Electrode control methodology for a scanning tunneling microscope

Abstract

A control methodology for scanning tunneling microscopy is disclosed. Instead of utilizing Integral-based control systems, the methodology utilizes a dual-control algorithm to direct relative advancement of a STM tip towards a sample. A piezo actuator and stepper motor advances an STM tip towards a sample at a given distance until measuring a current greater than or equal to a desired setpoint current. Readings of the contemporaneous step are analyzed to direct the system to change continue or change direction and also determine the size of each step. In simulations where Proportion and/or Integral control methodology was added to the algorithm the stability of the feedback control is decreased. The present methodology accounts for temperature variances in the environment and also appears to clean and protect the tip electrode, prolonging its useful life.

Claims

1. A control method for using a scanning tunneling microscope in an operation, the method comprising: a. providing a sample electrode and a tip electrode, at least one of which is positioned on a means for coarse movement and at least one of which is positioned on a means for fine movement; b. specifying a set point for a current to be used after tunneling occurs and also an initial value for average noise in the current before tunneling occurs; c. specifying: i. two different incremental voltages, one larger and one smaller, for incrementing the means for fine movement; ii. two different lengths of time, one larger and one smaller, to be used in averaging measured tunneling current; and iii. a current threshold between the average noise in the current before tunneling and the set point for the current after tunneling occurs; d. adjusting the means for fine movement and the means for coarse movement so that there is a measurable tunneling current; e. measuring the tunneling current and obtaining an average tunneling current over a designated time period chosen to be one of the two different lengths of time and determining if the average tunneling current is above or below the threshold; f. if the average tunneling current is below the threshold, actuating the means for coarse movement in a manner to bring the average tunneling current closer to the set point tunneling current value and use the larger time period for a next designated time period; g. if the average tunneling current is above the threshold, actuating the means for fine movement in a manner to bring the average tunneling current closer to the set point tunneling current value and set a smaller time period for a next designated time period; h. repeating steps e through g; wherein the larger incremental voltage and larger length of time are used for coarse approach and the smaller incremental voltage and smaller length of time are used for fine approach, thus more signal averaging is used for sensitivity when the current is small and higher resolution in positioning is possible once tunneling has been established.

2. The control method of claim 1, the given threshold being a current value based upon the geometric mean of the set point tunneling current and the average noise.

3. The control method of claim 2, the smaller period of time being longer than the reciprocal of a resonant frequency of the means for fine movement and the longer period of time being between 1 and 100 ms inclusively.

4. The control method of claim 3, the smaller incremental voltage being at least twice the resolution in a digital-to-analog converter driving the means for fine movement and the larger incremental voltage being less than of the voltage that would cause tip crash once tunneling has been established.

5. The control method of claim 4, further comprising a step of compensating for spreading resistance and thin-barrier corrections, based on simulations in order to specify the larger incremental voltage.

6. The control method of claim 1, the smaller period of time being longer than the reciprocal of a resonant frequency of the means for fine movement and the longer period of time being between 1 and 100 ms inclusively.

7. The control method of claim 6, the smaller incremental voltage being at least twice the resolution in a digital-to-analog converter driving the means for fine movement and the larger incremental voltage being less than of the voltage that would cause tip crash once tunneling has been established.

8. The control method of claim 7, further comprising a step of compensating for spreading resistance and thin-barrier corrections, based on simulations in order to specify the larger incremental voltage.

9. The control method of claim 1, the smaller incremental voltage being at least twice the resolution in a digital-to-analog converter driving the means for fine movement and the larger incremental voltage being less than of the voltage that would cause tip crash once tunneling has been established.

10. The control method of claim 9, further comprising a step of compensating for spreading resistance and thin-barrier corrections, based on simulations in order to specify the larger incremental voltage.

