s=Poisson's ratio=0.33, a = radius of the plate =.127 m, t = thickness of the plate= 1.9 cm, and Q =modulus of elasticity of the plate=1.86x1010 N/m2. With the indicated P, Y is only 8.7 pm. For frequencies on resonance, the amplitudes of vibration should be no larger than 10 times this value with the epoxy and polyurethane damping [67]. Since the assumed pressure variations were larger than expected and did not account for any attenuation due to the polyurethane foam, no further stiffening of the plate was performed.

Figure 28-Block diagram of tun

neling electronics.

Tunneling Electronics

The electronics used to measure the conduction properties of the tunneling devices are shown in figures 28 and 29. Requirements of the electronics were that it permit one to test devices whose impedances could range from 10-2 to 10" ohms with dc test voltages of typically 10 mV. The design shown in figure 28 utilized an operational amplifier in a follower configuration to insure that, other than voltage drops in the current leads, the

GDC VOLTMETER

Z IN Z 100 OHMS

output impedance of the voltage source would be less than 0.005 ohm. The operational amplifier was a 356H integrated circuit device. The four-wire lead system was carried through to the connection points on the electrode holders shown in figure 25. With all systems of the tunneling experiment in operation, i.e., vacuum system, temperature control system, high voltage power supply for the micropositioning assembly, and the tunneling electronics, the total system was carefully debugged for ground loop problems and 60 Hz pickup. The noise current in the tunneling electronics after this process was about 10-11 A. This value was measured with a 108 ohm test resistor substituted for the tunneling device and obtained from both the I-V characteristics of the resistor and the output of the logarithmic current to voltage converter. The major source of this noise was the operational amplifier and could have been reduced with a more elementary resistive voltage generator. However, the level was adequate for this experiment, and the alternative was a greatly increased source resistance.

Both dc voltmeters employed with the tunneling electronics had floating-guarded inputs with dc common-mode rejection ratios of greater than 140 dB. The voltmeter used to measure the bias voltage applied to the tunneling device had a gain of 10 with readout resolution to 10 μV. The voltmeter for measuring the tunneling current, in the I-V configuration of the electronics, had variable gains up to 10° with a meter noise of about 150 nV p-top.

The logarithmic current-to-voltage amplifier output was trimmed according to the manufacturer's specifications. After warmup, the offset was less than 100 μV. Specifications for the amplifier modules were that the output voltage would be a linear function of the logarithm of the input current over a range from 10-9 to 10-3 A to within 1%. Measurements with test resistors showed that, in addition, the nonlinearity was only 5% for the positive polarity module and less than 2% for the negative polarity module for currents of 10-10 A. To reduce the acoustical noise level of the chart recorder when the tunneling device formed an open circuit, a lowpass filter with a cutoff frequency of 32 Hz (see figure 29c) was installed.

In operation, the electronics were changed from the Log Icv-S configuration shown in figure 28 to the configuration for I-V measurements by first shorting the input of the Log module with the 1 ohm resistor, disconnecting the Log module and the piezoelectric sweep generator and finally connecting the dc voltmeter for current detection.

Changing back to the Log Icv-S configuration was performed in a similar manner.

4. Experimental Results and Analysis

Taking into account the extreme delicacy of the interelectrode spacing adjustments, the apparatus described in section 3 has proved to be very reliable and to give reproducible results. The data which will be presented were obtained with the same essential characteristics in two separate experiments with data being obtained over a period of several weeks in both instances.

After several unsuccessful attempts at getting the apparatus to perform as anticipated, a standard sequence of operations was evolved which permitted the experiment to be carried out in a consistent manner. Following formation of the electrodes and their installation into the holder and micropositioning assembly, as described in section 3, the assembly was placed on a temperature-controlled plate of copper. The temperature of the plate was maintained at (300.05) K which was the planned operating temperature for the experiment. The electrode spacing was then observed with a low power stereo-microscope and adjusted with the differential-screw mechanism until the electrodes appeared as shown in figure 30.

Concurrent with this adjustment the current flow through the electrodes for an applied voltage of 10 mV was monitored with the tunneling electronics. Final adjustment of the left electrode in the sense of figure 25, was such that with the PZ element at the maximum extension possible in air the electrodes would just make contact. Since the extension of the PZ element in air was only 0.7 of that possible in vacuum, slight misadjustments could be corrected after installation in the temperature-controlled vacuum system. Misadjustments out of range of the PZ element, either in contraction or expansion, could be corrected with small, ±0.5 K, changes in the operating temperature. Use of the temperature-controlled copper plate was required to overcome the expansion and contraction generated by unknown changes in temperature resulting from body heat during the adjustment pro

cess.

All parts of the electrode holder and micropositioning assembly were firmly clamped in place at this time. The assembly was then allowed to equilibrate with "hands-off." (Plastic gloves over cotton gloves were actually used at all times during the assembly to provide thermal insulation and to insure the cleanliness required for UHV.) After con

firming that an open and a short could be produced by contracting and expanding the PZ element, the electrode assembly was installed in the vacuum system and pumped to a pressure of approximately 1 X 10-8 Torr. This usually required several weeks with the small ion pump which was used on the vacuum system.

