Optimal Preamp for Tuning Fork signal detection Scanning Force Microscopy. Kristen Fellows and C.L. Jahncke St. Lawrence University

Transcription

1 Optimal Preamp for Tuning Fork signal detection Scanning Force Microscopy Kristen Fellows and C.L. Jahncke St. Lawrence University H. D. Hallen North Carolina State University Abstract In scanning probe microscopy it is critical to maintain small probe sample separations for high resolution imaging. Quartz crystal tuning forks are typically used for detecting shear forces in near-field scanning optical microscopy and normal forces in atomic force related microscopies. Small fiber vibration amplitudes[is THIS THE CASE FOR AFM?] are necessary to reduce imaging artifacts, and to maintain optical resolution. These small vibration amplitudes result in low signal levels. In this paper we compare several tuning fork based detection schemes to determine which solution gives the best signal to noise ratio. We find that a carefully guarded voltage preamp where the tuning fork is driven mechanically performs the best, however, an electrically driven current preamp offers simpler construction with only 30% lower signal to noise ratio.

2 Introduction Near-field scanning optical microscopy (NSOM) and atomic force microscopy (AFM) are both scanned probe techniques that provide high resolution topographical images. Optical information or force information respectively is simultaneously acquired. In each system probe sample separation is a critical parameter for obtaining and understanding high resolution images. One method for regulating the tip-sample separation uses a quartz crystal tuning fork, an idea developed by Karrai and Grober[Karrai 1995]. While this method was first developed for NSOM applications involving shear forces, it is also used for NSOM[DinPingTsai, Moyer] and AFM[Edwards 1997;King Lamb Nunes 2001; Giessibl 1998] with normal force detection. Others describe the advantages of tuning fork feedback vs. optical feedback for NSOM[Karrai 1995] and AFM[Edwards 1997], and there are many papers that discuss ways to improve the scan speed of tuning fork feedback microscopy[us, Giessibl 1998;Serebryakov 2002; Ruiter?]. Each of these developments involves driving the tuning fork and measuring the signal from the tuning fork with a preamplifier. The purpose of this note is to compare several preamplifier and drive techniques to determine the optimal solution with an emphasis on the best signal to noise ratio. When implementing force feedback frequently small fiber vibration amplitude (much less than the approach curve distancensomonly?) is critical in order to reduce scanning artifacts and produce high resolution images. These small vibration amplitudes result in very small signals; in turn these small signals require careful attention to preamplifiers. The question that we address in this paper is which what type of preamplifier and tuning fork driver does one use to obtain the best signal to noise ratio. Typically a high source impedance suggests the use of a current amplifier. However, we explore the possibility of a voltage preamplifier and find that for this application it often outperforms the current preamplifier. We also drive the fork both mechanically and electrically with both types of preamps. Additionally, we compare several different integrated circuits for the two types of amplifiers. We investigate four situations: a current preamp with a mechanical drive (CPMD), a current preamp with an electrical drive (CPED), a voltage preamp with a mechanical drive (VPMD) and a voltage preamp with an electrical drive (VPED).

