Measurement of hardness, surface potential, and charge
Transcript Of Measurement of hardness, surface potential, and charge
REVIEW OF SCIENTIFIC INSTRUMENTS
VOLUME 70, NUMBER 3
MARCH 1999
Measurement of hardness, surface potential, and charge distribution with dynamic contact mode electrostatic force microscope
J. W. Hong, Sang-il Park,a) and Z. G. Khimb) Department of Physics and Condensed Matter Research Institute, Seoul National University, Seoul 151-742, Korea
͑Received 21 August 1998; accepted for publication 30 November 1998͒
Dynamic contact mode electrostatic force microscopy ͑DC-EFM͒ was developed as a new operation mode of scanning probe microscope ͑SPM͒. By operating EFM in a contact mode with an ac modulation bias, we have improved the spatial resolution and also achieved a complete separation of the topographic effect from other electrostatic force effect overcoming the mixing problem of a topographic effect with other electrostatic effects frequently encountered in the conventional noncontact EFM measurement. DC-EFM can be utilized either as a force microscopy for the surface hardness, or as a potentiometry for the surface potential distribution, or as a charge densitometry for the surface charge density study. This is also applicable to the measurement and control of the domain structure in ferroelectric materials that have a bound surface charge. © 1999 American Institute of Physics. ͓S0034-6748͑99͒01703-7͔
I. INTRODUCTION
Scanning probe microscope ͑SPM͒ has matured and developed into a routine instrument for the investigation of the surface topography of insulating as well as conducting samples with an atomic resolution. Recent efforts have revealed a much broader potential for the measurement of local mechanical properties1 and electrical properties such as surface potential,2–4 surface charge,5,6 and ferroelectric domain7–9 by electrostatic force microscope ͑EFM͒.
Earlier force modulation microscopy ͑FMM͒ was achieved by applying a small mechanical sinusoidal force on the surface when the tip was close to the sample.1 Unfortunately, in the earlier FMM technique, either sample or probe cantilever is vibrated with a mechanical transducer. In either case, the mechanical transducer has a rather poor amplitude versus frequency response of the probe usually exciting several unwanted modes of vibration and noise. To avoid this problem, we have successfully employed tapping mode using an electrostatic force modulation technique10 for the study of the surface morphology by applying an ac modulation signal to the tip instead of the mechanical modulation force using a bimorph.
Conventional EFM is usually operated in a dynamic noncontact mode,11 where the change of the vibration amplitude due to a force gradient is used to detect the variation of the force gradient due to either topography or other interactions. Therefore, in the dynamic noncontact EFM, it is difficult to separate the effect of topography from that of the other origin. For example, abrupt changes in the surface potential and surface charge on the sample surface produce a large electrostatic force gradient. In such cases, the probe tip cannot follow a true topography but a force gradient contour
a͒Present address: PSIA Corp., Daelim Bldg., Seocho-dong 1600-3, Seoul 137-070, Korea.
b͒Electronic mail: [email protected]
including the electrostatic force gradient as well as van der Waals force gradient. Such a mixing of force gradients causes successive errors in measuring the electrical properties of the sample. In addition, the noncontact mode operation is rather complicated and its spatial resolution is significantly reduced compared to that of the contact mode operation, since the tip is far away, approximately 10 nm, from the surface.
We have overcome the problems of the conventional operation mode of EFM, and have successfully obtained images of surface topography, surface potential, and surface charge distribution by operating EFM in a contact mode with an ac electrostatic modulation, which we termed as dynamic noncontact mode EFM ͑DC-EFM͒12 to distinguish it from the conventional noncontact mode EFM.
In this report, we will explain the detection principle of DC-EFM for the measurement of the surface hardness, surface potential distribution, and surface charge density. Ferroelectric domain image obtained by DC-EFM is compared with that obtained by the conventional noncontact operation of EFM.
II. DETECTION METHOD
In DC-EFM, a contact mode atomic force microscope ͑AFM͒ is employed to maintain the tip-sample distance constant. A dc and ac bias voltage is applied between the conductive probe tip and sample in the contact mode. The probe tip used in this work is a heavily doped Si ͑doping level is 1019– 1020/cm3͒ with a spring constant kϭ1.9 N/m and a typical tip radius Rϭ20 nm. An insulating layer on the probe tip such as native oxide layer prevents electrical current flowing between the tip and sample.
The idea behind DC-EFM operation is, first, to utilize the sustained vibration of the cantilever even in the contact state, when an ac electrostatic modulation signal is applied to the tip. That is, even when the tip is in contact with the
0034-6748/99/70(3)/1735/5/$15.00
1735
© 1999 American Institute of Physics
1736 Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
Hong, Park, and Khim
FIG. 1. Schematic diagram of DCEFM. With the lock-in amplifier feedback off, output of lock-in amplifier can be used for the detection of surface potential or surface charge density. For the estimate of the absolute value of surface potential or the surface charge density, one can measure the lock-in feedback signal that controls Vdc such that the amplitude of component ͑lock-in amplifier output͒ vanishes.
sample surface, there still remains a finite vibration amplitude of the probe tip. The sustained vibration of the tip in a contact state was already confirmed in the force microscope.1 Then even in the presence of a strong atomic force in the contact mode, a weak electrostatic interaction between tip and sample surface can be detected by a lock-in technique. Second, by applying a bias to the tip one can for example control the induced charge on the tip, which in turn generates an additional controllable force between the tip and charged surface. Therefore we can simultaneously measure the topography and other electrostatic interaction effect such as surface potential or surface charge density with DC-EFM.
The general equation describing the force between the tip and sample at a surface position r in the presence of surface potential or surface charge density includes atomic force, capacitive force, and Coulombic force between the charge induced on the tip and sample surface charge:
F͑ r͒ϭFa͑ r͒ϩ1/2ץC͑ r͒/ץzV2ϩEs͑ r͒qtip .
