High ..resolution capacitance measurement and potentlometry by force microscopy Yves Martin. David W. Abraham, and H. Kumar Wickramasinghe IBM Research Division, T. J, Watson Research Center, P. O. Box 218, Yorktown Heights, New York 10598
(Received 1 December 1987; accepted for publication 26 January 1988) We demonstrate the usefulness and high sensitivity of the atomic force microscope (AFM) for imaging surface dielectric properties and for poientiometry through the detection of electrostatic forces. Electric forces as small as 1O~ 10 N have been measured, corresponding to a capacitance of 10- 19 farad. The sensitivity of our AFM should ultimately anow us to detect capacitances as low as 8 X 10- 22 F. The method enables us to detect the presence of dielectric material over Si, and to measure the voltage in a p~n junction with submicron spatial resolution.
The inventi.on of the atomic force microscope l (AFM) has provided the ability to profile insulators with unparalleled resolution. In our version of the AFM, 2 we accurately position a sharp tungsten tip within 50 A of the surface ofa sample by detecting the short-range Van der Waals force in the attractive regime. We have already demonstrated that the AFM with optical heterodyne detection can profile with 50 A resolution, 2 and can map, using a magnetic tip, domain structure in magnetic media.3,4 Here we show that the technique also allows the independent measurement of electrostatic forces with a high sensitivity and a spatial resolution of better than 1000 A. When a voltage is applied to the tip of the AFM, a force appears, 5 due to the separation-dependent capacitance between the tip and sample, of the form (1)
The capacitance can be inferred from an observation of the reduction in osci.Ilation amplitude versus tip-sample spacing z [which specifies the force gradient f' (z)], or by optical detection of the voltage-induced oscillation of the tip (giving a direct measure of force) . In Fig. 1 we plot the measured force versus separation for a grounded Si sample with de voltages ofO, 1.5, and 9 V applied to the tip. The capacitive force is detected at separations as large as 50 nm, and is dominant for separations greater than a few angstroms. The dotted lines represent the calculated force obtained by modeling the capacitance as two parallel plates of area (0.14 ,um)2, giving a minimum detected capacitance of 10- 18 F. The discrepancy offit in the 9 V data is due in part to the fact that the feedback loop was open during the measurement, and also to the simplicity of the model usedo However, it should be possible to measure force versus separation for dc tip bias voltage with the loop closed in order to improve the fit to the calculated curve. The ultimate sensitivity of this measurement can be derived as follows: the AFM can detect2 a force gradient as small as 3 X 1O~6 N/m, which corresponds to a minimum detectable second derivative of the capacitance 2Cm ,n loz = 2f'minIV2, obtained by differentiating 0). In a parallel plate capacitor of cross-sectional area A and dielectric constant E, the force gradient is given by f' = C 3 V 2/(EA)2.
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Appl. Phys. Lett. 52 {i 3),28 March 1988
Thus, solving for the minimum detectable capacitance, we find Cmin
= [I'min (
VEA )2]1/3
(2)
The model of a sphere and a conducting planetl yields the same dependence of capacitance on spacing z as the paranel plate model, for z much larger than the diameter of the tip, and gives the sensitivity described in (2) if A is replaced by the surface area of the hemisphere at the end of the tip. For an area of (O.l~m), E/Eo = 1, and 25 V bias, we estimate a sensitivity to capacitance for de measurement of 4 X 10-- 20 F, corresponding to a tip-to-surface spacing as great as 2.5 /lm.
A more convenient method for the measurement of the tip-sample capacitance is to apply an ac voltage at a frequency lU I to the tip, and detect the induced osciHation with the interferometer. In this experiment, the gap spacing z was 12.0 x 10-9
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FIG.!. Measured force (solid line) and calculated force (broken line) versus tip-sample separation. Data are presented for de tip voltages of 0, 1.5, and 9 V. The feedback loop was open during the measurement.
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@ 1988 American Institute of Physics
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FIG. 2. ac electric force inferred from induced tip oscillation {solid line) and model values calculated for parallel plate capacitor model (broken line), vs tip-sample separation. The induced vibration amplitude ranged from 0.1 to 5 A.