3 Experiment: The four primary circuits we studied are shown in figure 1. For the voltage preamps, the inputs are carefully guarded to produce optimal results. In each preamp we use an OPA655 operational amplifier (op-amp) from Burr Brown. As we will see, the choice of an op-amp is critical. Many high performance chips have too high of an input capacitance or require careful impedance balance to avoid large voltage noise. The electrically driven current preamp[grober] and the electrically driven voltage preamp have variable capacitors that allow for the subtraction of part of the background signal. Additionally we tested three other preamp circuits using different integrated circuits, ICs, all were driven mechanically. We used an AMP05 instrumentation amplifier with built in guarded inputs as a voltage preamp. (This chip is no longer available, therefore, we do not include the circuit diagram.) We also studied two current preamps. The first used an AD745 IC in a circuit very similar to the OPA655 current preamp except that careful attention was paid to compensating the chip to reduce noise; this required a 10 MW resistor to ground on the plus input and some extra capacitance in the feedback. The final circuit was built around a U430 MOSFET and is described in detail elsewhere [ref]. All of the voltage amplifiers have a gain of 100. All of the current amplifiers have a 10MW feedback resistor followed by a X10 gain stage (except for the U430). In order to oscillate the tuning fork we use either a mechanical or electrical drive. The circuits for the electrical drives are seen in figure 1 (b) and (c). Figure 2 shows the mechanical drive that we employ. One arm of the tuning fork is super glued to the edge of a glass slide, and the other arm of the fork is super glued to the optical fiber. On top of the glass slide we use silver epoxy to attach a shear piezo which drives the tuning fork and to coat the glass to create a ground plane to reduce noise. The shear piezo is driven at the tuning fork resonance generating a sound wave which couples through the glass to the tuning fork itself[ref Eric s PHD]. The use of a glass slide and shear piezo optimizes optical access by minimizing the blockage of reflected light. To determine which of these circuits is optimal for tuning fork detected force feedback, we measured signal to noise ratio for each preamp for several tuning forks

4 using the following experimental procedure. The tuning fork, with a fiber probe glued in place, is connected to the preamp and driven at resonance either electrically or mechanically depending on the preamp. The signal from the preamp is measured as a function of frequency with a SRS 830 Lock-in amplifier interfaced with a Macintosh computer running Labview for data acquisition. The background is subtracted from the peak to determine the total signal level. In order to determine the noise, the signal from preamplifier is measured in the same manner describe above at the tuning fork resonance as a function of time with a 1msec time constant. The standard deviation of this signal is calculated in order to determine the noise. In order to be sure that we are comparing equivalent signal levels between each circuit, we drove the tuning fork in such a manner that the fiber vibration amplitude was the same for each circuit. While this was inherent in the comparison of the mechanically driven amplifiers, in order to compare them with the electrical drive circuits, for each fiber/fork system and preamplifier we measured the fiber vibration amplitude using a method described by Wei Wei and Fann [ref]. The signal and noise measurements at equivalent vibration amplitude for each of the four circuits based on the OPA655 are summarized in the bar graph shown in figure 3. Here the signal levels are normalized across the four different trials to a probe vibration amplitude of 0.5 nm. (The test conditions involved probe vibration amplitudes of 0.2 nm, 0.3 nm, 0.5 nm and 0.85 nm.) Clearly the VPMD has the best performance. We found that both of the electrically driven preamps picked up noise as a function of driving voltage due to the limited common mode rejection ratio of the preamps(we can show a figure here), however, for the small voltages typically used for force feedback the pickup was minimal. We also compared four mechanically driven preamps built around several different integrated circuits, the AMP05 circuit, the U430 circuit, the AD745 circuit and the current and voltage circuits built with the OPA655(CP OPA655 and VP OPA655). Since each of these five circuits employed the same mechanical drive, it was not necessary to measure the tuning fork vibration amplitude; the voltage to the piezo produces the same fiber amplitude for all four circuits. These results are summarized in figure 4. Again, the VP OPA655 has the best performance, however, the OPA655

