Imaging high frequency dielectric dispersion of surfaces and thin films by heterodyne force-detected scanning Maxwell-stress microscopy

A

SURFACES

Colloids and Surfaces A: Physicochemical and Engineering Aspects 93 ( 1994) 359-373

Imaging high frequency dielectric dispersion of surfaces and thin films by heterodyne force-detected scanning Maxwell-stress microscopy Hiroshi Yokoyama, Mark J. Jeffery h#olrculur Physics

Section. Ekctrotechnicul

Laboratory,

l-l -4 fJme:ono.

Tsukubu

Ibaraki

305. Japan

Received 22 November 1993; accepted 19 February 1994

Abstract The design and performance of the heterodyne force-detected scanning Maxwell-stress microscope (HFD-SMM), a new tool for the microscopic observation of dynamic electrical phenomena at surfaces, are described. The HFD-SMM utilizes the non-linearity of the electric Maxwell stress with respect to the field strength which serves as a frequency mixer to create a low frequency heterodyne beat force from high frequency field components so as to make them observable even with a slowly responding cantilever. Combined with the tip-surface distance control based on capacitive forces, the HFD-SMM allows reliable dielectric-dispersion imaging at arbitrarily high frequencies, while carrying out simultaneous non-contact imaging of surface potentials and topography as in the original SMM. Images with clear frequency-dispersion contrast are presented for metal, semiconductor and polymer surfaces. Dielectric dispersion imaging: Dynamic electrical phenomena; Heterodyne force detection; Scanning Maxwell-stress microscopy

Keywords:

1. Introduction Dielectric spectroscopy, in its widest sense, is the study of voltage-charge relationships in electrodesample systems; it provides information about the dielectric constant, conductivity etc., and thereby about the underlying dynamical processes. The advent of scanning force microscopy (SFM) made it possible lo perform such studies for surfaces and thin films with an unprecedented spatial resolution ranging from submicron down to, hopefully, atomic and molecular dimensions [1.2]. Several non-contact force microscopy techniques have indeed been proposed so far for electrical surface imaging, and have been applied to electrostatic observations of dielectric constant [3]. isolated charges [4-6-j, insulating layer thickness [7] and 0927-7757/94/507.00 Q 199-I Elsevier Science B.V. All rights reserved SSDIO927-7757(94)01868-S

[8-131. The scanning Maxwellstress microscope (SMM) is a versatile electric force microscope, which, unlike its predecessors [3-93. relies only on the harmonic analysis of a.c.-voltage-induced oscillations of the cantilever under non-resonant conditions [ 10-14). The remarkable feature of the SMM is that it makes full use of the non-linear dependence of the electrical Maxwell stress on the field strength in all aspects of its functions. As shown below, it is this property that makes it possible to implement high frequency operations needed for dielectric spectroscopy [ 143. Knowing that SFMs depend on mechanical

surface potentials

deflection that they

of a cantilever,

one normally

suspects

would not be used for detection of high speed phenomena. Quite recently, however, it has

H. Yoko.wma.

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Surfuces A: Phwicochem.

been disclosed by a few research groups [ 14-173 that the non-linearity of the tip-sample interactions may resolve, partly at least, the apparent difficulty of limited time resolution of the SFMs, serving as a frequency mixer that allows downconversion of frequency to be observable even with a slowly responding cantilever. We designated this new scheme of force detection as heterodyne forcedetection (HFD) [ 143. We describe here the principle, design and performance of the HFD-SMM. and report on the first observations of high frequency dielectric dispersion images for metal. semiconductor and polymer samples. The dielectric dispersion arises from a variety of sources such as molecular dielectric relaxation, bulk and surface conductivity, etc. As such, the interpretations of some of the images remain as yet open; nevertheless. they clearly demonstrate the operational utility of the HFDSMM as giving a new dimension of frequency to electric force microscopy.