͑1͒
Here, Fa represents the repulsive atomic force on the tip. In the capacitive force term, ץC/ץz is the gradient of capaci-
tance between tip and sample, which depends on the tip-
sample geometry. The potential V between the tip and
sample surface may contain external dc bias Vdc and ac bias Vac cos t as well as the sample surface potential Vs . Es(r) and qtipϭC(VdcϩVac cos t) represent the electric field gen-
erated by the surface charge density of the sample and the
charge induced on the tip, respectively.
With Vϭ(VdcϪVsϩVac cos t) and ϩVac cos t), the force on the tip reduces to
q tipϭ C ( V dc
F͑ r ͒ϭFa͑ r ͒ϩ1/2ץC͑ r ͒/ץz͑ VdcϪVsϩVac cos t ͒2
ϩEs͑ r ͒C͑ r ͒͑ VdcϪVsϩVac cos t ͒
ϭ͓Fa͑ r ͒ϩ1/2ץC͑ r ͒/ץz͑ VdcϪVs͒2
ϩ1/4ץC͑ r ͒/ץzVa2cϩEs͑ r ͒C͑ r ͒͑ VdcϪVs͔͒
ϩ͓ץC͑ r ͒/ץz͑ VdcϪVs͒ϩEs͑ r ͒C͑ r ͔͒Vac cos t
ϩ
1/4
ץ
C
/
ץ
z
V
2 ac
cos
2
t
.
͑2͒
Since DC-EFM is operated in the contact mode, the dc component of the force ͑static deflection of the cantilever͒ is adjusted by the z servoloop such that the strong repulsive atomic force between tip and surface is maintained constant. Thus, the dc component provides the topographic image as in the conventional contact mode operation of AFM. On the other hand, the detection of the component, ͓ץC/ץz(Vdc ϪVs)ϩEsC͔, can provide information about Vs or Es depending on the experimental situation.
Now if the sample surface is not sufficiently hard and has variations in its hardness, then the surface may have certain compliance due to electrostatic force modulation. Therefore a strong electrostatic force can drive the probe tip to vibrate by indenting the sample surface. The vibration amplitude will depend on the surface hardness and the strength of the electrostatic force. In this case, the capacitance ͑or the gradient of the capacitance͒ between the tip and sample will show a dependence on the surface hardness. We can write the relationship between the hardness and relative amplitude of the tip vibration as follows:
F͑ r, ͒ϭkeff͑ r, ͒z͑ r, ͒,
͑3͒
where z(r,) represents the amplitude of the tip vibration at a position r caused by the electrostatic force F(r,). Thus in the absence of surface charge or potential distribution on the sample, we can approximate the electrostatic force to be constant over r. Furthermore, by keeping the ac and dc bias at a constant value, we can determine the variation of the effective mechanical hardness keff by measuring the component of the electrostatic vibration,
keff͑ r, ͒ϭF͑ r, ͒/z͑ r, ͒.
͑4͒
The lock-in amplifier was used to measure the vibration amplitude and phase of the probe at frequency . During this measurement, the dc part of the force is taken as the feedback signal to maintain a constant height in the contact mode operation thus avoiding any mixing of the topographic effect with the surface hardness effect.
Figure 1 shows a schematic diagram of the DC-EFM. The signal from the topographic feedback controller ͑z ser-
Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
Hong, Park, and Khim 1737
FIG. 2. Topography ͑a͒ and force modulation ͑b͒ image of a sample surface. Two hard GaAs regions are separated by a soft epoxy. The vibration amplitude at frequency force is much higher in soft epoxy than one in hard GaAs region.
vocontroller͒ that is to maintain the tip-sample height constant can be employed to image the surface morphology. With the feedback controller II off, the output of lock-in amplifier can be used for the detection of surface potential or surface charge density. For the estimate of the absolute value of surface potential or the surface charge density, one can measure the feedback controller II signal that controls Vdc such that the amplitude of component ͑lock-in amplifier output͒ vanishes.
III. EXPERIMENTAL RESULTS
As an example of DC-EFM, operation for the mechanical hardness measurement, images of the GaAs/epoxy/GaAs multilayer were taken by DC-EFM. Two GaAs wafers are glued together by a soft epoxy layer at the center. Figure 2 shows topography ͓Fig. 2͑a͔͒ and hardness ͓Fig. 2͑b͔͒ images obtained simultaneously for a polished surface which has regions of different mechanical hardness. In this measurement, applied dc bias, amplitude of ac bias, and frequency were 1 V, 5 V, and 40 kHz, respectively. Topography image barely reveals three separated regions of GaAs– epoxy–GaAs layers. However, the image obtained by the component clearly shows three distinctively separated layers. Because the central epoxy region is softer than both sides of the GaAs region, the amplitude of probe vibration at frequency in epoxy region is larger than the one in GaAs region. Thus the component of the tip vibration due to an electrostatic force in DC-EFM reflects the local mechanical hardness of a sample surface.
There are advantages of using DC-EFM for the mechanical hardness measurement compared to the earlier FMM technique using a bimorph driven mechanical modulation. In the FMM mode, the mechanical modulation usually generates several vibration modes of the microscope system, which can cause some ambiguity in the measurement. However the electrostatic modulation vibrates only the cantilever without shaking the entire part of the scanning or supporting cantilever system. Thus, we can get a clean vibration spectra. As a result, DC-EFM can prevent mixing or coupling of a main signal with unwanted noise sources.