5 current preamp worked very well and actually outperformed the voltage preamp in one trial. In the same series of experiments, we replaced the OPA655 chip with an AD745 chip. Unless we balance the input impedance of the AD745 chip, the noise is excessive. Balancing the input requires extra capacitance in the feedback and an extra 10 MW resistor from the plus input to ground increasing the calculated noise as we see below. The noise levels that we measure are consistent with what we calculate for the two types of circuits. For the current preamplifier, we use figure 1(d) as a model for the amplifier where the tuning fork is modeled as a resistor, R 1, capacitor (C s ) and inductor all in series together and in parallel with a capacitor, C 1 [ref???]. At resonance, the impedance due to the series capacitor and the inductor cancel, and we are left with a resistor, R 1, in parallel with a capacitor, C 1. We determine R 1 and C 1 by fitting data obtained using the CPED with the background subtraction part of the circuit removed. Each tuning fork/fiber is different, but typical values for the resistance are in the 50 to 80 MΩ range, and typical values of the capacitance are on the order of 1.7 pf. With these values we calculate the noise using the following equations: Vout = det det and È G1+ G2 + s(c1+ C2 + C3) -(G1+ sc1) gamma1 Í Í -(G1+ sc1) G1+ G3 + s(c1+ C3) gamma2 Î Í A -A 0 È G1+ G2 + s(c1+ C2 + C3) -(G1+ sc1) -G2 Í Í -(G1+ sc1) G1+ G3 + s(c1+ C3) 0 Î Í A -A -1 gamma1 = -vna(g1+g2+ s(c1+c2+c3))+g1vn1+ vnb(g1+ sc1)+ in1+g2vn2 gamma2 = -vnb(g1+g3+ s(c1+c3))- G1vn1+ vna(g1+ sc1)+ in2+g3vn3 (1) Here G is one over the resistance, A is the amplifier gain, and s is i2pf. The noise is given by the real part of Vout. The noise sources are the Johnson noise of the tuning fork and the resistors, R1, R2 and R3 respectively corresponding to vn1, vn2 and vn3. The amplifier noise is given by vna = vnb and the current noise is given by in1 = in2. The noise sources are determined individually and added in quadrature. We apply these equations to the OPA655 and AD745 current amplifiers where there are three important differences, the input capacitance (1.3 vs 20 pf), the gain bandwidth product (400MHz vs

6 20MHz/frequency), and a 10meg resistor to ground only on the latter. The noise calculated on the output is a voltage noise that is referenced to the input as a current noise by dividing by the feedback resistor. The noise calculations are summarized in table 1 where the primary noise source is the 10 MW resistor(s). The agreement between measurement and calculation is remarkable in both cases. We also find that if we add the 10 MW resistor to ground on the plus input of the OPA655 that the noise increases to 6µV/ Hz, which is exactly what we would calculate for this case. The noise on the voltage preamp is also primarily due to Johnson noise of the 10 MW resistor. For the calculation of the noise, we model the front end of the amplifier with the circuit shown in the inset of figure 1(a) where R 1 and C 1 are the tuning fork (as described above) and the R 2 and C 2 s are the10 MW resistors and stray capacitance to ground respectively. The circles indicate the Johnson noise, vn1 or vn2, of each resistor where 1 in the case of the tuning fork and 2 for the10 MW resistors. The stray capacitance is determined by measuring the frequency response of the amplifier with a known input and fitting the data using the equation described below. This gives a value on the order of 10 pf. The resulting noise, e, due to the Johnson noise of these three resistances is given by the following equation ( 4vn 1 2 G vn2 2 G 22 ) (2) ( 2G1+ G2) 2 + 4p 2 f 2 ( 2C 1 + C 2 ) 2 Once again G is one over the resistance. We calculate the noise for the AMP05 and OPA655 circuits. Here the primary difference is the voltage noise of the AMP05 which is rather large. A summary of the noise calculations is found in table 1. The calculated noise values are lower than the measured noise values in each case, although the agreement with the OPA655 mechanically driven circuit is much better. The calculation is very sensitive to the capacitance, and our measurement of this value is crude, so we suspect the capacitance is part of the reason for the discrepancy. Putting 10pF capacitors in parallel with the 10MW resistors to ground on the AMP05 circuit reduced the noise to 4µV/ Hz which has much better agreement with the calculation. We note that the VPED typically has a slightly higher noise than its mechanically driven counterpart which