2. Heterodyne forcedetectcd SMM

Eng. Aspects 93 ( 1994) 359-373

where the z axis is taken along the direction in which the cantilever bends, dS, is the : component of the surface element on the tip, and co the dielectric permittivity of vacuum. The frequency mixing property of the Maxwell stress, from which all the functions of the SMM derive, can readily be appreciated from the above equation, clearly showing the quadratic dependence on the surface charge density. In order to illustrate the basic principle of the SMM and heterodyne force-detection for dielectric spectroscopy, to such an extent necessary for understanding the later demonstrations, let us adopt here a simple parallel capacitor model for the tip-sample system. A more general analysis is found in Ref. [ 143. Then, the above equation simply reduces to F:(r) =

$0 p(‘(t)S

where S denotes the electrode area. When L’(t) is a single component sinusoidal voltage with frequency w, i.e. V(t) = VAccos ot. the charge density on the tip electrode may be written as p,( f ) = pc + c(u)) v*c cos [or f $(w,]

In the SMM, an alternating voltage V(r) is applied to a conductive tip, separated by a gap of length d from the surface, and the resultant forced oscillation of the tip is detected in the same manner as in the atomic force microscope (see Fig. I). The forced oscillation involves not only the fundamental but also the higher harmonics of the applied voltage, each carrying specific information about the electrical and topographical properties of the sample. The electrical force acting on the conductive tip is given by an integral of the Maxwell stress tensor over its surface [ 181. At the surface of a conductor, the Maxwell stress takes an especially simple form owing to the absence of transverse field components. Then, in terms of the surface charge density p,(r:r,) at a point r, on the tip, we can write the force in question as

$f(r:r,)

F,(f) = i dtip

0

dS,

(1)

(3)

where C(Q) and 4(w) are, rcspcctively, the capacitance per unit area and the phase delay due to dielectric dispersion at this frequency. and pc denotes the charge density induced, for example. by the contact potential difference of the tip and the substrate, or more generally, by the surface potential and/or by isolated charged species in the sample medium. For simplicity, we assume pe to be static. Our present goal is to achieve imaging of c(w) on a reliable basis at an arbitrary frequency. In view of Eqs. (2) and (3). one would imagine that such imaging should be possible by observing the force component at twice the applied frequency, 20. This way was actually taken by Martin et al. [3] for detecting the presence of a dielectric layer on a silicon wafer. However, this direct method presents a serious problem when we wish to perform measurements at higher frequencies, because the cantilever does not respond beyond its resonant frequency R,,,. which normally lies at a few tens to hundreds of kilohertz. To resolve this difficulty,

H. Yokownta.

Lasar :

M.J. Je~ery/Colioia5

Surfaces A: Ph_vsicochem Eng. Aspects 93 (1994)

361

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‘..

.

III controllt3t

NanoScqe

/-A Scanner

0

DC , wg

Low Pass Filter

0 z-signal

x.y-signal Fig. I. Schematic dingrnm of the heterodyne

we use a rather more elaborate

force-detected

voltage wave-form

V(t) = I/AF(f) + VRr(r)

(4)

V*r;( t) = VW + Vocos 0,f

cos(u,

(5)

-

WP)f +

(6)

where V&(r) denotes a low frequency component made up of a dc. bias voltage Vuc and a sinusoidal voltage with frequency w~<
modulated

and

VRF repre-

which is actu-

wave form with the

frequency

w, >>RIe, and the modulation frequency 0, <
quency components Substitution

below R,,,,

F:(t) =

2 cos 0,r

+ M COS(U, + u&)1]

ally an amplitude

restrictions on

oO,

w,

and w,,

nents below R,,,. which greatly reduces the number

+MCOSclJ~r)COSQJ,t

= $ V, [M

(HFD-SMM).

of rclcvant force components. Then, collecting only those oscillrttitt~ components which have frequency

where

v,(l

the aforementioned

microscop

we can safely assume that the coupling between VAI: and V& dots not contribute any force compo-

than the above [ 143:

&r(t)=

scanning Maxwell-stress

at d.c., wo, U, and W, +a..

of V(r) in Eqs. (2) and (3) gives rise

to non-linear coupling between frequency components, thereby creating altogether fifteen sum- and difference-frequency components in the resulting force. By a proper choice of frequencies based on

we obtain

$(2b,, +C(O)~$,-]C(UJ&J 0 X COS[Wot + $C’(OJo)v;

+ &Jo)] COS[2tfJ,t

f

2&o,]

+ f V:M (c(w, - W&o,) x cos cw, t + Q(w,

I- Q(w,- q ,I

+ c(w,)c(o,+ 0,) XCOS [a, t + ‘&Jr+ QJa) +~v$bz’c(uJ,

-

#@Jr)]

1

tfJ~)C(W, + 0,)

X COS[2w,t+~(OJr+WO)-$(O~-W.)])

