Fast low-noise transimpedance amplifier for scanning tunneling microscopy and beyond
Martin Štubian, Juraj Bobek, Martin Setvin, Ulrike Diebold, Michael Schmid
FFast low-noise transimpedance amplifier for scanning tunnelingmicroscopy and beyond
Martin Štubian, a) Juraj Bobek, a) Martin Setvin,
1, 2
Ulrike Diebold, and Michael Schmid b) Institute of Applied Physics, TU Wien, 1040 Vienna, Austria Department of Surface and Plasma Science, Faculty of Mathematics and Physics, Charles University, 180 00 Prague 8,Czech Republic (Dated: 2 June 2020)
Accepted manuscript, published in Rev. Sci. Instrum. 91, 074701 (2020); DOI: 10.1063/5.0011097A transimpedance amplifier has been designed for scanning tunneling microscopy (STM). The amplifier features lownoise (limited by the Johnson noise of the 1 G Ω feedback resistor at low input current and low frequencies), sufficientbandwidth for most STM applications (50 kHz at 35 pF input capacitance), a large dynamic range (0 . I. INTRODUCTION
Transimpedance amplifiers, also known as current-to-voltage converters (I/V converters) have many applications,for photodiode signals, biophysics, scanning tunneling mi-croscopy (STM), and much more. Due to parasitic capaci-tances, there is a tradeoff between bandwidth (speed) on theone hand and sensitivity (noise) on the other. For STM appli-cations, the following properties are essential:- Low noise and high sensitivity. STM is not an innocentprobe; even currents in the pA range can modify surfaces. Imaging poorly conducting samples such as wide-bandgapmaterials requires working at low currents. Thus, the ampli-fier should provide good performance at least down to the lowpA range, preferably below 1 pA.- Large dynamic range. Applications like single-atom ma-nipulation (tip-sample resistance R t ≈ Ω ) and themeasurement of conductive channels between the sample andthe tip upon contact formation (tip-sample resistance R t ≈
10 k Ω ) require high currents of at least tens of nA. STMimaging of metals with chemical contrast (tip-sample resis-tance R t ≈
100 k Ω –1 M Ω ) is often done at tunneling cur-rents around 5–10 nA. In constant-current mode, for adequateresponse of the feedback loop, the current range should belarger than the average tunneling current (i.e., the current set-point) by more than a factor of two. When also consideringthe requirements for low-current imaging discussed above, adynamic range in the order of 10 is desirable for a general-purpose STM preamplifier.- Sufficient bandwidth. The bandwidth of the amplifier lim-its the speed of data acquisition. While video-rate STM re-quires a bandwidth in the 500 kHz–1 MHz range, most STM a) Also at Brno University of Technology, 60190 Brno, Czech Republic b) Electronic mail: [email protected] controllers cannot handle such high data rates and are lim-ited to sampling rates of a few 10 kHz. Equally important,in constant-current mode of the STM, the preamplifier shouldnot introduce substantial phase shifts in the frequency rangewhere the feedback loop is active, since this will reduce thestability (phase margin) of the feedback.- Low input offset voltage. Measurements at low tip-sampleresistance require working at low bias voltages ( ≈ R t . For a com-bination of STM with non-contact atomic force microscopy(ncAFM), a low input impedance at the resonance frequencyof the ncAFM sensor (typically ≈
30 kHz) is also required tokeep the bias voltage between tip and sample constant, other-wise the voltage modulation by the variations of the input cur-rent causes electrostatic forces that excite the ncAFM sensor .- No phase inversion. Voltage pulses, mobile species at thesurface, or loose flakes (e.g. of a graphite sample) can lead to asudden short of the tunneling junction, overloading the pream-plifier. Some operational amplifiers produce output voltageswith the wrong polarity under overload conditions (“phase in-version”). When detecting a tunneling current with the wrongpolarity most STM controllers would crash the tip into thesample. Therefore, one should select operational amplifiersnot susceptible to phase inversion.- Finally, especially for low-temperature STMs with a long ca-ble between the STM (housed in a cryostat) and atmospheric-side electronics, the possibility of having the first amplifierstage in vacuum is desirable. As will be discussed below,the capacitance of a long cable is detrimental not only for thebandwidth but also for the noise performance of the amplifier.Figure 1(a) shows the basic design of a transimpedance am-plifier. Due to the unavoidable parasitic capacitance C f of thefeedback resistor R f , the bandwidth of this circuit is limited a r X i v : . [ phy s i c s . i n s - d e t ] J u l +– R f +– C c (a) C f R c small ≪ R c (b) +– R f (c) C f C i C c R c FIG. 1. (a) Basic design of a transimpedance amplifier, includingthe parasitic capacitance parallel to the feedback resistor, and (b) asecond stage for compensating the resulting low-pass behavior. (c)Basic design of a transimpedance amplifier