Now if there is a surface potential distribution Vs on the sample surface but in the absence of surface charge density, the component in Eq. ͑2͒ reduces simply to ץC/ץz(Vdc ϪVs). Therefore DC-EFM can be operated as a potentiom-
FIG. 3. Topography ͑a͒ and surface potential ͑b͒ image of an integrated test chip where one set of the trace is biased at ϩ1 V and the other set of the trace is biased at Ϫ1 V.
etry by detecting the component in the presence of a surface potential Vs(r) such as a pn junction or signal line in the integrated circuit. In order to measure the absolute value of the surface potential, a feedback loop is used to adjust the dc bias of the probe (Vdc,p) such that the vibration amplitude of the component vanishes.3,4 In this situation, the applied dc bias voltage to the probe is equal to the surface potential. An example is shown in Fig. 3, the topographic ͓Fig. 3͑a͔͒ and surface potential ͓Fig. 3͑b͔͒ image of a test pattern, where one set of the trace is biased at ϩ1 V and the other set of the trace is biased at Ϫ1 V. A thin SOG layer was covered on the top of the sample surface. Thus we can assume that the surface hardness is uniform through the entire surface. In the topographic image, two metal lines ͑bright region͒ are separated by the etched insulating region. From the surface potential image, we can find that the line profile of the potential is changing linearly across the etched region as expected. The resolution of this potentiometry is about ϳ20 mV.
In another case, if the sample surface has a bound surface charge density b , the electrostatic force is given as a sum of a capacitive force and Coulomb force between tip and sample. Since the probe tip-sample distance is very short in contact mode operation, one can approximate the effect of the bound surface charge density by a uniform surface electric field Es . If the area of the bound charge is smaller than the effective area of the tip end, this approximation is no more valid. Thus the lateral resolution will be limited by the size of the tip radius. However, with 20 nm in tip radius, this approximation will be valid for the investigation of the ferroelectric domain structure because the domain size is usually much larger than the tip radius. In this approximation, Coulomb force can be can be expressed simply as Esqt , where Esϭb/2⑀0 is the electric field due to the constant surface charge density b , and qtip is the charge, qtϭCV, induced at the tip by the applied voltage VϭVdcϩVac cos t.
Figure 4 shows the calculated electric field for ferroelectric strip domains with an alternating surface charge density Ϯb and width wϭ2 m which is a typical value for a triglycine sulfate ͑TGS͒ single crystal as a function of the position x and height z from the surface. For a tip height less than 10 nm, one can represent the effect of the surface charge density by a uniform surface electric field Esϭb/2⑀0 as we assumed above. A large electric field gradient appears near the domain boundary where two opposite charge densities collide. For a tip height greater than 10 nm, for example, a significant force gradient appears as shown in Fig. 4. Thus
1738 Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
Hong, Park, and Khim
FIG. 4. Plot of electric field as function of lateral position on the alternating charge strip of width 2 m at four different heights from surface.
the component of the electrostatic force in DC-EFM in the presence of a bound surface charge density becomes ץ)C/ץzVdcϩbC/2⑀0) which depends both on Vdc and the surface charge density b . Therefore, measurements on the amplitude of the component of the cantilever vibration lead to the detection of the surface charge density or the domain image, in the case of a ferroelectric surface. The topographic image can be obtained from the feedback signal due to the repulsive atomic force ͑dc component͒ that maintains a constant tip height ͑or a constant capacitance͒ during scanning of the tip in DC-EFM. Since the capacitance between tip and sample is kept constant in the operation of DC-EFM, the domain image obtained from the component ץ)C/ץzVdcϩbC/2⑀0) in DC-EFM is well separated from the topographic image unlike the conventional noncontact EFM which frequently shows mixed image of topography and domain structure. To understand the origin of the image mixing, we will describe the effect of the electrostatic force gradient in the detection of ferroelectric domains by the noncontact mode EFM. As shown in Fig. 4, a large electric field gradient appears near the domain boundary where two opposite charge distributions meet. Furthermore for the tipsample distance greater than 10 nm, for example, a significant force gradient appears along the lateral position. In the noncontact mode of EFM, the topography feedback loop adjusts the tip–sample distance in order to maintain constant vibration amplitude of the tip at resonance frequency of the cantilever. The electric properties of the sample can be simultaneously measured by applying dc and ac bias at another off-resonance frequency of cantilever. Therefore, in a noncontact EFM operation, the variation in the electrostatic force gradient due to the surface charge can shift a resonance frequency of probe oscillation, thus perturbing the topography measurement. In such a case, the probe tip follows a constant force gradient contour including the electrostatic force gradient as well as van der Waals force gradient. Thus the constant force gradient does not coincide with the real topography of the surface. However, in the operation of DCEFM, the tip-sample distance is controlled by the repulsive atomic force instead of the force gradient. Thus the topography image is well separated from the electrical property of a surface.
Figure 5 shows topography and domain contrast images
FIG. 5. Comparison the surface charge image obtained by DC-EFM and noncontact EFM. Images taken by DC-EFM do not show any correlation between topography ͑a͒ and surface charge ͑b͒ image. However, the images taken by noncontact EFM show a strong coupling between topography ͑c͒ and charge ͑d͒ image.
