Figure 23-Block diagram of temperature control electronics. was to use the output of a bridge to drive a high gain amplifier and compensation network to account for the lags of the detectors and stagemasses, then to close the control loop by incorporating a thermistor detector as one element of the bridge. A full discussion of the electronics of both control stages is given in Appendix V. There it is shown that one of the most important parameters of the control loop is the time response of the thermistors with respect to changes in power input to the heaters. For this reason, the thermistors were mounted in a manner to allow the closest possible coupling between the heaters and the thermistors.

The principal difference between the two stages of temperature control was that a dc bridge and a sensor amplifier were used for the outer stage while an ac excited bridge and lock-in amplifier were used for the inner stage. The compensation

OVERPRESSURE RELEASE

network, power amplifier and heaters were tailored for the requirements of each stage. Values for the heat capacities, thermal resistances, and masses of each stage are given in Appendix V.

Both controllers were designed to allow convenient and accurate changes in operating temperature. The outer stage's setpoint could be changed in 2 mK increments with the use of a switched resistor network. Setpoints for the inner stages were changed with a seven-digit ratio transformer which permitted 10 μK increment changes.

Performance of the outer control stages was checked by using the inner stage detector system as a temperature monitor. When this stage's compensation network was adjusted as described in Appendix V, temperature deviations from the setpoint, measured over a 10-hour period, were no greater than 0.5 mK. The only check on the inner control stage's performance was to monitor the stability of the interelectrode spacing. The results of this check are given in section 4 where it is shown that no changes in electrode spacing due to temperature variations were observed. A major indication of the sensitivity of the inner stage controller was that a setpoint change of 30 μK would cause an observable change in the output of this stage's sensor amplifier. The response of both stages to setpoint changes is described in Appendix V.

Vacuum System for the Tunneling Experiment

A schematic diagram of the vacuum system used for the tunneling experiment is given in figure 24.

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TITANIUM SUBLIMATION PUMP

in figure 26 provides a system which is compatible with ultra-high vacuum, has mechanical rigidity to maintain electrode spacings to stabilities of approximately 1 pm, and permits the electrodes to be assembled into a tunneling structure on a laboratory scale. In addition, the assembly is capable of producing interelectrode spacings of 1 to 2 nm and has the facility to change the electrode spacing in a rapid and convenient manner.

The basic approach of this design is that a precision-differential screw mechanism is inserted at point 11 in figure 25 to position the left electrode clamp, item 10, which contains one gold electrode until the electrode spacing is less than the distance which can be spanned by the piezoelectric (PZ) element. At this point, all components of the assembly are clamped rigidly in place, the differential-screw mechanism is removed, and final fine tuning of the electrode spacing is achieved by temperature adjustment and piezoelectrically generated displacements of the second electrode holder. With reference to figure 25, the left electrode holder is composed of the electrode clamp, and a differential-screw-mount. Both were made of OFHC copper to obtain minimum thermal resis

tance between the electrode and the holder housing and minimum electrical resistance between the electrode and its electrical connection. The electrode clamp was essentially two half-cylinders connected together by a 0.25 mm × 0.5 mm flexure along the length of the clamp and located next to the hole for the electrode. A separate screw is provided for clamping the electrode into place. The mount for the differential-screw had a similar form. All other clamping is performed with the electrode-holder housing which is cut only in the shaded area of the drawing.

Each vernier division of the differential-screwmechanism corresponded to an output displacement of about 25 nm. This resolution was such that approximately one-quarter turn of the differentialscrew's input covered the PZ element's 500 nm range.

The right electrode holder consisted of an electrode clamp mounted to a double diaphragm-flexure support to insure axial motion of the electrode, a PZ element, and a mechanism to prestress the driving element-flexure combination so that microscopic motion losses would be minimized. End caps for the PZ element and the prestressing mechanism were made from hardened steel. The di

aphragm-flexures and piezoelectric element were prestressed with a force of approximately 890 N (200 pounds). All other parts of the electrode holder, except the 304 stainless steel fasteners, were machined from OFHC copper. The PZ element was electrically insulated from the rest of the holder with four sapphire spheres.

The PZ element consisted of six ceramic discs, each 1.27 cm in diameter by 0.25 cm thick. The ceramic was a barium-titanate-zirconate composition which has very low hysteresis, linear characteristics [61]. The relevant expansion coefficient for the material is d33=225 pm/V for fields along the poled direction of the ceramic; here perpendicular to the disc faces. The individual disks and end caps were bonded into one element with the use of a low viscosity, electrically conductive epoxy. The epoxy's electrical resistivity was less than 0.002 ohm-cm [51]. After baking in air at 100 °C for one hour, the outgassing rate was sufficiently low that the 10-10 Torr base pressure of a bell jar system with a 50 1/s ion pump was unaffected by the presence of the epoxy bonded piezoelectric element.