with compensation in thefeedback loop. to ω − = / ( R f C f ) . For a feedback resistor of 1 G Ω anda typical parasitic capacitance of 0.1 pF, this corresponds to f − = . but not reach the desired band-width of at least tens of kHz. The easiest solution for thebandwidth problem is using a lower feedback resistor, eitherdriven by a voltage divider or with post-amplification. Asdiscussed below, this comes at the cost of increased (Johnson)noise.The low-pass behavior caused by the stray capacitance C f can be compensated by a second stage having a gain increas-ing at high frequencies, as shown in Fig. 1(b). It has beennoted earlier that then the input voltage noise of the secondstage becomes an issue at high frequencies (where its gainmust be high to compensate for the low-pass behavior of thefirst stage). Although the design of the amplifier in Ref. 8 hasnot been published, it is likely that it involves a similar circuitand the increase of its noise being more than proportional tothe bandwidth is due to this problem.Another method of compensating for the low-pass behaviorof the amplifier in Fig. 1(a) is adding a low-pass filter to thefeedback path, again with R c C c = R f C f [Fig. 1(c)]. Thebasic circuit in Fig. 1(c) is not stable, however: At high fre-quencies, ω (cid:29) / ( R f C f ) , where R f plays no role, C f forms acapacitive voltage divider with the parasitic input capacitance C i (including the input capacitance of the operational ampli-fier, and the capacitance of the cable from the input to theamplifier, if any) with a phase shift near 0 ◦ . Thus, the phaseshift of the R c C c low-pass circuit will add to the phase shift ofthe operational amplifier’s open loop gain; both near − ◦ athigh frequencies, leading to a phase margin close to 0 ◦ . This problem can be solved by either a capacitor parallel to R c16 or using an amplifier with a low phase shift in the relevantfrequency range, i.e., an amplifier with fixed (and rather lim-ited) gain. The first approach, though delivering excellentperformance, is not trivial since it either involves a capacitiveload to the operational amplifier (which may also induce in-stability) or a high R c value, which makes the node between R f and R c sensitive to pickup of interference signals. This ap-proach also requires a very careful design of the environmentof the feedback resistor to ensure stability of the circuit inspite of various stray capacitances. Furthermore, it is unclearin which range of input capacitances the circuit in Ref. 16 canbe stable if there is a cable between the STM and the ampli-fier (only cables up to 2 cm length are mentioned in Ref. 16).The performance of this circuit is impressive, however, witha bandwidth of 1 MHz reported even with a feedback resistorof 10 G Ω . The main drawback of the circuit in Ref. 16 isthe use of a dual-JFET input with a large input offset voltage( ≈
25 mV), not acceptable for many STM applications.The other approach to obtain stable operation of the cir-cuit in Fig. 1(c), using an amplifier with fixed gain (and lowphase shift) , is a known solution of the C i -induced stabil-ity problem . The operational amplifier in Fig. 1(c) was re-placed by a circuit consisting of a noninverting input stagefollowed by an inverting stage (in Ref. 17, with gains of 25.9and − R f = Ω , clearly sufficient formost STM applications, and the circuit also works at input ca-pacitance values of 47 or 100 pF, though with reduced band-width. For STM applications, it has to be noted, however,that the input impedance of this amplifier is roughly equal to R f / | A | , where A is the gain of the amplifier. With the valuesof Ref. 17, the DC input impedance is 77 k Ω , so switchingof the feedback resistor would be required for measurementsinvolving low values of the tip-sample resistance R t . A fur-ther problem comes from the fact that the input of this am-plifier is at the noninverting input of the operational amplifier,which is on the IC housing usually next to the negative supply.Thus, a leakage resistance between neighboring pins of 1 T Ω will cause a leakage current of a several pA (depending on thesupply voltage). The amplifier described in the current paper is based on thecircuit of Figure 1(c), but solves the stability problem by plac-ing a resistor in series to C c . Before discussing the details ofthe circuit and its performance, the following two sections willbe devoted to basics of the noise of transimpedance amplifiersand the measurement of their frequency response. II. NOISE CONSIDERATIONS
For reducing the noise, several contributions have to betaken into account (Fig. 2). The thermal (Johnson) currentnoise density of the feedback resistor, (cid:112) k B T / R f , decreaseswith increasing value of R f . As described above, a high valueof R f leads to a lower bandwidth, furthermore the input currentrange also decreases. Thus, there is no point in increasing R f ifother sources of noise dominate. Except for low input currents −15 c u rr e n t no i s e d e n s it y ( A / √ H z ) −14 −13 −12 GΩ10