(7)

The third and fourth terms, coming from the internal coupling of V&t). are the heterodyne beat forces we seek. whereby high frequency capacitances can be approached

in terms of slow canti-

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H. Yokowmu. M. J. Je~ery/Colloidr Surfuces A: Physi~ochm. Eng. Aspects 93 ( 1994) 359-373

lever oscillations. Noting that o, BUJ,. we can further approximate these terms to obtain F:(t) = f

2CP, +

4O,b,l4%)b

0 I

x

ax

cue

+

+c2(too)v;

t +

$(w,

,I

cos[l~oot

+

2~(00)]

at +

UJ

&%J,)

=

&or 1

II

@(~fJr 1

hJ,f

+

2U4,-

&J,

(8) In principle, the oscillation amplitude and phase at either o, or ihu, give identical about dielectric at a~,. As this equation shows, however, the magnitude of the third term is always at least four times larger than that of the fourth term for the present wave form with 0 GM < 1. so that the third term is cxpcctcd to offer a bet&r signal-to-noise ratio. In what follows. therefore, we focus attention on the third term, omitting the fourth, although it dots exist and is certainly mcasurablc in reality. The first and the second terms arc utilized in the SMM to get information about the surface potential and the topography, rcspcctivcly. In particular, the control of tip-surface distance, which is obviously an indispcnsablc function in SFM. is achieved in the SMM in such a way that the amplitude of 2w,-oscillation is fixed at a certain value. Since ~((0,) scales as l/d and hence the amplitude at 2w, as I/rf’. the closer the tip is to the surface, the better the lateral as well as vertical resolutions: however, as will be mentioned in the next section, when the distance is extremely small, various short-ranged surface forces and hydrodynamic effects set in, and such a scaling relation breaks down. This mode of distance control is a unique function of the SMM and is a trcmcndous advantage for frequency-dispersion imaging. The capacitance to be measured is always a mixture of dielectric and geometric propcrtics of the sample-clcctrodc system. Consequently. in order to say something

about the dielectric properties alone, geometrical factors must be controlled in one way or another. As readily understandable in Eqs. (7) and (8). fixing the 20~ oscillation amplitude automatically insures that if the capacitance does not have a frequency dispersion, i.e. if c(Q,) = c((uo), the heterodyne beat oscillation also remains constant. This occurs because amplitudes at 2uo and CO, have the same quadratic dependence on their respective capacitances. So, the capacitance image taken by the HFD-SMM can be said to reflect faithfully the difference of dielectric properties at (u, and (11~. Finally. the surface potential of the sample is obtained basically from the observation of the (u. oscillation amplitude. There are two equivalent ways in the SMM to extract the surface potential. V,= -,1,/c(0): one is. as in the Kelvin method. to determine the VW that makes the (u. oscillation vanish by forming a closed feedback loop [S-IO], and the other. which is unique in the SMM. is to just measure the w,) amplitude [IO]. AS the 2too amplitude is fixed in the SMM. both methods give the same result in the abscncc of low frequency dispersion. cxccpt for a constant factor of difference in the latter.

The dctailcd design of the HFD-SMM is shown in Fig. I. It consists of a commerical atomic force microscope (AFM) (NanoScope 111, Digital Instruments) and some other external electronic components. The AF voltage, set at wo= 2n x 7.72 kHz here. is combined with a d.c. bias and is then fed to the substrate with the tip grounded through a low pass filter with I5 kHz cut-off frequency. The magnitude of the a.c. voltage is normally taken between I and 5 V (peak to peak), depending on the signal-to-noise ratio attained. The amplitude-modulated r.f. voltage is generated by a synthesized function generator (PMSl93, Philips) covering the frcqucncy range up to 50 MHz. The r.f. output is conncctcd to the tip and substrate through a high pass filter I50

H. Yokoyama. M.J. Je~ery/Colloids Surfaces A: Ph_vsicochemEng. Aspects 93 (1994)359-373

control the tip-surface distance in such a way that the 20~ amplitude is fixed at an externally given set-point value. In the actual circuitry, the error from this set-point value is amplified with a high voltage (HV) amplifier and is applied to the z-piezo scanner. Although this function may in principle be realized by the NanoScope controller, we prefer an external control, since it often happens in SMM observations that the z-feedback loop has to be quickly turned off while the tip is engaged, when the tip accidentally makes a direct confacr with the surface and ceases to oscillate. This occurs because, unlike scanning tunneling microscopy (STM) and AFM, the capacitive force scheme of tip-surface distance control is not absolutely stable in the sense that when the separation is reduced below a certain threshold level, the feedback becomes unstable. In other words, the stability of this scheme requires that the oscillation amplitude should be increasing when the separation is reduced. but this condition can not be met when the tip is so close to the surface that short-range surface forces such as steric repulsion and/or hydrodynamic damping forces become comparable to the electrical force. In operation, we monitor the occurrcncc of such an instability and, once it