Description

BRIEF DESCRIPTION OF THE DRAWING

(1) The FIGURE is a flowchart detailing steps of a methodology to control electrode approach and separation in an STM.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENT

(2) With reference now to the drawing, a preferred embodiment of the control methodology is herein described. It should be noted that the articles a, an, and the, as used in this specification, include plural referents unless the content clearly dictates otherwise.

(3) The tip electrode in the scanning tunneling microscope is moved relative to the sample in order to be close enough to create a measurable current by quantum tunneling and then feedback control is used to maintain a current to approximate a specified set-point for the current.

(4) In order to obtain sub-nanometer resolution over a range which may be as large as 1 mm, it is generally necessary to combine two different devices to control the tip-sample distance D. A stepper motor for coarse movement, and a piezoelectric actuator (or piezo) for fine movement, may be used for this purpose, which is generally done in scanning probe microscopy. Let D=D.sub.0nCV.sub.p where the stepper motor is moved incrementally in steps having length meters, V.sub.p is the voltage applied to the piezo actuator, and C is the gain of the piezo actuator defined as the linear extension in meters per volt. Here D.sub.0 is the tip-sample distance in meters for n=0 and Vp=0. If V.sub.maxVpV.sub.max, then with a fixed setting of n on the stepper motor, D.sub.0nCV.sub.max<D<D.sub.0n+CV.sub.max. It is necessary for Vmax>/2C so that the total peak-to-peak displacement caused by the piezoelectric actuator exceeds the step-size for incremental motion by the stepper motor in order to continuously cover all values of the distance D with this system. For example, with V.sub.max>/C so that the span covered by the piezo actuator exceeds 2, a value of D in a span of 2 may be centered within the span of the piezo actuator by incrementing the stepper motor by one step of . This synergistic means for combining the stepper motor with a piezoelectric actuator is efficiently and effectively implemented in the algorithm. It is of course to be understood that any other means known or later discovered to control the distance between the tip and sample may also be incorporated into this algorithm. The key functionality is that there is a system for coarse movement and a separate, overlying system for finer movement.

(5) In this algorithm, as well as in applications, it is necessary to use expressions for the tunneling current that correct for the effects of the spreading resistance in the sample [F. Flores and N. Garcia, Voltage drop in experiments of scanning tunneling microscopy for Si, Phys. Rev. B, Vol. 30, August 1984, pp. 2289-2291] and make thin-barrier corrections for small tip-sample distances [J. M. Blanco, C. Gonzalez, P. Jelinek, J. Ortega, F. Flores and R. Perez, First-principles simulations of STM images: From tunneling to the contact regime, Phys. Rev. B, Vol. 70, August 2004, 085405] in order to properly specify E.sub.p1. The basic control algorithm consists of 4 distinct steps, including establishing initial parameters, which may be repeated on various occasions to accomplish the desired separation distance and desired tunneling current between the tip and sample electrodes of an STM. The following variables are defined in the method:

(6) C is the ratio of the length change for the piezo actuator to the voltage, in meters per volt.

(7) D is the distance between the tip and the sample in meters.

(8) D.sub.0 is the tip-sample distance in meters below which I.sub.T is greater than I.sub.T0.

(9) E.sub.P is the voltage step by which V.sub.p is incremented, either E.sub.P1 or E.sub.P2.

(10) E.sub.P1 is the voltage step by which V.sub.p is incremented in the initial approach of the tip, before there is a measurable current.

(11) E.sub.P2 is the voltage step by which V.sub.p is incremented when I.sub.T is significantly greater than I.sub.TN.

(12) I.sub.T is the tunneling current in amperes.

(13) I.sub.TM is the average value of the current I.sub.T in amperes obtained by averaging I.sub.T over time T.

(14) I.sub.TN is the measured rms noise in the current in amperes.

(15) I.sub.T0 is the set-point current specified for the tunneling current in amperes.

(16) n is the number of steps by the stepper motor.

(17) T is the delay time in seconds for each cycle of the algorithm.