GΩ10
MΩ100
MΩ100 kΩ1
MΩ 1 nA10 nA100 nA100 pA10 pA I f o r s ho t no i s e R f o r J ohn s on no i s e n V / √ H z : p F p F FIG. 2. Contributions to the noise of a transimpedance amplifier.The thermal (Johnson) noise for different values of the feedback re-sistor at T =
300 K is given by blue, short dashes, the shot noise fordifferent current values by red, long dashes. The diagonal lines showthe impact of the voltage noise of the operational amplifier assum-ing a frequency-independent input voltage noise of 10 nV/ √ Hz and(effective) input capacitance values of 10 and 100 pF. I , the shot noise, (cid:112) e | I | (with e being the elementary charge),has to be considered. It follows from these equations that theshot noise dominates over the thermal noise if the voltage dropacross the feedback resistor is higher than V = k B T / e , whichis 52 mV for the feedback resistor at 300 K. Thus, assumingthat the input current range is limited by the maximum volt-age at the feedback resistor of ±
10 V (provided by a typicalopamp output), the Johnson noise will dominate only if theinput current is 0.5% of the full scale or less. Considering thelarge dynamic range desirable for an STM current amplifier,it is nevertheless important to reduce the Johnson noise (keep-ing R f as high as possible, and taking advantage of keeping itcold in low-temperature STMs) for optimum performance atlow currents.The input current noise of operational amplifiers relevantfor this application is typically ≈ √ Hz or better, belowthe thermal noise of a 1 G Ω resistor (4.1 fA / √ Hz at roomtemperature) . The input voltage noise v n , together with theinput capacitance C i (of the amplifier, plus stray capacitanceand that of the cable, if any), is usually more important. As-suming an otherwise ideal operational amplifier and feedbacknetwork, the current through the input capacitor caused by theinput voltage noise v n is supplied by the feedback resistor, andthus measured the same way as the input current . This noisecontribution therefore corresponds to an input current noise of i n = ω C i v n . (1)For amplifiers with large bandwidth, this source of noise willdominate (Fig. 2), which underlines the importance of keep- C GS − supplynoninvertinginputinvertinginput v nS C in R f i nS v ni amplifierinput FIG. 3. Simplified view of the input stage of an operational amplifierused as transimpedance amplifier. Noise of the current source in theinput stage leads to a voltage noise v nS at the source terminals of theFETs. Due to the unbalanced input impedances, this leads to a noisevoltage v ni at the input. The circuit has been drawn for n-channelJFETs, but the same applies for p-channel FETs and MOSFETs inthe input stage. ing the input capacitance as low as possible. This can be easilyexplained by the operational amplifier being a voltage ampli-fier: The input current needs to be converted to a voltage to bedetected; if the input is bypassed by a capacitor, that voltagewill be lower and more susceptible to the influence of voltagenoise.Our experiments provide evidence of an additional noisecontribution that also increases proportional to the frequencyand is usually not considered. It has been noted previouslythat the experimentally observed noise of transimpedance am-plifiers could be explained if the input capacitances of opera-tional amplifiers were higher than stated in datasheets . Wesuggest the following reason for this: The input voltage noiseof operational amplifiers is usually measured with a very lowinput impedance for both inputs. Transimpedance amplifiershave a high input impedance for the non-inverting input, how-ever. Figure 3 shows a simplified view of an operational am-plifier’s input stage in such a configuration. Assuming a noisecontribution i nS of the current supply for the source terminalsof the input FETs, a noise voltage v nS will appear there, andbe coupled into the gate by the gate-source capacitance C GS .As the gate of the other FET is tied to ground, it acts as adifferential-mode input voltage. This noise contribution is re-lated to a noise source of field effect transistors named “in-duced gate noise” (IGN) . This noise type has been foundearly and been linked to noise of the drain current, such asshot noise, leading to a modulation of the channel potential,which couples capacitively to the gate . Therefore, IGNcan be observed in common-source circuits. In our case, weconsider it likely that the main source of the noise of the FETchannel current does not have its root in the FETs themselves(the FETs do not determine the overall current) but rather inthe current source driving the input FETs. In any case, even ifIGN contributions in the usual sense play a role, they can beadded to the noise v nS and will affect the gate voltage throughessentially the same (gate-source or gate-channel) capacitance C GS . The noise at the common source point of the FETs, v nS ,leads to a noise voltage at the inverting input (FET gate), v