modulation frequency was fixed at w, = 2x x 4.1 kHz and the modulation depth at M = 1. The NanoScope AFM head is used as provided by the manufacturer, except that the connection is interrupted between the head and the controller to extract the preamplifier output and to return the SMM height-signal in place of the original one. The alternating multicomponent voltage applied between the tip and the substrate causes oscillations of the cantilever at frequencies wO, 2to,, w, and Zw,. The former three components are detected with dedicated lock-in amplifiers. The amplitude and the phase of oscillation at the modulation frequency w, are led to an auxiliary input of the NanoScope III to form frequencydispersion images simultaneously with the topography or the surface potential. The amplitude of the we component gives information about the surface potential or isolated charges, and is either directly fed to an auxiliary input of the NanoScope III controller or once fed back to the AF generator to determine the I& that eliminates the oO amplitude, thereby giving a direct reading of the surface potential (Kelvin null method). The amplitude of the 2w, signal is used to

o.ol .

I

.

0

1

2000

.

I

4000

.

I

6000

Tip-Surface Distance Fig. 2. Oscillation

amplitude

vs. tip-surface

(peak to peak)) and the hctcrodync The &,

amplitude

is rcprcscntcd

363

.

I

.

6000

I

.

I,,,,

1000012000

(nm)

distance curves (force curves) for the second harmonic (LJ,, = 2n x 15.44 kHz, V, = 3.0 V w, = Zn x 4.1 kHz. V, = 1.0 V (peak to peak), AI = I) oscillations.

beat force (w, = Zn x 50 MHz.

by a solid line and is rcfcrrcd to the left ordinate

line and circles. and is refcrrcd to the right ordinate

axis.

axis. The w,, amplitude

is represented by shaded

364

H. Yokoyama. M. J. Je~ery/Colloids Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 359-3 73

happens, the z-feedback is turned off manually. the tip is detached from the surface and is made to approach again. From the operational point of view, this might seem a nuisance; actually, however, we believe this is one of the most crucial advantages of the SMM compared to other electric force microscopes. Thanks to this property, we can be quite confident under normal operating conditions that the tip is definitely away from the surface, quite free from ill-controlled surface processes. The phase of the second harmonic signal 4 offers an independent indicator of such an instability, by giving a hydrodynamic estimate of the tip-surface distance, d,, based on the following relation: tanQayo

mercially by Digital Instruments, were used after coating the tip surface with a platinum film by sputtering. The nominal spring constant of the cantilever is 0.58 N m-‘, and the resonant frequency lies at about 30 kHz. Under normal operating conditions, the time constants of the lock-in amplifiers are set at 10 ms, and the line scan rate is chosen to be smaller than 0.5 Hz to get meaningful data for each pixel.

3. Results and discussion 3.1. Force curve Fig. 2 shows the force curves for oscillations at 20~~ and w,. taken against a silicon wafer as a function of tip-surface distance. The r.f. frequency was 50 MHz and the amplitude was V, = 1.0 V (peak to peak). The AF frequency was 7.72 kHz and the amplitude was V, = 3.0 V (peak to peak). Despite the nearly four orders of magnitude difference in the driving frequencies, the two force curves almost exactly follow each other from distances larger than IO urn down to the point of direct contact located presumably below a few nanometers. This correspondence was found to be independent of the level of applied voltages, both AF and r.f., although the instability at the closest approach

(9)

where y denotes the friction coefficient for the cantilever motion which is given by

3s2

(10)

Y=L+w9

with q being the viscosity of air and ym the friction coefficient when the distance is infinitely large [ 193. This facility isof particular significance when a thick insulating layer is present on the substrate, in which case the topographic feedback based on the 2~0~amplitude often fails to work properly. Silicon nitride cantilevers, distributed com-

-132

4

-134

1.5 E

-136 -138

1.0 5 Y Z

E

-140 -142

0.5 -

a -144 o.ol -2000

.

I

.

0

I

2000

I

.

Tip-Surface Fig. 3. Amplitude

.