fixed by the feedback ioop, and was adjusted by changing the set point which determined the oscillation amplitude at the resonant frequency W o, thereby increasing the stability of the measurement. In Fig. 2 we plot the measured capacitive force versus separation for a tip bias of 2.5 peak-to-peak and a frequency of 40 kHz, well below the first resonant frequency of 109 kHz. The force amplitude equals the oscillation amplitude divided by the spring constant k, estimated from scanning electron micrographs to be 19 N/m for this tip. Also plotted in Fig. 2 is the theoretical force versus separation for the parallel plate capacitor mode!, showing good agreement between experiment and theory. Very small capacitances can be detected by choosing the frequency of the bias voltage WI to be at a tip resonance (different from that used in the feedback loop), increasing the induced oscillation amplitude by Q. The minimum detectable oscillation is limited by the thermal excitation of the beam which causes an average motion 2 at a frequency w, of N .~·~4kB TQB lk,w 1 for temperature T and bandwidth B. Setting the signal-to-noise ratio to unity, we obtain
frequency UJI = 35 MHz, and Q = 200, the minimum detectable capacitance in a 1 Hz bandwidth at room temperature is 8X 10- 22 F. This sensitivity is comparable to that of the scanning capacitance microscope,s but with enhanced resolution. For both de and ac detection the signal only depends on that portion of the capacitance which varies with the gap spacing, which can be orders of magnitude smaller than typical stray capacitances. The ac method has the dear advantage, however, that it provides independent measures of capacitance and topography simultaneously. With the feedback loop closed, the tip traces contours of constant force gradient. 3 The capacitive force is detected at a frequency 2w 1, outside of the bandwidth of the feedback loop. The measured topography will change slightly to reflect the de contribution of the bias voltage VI cos(w!t) to the force gradient aj' = !Vr ae /az. For sman bias voltage Vi' the topographic image will not change appreciably, and new sample properties and topography can be measured simultaneously and independently. We now consider two ways in which changes in the induced amplitude of oscillation can be related to variations of sample properties. Referring to ( 1), either a change in BC loz, and therefore dielectric constant € of the material between the tip and the conductive portion of the sample, or in bias voltage VI' will cause a change in driving force, and hence in amplitude of oscillation. The images in Figs. 3(a) and 3(b) are the topography and electric field-induced tip oscillation amplitude, respectively, of the edge of a photoresist line on a Si wafer. The tip was biased with a voltage of 0.2 V peak-to-peak at a frequen-
oCmin
(16k B TBk)1I2 (3) V 4 Qw! The sensitivity for ac detection is thus expressed in terms of the first derivative of the capacitance, rather than the capacitance itself. For a paranel plate or a sphere-plate capacitor taken as previously, whereoC laz = C 2 1t?A, we find the minimum detectable variation in capacitance to be --=
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= (16kBTB(€A)2k)J/4 V 4 QUJ
(4) 1
For a Si beam 7 with spring constant k 1104
= 2,5 N/m, resonant
Appl. Phys. Lett., Vol. 52, No. 13,28 March 1988
(b)
FIG. 3. (a) Topography and (b) capacitive signal for photoresist on Si. Left half of image is covered with 1 ~m of photoresist, while right half is bare Si. Contrast in (0) is due to change in capacitive gradient ac I Jz. Martin, Abraham, and Wickramasinghe
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FIG. 4. (a) Topography and (b) capacitive signal on a pn junction of a commercisJ transistor. Schematic illustration of the biased junction is shown. Total range in height in (a) is 200 A, and the junction appears only weakly as a change in slope. (Note difference in vertical and horizontal scales.) In (b) the junction is revealed by an abrupt change in signal due to the voltage drop in the reverse-biased junction.
cy of 210 kHz. The difference between the induced oscillation over the coated and bare Si is due to the increase in capacitive gradient ac laz in the latter case. The tip radius and the dielectric constant of the photoresist largely determine the capacitance while the thickness of the photoresist plays only a minor role, due to the relatively large fringe fields near the tip. A rough estimate of the ratio of ac I az over photoresist-coated and bare 8i, which models the tip, photoresist layer and conducting sample as concentric spheres, gives order-or-magnitude agreement with the observed ratio of 0.6. The drop in capacitive signal over the sloping portion of the photoresist is due to geometric effects.
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Appl. Phys, Lett., Vol. 52, No. i 3,28 March 1968
An accurate measurement of the dielectric constant would require an independent determination of the tip-tosample spacing in order to provide calibration. However, for fiat and uniform samples, comparison can stm be made between regions of differing dielectric constant. The technique can also be used to map spatial variation of voltage on the sample. Potentiometry oftnis sort has been done with the tunneling microscope,9 but is limited to samples with the conductive path exposed in order to allow tunnel current to flow. We have performed measurements on the junction region of a commerical transistor. IV In Figs. 4(a) and 4(b), respectively, are topography and capacitive signal obtained over the emitter-base junction, reverse biased with a de voltage of7 V and an ae component of2.5 V pp. The capacitive signal shows an abrupt change in amplitude, attributable to a spatially localized drop in voltage across the junction. The quantitative interpretation of the image in Fig. 4(b) as voltage is difficult, since the sample, a semiconducting device, is nonlinear, and additionally is coated with a passivation layer of unknown thickness, dielectric properties and which may contain trapped charge. However, systematic analysis on a well-characterized sample should yield more quantitative data. We have shown that the AFM can accurately detect electric forces, corresponding to capacitances as low as 10- 21 F. This sensitivity can be used to image variations in the sample dielectric constant, as wen as perform potentiometric measurements on passivated conducting samples. We thank C. C. Williams for many useful discussions and comments.
10. Binnig, C. Quate, and Ch. Gerber, Phys. Rev. l.ett. 56, 930 (1986). Martin, C. C. Williams, and H. K. Wickramasinghe, J. App1. Phys. 61,
2y'
4723 (1987).
3y. Martin andH, K. Wickramasinghe. App!. Phys. Lett. 50,1455 (1987). ·Y. Martin, D. Rugar, and H. K. Wickra.:nasinghe, Appl. Phys. Lett. 52, 244 (1988), 5G. M. McClelland. R. Edandsson, and S. Chiang. in Review ofProgress in Quantitative Nondestructive Evaluation, edited by D. O. Thompson and D. E. Chimenti (Plenum, New York, 1987). Vo. 6B. p. 1307. 6p, Lorrain and D. Corson, Electromagnetic Fields and Waves, 2nd ed. (Freeman, San FrancEsco, 1970), p. 150. 7T. Albrecht and C. Quate, STM'87 Conference Proceedings, J. Vac. Sci. TechnoL A 6,271 (1988). 8J. R. Matey alld J. Blanc, J. Appl. Phys. 57, 1437 (1985). "p, Muralt and D. Pohl, App\. Phys. Lett. 48. 514 (1986). IOMeasurements were made on an npn power transistor, mode12N3439.
Martin, Abraham, and Wickramasinghe
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