7 increases with drive voltage (due to electrical pickup and limited common mode rejection ratio). Conclusions: Typically high source impedance applications benefit from current preamp configurations, so surprisingly the mechanically driven voltage preamp built with the OPA655 IC has the best signal to noise ratio of all of the circuits tested. If signal to noise is the primary or only consideration, this circuit is the best choice. However, there are other factors that might favor the CPED. Using an electrical drive has tremendous practical advantages over the mechanical drive in terms of the flexibility of implementation; the attachment of the tuning fork to the microscope does not require a bulky drive piezo. The CPED also allows for background subtraction, which is important since the resonance produced by the current preamps can be asymmetric. Additionally, the circuit is somewhat smaller, easier to build, and less expensive. In either case, the choice of the IC to use in the circuit is very important; the OPA655 outperforms all of the other ICs that we tested. The mechanical drive was less susceptible to pickup from the drive voltage than the electrical drive circuits, however, for small voltages (less than 20 mv) the pickup is negligible. This work was supported by the National Science Foundation through grant DMR and by the Research Corporation through grant CC5342. We thank Denny Brandt for many hours of useful conversations about noise. drive voltage. We could include other figures: resonance scans, preamp noise as a function of

8 (a) Guard "-" "+ 10M 10M Guard OPA OPA pf 40 pf OP 27 + OP k 20 pf 100k - out OP pf 1 2 e 2 (b) tuning fork ~ 2-15 pf a b a b 10 M - + OPA k 100 k - + OP 27 (c) ~ 10k 10k 10M 1-10 pf V 10M (d) R1 C1 R3 C3 C3 C2 R2 A Figure 1 (a) is the guarded voltage preamp with a mechanical drive. (b) shows the electrically driven current preamp which consists of three parts: the electrical drive/background subtraction, the current preamp, and a X10 gain stage. The mechanically driven current preamp is similar except the first stage is removed, and the tuning fork is attached across a and b, the OPA655 inputs. (c) is the electrical drive part of the voltage preamp. The inset shown in (a) is a model for the front stage of the voltage amplifier where the circles are the voltage noise of the resistors, and the number 1 represents tuning fork at resonance which consists of R1 and C1 in parallel and the number 2 represents the 10Mohm resistors to ground, R2, with stray capacitance, C2. Similarly (d) is the model used to calculate the noise for the current amplifier. Again R1 and C1 model the tuning fork at resonance and A is the amplifier gain.

9 Figure 2 The elements seen in the figure from the bottom to the top are the glass fiber, the tuning fork, the silver coated glass slide, and the shear piezo. An arrow is shown to indicate the direction of motion of the shear piezo.

10 Current Current Voltage Voltage OPA655 AD745 AMP05 OPA655 Johnson TF fa/ Hz Johnson 10meg fa/ Hz I amplifier fa/ Hz V amplifier fa/ Hz Tot Input Noise fa/ Hz Measured Noise Input (fa/ Hz) Measured noise (output) µv/ Hz Johnson TF nv/ Hz Johnson 10meg nv/ Hz I amplifier nv/ Hz V amplifier nv/ Hz Tot Input Noise nv/ Hz Measured Input Noise (nv/ Hz) Measured noise (output) µv/ Hz Table 1 summarizes the noise calculations for several preamplifiers and compares them with the measured noise.

11 Signal to Noise Ratio VPMD VPED CPMD CPED Figure 3 shows the average signal to noise ratio for the four circuits described in figure 1 all built around the OPA655. The voltage preamp with the mechanical drive has the best performance.

12 Mechanically Driven Preamplifiers average signal to noise ratio (/ Hz) average S/N average noise Noise (µv/ Hz) 0 0 OPA655CP U430 x10 OPA655VP AMP05 AD745 Figure 4 shows the average noise and signal to noise ratio for the five mechanically driven preamps over 3 trials. The U430 amplifier noise was multiplied by 10 to account for the lack of a X10 stage. The voltage preamp using the OPA655 chip has the best performance, and the voltage preamp with the AMP05 chip has the worst performance.

13 AD745 OPA655CP U430 x10 OPA655VP AMP We are probably too long already, but here are some resonance curves.