4000

I

6000

Distance

and phnsc ol the lwo oscillation.

.

I

8000

.

I

10

.

1_,46 12000

(nm)

The mcasuremcnt

conditions

are the same as Fig. 2.

H. Yokoyama, M. J. Jeflery/Colloiak Surfaces A: Physicochem Eng. Aspects 93 (1994) 359-373

365

Fig .4. (a) Non-comasct topography image taken by the HFD-SMM for a hydrogenated microcrystalline amorvphous silicon 2%: H) layer (dark region at right). partly covered with a 30 nm thick platinum film (bright region at left) (velrtical hullscale, nm: scan area. 5.017urn x 5.07 pm). (b) Simultaneously captured surface potential image (vertical fullscale. 500 mV ‘). Tip- -surface ance was fixed at about 30 nm: k’, = 3 V (peak to peak), w,, = Zn x 7.72 kHz and the scan rate was 3.3 s per line. The hump in the topography image represents platinum accumulated during the deposition on ac-Si : H through a proximity mask.

H. Yokoyama. M. 1. Jeffer_v’Colloids Surfaces A: Physicochem Eng. Aspects 93 ( 1994) 359-373

366

to the surface seemed to be slightly enhanced with voltage increase. The shape of the force curve reflects mostly the geometry of the tip-surface system as clear from the quasi-static formula FE--

vzSC

where C is the total capacitance of the tip. As the tip approaches the surface, the observed amplitudes increase gradually. when the distance is larger than 100 nm, while they show a steep increase when the distance is reduced below 30 nm. The distance dependence observed at large separations is much slower than the l/d2 dependence expected from the parallel capacitor model. This behavior is caused by the rather blunt shape of the pyramidal tip used, typically of size a few microns. As the tip approaches the surface, the contributions from the tip apex become relatively more important, and finally, when the tip-surface distance becomes comparable to the radius of curvature of the tip apex, it begins to behave practically as a parallel plate capacitor showing the i/d* dependence. In the present case, we observed a markedly incrcasing behavior below about 30 nm, which indicates that the tip apex should be of this size. In particular, the fact that this trend is independent of frequency implies that the tip surface is sufficiently conductive up to the tip apex for the surface charge distribution to remain the same regardless of the frequency. The phase of the 20, oscillation was also measured as a function of the tip-surface distance (Fig. 3). As can be clearly seen, as the tip approaches the surface, the phase undergoes a concomitant decrease, and just as for the amplitude, it exhibits an extremely sharp drop in the vicinity of the surface. This confirms the validity of Eqs. (9) and (lo), and states that for the silicon surface used, the hydrodynamically detected sur-

view of frequency-dispersion

imaga

(c) CO,= 2n x 130 kHz for the platinum/pc-Si: the oscillation

amplitude.

at 0.7 nm. Other

taken

H boundary

As a first example of frequency-dispersion imaging, we selected a rather straightforward case of frequency dispersion caused by surface conductivity. The sample we prepared is a 700 nm thick film of hydrogenated microcrystalline amorphous silicon (~c-Si : H) deposited on a glass microscope slide, which has a surface conductivity of about lo-‘R-l. To make a well-defined conductivity distribution over the surface, suitable for imaging, the surface of the pc-Si : H tilm was partly covered with a 30 nm thick platinum film by sputtering. Fig. 4(a) shows the non-contact topography image of the boundary between the platinum film (left half) and the bare pc-Si : H surface (right half), taken by the SMM. At the boundary is a hump of platinum as tall as 50 nm, making this a rather challenging sample to test the interference between topography and other properties to be imaged. Fig. 4(b) shows the surface potential image, which was taken simultaneously with the topography. From this figure, we see that itc-Si: H has a higher surface potential, due probably to the contact potential difference, about 300 mV higher than that of the platinum film. Since the tip is also covered with platinum, the absolute value of V, was found to be nearly 0 mV within experimental error for the platinum film. There is no noticeable structure in the surface potential corresponding to the platinum hump at the boundary. We then took high frequency capacitive force images by the HFD-SMM for the same part of the sample (Fig. 5). At 50 MHz, we observed a dramatically reduced oscillation amplitude over the

by the HFD-SMM

(b) w, =2~

contrast corresponds

obscrvcd topography

x

I

MHz,

and

to a 0.5 nm difference in

(also top view). The beat amplitude

frequency of (9). = 2x x 4.1 kHx and the r.f. voltage level was chosen to set the average beat oscillation

imaging conditions

the r.f. frequency is incrcascd.

at (a) U, = 2x x 50 MHz,

(right half). The maximum

The lch halC image shows the simultaneously

was detected at the modulation amplitude

3.2. Boundary between amorphous silicon and platinum thin film

(11)

2 ad

Fig. 5. Top

face :ispractically identical with the electrical working surface as far as the SMM observation is concerned.

arc the same as in Fig. 4. Note that clear frcqucncy-dispersion

contrast emerges as

H. Yokoyama. M. J. JefleryiColloia!s

Fig. 5. (Caption

opposite.)