(18) T.sub.1 is the delay time during the initial approach of the tip, before there is a measurable current.

(19) T.sub.2 is the delay time when I.sub.T is significantly greater than I.sub.TN.

(20) V.sub.b is the bias voltage applied between the tip and the sample.

(21) V.sub.max is the maximum magnitude for voltage applied to the piezo actuator.

(22) Vp is the voltage applied to the piezo actuator.

(23) V.sub.RES is the DAC resolution for Vp in volts.

(24) is the step size for the stepper motor in meters.

(25) The steps in the exemplary algorithm are as follows:

(26) 1. Initial determinations and settings must be made.

(27) 1.1. Enter the parameters C, I.sub.TN, I.sub.T0, V.sub.b, V.sub.max, V.sub.RES, , as well as the properties of the tip and sample that are required for simulations.

(28) 1.2. Use simulations to approximate the parameter D.sub.0.

(29) 1.3. Calculate E.sub.P1 and E.sub.P2, the steps by which the V.sub.p is incremented, where E.sub.P1 is used in the initial approach and E.sub.P2 is used when I.sub.T is significantly greater than I.sub.TN. E.sub.p2 being at least twice V.sub.RES and the E.sub.p1 being less than of the voltage that would cause tip crash once tunneling has been established. For example, E.sub.P2=4*V.sub.RES and E.sub.P1=D.sub.0/(6*C).

(30) 1.4. Initialize n=0, V.sub.p=0, and E.sub.P=E.sub.P1.

(31) 1.5. Calculate T.sub.1 and T.sub.2, the delay times for pauses in each cycle of the algorithm, where T.sub.1 is used in the initial approach to provide greater accuracy when the tunneling current is small and thus difficult to measure (usually between 1 and 100 ms inclusively to provide greater signal averaging to detect a weaker current), and T.sub.2 is used when I.sub.T is significantly greater than I.sub.TN. For example, T.sub.2 may be as short as 100 svarying with the reciprocal of the resonant frequency of a piezoelectric actuator and the filtering used to smooth the change in V.sub.p. However, T.sub.1 may be 100 times greater, such as 10 ms, to reduce the noise by a factor of 10 by increasing the time for signal averaging.

(32) 1.6. Initialize T to T.sub.1.

(33) 2. Determine I.sub.TM.

(34) 2.1. Set I.sub.TM to zero and start measuring I.sub.T.

(35) 2.2. Measure for time T.

(36) 2.3. Average measured I.sub.T over time T to obtain I.sub.TM.

(37) 3. Increment the stepper motor so that V.sub.p satisfies V.sub.max<V.sub.p<V.sub.max.

(38) IF ((C*V.sub.p>) AND (C*V.sub.p<) GOTO step 4.

(39) IF (C*V.sub.p>) THEN set V.sub.p=0, PAUSE 1 ms, and set n=n+1 ENDIF

(40) IF (C*V.sub.p<) THEN set n=n1, PAUSE 1 ms, and set V.sub.p=0 ENDIF

(41) WRITE n.

(42) WRITE V.sub.p.

(43) GOTO step 2.

(44) 4. Update V.sub.p for the piezo and T for the delay based on I.sub.TM, the average value of I.sub.T.

(45) 4.1. Change E.sub.P between E.sub.P1 and E.sub.P2 and T between T.sub.1 and T.sub.2 as necessary.

(46) IF (I.sub.TM<SQRT(I.sub.T0*I.sub.TN)) set E.sub.P=E.sub.P1 and T=T.sub.1 ENDIF

(47) IF (I.sub.TMSQRT(I.sub.T0*I.sub.TN)) set E.sub.P=E.sub.P1 and T=T.sub.2 ENDIF

(48) 4.2. Update V.sub.p, the voltage on the piezo actuator.