Determining the PZ element voltage and operating temperature at which the electrodes were positioned to within 1 to 2 nm of each other was accomplished by searching for the abrupt change in tunneling current as the electrode spacing was swept through the tunneling region. With the circuit shown in figure 27 the sweep rate for a range of 5 nm was approximately 0.1 nm/s. The search was greatly facilitated with the logarithmic current amplifier. In fact, all attempts at finding the required PZ voltage and temperature settings without the use of a logarithmic amplifier were unsuccessful. After completing this procedure to locate the tunneling region the first time, successive searches were not difficult.

Data and Analysis

The first sets of Log Iv-S data, while exhibiting the character of many orders of magnitude change in current over 1 to 2 nm change in electrode spacing, contained much structure akin to noise; see figure 31. However, some of the structure may be due to the oscillations in the tunneling probability predicted by numerical calculations based on an exact solution to Schrödinger's equation [45]. Regardless of the possibilities, the exploration of the phenomenon was prevented by an accidental electrical discharge as an attempt was being made to measure the constant-current characteristics which were measured in both previous vacuum tunneling experiments [12].

The series of measurements which was made subsequent to this accidental discharge of the constant-current power supply will be referred to as the first experiment. Representative Log Icv-S data obtained during this experiment are given in figures 32a and 32b. A comparison of figures 32 and 31 shows that much of the structure present in figure 31 was probably due to fluctuating surface conditions. The larger scale oscillations in figure 31 were not found in any subsequent Log Icv-S measurements even though they were consistently

present in all measurements prior to the accidental discharge. Exploration of the meaning of the oscillations and the conditions necessary for their observation was left for future experiments."

The overall shape and features of the data shown in figure 32 were reproduced about 50 times over a period of several weeks. Small changes in average slope and local details were observed as the electrodes were brought into contact during repeated closing and opening of the electrode spacing. All the Log Icv-S data had three characteristic regions. Expressed in terms of the tunneling current, the first of these regions was the initial transition into the current range of the Log amplifier. This region extended up to currents of approximately 10-10 A and covered the non-linear part of the Log amplifier's response. The direct tunneling region usually extended from currents of 10-10 A up to 10- A for bias voltages of 10 mV. The final region occurred as the spacing of the electrodes was such that multiple portions of the electrode surface, other than the previously dominant part, began to make significant contributions to the total current

"Subsequent investigations of this phenomenon have proved very interesting. R. S. Becker, J. A. Golovchenko, and B. S. Swartzentruber (Electron Interferometry at Crystal Surfaces, Phys. Rev. Lett. 55 (1985) 987) and G. Binnig, K. H. Frank, H. Fuchs, N. Garcia, B. Reihl, H. Rohrer, F. Salvan, and A. R. Williams (Tunneling Spectroscopy and Inverse Photoemission: Image and Field States, Phys. Rev. Lett. 55 (1985) 991) demonstrated oscillations in the tunneling voltage as a function of electrode spacing for a constant tunnel current. Figure 31 is a graph of tunneling current as a function of electrode spacing for a constant bias voltage. The scale of the structure here is similar to that shown in the two references cited.

and as the initially dominant portions made contact."

A second attempt at obtaining constant-current measurements was made with a different power supply. In this attempt the transient discharge occurred again and was sufficient to microscopically weld the electrodes. Efforts to melt the bridge resulted in broken lead wires. The entire tunneling system was therefore disassembled, new lead wires installed, repositioned as described earlier, reassembled and all of the set-up operation repeated. Once the vacuum was at the 10-8 Torr level, the electrodes were cleaned with controlled capacitive discharges. A representative Log Icv-S graph from this second experiment is given in figure 33. Five discharges of both polarities obtained from a 0.47 ufd capacitor charged to 14 V were used for the cleaning and/or shaping of the electrode surfaces. The surface condition of the electrodes for the data of figure 33 is obviously different from that of figure 32, but the average slopes in the direct tunneling region of the two sets of data are approximately equal. The data in figure 33 were also reproduced a large number of times over several weeks.

The electrode surfaces were examined in detail in a SEM after the completion of both experiments. No evidence of the discharges could be found.

To confirm that the shape and magnitude of the Log Icv-S graphs were not being significantly affected by the time response of the Log amplifier, a very slow scan of the PZ element's voltage was performed. The data shown in figure 34 were obtained at a scan rate of 0.01 nm/s. One may conclude from a comparison of figures 33 and 34 that the shape of the Log curves was not affected.

A Log Icv versus time measurement was also performed to check for temperature and any other instabilities in the experiment. Results are shown in figure 35. None of the changes in current appears to be the result of temperature variations since the transitions occur so rapidly. Changes such as the ones shown in figure 35 could be due to either sudden changes in surface conditions generated by the relatively large electric fields involved or to mo

"There have been two subsequent observations of the exponential variation of tunneling current as a function of electrode spacing for a constant bias voltage: G. Binnig, H. Rohrer, Ch. Gerber, and E. Weibel, Tunneling Through a Controllable Vacuum Gap, Appl. Phys Lett. 10 (1982) 178; and C. F. Quate, Low-Temperature Vacuum Tunneling Spectroscopy, Appl. Phys. Lett. 45 (1984) 1240. The capability for making such observations is implicit in the work by Becker, et al. cited in footnote (d) and in the work by Moreland, et al., cited in footnote (g), but no explicit graphs of current versus distance or equivalent are given.