Surfices A: Physicochem.

Eng. Aspects 93 ( 1994) 359-373

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Fig. 6. (a) Non-contact topograp&.image~ken by the HFD-SMM for a microfabricated tungsten square (50 nm thick, 6 pm x 6 pm) on silicon wafer (vertical fullscale, 200 nm; scan area, 10 pm x 10 pm). (b) Simultaneously taken surface potential image (vertical fullscale. 100 mV): tip-surface distance was fixed at about 30 nm. If, = 3 V (peak to peak), w,, = 2x x 7.72 kHz and the scan rate is 5 s per line.

pc-Si: H region, obtaining a clear contrast across the boundary (right half of Fig. 5(a)). As the frequency was lowered. the contrast was rapidly lost, finally becoming almost indistinguishable at the

frequency of 130 kHz (right half of Fig. 5(c)). This result clearly demonstrates the occurrence of frequency dispersion. It should be emphasized, however, that the loss of amplitude contrast at low

H. Yokowma.

M. 1. Jeffqv/Colloids

Surfaces A: Physicochem.

of dielectric response at w, from that at wO where the distance control is carried out. The source of the observed frequency dispersion may be simply understood as coming from the low

frequencies does not necessarily imply the absence of frequency dispersion in this frequency region; rather, this may be, first of all, a consequence of the fact that we are measuring the relative change

Fig. 7. Frequency-dispersion on silicon w&r

(vertical

images taken by the HFD-SMM

fullsc~lc.

I

nm). The beat amplitude

at (a) OJ,= Zn x 50 MHz_ (b) w, = 2n x 130 ktiz was detected at the modulation

the r.f. voltage level was chosen IO set the average beat oscillation in Fig. 6.

369

Eng. Aspects 93 ( 1994~ 359-373

amplitude

at 0.7 nm. Other

for a tungsten square

frcqucncy of CU.= Zn x 4.1 kfld and imaging conditions

are the same as

. H. Yokowma.

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93 ( 1994) 359-373

Fig. 8. Non-contact topography image taken by the HFD-SMM for platinum-coated Nuclepore membrane having I )tm diameter ports (vertical fullscalc. 200 nm; scan area, 4 pm x 4 pm). Tip-surface distance was fixed at about 30 nm. V, = 3 V (peak to peak). q, = ?n x 7.72 kHz and the scan rate is 5 s per line.

surf&c

conductivity of @ji: H. In general, a the SMM as a resistor through which the tip capacitance is charged. As a result, there must always be a series resistor-capacitor (RC) type relaxation, although the actual relaxation frequency will vary greatly depending on the value of conductivity. Referring to Eq. ( 1I ), we can estimate the tip capacitance by integrating the force curve in Fig. 2. With the spring constant 0.58 N m-’ listed by the manufacturer, we then obtain Cz4 x IO-” F for the present tip. The effective resistance the tip feels can also be easily estimated by assuming a two-dimensional current Row in a semi-infinite plane bounded by an ideal sink (which is meant to model the platinum film). Denoting the typical radius of the tip-sample interaction area by r, the separation of its center from the line sink by h, and the surface conductivity by 6. the etTective resistance is given by [20] sample

R, = -&

acts iii

In [k/r + (h’/r2 - I )*/‘]

(12)

Then. by substituting relevant values, we see that the relaxation frequency fc = I/(2nR,C) is of the

order of 10 MHz or less, supporting the present observation. Eq. (12), furthermore, indicates that the rclaxation frequency shows an appreciable change only when the separation h moves several multiples of r. As the above argument shows, the relaxation frequency is responding to the entire tip capacitance, not to its gradient as in topography imaging. In view of the gradual decay of the force curve as shown in Fig. 2, we can conclude that the major contribution to the tip capacitance is made by the base part of the tip, so the above mentioned effective interaction area should extend over the whole tip area. This explains why the frequencydispersion images shown in Fig. 5 are much less space resolved compared to the topography or even to the surface potential images. 3.3. Tungsten film on silicon wr$er We also made HFD-SMM observations of a sample made up of highly conductive materials to avoid the influence of the series RC-type frequency dispersion shown above. The non-contact topogra-

