- Email: [email protected]
The waveform separation of displacement current and tunneling current using a scanning vibrating probe
Thin Solid Films 393 Ž2001. 204᎐209
The waveform separation of displacement current and tunneling current using a scanning vibrating probe Yutaka MajimaU , Setsuri Uehara, Tomohiko Masuda, Atsushi Okuda, Mitsumasa Iwamoto Department of Physical Electronics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Abstract A measuring system that separates the both waveforms of displacement and tunneling current using a scanning vibrating probe is described. In the measuring system, the displacement and tunneling current flow periodically in accordance with the perpendicular vibration of the probe. The external circuit current is measured by oscilloscope and is separated into both waveforms of the displacement and tunneling current by utilizing the phase difference of them. The waveform of the displacement current is also analyzed by assuming the presence of excessive surface charges above the sample. Consequently, we can determine the mean distance between the probe and sample, and the offset voltage which is built up by excessive surface charges and work function difference of the probe and sample. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Displacement current; Tunneling current; Oscilloscope; Scanning vibrating probe; Surface charge
1. Introduction Recently, many scanning probe microscopes ŽSPM., e.g. scanning tunneling microscope ŽSTM., atomic force microscope ŽAFM., electrostatic force microscope ŽEFM., and scanning capacitance microscope ŽSCM. have been developed and, thus, used to investigate physical properties of organic thin films w1᎐6x. EFM can measure electrostatic properties on the surface, e.g. a non-uniform charge distribution and variations in surface work function by detecting a change in the mechanical resonant frequency of a cantilever w4,5x. In SCM, oscillation voltage is applied to the scanning probe, and the change in capacitance between the probe and sample is detected as a change in resonance frequency using an ultrahigh frequency resonant capac-
U
Corresponding author. Tel.: q81-3-5734-2673; fax: q81-3-57342673. E-mail address: [email protected] ŽY. Majima..
itance sensor w6x. Both EFM and SCM are useful tools to map two-dimensional electrostatic distributions, and use the resonant phenomena. On the other hand, when the probe is vibrated perpendicular to the sample by applying a d.c. probe voltage, both displacement and tunneling current flow periodically in accordance with the vibration of the probe w7,8x. Recently, we have successfully separated the external circuit current across semiconductors into displacement and tunneling current, and then established the measuring method of determining semiconductor local carrier concentration from displacement current᎐voltage curves w9x. Simultaneous measurement of the displacement current and the tunneling current should be significant in characterizing electrical surface properties, e.g. surface potential of organic thin films built up by excessive surface charges and semiconductor carrier concentration. In this paper, we demonstrate the measuring system that separates both waveforms of the displacement and tunneling currents. The waveform of the displacement
0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 1 . 0 1 0 7 0 - 7
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
current is also analyzed by assuming the presence of excessive surface charges above the sample. The measuring methods of determining the mean distance between the probe and sample, and the offset voltage, which is built up by the excessive surface charges and the work function difference of the probe and the sample are also described. 2. Analysis 2.1. The external circuit current with the ¨ ibrating probe Fig. 1 shows a schematic diagram of the measuring system. When the probe is vibrated, the distance dŽ t . between the probe and sample changes as d Ž t . s d 0 y d1cos t
Ž1.
where is the angler vibration frequency given by s 2 f Ž f s frequency., d1 is the amplitude of vibration, and d 0 is the mean distance between the probe and sample. If the probe is closed to the sample and is vibrated within dŽ t . of 10 nm, the external circuit current I Ž t . includes both the displacement current ID Ž t . and the tunneling current IT Ž t ., and is given by I Ž t . s ID Ž t . q IT Ž t .
Ž2.
where ID Ž t . is the displacement current due to the change in the induced charges on the probe Q1Ž t ., and IT Ž t . is the tunneling current across the vacuum gap between the probe and the sample.
205
2.2. The analysis of the wa¨ eform of the displacement current with surface charges Although the probe has an arbitrary shape, it is assumed to be a sphere because the distance dŽ t . is more than one hundred times smaller than the peak radius R of the probe w dŽ t . < R x w8x. By applying an image method, the capacitance between the probe and a metal sample C Ž t . is approximately given by w8,9x C Ž t . s 4 0 R 0.93y
ž
1 dŽ t . ln . 2 R
/
Ž3.
When uniform excessive surface charges exists at d 2 above the sample, the charges induced on the probe Q1Ž t . is expressed by applying the Green’s reciprocity theorem as w10x Q1Ž t . s C Ž t . V1 y
⬁
H0
V2 Ž r ,d 2 . 2 rd r V1
Ž4.
where V1 is the potential across the vacuum between the probe and the sample, r is the radius from the center of the surface, V2 Ž r, d 2 . is potential built up voltage at position Ž r, d 2 . without the uniform excessive surface charges, and is the charge density of the excessive surface charges. Assuming dŽ t . < R, the electric flux from the sample to the probe becomes perpendicular to the sample at the position Ž r, d 2 ., and the voltage ratio V2 Ž r, d 2 .rV1 becomes V2 Ž r ,d 2 . d s 2 V1 lŽ r .