(49) IF (I.sub.TM<I.sub.T0) set V.sub.p=V.sub.p+E.sub.P ENDIF

(50) IF (I.sub.TMI.sub.T0) set V.sub.p=V.sub.pE.sub.P ENDIF

(51) WRITE T

(52) WRITE V.sub.p.

(53) GOTO step 2.

(54) There is an optimum value for the pause T and the voltage step E.sub.P for the piezo actuator during each cycle of the algorithm. During the initial approach before the tunneling current is measurable, set T to the larger value of T.sub.1 for increased signal averaging to provide greater accuracy for earlier response to the tunneling current. However, when I.sub.T is significantly greater than the noise I.sub.TN, set T to the smaller value of T.sub.2 to provide faster response to prevent tip crash. Similarly, during the initial approach before the tunneling current is measurable, set E.sub.p, the voltage step for the piezo actuator, to the larger value of E.sub.p1 to reduce the time that is required to achieve tunneling. However, when I.sub.T is significantly greater than the noise I.sub.TN, set E.sub.p to the smaller value of E.sub.p2 to provide finer resolution in the motion to prevent tip crash.

(55) In initial testing of an earlier version of this algorithm (as described in the parent provisional application), a test fixture similar to that shown in a previous design patent (U.S. Pat. No. D695,801) was used in which coarse positioning is done using a 3-axis stepper motor system (Thor Labs Nanomax) having a step size of 60 nm and total travel of 4 mm on each axis. The piezo actuator (Boston Piezo-Optics PZT-5H radial tube with 0.024 inch wall, 0.394 inch OD, 0.984 inch length) has a travel of 13 nm/V, and has a voltage rating of 288 VDC. However, in order to obtain unusually high resolution, the applied bias was limited to 10V with the D/A converter set for 16-bit resolution in this interval to provide a range of 265 nm with a voltage step size of 300 V corresponding to a nominal displacement of 0.004 nm. The test fixture was mounted on a negative-stiffness vibration isolation platform and placed in an acoustical isolation box. A low-noise current preamplifier (Stanford Research Systems SR570) was used to measure the tunneling current, and this system was interfaced to a desktop computer using LabVIEW. This system has relatively slow operation, with approximately 30 steps of the piezo actuator per second, but the speed will be increased later by using a FPGA and optimal shaping of the waveform of the piezo voltage to minimize effects of the piezo resonance. Thus far, all measurements with this system have been made in air.

(56) The STM system is unusually stable and robust. Typically, the standard deviation of the tunneling current is less than 10% of the mean, and the instrument is stable even when using tunneling currents of 1 A even though the tip is quite close to the sample. The time to establish tunneling is typically less than 10% of that in the commercial systems. Of further note, tungsten tips prepared by electrochemical etching followed by vacuum annealing were used. Typically, with commercial scanning tunneling microscopes, many have found it necessary to anneal each tungsten tip immediately before it is used and the tip lifespan is typically no more than one hour. However, tips used in an STM according to the practices of this methodology have repeatedly been used during a two-week period, and even continuously for periods of over 48 hours, with no further treatment. It is hypothesized that this improvement may be caused by the high stability of the tip approach, which makes tip crash less likely, as well as the more nearly constant characteristics of the electric field. A more nearly constant field may enable cleaning of contaminants from the surface of the tip electrode. Likewise, the lack of fluctuations in the electric field may reduce the stress on the tip electrode by reducing the peak values of the electric field.

(57) Although the present invention has been described with reference to preferred embodiments, numerous modifications and variations can be made and still the result will come within the scope of the invention. As an example, additional step sizes may be incorporated, as may multipliers and dividers to step sizes to provide more dynamic range of motion. Determinations on what to do in the algorithm when a determined value equals a target value are also arbitrary and may be switched. The threshold value to the measured average tunneling current is set as the geometric mean of the targeted tunneling current and the noise current. Other functions, such as a multiple of the noise level may be utilized. No limitation with respect to the specific embodiments disclosed herein is intended or should be inferred.