Displacement characteristics of the completely assembled micropositioning system were measured before and after the tunneling experiments described in section 4. Before the experiments, the displacements were measured with a precise but uncalibrated mechanical gauge to be (.56±.06) nm/V. After the experiment, the displacements were measured with a Hewlett-Packard 5526A laser interferometer measurement system in combination with a 10565B remote interferometer and retroreflector. This measurement system enabled displacements to be measured with an accuracy of

±25 nm. For both expansion and contraction of the piezoelectric element, the displacements were measured as (0.47±.03) nm/V. Thus, taking into account the uncalibrated state of the mechanical gauge, the displacement characteristics of the micropositioning system were stable throughout the experiment.

The need for 1 pm electrode spacing stability combined with the 470 pm/V sensitivity of the PZ element requires that the high voltage power supply used to drive the PZ element have a very low voltage noise level, less than 2 mV. The power supply used for this purpose had a noise level of less than 75 μV peak-to-peak and the capability of being switched in 1 mV increments from -1100 volts to +1100 volts [64]. To enable continuous voltage sweeps over ±10 volts, a ramp generator was added in series with this power supply. The circuit diagram of the ramp generator and a filter circuit to suppress switching transients are shown in figure 27.

Two other experimental techniques for holding and positioning the tunneling electrodes were thoroughly explored before finally adopting the electrode holder and micropositioning assembly design just described. The technique first explored was to fabricate the tunneling structure as a microelectronic device with the use of photolithographic methods. This approach was not adopted because the technology to which the author had access could not meet the dimensional requirements of the tunneling device. However, as a byproduct of this work, the approach may result in an electronic device with a very high transconductance; values up to 1 mho appear feasible. A patent application

on the concept is being submitted to the National Bureau of Standards Patent Review Committee. The concept and a prototype device are described in Appendix IV.5

Lever amplification of the piezoelectric element's length changes was also explored as a possible means to bridge the gap between laboratory scale distances and the microscopic dimensions required by the tunneling experiment. While this technique proved to have excessive vibration levels for the tunneling experiment, it has characteristics which are very useful for scanning-electron and optical microscope stages [65].

Vibration and Acoustical Isolation

In the previous metal-vacuum-metal tunneling experiment [12] similar to this work and in all earlier attempts made in connection with this work, vibrations of the tunneling device structure at the 1 nm level have limited a successful execution of the experiment. Every effort was made, therefore, to carefully examine the mechanical design of each part of the apparatus to insure that all known sources of vibrational energy were attenuated to levels which would not result in detrimental changes in the electrode spacing. The vibrational properties of what was thought to be the most likely contributors to changes in electrode spacing will now be described in terms of one-dimensional models.

Starting with the electrode holder and micropositioning assembly, the most likely contributor is vibrational motion of the right electrode holder as the entire assembly is vibrated along the assembly's axis. This motion could be produced either from acoustical pressure variations on the bottom of the vacuum chamber or from building vibrations driving the isolation table top and, thus, the entire vacuum chamber. As a model of this motion, let a mass, m, be connected by a spring with force constant k, and a viscous damper characterized by the constant C, to a vibrating wall whose displacement is given by x=Ao sin wt. Then the equation of motion of m in terms of x, measured relative to the wall is

Thus, if wo is the lowest resonant mode frequency of the micropositioning assembly for axial vibrations and the full amplitude of the isolation table top's horizontal motion is transmitted along the axis to the electrode holder housing, fo(= wo 2π) must be greater than 6 kHz. This follows with the use of an w of (27)30 radians/s, an x of 40 nm, and a requirement that x be less than 1 pm. The only mechanical element with a resonant frequency near this value is the diaphragm flexures, which were designed to have a resonant frequency of 10 kHz, when unstressed. When stressed, the frequency would be even higher and motion would then be determined almost entirely by the prestressing mechanism.

For motions normal to the axis of the assembly all resonant frequencies are much higher than 10 kHz. The relatively large gold wires were used to avoid low resonant frequencies in those directions. For example, even with a very high modulus of elasticity material such as tungsten, the transverse vibrational resonant frequency of a cantilever only 2 mm long and .025 mm in diameter is 4 kHz [66]. To minimize the affects of any acoustically generated vibrations, the electrode holder and micropositioning assembly are only connected mechanically to the laboratory environment by the bottom plate of the vacuum chamber. This plate is heavily damped both by the epoxy layer for attaching the heater wires and by the polyurethane foam. The four lowest eigenfrequencies of the bottom plate are approximately: 884 Hz, 1.85 kHz, and 3.0 kHz, and 3.5 kHz [66]. These neglect any mass loaded decreases in the frequencies due to the mass of the tunneling assembly, which is supported by the plate and any increases in the frequencies due to the epoxy damping. The lowest of these frequencies again is the most likely source of transmitting acoustical pressure variations to the electrode assembly. As a safety factor for design, a 40 dB white noise spectrum was assumed to exist up to one kHz, i.e., pressure variations, P, with amplitudes of 2× 10-3 N/m2. For frequencies much less than the eigenfrequencies, the vibrational amplitudes, Y, of the plate at the center of the plate would be [55]