Ž5.
where l Ž r . is the length of the electric flux from the sample to the probe at the position r. Substituting Eq. Ž5. into Eq. Ž4., Q1Ž t . becomes Q1Ž t . s C Ž t . V1 y
Fig. 1. Schematic diagram of a tunneling and displacement current simultaneous measurement system. The current which flows between the probe and the sample due to the static probe bias voltage VP , and the time varying probe᎐sample distance dŽ t . is the sum of the waveforms of a tunneling current IT Ž t . and displacement current ID Ž t ., which is measured by a digital storage oscilloscope. The mean tunneling current, IT Ž VP ., and the mean displacement current, ID Ž VP . are separated using a 2-phase lock-in amplifier.
⬁
d2
H0 l Ž r . 2 rd r .
Ž6.
The second term of Eq. Ž6. includes the surface integral of the capacitance between the probe and the sample, because l Ž r . is the length of the electric flux from the sample to the probe. Consequently, Eq. Ž6. is re-expressed as Q1Ž t . s C Ž t . V1 y
ž
d 2 . 0
/
Ž7.
The probe voltage VP is shared by the potential V1
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
206
and the work function difference between the probe and the sample PS , and is given by VP s V1 q PS .
Ž8.
Consequently, the displacement current ID Ž t . is given by differentiating Eq. Ž7. as d 2 ID Ž t . s 4 0 R VP y P S y 0
ž
=
ž
ysin t d 0rd1 y cos t
uniform excessive surface charges to ID Ž t . appears as the voltage shift yd 2r 0 as in the case with PS . Since the differentiation of Eq. Ž9. with t becomes 0 at the peak Žd ID Ž t .rdt s 0., both the peak value ID Ž t . max and peak phase max of the displacement are given by ID Ž t . max s "4 0 R VP y PS y
/ž
2
ž
/
=
ž 2 / 'Ž d rd1 0
/
.
1
d 2 0
.2 y 1
,
/ Ž 10 .
Ž9.
Fig. 2a shows the theoretical displacement current waveforms as a function of the ratio d 0rd1. The displacement current waveforms strongly depend on the d 0rd1. It should be noted that the contribution of the
and cosmax s d1rd 0 ,
Ž 11 .
respectively. Fig. 2b shows the theoretical peak phase of the displacement current as a function of the ratio d 0rd1. It should be noted that the peak phase, max , changes steeply with decreasing d 0rd1 , especially in the region d 0rd1 - 4. From Eq. Ž11., the mean distance d 0 can be estimated since the amplitude of vibration d1 can be controlled by changing the oscillation voltage of the z-axes piezo. 2.3. The analysis of the wa¨ eform of the tunneling current Tunneling current IT Ž t . depends on dŽ t ., and is given by w11,12x IT Ž t . A exp
ž
'8 me
AP
ប
d1cos t
/
Ž 12 .
where m is the mass of the electron, e is the unit charge, AP is the apparent barrier height, and ប is the Planck constant divided by 2 . From Eq. Ž12., the tunneling current flows exponentially with d1cos t and reaches a maximum at t s 0 where dŽ t . reaches a minimum value of d 0 y d1. 2.4. The separation of the wa¨ eform of the displacement current from the wa¨ eform of the tunneling current
Fig. 2. Ža. Theoretical waveforms of displacement current as a function of the ratio d 0rd1. The waveforms of displacement current are normalized and calculations are shown for the ratios d 0rd1 s ⬁, 10, 5, 2 and 1.1. Žb. Theoretical peak phase of displacement current as a function of the ratio d 0rd1 .
As mentioned above, the waveform of the external circuit current I Ž t . is the sum of the waveforms of the displacement and tunneling current. From Eqs. Ž9. and Ž12., it is clear that the waveforms of the displacement and tunneling currents are odd and even functions with respect to time, respectively. Consequently, the displacement current ID Ž t . and the tunneling current IT Ž t . are given as ID Ž t . s
I Ž t . y I Ž yt . , 2
Ž 13 .
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
and IT Ž t . s
I Ž t . q I Ž yt . , 2
Ž 14 .