of TGS single crystal obtained simultaneously. Images are obtained by both DC-EFM and conventional noncontact mode EFM for the purpose of comparison. Cleaved TGS single crystal has 180° domains with the polarization direction perpendicular to the ac plane. Therefore the bound surface charge density bϭP–n of each domain is either positive or negative depending on the polarity. As shown in Figs. 5͑a͒ and 5͑b͒, topography and domain image, which are obtained by DC-EFM simultaneously, are well separated from each other. Domain contrast image shown in Fig. 5͑b͒ shows sharply divided two distinct levels only as can be expected for 180° domains. However, topography ͓Fig. 5͑c͔͒ and surface charge image ͓Fig. 5͑d͔͒ obtained by the noncontact mode EFM show coupled or blurred images. In the topographic image, an enhanced contrast appears along the domain boundary where a strong electrostatic force gradient exists. In the noncontact operation, topography image is a convolution of van der Waals force gradient with electrostatic force gradient. Thus, the probe tip will show a constant force-gradient contour rather than a constant tip-sample separation contour. Domain contrast obtained by the noncontact operation ͓Fig. 5͑d͔͒ shows a much blurrier image, as if it is unfocused, compared to the one ͓Fig. 5͑b͔͒ obtained by DC-EFM. Yet we can distinguish the polarity for a wide domain. This grey level contrast can be explained by the behavior of the surface electric field as shown in Fig. 4. For a tip distance higher than 10 nm, the electric field changes gradually near the domain boundary. In addition, the electric field intensity over a narrow domain is much weaker than the one over a wide domain region. When the tip is far away from the surface, the electrostatic force exerted on the tip will be reduced by the decrease in the surface electric field intensity and also by the decrease of the induced charge on the tip due to decrease in the capacitance between the tip and electrode. Thus domain image shows a spatially averaged contrast, which in turn decreases the lateral resolution, therefore a contact operation such as in DC-EFM provides a better
Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
domain contrast image as well as a better spatial resolution
than a noncontact method. The advantage of DC-EFM com-
pared to other similar methods such as the piezoresponse method13 or lateral force mocroscope14 for the detection of
domain images is that it can provide a way for a quantitative
evaluation of the surface change density and a direct control
of the domain structure in ferroelectric materials. In the null-
ing method, the feedback signal of the feedback controller controls Vdc such that the amplitude of component, ץ)C/ץzVdcϩbC/2⑀0), vanishes. The surface charge density is, therefore, related to the nulling dc voltage Vdc,n as
bϭϪ2⑀0Vdc,n͑ ץC/ץz ͒/C.
͑5͒
Since DC-EFM is operated in a contact mode with the effective tip-sample distance d as small as 1 nm, the capacitance between tip and sample can be regarded as a parallel plate capacitor with the resulting ץ)C/ץz)/CХ1/d. Thus, one can estimate the surface charge density of ferroelectrics directly from the nulling feedback signal in DC-EFM. If one applies a strong dc bias to the tip, a control of the domain structure ͑domain reversal͒ is also possible with DC-EFM.
IV. DISCUSSIONS
Electrostatic force modulation by applying an ac modulation bias between the tip and the electrode generates the vibration of the cantilever even in the contact state and also induces charges on the tip. The sustained vibration and the induced charge on the tip allows the detection of a weak electric force by a lock-in technique even in the presence of a strong atomic force at the surface.
Thus DC-EFM can be used either as a force modulation microscopy for the surface hardness, or as a potentiometry for the surface potential distribution, or as a charge densitometry for the ferroelectric domain study. Much better spatial resolution and clear detection of surface electrical properties can be achieved in DC-EFM than in the conventional noncontact EFM. Furthermore, topography, surface potential, and surface charge image are well separated from each other
Hong, Park, and Khim 1739
in DC-EFM, that allows a quantitative evaluation of the bound surface charge density and control of the domain structure. For the quantitative evaluation of the surface charge density, however, it is required to measure the gap distance between tip and sample more accurately. In this work, we estimated the gap value from the force distance curve of the cantilever with an uncertainty of 10% which limits the accuracy of the estimated value of the surface charge density.
ACKNOWLEDGMENTS
This work was supported in part by the Nano-Structure Technology Project and also by the Ministry of Education in Korea under Grant No. BSRI-98-2416.
1 P. Maviald, H. J. Butt, S. A. C. Gould, C. B. Prater, B. Drake, J. A. Gurley, V. B. Elings, and P. K. Hansma, Nanotechnology 2, 103 ͑1991͒. 2 Y. Martin, D. W. Abraham, and H. K. Wickramasinghe, Appl. Phys. Lett. 52, 1103 ͑1988͒. 3 J. M. R. Weaver, D. W. Abraham, J. Vac. Sci. Technol. B 9, 1559 ͑1991͒. 4 A similar method based on the nulling condition of the force between tip and sample also yielded a simultaneous measurement of the topographic and surface potential. See, for example, M. Nonnenmacher, M. P. Boyle, and H. K. Wickramashinge, Appl. Phys. Lett. 58, 2921 ͑1991͒. 5 J. E. Stern, B. D. Terris, H. J. Mamin, and D. Rugar, Appl. Phys. Lett. 53, 2117 ͑1988͒. 6 B. D. Terris, J. E. Stern, D. Rugar, and H. J. Mamin, J. Vac. Sci. Technol. A 8, 374 ͑1989͒. 7 F. Saurenbach and B. D. Terris, Appl. Phys. Lett. 56, 1703 ͑1990͒. 8 R. Luthi, H. Haefke, K.-P. Meyer, E. Meyer, L. Howald, and H.-J. Guntherodt, J. Appl. Phys. 74, 7461 ͑1993͒. 9 H. Bluhm, A. Wadas, R. Wiesendanger, K.-K. Meyer, and L. Szczesniak, Phys. Rev. B 55, 4 ͑1996͒. 10 J. W. Hong, Z. G. Khim, A. S. Hou, and S.-I. Park, Appl. Phys. Lett. 69, 2831 ͑1996͒. 11 Y. Martin, C. C. Williams, and H. K. Wickramasinghe, J. Appl. Phys. 61, 4723 ͑1987͒. 12 J. W. Hong, K. H. Noh, S.-I. Park, S. I Kwun, and Z. G. Khim, Phys. Rev. B 58, 5078 ͑1998͒. 13 A. Gruverman, O. Auciello, R. Ramesh, and H. Tokumoto, Nanotechnology 8, A38 ͑1997͒. 14 H. Bluhm, U. D. Schwarz, and R. Wiesendanger, Phys. Rev. B 57, 161 ͑1998͒.
