5.

  • Fig. 5

  • 5. AFM canClevers and probes. There are two basic types of can7levered probes used in the AFM: a.) Silicon nitride for Contact AFM modes. Four-sided, 70 Si3N4 pyramid on a triangular Si3N4 can7lever ( Fig. 6 ). The highest measurable angle using these probes is approximately 65 ( Fig. 7). Resonant frequency 5 50 kHz.

    Fig. 6

  • Fig. 7

  • b.) Etched silicon for Tapping Mode. Resonant frequency 200 400 kHz.

    Fig. 8

  • Four-sided asymmetric pyramid, with a 17 +/- 2 from side to side half cone angle. The front edge half angle 25, and the back edge half angle 10 ( Fig. 9). Using the back edge, the highest measurable angle of 80 can be achieved rou7nely.

    Fig. 9

  • 6. Tip-sample convoluCon eects.

    The convolu7on eects are always present when the radius of curvature Rp of the sample surface feature is comparable or smaller then the radius Rt of curvature of the 7p apex.

    Fig. 10

  • For a spherical surface feature which interacts with both the 7p apex and walls, the resul7ng composite image can be described by the following equa7on: W = C1( h Rp ) + C2Rp + C3Rt , ( 5 ) Where W is the image width, h is a ver7cal distance between the top of the sphere and a lower point, Rp is a true radius of the spherical par7cle, Rt is the radius of curvature of the 7p apex. The coecients C1, C2 and C3 are related to the 7p symmetry, C3 = C2 C1. If W is measured where h = Rp, that is, at half the maximum height, a plot of W versus Rp for a number of spheres with dierent radii yields a line with a slope of C2 and intercept of C3Rt. C1 is obtained by plopng sets of W versus h Rp for a given sphere. With Ci in hand, Rt may be calculated.

  • Once the 7p is characterized, the value for Rt can be used to calculate the true radius of the spherical feature:

    t

    22

    p Rh8h4WR += ( 6 )

    t3

    1p RC

    hCWR = ( 7 )

    Eq.( 6 ) is used at heights h on the par7cle at which only the 7p apex is interac7ng with the par7cle, that is near the top of a given sphere. Eq.( 7 ) is used at heights where signicant interac7on between the 7p edge and the sphere is taking place. In case Rt >> Rp, Eq.( 6 ) is always valid, and can be used for direct es7mate of the 7p radius Rt by measuring image width W at the par7cle base, where h = h0 = 2Rp : Rt = W2/8h0 ( 8 )

  • III. SPM applica7ons. 1. Surface Topography. a.) Contact AFM b.) Tapping Mode AFM 2. Lateral Force Microscopy ( LFM ). The AFM can7lever is most suscep7ble to fric7onal eects when the scan direc7on runs perpendicular to the major axis of the can7lever. This regime of imaging can be accomplished by simply sepng scan angle at 90 or 270.

  • 3. Force imaging. Lets consider a contact AFM force plot using a silicon nitride 7p, sensi7ve both to arrac7ve and repulsive forces.

    Fig. 11

  • The graph reveals at least two very important things: a.) Tip-sample aPrac9on As the 7p approaches the sample, arrac7ve forces reach out and grab the 7p, that is evidenced at point 2 in the graph. b.) Material elas9city AQer contact is established and 7p is pressed further into the material (Fig. 12, part of the curve between points 2 and 3). The amount of the can7lever exion for a given amount of downward 7p movement gives an indica7on of the material elas7city.

    Fig. 12

  • Piezo extends; 7p descends. No contact with surface yet.

    Tip is pulled down by arrac7ve forces near surface (jump- to-contact point.)

    As 7p presses into a surface, can7lever bends upward.

    Piezo retracts; 7p ascends. Can7lever relaxes downward un7l 7p force is balanced by surface forces.

    Piezo con7nues retrac7on; 7p ascends further. Can7lever bends downward as surface arrac7on holds on to the 7p As 7p con7nues ascent, 7p nally breaks free of surface arrac7on. Can7lever rebounds sharply upward. As piezo con7nues its retrac7ng, 7p con7nues its ascent. no further contact with surface this cycle.

  • Tip-sample interac7on during a force plot.

    Fig. 13

  • Interpre9ng force curves: An examina7on of force curves can be useful in determining adhesion and hardness characteris7cs of samples. Fig. 14 represents some of the general varia7ons in force curves.

    Fig. 14

  • 4. MagneCc force ( MFM ) imaging. In Magne7c force imaging, a tapping can7lever with a special 7p is rst scanned over the surface of the sample to obtain topographic informa7on. Then, using LiQMode the 7p is raised just above the sample surface ( 10 100 nm ), and the surface is scanned while being monitored for the inuence of magne7c forces ( Fig. 15 ). This inuence is measured using the principle of force gradient detec9on.

    Fig. 15

    MagneCc or

  • In the presence of magne7c forces the resonance frequency of the can7lever f0 is shiQed by an amount f propor9onal to the magne9c force ver9cal gradient. This frequency shiQ usually amounts to 1 50 Hz for can7levers having resonance frequency f0 ~ 100 kHz. These frequency shiQs can be detected and converted into the magne7c force gradient images.

    5. Electric force ( EFM ) imaging. Electric eld gradient imaging is analogous to standard MFM, except that gradients being sensed are due to electrosta7c forces. The can7lever resonance frequency changes in response to the electrical force gradient.

  • Arrac7ve forces make the can7lever eec7vely soQer, reducing the can7lever resonance frequency. Conversely, repulsive forces make the can7lever eec7vely s7er, increasing the resonance frequency, ( Fig. 16).

    Fig. 16

  • Literature 1. Mul7mode Scanning Probe Microscope Instruc7on Manual, Digital Instruments Inc., (1996). 2. Sarid D., Scanning Force Microscopy With Applica7ons to Electric, Magne7c, and Atomic Forces, Oxford Series in Op7cal Sciences (Oxford University Press, New York, 1991). 3. Chen G.Y., Warmack R.J., Huang A., and Thandat T., Harmonic response of near-contact scanning force microscopy, J. Appl. Phys. vol. 78, No.3, p.1465 (1995). 4. Ramirez-Aguilar K., Rowlen K., Tip characteriza7on from AFM images of nanometric spherical par7cles, Langmur, vol.14, No.9, p.2562 (1998).