respectively. 3. Experiment The apparatus used in this paper is based on the ultra high vacuum STM system ŽUNUISOKU, USM501. w9x. Some improvements, e.g. electrical shields of the tip piezo, voltage source for z-axis piezo, methods of approaching and maintaining the distance between the probe and the sample, and programs for measurements have been made using it. The probe is vibrated by applying a sinusoidal oscillating voltage with a multifunction synthesizer ŽNF, 1945.. The vibrating frequency of the z-axis piezo is 1632 Hz, which is smaller than the resonance frequency Ž4 kHz. of the piezo. The vibrating amplitude, d1 s 4.16 nm. The mean distance between the probe and the sample, d 0 , is approximately 2᎐15 nm, and is adjusted using a tunneling current feedback loop whilst vibrating the probe at a constant VP . When the feedback loop is turned off, the waveform measurement of the external circuit current I Ž t . is carried out. I Ž t . is of the orders of femto- to picoamps. A high-speed current amplifier ŽKeithley, 428. is used for converting an I Ž t . signal to a voltage type signal. This signal voltage is applied to a digital storage oscilloscope ŽTektronix, TDS 540D., and the I Ž t . waveform is averaged over 2000 cycles. The determination of a datum point which corresponds to t s 0 from the experimental waveform data is important. As shown in Fig. 2a, ID Ž t . is an odd function with angler frequency , and becomes a sine wave when the ratio d 0rd1 is large enough. Under experimental conditions, it is easy to set d 0rd1 for a large value, e.g. d 0rd1 s 13.3 Ž d 0 s 10.0 nm, and d1 s 0.75 nm. w9x and to make the ID Ž t . waveform sinusoidal. When a square wave with angler frequency 2 is multiplied to the ID Ž t . waveform under large d 0rd1 conditions, the integrated value with respect to t between yr and r always becomes zero. At the same time, the integrated value due to the multiplication of IT Ž t . and the square wave with angular frequency 2 , which becomes zero only when the phase is set to the datum point. It should be noted that this multiplication process of the square wave with angular frequency 2 to the external circuit current I Ž t . can also cancel the current offset due to the intrinsic offset of the current amplifier. In this experiment, the datum point, t s 0, is determined numerically. Briefly, one period Žyr- t - r . of the I Ž t . waveform data is divided into four parts. The I Ž t . data in each quarter part are multiplied by q1 or y1 so as to multiply the
207
square function of 2 , and are integrated in the region yr- t - r. We can determine the datum point of t s 0 where the integration becomes zero. Finally, the measured waveform of I Ž t . is separated into the waveform of displacement current ID Ž t . and that of the tunneling current IT Ž t . using Eqs. Ž13. and Ž14. by applying the evaluated datum point of t s 0. The mean displacement current and the mean tunneling current are also measured by using the twophase lock-in amplifier ŽNF, 5640. as in the same manner in our previous paper w7᎐9x. The tungsten probe is made using an electrochemical etching method w7,13,14x. The radius of the probe was 6.7 m, which was determined by scanning electron microscopy ŽSEM.. The sample was highly oriented pyrolytic graphite ŽHOPG., which was cleaved by polyimide tape in the air, and was introduced in the measurement chamber without further treatment. All measurements were carried out at room temperature in vacuum pressure, which was maintained below 3 = 10y9 torr throughout the experiment. 4. Results and discussions Fig. 3 shows typical waveforms of the external circuit current I Ž t . at VP s y3.0 V. The current set-points for tunneling current feedback were set to y3.5 and y2.5 pA. In Fig. 3, the external circuit current I Ž t . Žthe sum of the tunneling current IT Ž t . and displacement current ID Ž t .. are observed. Briefly, when the distance dŽ t . is close to a minimum at t s 0, the tunneling current IT Ž t . flows since IT Ž t . is exponentially proportional to ydŽ t .. On the other hand, the displacement current ID Ž t . is clearly observed in the range 0.1- t -
Fig. 3. The waveform measurements of the external circuit current as a function of time. The waveforms are shown for the set point current of y3.5 Žsolid line. and y2.5 pA Žbroken line.. The peak radius of the probe R s 2.5 m, the frequency s 1632 Hz, and the amplitude of the vibration d1 s 4.2 nm.
208
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
Fig. 4. Calculated waveforms of the tunneling and displacement current from the waveforms given in Fig. 3. The waveforms are shown for the set point current of y3.5 Žsolid line. and y2.5 pA Žbroken line..
0.3 ms, because I Ž t . flows in the negative direction compared to the probe voltage VP . Fig. 4 shows the waveforms of the displacement current ID Ž t . and the tunneling current IT Ž t . calculated from the experimental results of I Ž t . in Fig. 3 using Eqs. Ž13. and Ž14., respectively. From Fig. 4, we can see that the waveforms of IT Ž t . and ID Ž t . are successfully separated. In Fig. 4, the waveforms of the displacement current are similar to a sine wave; however, the peak positions are slightly centered as shown in Fig. 2a. The peak values of the displacement current Žset point current . are approximately y2.1 Žy3.5. and y1.8 Žy2.5. pA, respectively. The change in peak value of the displacement current was smaller than that in the tunneling current. This result is reasonable since the peak value of ID Ž t . wEq. Ž10.x does not strongly depend on the mean distance d 0 compared to IT Ž t .. As shown in Fig. 2b, the mean distance d 0 should be evaluated when the peak phase of ID Ž t . is experimentally obtained. In Fig. 4, the peak phase of ID Ž t . Žwith a set point current of y3.5 pA. s "0.36. In this experiment, as the vibration frequency of 1632 Hz is smaller than the resonance frequency of the piezo, the amplitude of the vibration, d1 , is proportional to the applied a.c. voltage of the z-axis piezo, and is calculated as 4.16 nm. Consequently, the mean distance d 0 becomes 9.8 nm by substituting the peak phase and d1 into Eq. Ž11.. Fig. 5 shows the comparison between the theoretical curve and the measurement of the waveform of ID Ž t ..