H. Yokoyawia. M. J. Jeffery/CoNoidTSurfaces A: Physicodem Eng. Aspects 93 ( 1994) 359-373

371

Fig. 9. Frequency-dispersion images taken by the HFD-SMM at (a) w, i 2n x 50 MHz and (b) W, = 2n x 130 kHz for platinumcoated Nuclepore membrane (vertical fullscale: (a) 0.6 nm; (b) 0.2 nm). The beat amplitude was detected at the modulation frequency of W, = 2n x 4.1 kHz and the r.f. voltage level was chosen to set the average beat oscillation amplitude at 0.7 nm.

phy of the sample surface is shown in Fig. 6(a). The sample is a microfabricated structure comprised of a 6 pm x 6 pm area, 50 nm thick tungsten square film on a silicon wafer. The surface potential

structure, due also to the contact potential difference, is also clearly visible as shown in Fig. 6(b) with the potential on the tungsten area being about 20mV lower than that on the silicon surface. In

372

H. Yokoyuna. ht. J. Jrflery/Colloidc Surfaces A: Physicochem. Eng. Aspects 93 ( 1994) 359-373

the topography image, we can also see submicronsize string-like objects, which have also been confirmed to exist all over the processed area by scanning electron microscopy and are ascribed to etching remainders of tungsten grain boundaries. As shown in Fig. 7(a), the results of HFD-SMM observation of this sample showed, somewhat unexpectedly, a frequency-dispersion contrast at 50 MHz with a fairly good correspondence with the base structure of the sample. The frequencydispersion contrast was found to disappear rapidly as the frequency was reduced and it became virtually undetectable at 130 kHz. The mechanism for producing such a frequency dispersion is not clear at the present stage, though it might well be suspected that properties of the metal-semiconductor interface are playing some role, giving rise to temporary structures such as those inferred by isothermal capacitance transient spectroscopy. 3.4. Metal-coated

porous polymer membrane

Finally, we present an observation of a polymeric sample. We used a porous polycarbonate membranc {Nuclepore filter) having 1 urn diameter pores. To make the surface sufficiently conductive to allow SM M observations, we applied a platinum coating over the membrane surface to the thickness of 20 nm by sputtering. The membrane was then glued on a piece of chromatography paper placed on a glass slide by applying 1 wt.% aqueous solution of polyvinylalcohol (PVA). The chromatography paper prevents an excessive amount of PVA solution from remaining in the membrane and eventually clogging the pores. Fig. 8 shows the non-contact topography image of the porous membrane. The pores are clearly imaged with the correct size of 1 urn diameter. Simultaneously taken frequency-dispersion images are shown-in Fig 9. As expected, no visible structure emerged at w, = 27t x 130 kHz (Fig. 9(b)). At 50 MHz, however, we obtained an image with a clear dispersion contrast, revealing good correspondence with the pore positions (Fig. 9(a)). Although it is difficult to identify the underlying mechanism of the observed frequency dispersion, the molecular relaxation of polymers or the contribution of surface conductivity inside the pores

might be a plausible candidate, since the pore walls are thought to be left uncovered with platinum.

4. Conclusions We have described the principle, design and performance of the heterodyne force-detected scanning Maxwell-stress microscope (HFD-SMM), and reported for the first time the frequencydispersion images for a variety of samples. In particular, non-contact conductivity imaging was successfully performed for the boundary of a platinum film and an amorphous silicon layer. Additional preliminary observations performed on a microfabricated metal/semiconductor sample and on a metal-coated porous polymer membrane also exhibited characteristic frequency-dispersion images, though their interpretation is as yet an open question. Local motion of molecules and charges is an important subject in the complete understanding of every colloidal and surface phenomenon. We believe the HFD-SMM will be a powerful realspace analytical technique to explore this intriguing field.

Acknolwedgments

The authors wish to thank Dr. J. ltoh for invaluable assistance in microfabrication. Dr. S. Yamasaki for amorphous silicon samples, and Dr. T. Inoue for helpful discussions.

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