VOLUME 70, NUMBER 3
MARCH 1999
Measurement of hardness, surface potential, and charge distribution with dynamic contact mode electrostatic force microscope
J. W. Hong, Sang-il Park,a) and Z. G. Khimb) Department of Physics and Condensed Matter Research Institute, Seoul National University, Seoul 151-742, Korea
͑Received 21 August 1998; accepted for publication 30 November 1998͒
Dynamic contact mode electrostatic force microscopy ͑DC-EFM͒ was developed as a new operation mode of scanning probe microscope ͑SPM͒. By operating EFM in a contact mode with an ac modulation bias, we have improved the spatial resolution and also achieved a complete separation of the topographic effect from other electrostatic force effect overcoming the mixing problem of a topographic effect with other electrostatic effects frequently encountered in the conventional noncontact EFM measurement. DC-EFM can be utilized either as a force microscopy for the surface hardness, or as a potentiometry for the surface potential distribution, or as a charge densitometry for the surface charge density study. This is also applicable to the measurement and control of the domain structure in ferroelectric materials that have a bound surface charge. © 1999 American Institute of Physics. ͓S0034-6748͑99͒01703-7͔
I. INTRODUCTION
Scanning probe microscope ͑SPM͒ has matured and developed into a routine instrument for the investigation of the surface topography of insulating as well as conducting samples with an atomic resolution. Recent efforts have revealed a much broader potential for the measurement of local mechanical properties1 and electrical properties such as surface potential,2–4 surface charge,5,6 and ferroelectric domain7–9 by electrostatic force microscope ͑EFM͒.
Earlier force modulation microscopy ͑FMM͒ was achieved by applying a small mechanical sinusoidal force on the surface when the tip was close to the sample.1 Unfortunately, in the earlier FMM technique, either sample or probe cantilever is vibrated with a mechanical transducer. In either case, the mechanical transducer has a rather poor amplitude versus frequency response of the probe usually exciting several unwanted modes of vibration and noise. To avoid this problem, we have successfully employed tapping mode using an electrostatic force modulation technique10 for the study of the surface morphology by applying an ac modulation signal to the tip instead of the mechanical modulation force using a bimorph.
Conventional EFM is usually operated in a dynamic noncontact mode,11 where the change of the vibration amplitude due to a force gradient is used to detect the variation of the force gradient due to either topography or other interactions. Therefore, in the dynamic noncontact EFM, it is difficult to separate the effect of topography from that of the other origin. For example, abrupt changes in the surface potential and surface charge on the sample surface produce a large electrostatic force gradient. In such cases, the probe tip cannot follow a true topography but a force gradient contour
a͒Present address: PSIA Corp., Daelim Bldg., Seocho-dong 1600-3, Seoul 137-070, Korea.
b͒Electronic mail: [email protected]
including the electrostatic force gradient as well as van der Waals force gradient. Such a mixing of force gradients causes successive errors in measuring the electrical properties of the sample. In addition, the noncontact mode operation is rather complicated and its spatial resolution is significantly reduced compared to that of the contact mode operation, since the tip is far away, approximately 10 nm, from the surface.
We have overcome the problems of the conventional operation mode of EFM, and have successfully obtained images of surface topography, surface potential, and surface charge distribution by operating EFM in a contact mode with an ac electrostatic modulation, which we termed as dynamic noncontact mode EFM ͑DC-EFM͒12 to distinguish it from the conventional noncontact mode EFM.
In this report, we will explain the detection principle of DC-EFM for the measurement of the surface hardness, surface potential distribution, and surface charge density. Ferroelectric domain image obtained by DC-EFM is compared with that obtained by the conventional noncontact operation of EFM.
II. DETECTION METHOD
In DC-EFM, a contact mode atomic force microscope ͑AFM͒ is employed to maintain the tip-sample distance constant. A dc and ac bias voltage is applied between the conductive probe tip and sample in the contact mode. The probe tip used in this work is a heavily doped Si ͑doping level is 1019– 1020/cm3͒ with a spring constant kϭ1.9 N/m and a typical tip radius Rϭ20 nm. An insulating layer on the probe tip such as native oxide layer prevents electrical current flowing between the tip and sample.
The idea behind DC-EFM operation is, first, to utilize the sustained vibration of the cantilever even in the contact state, when an ac electrostatic modulation signal is applied to the tip. That is, even when the tip is in contact with the
0034-6748/99/70(3)/1735/5/$15.00
1735
© 1999 American Institute of Physics
1736 Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
Hong, Park, and Khim
FIG. 1. Schematic diagram of DCEFM. With the lock-in amplifier feedback off, output of lock-in amplifier can be used for the detection of surface potential or surface charge density. For the estimate of the absolute value of surface potential or the surface charge density, one can measure the lock-in feedback signal that controls Vdc such that the amplitude of component ͑lock-in amplifier output͒ vanishes.
sample surface, there still remains a finite vibration amplitude of the probe tip. The sustained vibration of the tip in a contact state was already confirmed in the force microscope.1 Then even in the presence of a strong atomic force in the contact mode, a weak electrostatic interaction between tip and sample surface can be detected by a lock-in technique. Second, by applying a bias to the tip one can for example control the induced charge on the tip, which in turn generates an additional controllable force between the tip and charged surface. Therefore we can simultaneously measure the topography and other electrostatic interaction effect such as surface potential or surface charge density with DC-EFM.
The general equation describing the force between the tip and sample at a surface position r in the presence of surface potential or surface charge density includes atomic force, capacitive force, and Coulombic force between the charge induced on the tip and sample surface charge:
F͑ r͒ϭFa͑ r͒ϩ1/2ץC͑ r͒/ץzV2ϩEs͑ r͒qtip .