In Fig. 5, the theoretical curve of ID Ž t . is calculated by Eq. Ž10. using the values of Ž VP y PS y d 2r 0 . s y1.2 V, d 0rd1 s 2.33 ws 1rcosŽ0.36 .x, and R s 6.7 m. There is good agreement between the theoretical and measured values of ID Ž t .. From Fig. 5, the offset voltage due to the work function difference y PS , and excess surface charge yd 2r 0 is found to be 1.8 V, since the applied probe voltage VP was y3 V. The contribution of yd 2r 0 is almost 1.3 V where the work function difference y PS should be approximately 0.5 eV w15x. It should be noted that the mean displacement current ID Ž VP . y VP curve between the W probe and HOPG becomes a straight line w7x, and crosses the VP axis at approximately y1.8 V in this investigation. Since the mean displacement current ID Ž VP . is proportional to ID Ž t ., the voltage shift of y PS y d 2r 0 estimated from ID Ž t . waveform in Fig. 5 corresponds well with the ID Ž VP . y VP dependence. However, the origin of the excessive surface charges has not been clarified in this paper. We recommend surface treatments to clean the surface of both the probe and the sample for future studies. The tunneling current IT Ž t . only flows in the range y0.14- t - 0.14 ms, and the peak value depends on the current set point. The peak values of tunneling current are y16.9 and y8.6 pA with a set point current of y3.5 and y2.5 pA, respectively. The peak tunneling current should be proportional to the set point current; however, the ratio of the peak values of IT Ž t . Ž2.0. in the measurement differs from the ratio of the set point current Ž1.4. in the SPM controller. This difference is found to be due to the internal offset of the external circuit current monitor in the SPM controller. From Fig. 4, the apparent barrier height AP is estimated by substituting the experimental results into Eq. Ž12., which equaled 10 meV. The estimated AP is
Fig. 5. Comparison between the theoretical and experimental displacement current waveforms as a function of time. The theoretical displacement current waveform is calculated by Eq. Ž9. with voltage Ž VP y PS y d 2 r 0 . s y1.2 V, and the ratio d 0 rd1 s 2.33.
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
much smaller than in previous investigations by a few electronvolts w11,12x. It is well known that AP depends on the vibration amplitude and cleanliness of the probe and sample. We think that experimental conditions in which the offset voltage Žy PS y d 2r 0 . and the apparent barrier height is in good agreement with the theoretical values, should be clarified in the next step. As discussed above, we have demonstrated that the mean distance, d 0 , and the offset voltage due to y PS and yd 2r 0 , can be determined by measuring the waveform of ID Ž t .. This method would be useful for investigating local excess charge density of organic thin films. 5. Conclusions We have successfully separated both waveforms of displacement and tunneling currents using a scanning vibrating probe. The waveform of the displacement current is analyzed by assuming the presence of excessive surface charges above the sample. The measured waveform of the displacement current is in good agreement with the theoretical curve. The mean distance between the probe and the sample, and the offset voltage due to excess surface charges and work function difference, are determined from the waveform of displacement current.
209
References w1x G. Binnig, H. Rohrer, C.h. Gerber, E. Weibel, Phys. Rev. Lett. 49 Ž1982. 57. w2x G. Binnig, C.F. Quate, C.h. Gerber, Phys. Rev. Lett. 56 Ž1986. 930. w3x L.A. Bumm, J.J. Arnold, M.T. Cygan et al., Science 271 Ž1996. 1705. w4x J. Ohgami, Y. Sugawara, S. Morita, E. Nakamura, T. Ozaki, Jpn. J. Appl. Phys. 35 Ž1996. 2734. w5x Y. Sugawara, T. Uchihashi, M. Abe, S. Morita, Appl. Surf. Sci. 140 Ž1999. 371. w6x C.C. Williams, W.P. Hough, S.A. Rishton, Appl. Phys. Lett. 55 Ž1989. 203. w7x Y. Majima, S. Miyamoto, Y. Oyama, M. Iwamoto, Jpn. J. Appl. Phys. 37 Ž1998. 4557. w8x Y. Oyama, Y. Majima, M. Iwamoto, J. Appl. Phys. 86 Ž1999. 7087. w9x Y. Majima, Y. Oyama, M. Iwamoto, Phys. Rev. B 62 Ž2000. 1971. w10x Ža. P.M. Morse, H. Freshbach, Methods of Theoretical Physics, Part I, McGraw-Hill, New York, 1953; Žb. B.I. Bleaney, B. Bleany, Electricity and Magnetism, Oxford University Press, London, 1965. w11x G. Binnig, N. Garcia, H. Rohrer, J.M. Soler, F. Flores, Phys. Rev. B 30 Ž1984. 4816. w12x J.K. Gimzewski, R. Moller, Phys. Rev. B 36 Ž1987. 1284. ¨ w13x P.J. Bryant, H.S. Kim, Y.C. Zheng, R. Yang, Rev. Sci. Instrum. 58 Ž1987. 1115. w14x R. Zhang, D.G. Ivey, J. Vac. Sci. Technol. B 14 Ž1996. 1. w15x S.M. Sze, Physics of Semiconductor Devices, Wiley, New York, 1981.
The waveform separation of displacement current and tunneling current using a scanning vibrating probe Yutaka MajimaU , Setsuri Uehara, Tomohiko Masuda, Atsushi Okuda, Mitsumasa Iwamoto Department of Physical Electronics, Tokyo Institute of Technology, 2-12-1 O-Okayama, Meguro-ku, Tokyo 152-8552, Japan
Abstract A measuring system that separates the both waveforms of displacement and tunneling current using a scanning vibrating probe is described. In the measuring system, the displacement and tunneling current flow periodically in accordance with the perpendicular vibration of the probe. The external circuit current is measured by oscilloscope and is separated into both waveforms of the displacement and tunneling current by utilizing the phase difference of them. The waveform of the displacement current is also analyzed by assuming the presence of excessive surface charges above the sample. Consequently, we can determine the mean distance between the probe and sample, and the offset voltage which is built up by excessive surface charges and work function difference of the probe and sample. 䊚 2001 Elsevier Science B.V. All rights reserved. Keywords: Displacement current; Tunneling current; Oscilloscope; Scanning vibrating probe; Surface charge
1. Introduction Recently, many scanning probe microscopes ŽSPM., e.g. scanning tunneling microscope ŽSTM., atomic force microscope ŽAFM., electrostatic force microscope ŽEFM., and scanning capacitance microscope ŽSCM. have been developed and, thus, used to investigate physical properties of organic thin films w1᎐6x. EFM can measure electrostatic properties on the surface, e.g. a non-uniform charge distribution and variations in surface work function by detecting a change in the mechanical resonant frequency of a cantilever w4,5x. In SCM, oscillation voltage is applied to the scanning probe, and the change in capacitance between the probe and sample is detected as a change in resonance frequency using an ultrahigh frequency resonant capac-
U
Corresponding author. Tel.: q81-3-5734-2673; fax: q81-3-57342673. E-mail address: [email protected] ŽY. Majima..
itance sensor w6x. Both EFM and SCM are useful tools to map two-dimensional electrostatic distributions, and use the resonant phenomena. On the other hand, when the probe is vibrated perpendicular to the sample by applying a d.c. probe voltage, both displacement and tunneling current flow periodically in accordance with the vibration of the probe w7,8x. Recently, we have successfully separated the external circuit current across semiconductors into displacement and tunneling current, and then established the measuring method of determining semiconductor local carrier concentration from displacement current᎐voltage curves w9x. Simultaneous measurement of the displacement current and the tunneling current should be significant in characterizing electrical surface properties, e.g. surface potential of organic thin films built up by excessive surface charges and semiconductor carrier concentration. In this paper, we demonstrate the measuring system that separates both waveforms of the displacement and tunneling currents. The waveform of the displacement
0040-6090r01r$ - see front matter 䊚 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 0 - 6 0 9 0 Ž 0 1 . 0 1 0 7 0 - 7
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
current is also analyzed by assuming the presence of excessive surface charges above the sample. The measuring methods of determining the mean distance between the probe and sample, and the offset voltage, which is built up by the excessive surface charges and the work function difference of the probe and the sample are also described. 2. Analysis 2.1. The external circuit current with the ¨ ibrating probe Fig. 1 shows a schematic diagram of the measuring system. When the probe is vibrated, the distance dŽ t . between the probe and sample changes as d Ž t . s d 0 y d1cos t
Ž1.
where is the angler vibration frequency given by s 2 f Ž f s frequency., d1 is the amplitude of vibration, and d 0 is the mean distance between the probe and sample. If the probe is closed to the sample and is vibrated within dŽ t . of 10 nm, the external circuit current I Ž t . includes both the displacement current ID Ž t . and the tunneling current IT Ž t ., and is given by I Ž t . s ID Ž t . q IT Ž t .
Ž2.
where ID Ž t . is the displacement current due to the change in the induced charges on the probe Q1Ž t ., and IT Ž t . is the tunneling current across the vacuum gap between the probe and the sample.
205
2.2. The analysis of the wa¨ eform of the displacement current with surface charges Although the probe has an arbitrary shape, it is assumed to be a sphere because the distance dŽ t . is more than one hundred times smaller than the peak radius R of the probe w dŽ t . < R x w8x. By applying an image method, the capacitance between the probe and a metal sample C Ž t . is approximately given by w8,9x C Ž t . s 4 0 R 0.93y
ž
1 dŽ t . ln . 2 R
/
Ž3.
When uniform excessive surface charges exists at d 2 above the sample, the charges induced on the probe Q1Ž t . is expressed by applying the Green’s reciprocity theorem as w10x Q1Ž t . s C Ž t . V1 y
⬁
H0
V2 Ž r ,d 2 . 2 rd r V1
Ž4.
where V1 is the potential across the vacuum between the probe and the sample, r is the radius from the center of the surface, V2 Ž r, d 2 . is potential built up voltage at position Ž r, d 2 . without the uniform excessive surface charges, and is the charge density of the excessive surface charges. Assuming dŽ t . < R, the electric flux from the sample to the probe becomes perpendicular to the sample at the position Ž r, d 2 ., and the voltage ratio V2 Ž r, d 2 .rV1 becomes V2 Ž r ,d 2 . d s 2 V1 lŽ r .