͑1͒
Here, Fa represents the repulsive atomic force on the tip. In the capacitive force term, ץC/ץz is the gradient of capaci-
tance between tip and sample, which depends on the tip-
sample geometry. The potential V between the tip and
sample surface may contain external dc bias Vdc and ac bias Vac cos t as well as the sample surface potential Vs . Es(r) and qtipϭC(VdcϩVac cos t) represent the electric field gen-
erated by the surface charge density of the sample and the
charge induced on the tip, respectively.
With Vϭ(VdcϪVsϩVac cos t) and ϩVac cos t), the force on the tip reduces to
q tipϭ C ( V dc
F͑ r ͒ϭFa͑ r ͒ϩ1/2ץC͑ r ͒/ץz͑ VdcϪVsϩVac cos t ͒2
ϩEs͑ r ͒C͑ r ͒͑ VdcϪVsϩVac cos t ͒
ϭ͓Fa͑ r ͒ϩ1/2ץC͑ r ͒/ץz͑ VdcϪVs͒2
ϩ1/4ץC͑ r ͒/ץzVa2cϩEs͑ r ͒C͑ r ͒͑ VdcϪVs͔͒
ϩ͓ץC͑ r ͒/ץz͑ VdcϪVs͒ϩEs͑ r ͒C͑ r ͔͒Vac cos t
ϩ
1/4
ץ
C
/
ץ
z
V
2 ac
cos
2
t
.
͑2͒
Since DC-EFM is operated in the contact mode, the dc component of the force ͑static deflection of the cantilever͒ is adjusted by the z servoloop such that the strong repulsive atomic force between tip and surface is maintained constant. Thus, the dc component provides the topographic image as in the conventional contact mode operation of AFM. On the other hand, the detection of the component, ͓ץC/ץz(Vdc ϪVs)ϩEsC͔, can provide information about Vs or Es depending on the experimental situation.
Now if the sample surface is not sufficiently hard and has variations in its hardness, then the surface may have certain compliance due to electrostatic force modulation. Therefore a strong electrostatic force can drive the probe tip to vibrate by indenting the sample surface. The vibration amplitude will depend on the surface hardness and the strength of the electrostatic force. In this case, the capacitance ͑or the gradient of the capacitance͒ between the tip and sample will show a dependence on the surface hardness. We can write the relationship between the hardness and relative amplitude of the tip vibration as follows:
F͑ r, ͒ϭkeff͑ r, ͒z͑ r, ͒,
͑3͒
where z(r,) represents the amplitude of the tip vibration at a position r caused by the electrostatic force F(r,). Thus in the absence of surface charge or potential distribution on the sample, we can approximate the electrostatic force to be constant over r. Furthermore, by keeping the ac and dc bias at a constant value, we can determine the variation of the effective mechanical hardness keff by measuring the component of the electrostatic vibration,
keff͑ r, ͒ϭF͑ r, ͒/z͑ r, ͒.
͑4͒
The lock-in amplifier was used to measure the vibration amplitude and phase of the probe at frequency . During this measurement, the dc part of the force is taken as the feedback signal to maintain a constant height in the contact mode operation thus avoiding any mixing of the topographic effect with the surface hardness effect.
Figure 1 shows a schematic diagram of the DC-EFM. The signal from the topographic feedback controller ͑z ser-
Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
Hong, Park, and Khim 1737
FIG. 2. Topography ͑a͒ and force modulation ͑b͒ image of a sample surface. Two hard GaAs regions are separated by a soft epoxy. The vibration amplitude at frequency force is much higher in soft epoxy than one in hard GaAs region.
vocontroller͒ that is to maintain the tip-sample height constant can be employed to image the surface morphology. With the feedback controller II off, the output of lock-in amplifier can be used for the detection of surface potential or surface charge density. For the estimate of the absolute value of surface potential or the surface charge density, one can measure the feedback controller II signal that controls Vdc such that the amplitude of component ͑lock-in amplifier output͒ vanishes.
III. EXPERIMENTAL RESULTS
As an example of DC-EFM, operation for the mechanical hardness measurement, images of the GaAs/epoxy/GaAs multilayer were taken by DC-EFM. Two GaAs wafers are glued together by a soft epoxy layer at the center. Figure 2 shows topography ͓Fig. 2͑a͔͒ and hardness ͓Fig. 2͑b͔͒ images obtained simultaneously for a polished surface which has regions of different mechanical hardness. In this measurement, applied dc bias, amplitude of ac bias, and frequency were 1 V, 5 V, and 40 kHz, respectively. Topography image barely reveals three separated regions of GaAs– epoxy–GaAs layers. However, the image obtained by the component clearly shows three distinctively separated layers. Because the central epoxy region is softer than both sides of the GaAs region, the amplitude of probe vibration at frequency in epoxy region is larger than the one in GaAs region. Thus the component of the tip vibration due to an electrostatic force in DC-EFM reflects the local mechanical hardness of a sample surface.
There are advantages of using DC-EFM for the mechanical hardness measurement compared to the earlier FMM technique using a bimorph driven mechanical modulation. In the FMM mode, the mechanical modulation usually generates several vibration modes of the microscope system, which can cause some ambiguity in the measurement. However the electrostatic modulation vibrates only the cantilever without shaking the entire part of the scanning or supporting cantilever system. Thus, we can get a clean vibration spectra. As a result, DC-EFM can prevent mixing or coupling of a main signal with unwanted noise sources.