Ž5.
where l Ž r . is the length of the electric flux from the sample to the probe at the position r. Substituting Eq. Ž5. into Eq. Ž4., Q1Ž t . becomes Q1Ž t . s C Ž t . V1 y
Fig. 1. Schematic diagram of a tunneling and displacement current simultaneous measurement system. The current which flows between the probe and the sample due to the static probe bias voltage VP , and the time varying probe᎐sample distance dŽ t . is the sum of the waveforms of a tunneling current IT Ž t . and displacement current ID Ž t ., which is measured by a digital storage oscilloscope. The mean tunneling current, IT Ž VP ., and the mean displacement current, ID Ž VP . are separated using a 2-phase lock-in amplifier.
⬁
d2
H0 l Ž r . 2 rd r .
Ž6.
The second term of Eq. Ž6. includes the surface integral of the capacitance between the probe and the sample, because l Ž r . is the length of the electric flux from the sample to the probe. Consequently, Eq. Ž6. is re-expressed as Q1Ž t . s C Ž t . V1 y
ž
d 2 . 0
/
Ž7.
The probe voltage VP is shared by the potential V1
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
206
and the work function difference between the probe and the sample PS , and is given by VP s V1 q PS .
Ž8.
Consequently, the displacement current ID Ž t . is given by differentiating Eq. Ž7. as d 2 ID Ž t . s 4 0 R VP y P S y 0
ž
=
ž
ysin t d 0rd1 y cos t
uniform excessive surface charges to ID Ž t . appears as the voltage shift yd 2r 0 as in the case with PS . Since the differentiation of Eq. Ž9. with t becomes 0 at the peak Žd ID Ž t .rdt s 0., both the peak value ID Ž t . max and peak phase max of the displacement are given by ID Ž t . max s "4 0 R VP y PS y
/ž
2
ž
/
=
ž 2 / 'Ž d rd1 0
/
.
1
d 2 0
.2 y 1
,
/ Ž 10 .
Ž9.
Fig. 2a shows the theoretical displacement current waveforms as a function of the ratio d 0rd1. The displacement current waveforms strongly depend on the d 0rd1. It should be noted that the contribution of the
and cosmax s d1rd 0 ,
Ž 11 .
respectively. Fig. 2b shows the theoretical peak phase of the displacement current as a function of the ratio d 0rd1. It should be noted that the peak phase, max , changes steeply with decreasing d 0rd1 , especially in the region d 0rd1 - 4. From Eq. Ž11., the mean distance d 0 can be estimated since the amplitude of vibration d1 can be controlled by changing the oscillation voltage of the z-axes piezo. 2.3. The analysis of the wa¨ eform of the tunneling current Tunneling current IT Ž t . depends on dŽ t ., and is given by w11,12x IT Ž t . A exp
ž
'8 me
AP
ប
d1cos t
/
Ž 12 .
where m is the mass of the electron, e is the unit charge, AP is the apparent barrier height, and ប is the Planck constant divided by 2 . From Eq. Ž12., the tunneling current flows exponentially with d1cos t and reaches a maximum at t s 0 where dŽ t . reaches a minimum value of d 0 y d1. 2.4. The separation of the wa¨ eform of the displacement current from the wa¨ eform of the tunneling current
Fig. 2. Ža. Theoretical waveforms of displacement current as a function of the ratio d 0rd1. The waveforms of displacement current are normalized and calculations are shown for the ratios d 0rd1 s ⬁, 10, 5, 2 and 1.1. Žb. Theoretical peak phase of displacement current as a function of the ratio d 0rd1 .
As mentioned above, the waveform of the external circuit current I Ž t . is the sum of the waveforms of the displacement and tunneling current. From Eqs. Ž9. and Ž12., it is clear that the waveforms of the displacement and tunneling currents are odd and even functions with respect to time, respectively. Consequently, the displacement current ID Ž t . and the tunneling current IT Ž t . are given as ID Ž t . s
I Ž t . y I Ž yt . , 2
Ž 13 .
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
and IT Ž t . s
I Ž t . q I Ž yt . , 2
Ž 14 .
respectively. 3. Experiment The apparatus used in this paper is based on the ultra high vacuum STM system ŽUNUISOKU, USM501. w9x. Some improvements, e.g. electrical shields of the tip piezo, voltage source for z-axis piezo, methods of approaching and maintaining the distance between the probe and the sample, and programs for measurements have been made using it. The probe is vibrated by applying a sinusoidal oscillating voltage with a multifunction synthesizer ŽNF, 1945.. The vibrating frequency of the z-axis piezo is 1632 Hz, which is smaller than the resonance frequency Ž4 kHz. of the piezo. The vibrating amplitude, d1 s 4.16 nm. The mean distance between the probe and the sample, d 0 , is approximately 2᎐15 nm, and is adjusted using a tunneling current feedback loop whilst vibrating the probe at a constant VP . When the feedback loop is turned off, the waveform measurement of the external circuit current I Ž t . is carried out. I Ž t . is of the orders of femto- to picoamps. A high-speed current amplifier ŽKeithley, 428. is used for converting an I Ž t . signal to a voltage type signal. This signal voltage is applied to a digital storage oscilloscope ŽTektronix, TDS 540D., and the I Ž t . waveform is averaged over 2000 cycles. The determination of a datum point which corresponds to t s 0 from the experimental waveform data is important. As shown in Fig. 2a, ID Ž t . is an odd function with angler frequency , and becomes a sine wave when the ratio d 0rd1 is large enough. Under experimental conditions, it is easy to set d 0rd1 for a large value, e.g. d 0rd1 s 13.3 Ž d 0 s 10.0 nm, and d1 s 0.75 nm. w9x and to make the ID Ž t . waveform sinusoidal. When a square wave with angler frequency 2 is multiplied to the ID Ž t . waveform under large d 0rd1 conditions, the integrated value with respect to t between yr and r always becomes zero. At the same time, the integrated value due to the multiplication of IT Ž t . and the square wave with angular frequency 2 , which becomes zero only when the phase is set to the datum point. It should be noted that this multiplication process of the square wave with angular frequency 2 to the external circuit current I Ž t . can also cancel the current offset due to the intrinsic offset of the current amplifier. In this experiment, the datum point, t s 0, is determined numerically. Briefly, one period Žyr- t - r . of the I Ž t . waveform data is divided into four parts. The I Ž t . data in each quarter part are multiplied by q1 or y1 so as to multiply the
207
square function of 2 , and are integrated in the region yr- t - r. We can determine the datum point of t s 0 where the integration becomes zero. Finally, the measured waveform of I Ž t . is separated into the waveform of displacement current ID Ž t . and that of the tunneling current IT Ž t . using Eqs. Ž13. and Ž14. by applying the evaluated datum point of t s 0. The mean displacement current and the mean tunneling current are also measured by using the twophase lock-in amplifier ŽNF, 5640. as in the same manner in our previous paper w7᎐9x. The tungsten probe is made using an electrochemical etching method w7,13,14x. The radius of the probe was 6.7 m, which was determined by scanning electron microscopy ŽSEM.. The sample was highly oriented pyrolytic graphite ŽHOPG., which was cleaved by polyimide tape in the air, and was introduced in the measurement chamber without further treatment. All measurements were carried out at room temperature in vacuum pressure, which was maintained below 3 = 10y9 torr throughout the experiment. 4. Results and discussions Fig. 3 shows typical waveforms of the external circuit current I Ž t . at VP s y3.0 V. The current set-points for tunneling current feedback were set to y3.5 and y2.5 pA. In Fig. 3, the external circuit current I Ž t . Žthe sum of the tunneling current IT Ž t . and displacement current ID Ž t .. are observed. Briefly, when the distance dŽ t . is close to a minimum at t s 0, the tunneling current IT Ž t . flows since IT Ž t . is exponentially proportional to ydŽ t .. On the other hand, the displacement current ID Ž t . is clearly observed in the range 0.1- t -
Fig. 3. The waveform measurements of the external circuit current as a function of time. The waveforms are shown for the set point current of y3.5 Žsolid line. and y2.5 pA Žbroken line.. The peak radius of the probe R s 2.5 m, the frequency s 1632 Hz, and the amplitude of the vibration d1 s 4.2 nm.
208
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
Fig. 4. Calculated waveforms of the tunneling and displacement current from the waveforms given in Fig. 3. The waveforms are shown for the set point current of y3.5 Žsolid line. and y2.5 pA Žbroken line..
0.3 ms, because I Ž t . flows in the negative direction compared to the probe voltage VP . Fig. 4 shows the waveforms of the displacement current ID Ž t . and the tunneling current IT Ž t . calculated from the experimental results of I Ž t . in Fig. 3 using Eqs. Ž13. and Ž14., respectively. From Fig. 4, we can see that the waveforms of IT Ž t . and ID Ž t . are successfully separated. In Fig. 4, the waveforms of the displacement current are similar to a sine wave; however, the peak positions are slightly centered as shown in Fig. 2a. The peak values of the displacement current Žset point current . are approximately y2.1 Žy3.5. and y1.8 Žy2.5. pA, respectively. The change in peak value of the displacement current was smaller than that in the tunneling current. This result is reasonable since the peak value of ID Ž t . wEq. Ž10.x does not strongly depend on the mean distance d 0 compared to IT Ž t .. As shown in Fig. 2b, the mean distance d 0 should be evaluated when the peak phase of ID Ž t . is experimentally obtained. In Fig. 4, the peak phase of ID Ž t . Žwith a set point current of y3.5 pA. s "0.36. In this experiment, as the vibration frequency of 1632 Hz is smaller than the resonance frequency of the piezo, the amplitude of the vibration, d1 , is proportional to the applied a.c. voltage of the z-axis piezo, and is calculated as 4.16 nm. Consequently, the mean distance d 0 becomes 9.8 nm by substituting the peak phase and d1 into Eq. Ž11.. Fig. 5 shows the comparison between the theoretical curve and the measurement of the waveform of ID Ž t ..