Now if there is a surface potential distribution Vs on the sample surface but in the absence of surface charge density, the component in Eq. ͑2͒ reduces simply to ץC/ץz(Vdc ϪVs). Therefore DC-EFM can be operated as a potentiom-
FIG. 3. Topography ͑a͒ and surface potential ͑b͒ image of an integrated test chip where one set of the trace is biased at ϩ1 V and the other set of the trace is biased at Ϫ1 V.
etry by detecting the component in the presence of a surface potential Vs(r) such as a pn junction or signal line in the integrated circuit. In order to measure the absolute value of the surface potential, a feedback loop is used to adjust the dc bias of the probe (Vdc,p) such that the vibration amplitude of the component vanishes.3,4 In this situation, the applied dc bias voltage to the probe is equal to the surface potential. An example is shown in Fig. 3, the topographic ͓Fig. 3͑a͔͒ and surface potential ͓Fig. 3͑b͔͒ image of a test pattern, where one set of the trace is biased at ϩ1 V and the other set of the trace is biased at Ϫ1 V. A thin SOG layer was covered on the top of the sample surface. Thus we can assume that the surface hardness is uniform through the entire surface. In the topographic image, two metal lines ͑bright region͒ are separated by the etched insulating region. From the surface potential image, we can find that the line profile of the potential is changing linearly across the etched region as expected. The resolution of this potentiometry is about ϳ20 mV.
In another case, if the sample surface has a bound surface charge density b , the electrostatic force is given as a sum of a capacitive force and Coulomb force between tip and sample. Since the probe tip-sample distance is very short in contact mode operation, one can approximate the effect of the bound surface charge density by a uniform surface electric field Es . If the area of the bound charge is smaller than the effective area of the tip end, this approximation is no more valid. Thus the lateral resolution will be limited by the size of the tip radius. However, with 20 nm in tip radius, this approximation will be valid for the investigation of the ferroelectric domain structure because the domain size is usually much larger than the tip radius. In this approximation, Coulomb force can be can be expressed simply as Esqt , where Esϭb/2⑀0 is the electric field due to the constant surface charge density b , and qtip is the charge, qtϭCV, induced at the tip by the applied voltage VϭVdcϩVac cos t.
Figure 4 shows the calculated electric field for ferroelectric strip domains with an alternating surface charge density Ϯb and width wϭ2 m which is a typical value for a triglycine sulfate ͑TGS͒ single crystal as a function of the position x and height z from the surface. For a tip height less than 10 nm, one can represent the effect of the surface charge density by a uniform surface electric field Esϭb/2⑀0 as we assumed above. A large electric field gradient appears near the domain boundary where two opposite charge densities collide. For a tip height greater than 10 nm, for example, a significant force gradient appears as shown in Fig. 4. Thus
1738 Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
Hong, Park, and Khim
FIG. 4. Plot of electric field as function of lateral position on the alternating charge strip of width 2 m at four different heights from surface.
the component of the electrostatic force in DC-EFM in the presence of a bound surface charge density becomes ץ)C/ץzVdcϩbC/2⑀0) which depends both on Vdc and the surface charge density b . Therefore, measurements on the amplitude of the component of the cantilever vibration lead to the detection of the surface charge density or the domain image, in the case of a ferroelectric surface. The topographic image can be obtained from the feedback signal due to the repulsive atomic force ͑dc component͒ that maintains a constant tip height ͑or a constant capacitance͒ during scanning of the tip in DC-EFM. Since the capacitance between tip and sample is kept constant in the operation of DC-EFM, the domain image obtained from the component ץ)C/ץzVdcϩbC/2⑀0) in DC-EFM is well separated from the topographic image unlike the conventional noncontact EFM which frequently shows mixed image of topography and domain structure. To understand the origin of the image mixing, we will describe the effect of the electrostatic force gradient in the detection of ferroelectric domains by the noncontact mode EFM. As shown in Fig. 4, a large electric field gradient appears near the domain boundary where two opposite charge distributions meet. Furthermore for the tipsample distance greater than 10 nm, for example, a significant force gradient appears along the lateral position. In the noncontact mode of EFM, the topography feedback loop adjusts the tip–sample distance in order to maintain constant vibration amplitude of the tip at resonance frequency of the cantilever. The electric properties of the sample can be simultaneously measured by applying dc and ac bias at another off-resonance frequency of cantilever. Therefore, in a noncontact EFM operation, the variation in the electrostatic force gradient due to the surface charge can shift a resonance frequency of probe oscillation, thus perturbing the topography measurement. In such a case, the probe tip follows a constant force gradient contour including the electrostatic force gradient as well as van der Waals force gradient. Thus the constant force gradient does not coincide with the real topography of the surface. However, in the operation of DCEFM, the tip-sample distance is controlled by the repulsive atomic force instead of the force gradient. Thus the topography image is well separated from the electrical property of a surface.
Figure 5 shows topography and domain contrast images
FIG. 5. Comparison the surface charge image obtained by DC-EFM and noncontact EFM. Images taken by DC-EFM do not show any correlation between topography ͑a͒ and surface charge ͑b͒ image. However, the images taken by noncontact EFM show a strong coupling between topography ͑c͒ and charge ͑d͒ image.