In Fig. 5, the theoretical curve of ID Ž t . is calculated by Eq. Ž10. using the values of Ž VP y PS y d 2r 0 . s y1.2 V, d 0rd1 s 2.33 ws 1rcosŽ0.36 .x, and R s 6.7 m. There is good agreement between the theoretical and measured values of ID Ž t .. From Fig. 5, the offset voltage due to the work function difference y PS , and excess surface charge yd 2r 0 is found to be 1.8 V, since the applied probe voltage VP was y3 V. The contribution of yd 2r 0 is almost 1.3 V where the work function difference y PS should be approximately 0.5 eV w15x. It should be noted that the mean displacement current ID Ž VP . y VP curve between the W probe and HOPG becomes a straight line w7x, and crosses the VP axis at approximately y1.8 V in this investigation. Since the mean displacement current ID Ž VP . is proportional to ID Ž t ., the voltage shift of y PS y d 2r 0 estimated from ID Ž t . waveform in Fig. 5 corresponds well with the ID Ž VP . y VP dependence. However, the origin of the excessive surface charges has not been clarified in this paper. We recommend surface treatments to clean the surface of both the probe and the sample for future studies. The tunneling current IT Ž t . only flows in the range y0.14- t - 0.14 ms, and the peak value depends on the current set point. The peak values of tunneling current are y16.9 and y8.6 pA with a set point current of y3.5 and y2.5 pA, respectively. The peak tunneling current should be proportional to the set point current; however, the ratio of the peak values of IT Ž t . Ž2.0. in the measurement differs from the ratio of the set point current Ž1.4. in the SPM controller. This difference is found to be due to the internal offset of the external circuit current monitor in the SPM controller. From Fig. 4, the apparent barrier height AP is estimated by substituting the experimental results into Eq. Ž12., which equaled 10 meV. The estimated AP is
Fig. 5. Comparison between the theoretical and experimental displacement current waveforms as a function of time. The theoretical displacement current waveform is calculated by Eq. Ž9. with voltage Ž VP y PS y d 2 r 0 . s y1.2 V, and the ratio d 0 rd1 s 2.33.
Y. Majima et al. r Thin Solid Films 393 (2001) 204᎐209
much smaller than in previous investigations by a few electronvolts w11,12x. It is well known that AP depends on the vibration amplitude and cleanliness of the probe and sample. We think that experimental conditions in which the offset voltage Žy PS y d 2r 0 . and the apparent barrier height is in good agreement with the theoretical values, should be clarified in the next step. As discussed above, we have demonstrated that the mean distance, d 0 , and the offset voltage due to y PS and yd 2r 0 , can be determined by measuring the waveform of ID Ž t .. This method would be useful for investigating local excess charge density of organic thin films. 5. Conclusions We have successfully separated both waveforms of displacement and tunneling currents using a scanning vibrating probe. The waveform of the displacement current is analyzed by assuming the presence of excessive surface charges above the sample. The measured waveform of the displacement current is in good agreement with the theoretical curve. The mean distance between the probe and the sample, and the offset voltage due to excess surface charges and work function difference, are determined from the waveform of displacement current.
209
References w1x G. Binnig, H. Rohrer, C.h. Gerber, E. Weibel, Phys. Rev. Lett. 49 Ž1982. 57. w2x G. Binnig, C.F. Quate, C.h. Gerber, Phys. Rev. Lett. 56 Ž1986. 930. w3x L.A. Bumm, J.J. Arnold, M.T. Cygan et al., Science 271 Ž1996. 1705. w4x J. Ohgami, Y. Sugawara, S. Morita, E. Nakamura, T. Ozaki, Jpn. J. Appl. Phys. 35 Ž1996. 2734. w5x Y. Sugawara, T. Uchihashi, M. Abe, S. Morita, Appl. Surf. Sci. 140 Ž1999. 371. w6x C.C. Williams, W.P. Hough, S.A. Rishton, Appl. Phys. Lett. 55 Ž1989. 203. w7x Y. Majima, S. Miyamoto, Y. Oyama, M. Iwamoto, Jpn. J. Appl. Phys. 37 Ž1998. 4557. w8x Y. Oyama, Y. Majima, M. Iwamoto, J. Appl. Phys. 86 Ž1999. 7087. w9x Y. Majima, Y. Oyama, M. Iwamoto, Phys. Rev. B 62 Ž2000. 1971. w10x Ža. P.M. Morse, H. Freshbach, Methods of Theoretical Physics, Part I, McGraw-Hill, New York, 1953; Žb. B.I. Bleaney, B. Bleany, Electricity and Magnetism, Oxford University Press, London, 1965. w11x G. Binnig, N. Garcia, H. Rohrer, J.M. Soler, F. Flores, Phys. Rev. B 30 Ž1984. 4816. w12x J.K. Gimzewski, R. Moller, Phys. Rev. B 36 Ž1987. 1284. ¨ w13x P.J. Bryant, H.S. Kim, Y.C. Zheng, R. Yang, Rev. Sci. Instrum. 58 Ž1987. 1115. w14x R. Zhang, D.G. Ivey, J. Vac. Sci. Technol. B 14 Ž1996. 1. w15x S.M. Sze, Physics of Semiconductor Devices, Wiley, New York, 1981.