of TGS single crystal obtained simultaneously. Images are obtained by both DC-EFM and conventional noncontact mode EFM for the purpose of comparison. Cleaved TGS single crystal has 180° domains with the polarization direction perpendicular to the ac plane. Therefore the bound surface charge density bϭP–n of each domain is either positive or negative depending on the polarity. As shown in Figs. 5͑a͒ and 5͑b͒, topography and domain image, which are obtained by DC-EFM simultaneously, are well separated from each other. Domain contrast image shown in Fig. 5͑b͒ shows sharply divided two distinct levels only as can be expected for 180° domains. However, topography ͓Fig. 5͑c͔͒ and surface charge image ͓Fig. 5͑d͔͒ obtained by the noncontact mode EFM show coupled or blurred images. In the topographic image, an enhanced contrast appears along the domain boundary where a strong electrostatic force gradient exists. In the noncontact operation, topography image is a convolution of van der Waals force gradient with electrostatic force gradient. Thus, the probe tip will show a constant force-gradient contour rather than a constant tip-sample separation contour. Domain contrast obtained by the noncontact operation ͓Fig. 5͑d͔͒ shows a much blurrier image, as if it is unfocused, compared to the one ͓Fig. 5͑b͔͒ obtained by DC-EFM. Yet we can distinguish the polarity for a wide domain. This grey level contrast can be explained by the behavior of the surface electric field as shown in Fig. 4. For a tip distance higher than 10 nm, the electric field changes gradually near the domain boundary. In addition, the electric field intensity over a narrow domain is much weaker than the one over a wide domain region. When the tip is far away from the surface, the electrostatic force exerted on the tip will be reduced by the decrease in the surface electric field intensity and also by the decrease of the induced charge on the tip due to decrease in the capacitance between the tip and electrode. Thus domain image shows a spatially averaged contrast, which in turn decreases the lateral resolution, therefore a contact operation such as in DC-EFM provides a better
Rev. Sci. Instrum., Vol. 70, No. 3, March 1999
domain contrast image as well as a better spatial resolution
than a noncontact method. The advantage of DC-EFM com-
pared to other similar methods such as the piezoresponse method13 or lateral force mocroscope14 for the detection of
domain images is that it can provide a way for a quantitative
evaluation of the surface change density and a direct control
of the domain structure in ferroelectric materials. In the null-
ing method, the feedback signal of the feedback controller controls Vdc such that the amplitude of component, ץ)C/ץzVdcϩbC/2⑀0), vanishes. The surface charge density is, therefore, related to the nulling dc voltage Vdc,n as
bϭϪ2⑀0Vdc,n͑ ץC/ץz ͒/C.
͑5͒
Since DC-EFM is operated in a contact mode with the effective tip-sample distance d as small as 1 nm, the capacitance between tip and sample can be regarded as a parallel plate capacitor with the resulting ץ)C/ץz)/CХ1/d. Thus, one can estimate the surface charge density of ferroelectrics directly from the nulling feedback signal in DC-EFM. If one applies a strong dc bias to the tip, a control of the domain structure ͑domain reversal͒ is also possible with DC-EFM.
IV. DISCUSSIONS
Electrostatic force modulation by applying an ac modulation bias between the tip and the electrode generates the vibration of the cantilever even in the contact state and also induces charges on the tip. The sustained vibration and the induced charge on the tip allows the detection of a weak electric force by a lock-in technique even in the presence of a strong atomic force at the surface.
Thus DC-EFM can be used either as a force modulation microscopy for the surface hardness, or as a potentiometry for the surface potential distribution, or as a charge densitometry for the ferroelectric domain study. Much better spatial resolution and clear detection of surface electrical properties can be achieved in DC-EFM than in the conventional noncontact EFM. Furthermore, topography, surface potential, and surface charge image are well separated from each other
Hong, Park, and Khim 1739
in DC-EFM, that allows a quantitative evaluation of the bound surface charge density and control of the domain structure. For the quantitative evaluation of the surface charge density, however, it is required to measure the gap distance between tip and sample more accurately. In this work, we estimated the gap value from the force distance curve of the cantilever with an uncertainty of 10% which limits the accuracy of the estimated value of the surface charge density.
ACKNOWLEDGMENTS
This work was supported in part by the Nano-Structure Technology Project and also by the Ministry of Education in Korea under Grant No. BSRI-98-2416.
1 P. Maviald, H. J. Butt, S. A. C. Gould, C. B. Prater, B. Drake, J. A. Gurley, V. B. Elings, and P. K. Hansma, Nanotechnology 2, 103 ͑1991͒. 2 Y. Martin, D. W. Abraham, and H. K. Wickramasinghe, Appl. Phys. Lett. 52, 1103 ͑1988͒. 3 J. M. R. Weaver, D. W. Abraham, J. Vac. Sci. Technol. B 9, 1559 ͑1991͒. 4 A similar method based on the nulling condition of the force between tip and sample also yielded a simultaneous measurement of the topographic and surface potential. See, for example, M. Nonnenmacher, M. P. Boyle, and H. K. Wickramashinge, Appl. Phys. Lett. 58, 2921 ͑1991͒. 5 J. E. Stern, B. D. Terris, H. J. Mamin, and D. Rugar, Appl. Phys. Lett. 53, 2117 ͑1988͒. 6 B. D. Terris, J. E. Stern, D. Rugar, and H. J. Mamin, J. Vac. Sci. Technol. A 8, 374 ͑1989͒. 7 F. Saurenbach and B. D. Terris, Appl. Phys. Lett. 56, 1703 ͑1990͒. 8 R. Luthi, H. Haefke, K.-P. Meyer, E. Meyer, L. Howald, and H.-J. Guntherodt, J. Appl. Phys. 74, 7461 ͑1993͒. 9 H. Bluhm, A. Wadas, R. Wiesendanger, K.-K. Meyer, and L. Szczesniak, Phys. Rev. B 55, 4 ͑1996͒. 10 J. W. Hong, Z. G. Khim, A. S. Hou, and S.-I. Park, Appl. Phys. Lett. 69, 2831 ͑1996͒. 11 Y. Martin, C. C. Williams, and H. K. Wickramasinghe, J. Appl. Phys. 61, 4723 ͑1987͒. 12 J. W. Hong, K. H. Noh, S.-I. Park, S. I Kwun, and Z. G. Khim, Phys. Rev. B 58, 5078 ͑1998͒. 13 A. Gruverman, O. Auciello, R. Ramesh, and H. Tokumoto, Nanotechnology 8, A38 ͑1997͒. 14 H. Bluhm, U. D. Schwarz, and R. Wiesendanger, Phys. Rev. B 57, 161 ͑1998͒.