ni = v nS C GS C in + C GS , (2)where C in is the capacitance between the input and ground(not exactly identical to the C i mentioned above; C i also in-cludes contributions from C GS ). Similar to the “usual” inputvoltage noise v n of the operational amplifier, this noise voltagehas to be compensated by a current through R f , which yieldsa noise current contribution of i n = ω C i v nS C GS C in + C GS ≈ ω v nS C GS . (3)The latter approximation is justified if C GS (cid:28) C i or C i ≈ C in + C GS , which is usually fulfilled. This contribution hasthe same frequency dependence as (1), thus the two can beadded and also written as in (1), but with a larger, effectiveinput capacitance C eff ≈ (cid:115) C + v v C . (4)In a circuit with balanced input impedances, or in ampli-fiers where the input impedance of both inputs is low, thesource of noise in (2), (3) can be neglected. For some oper-ational amplifier types, we have indeed observed a reductionof noise in a balanced circuit, where the noninverting input isconnected to ground via a resistor equal to R f and a capacitorequal to the input capacitance. Unfortunately, for our appli-cation this approach turned out to be impractical, because (i)that resistor increases the noise at low frequencies (additionalJohnson noise), (ii) it reduces the bandwidth of the circuit,and (iii) it introduces another adjustment point (the input ca-pacitance and the capacitance in the noninverting branch haveto be matched), and adjusting that balancing capacitance re-quires readjusting the frequency compensation. Thus we optto select operational amplifier types where the “additional”high-frequency noise (beyond that expected from v n and C i ) islow. In principle, problem (i) could be alleviated by using alower resistor value than R f at the noninverting input (resultinglower voltage noise). The resulting imbalance will be relevantat low frequencies only, where the noise contribution of (3)is negligible. First experiments in this direction did not yielda noise reduction as high as with a value of R f at the nonin-verting input, however. Nevertheless, support for this analysiscomes from observation that some operational amplifiers ben-efit more from a balanced design than others, and those thatbenefit more indeed have a large contribution of this “addi-tional” high-frequency noise beyond that expected from eq.(1) (cf. section VI). A further observation consistent with ourmodel is the increase of noise of the AD8615 when the posi-tive supply voltage is lower than ≈ III. MEASURING THE FREQUENCY RESPONSE
Measuring the frequency response of a transimpedance am-plifier is not simple: If the input current is derived from a fre-quency generator with a series resistor, its stray capacitancewill strongly influence the result. It is difficult to determinethat stray capacitance with sufficiently high accuracy to cor-rect for it numerically. Similar as for the stray capacitance ofthe feedback resistor, this problem can be alleviated by usinglow resistance values (though at the cost of increased noise)and placing several of them in series . We use a much sim-pler method, putting a small capacitor (1 pF) between the fre-quency generator and the amplifier input. It is easy to correctfor the capacitor’s frequency-dependent impedance in the dataanalysis, and any stray capacitance will only affect the abso-lute value of the gain, not the frequency dependence or thephase. If required, the absolute value of the gain can be easilydetermined by a separate DC measurement. With the ampli-fier already connected to an STM, the frequency response canbe measured in exactly the same fashion by retracting the tipand using an AC bias voltage and the tip-sample capacitanceas a high-impedance AC current source.For an amplifier with compensation of parasitic capaci-tances, there will be usually adjustment points such as poten-tiometers to obtain a flat frequency response. Using a smallcapacitor at the input also provides an elegant way for adjust-ing: When applying a triangle waveform via a small capacitorto the input, the transimpedance amplifier will act as a differ-entiator, and, with a flat frequency response, provide a squarewave at the output. Adjustment of the frequency response ofthe amplifier is then similar to adjusting a 1:10 oscilloscopeprobe. In our STM amplifier, we have added a 1 kHz trian-gle generator [Fig. 4(b)], whose output can be used insteadof the STM bias. With the tip not in tunneling contact, wesimply apply the triangular waveform instead of the tunnelingbias and make use of the capacitance between tip and sample(typically 0.3–1 pF) to examine the frequency response of theamplifier (and adjust it if required, e.g., after modifications ofthe cabling, changing the input capacitance). An example ofsuch square wave output is presented in section VI. The trian-gle generator is also helpful for troubleshooting, e.g. in casea bad contact or a shorted bias voltage is suspected: One canquickly check the correct operation of the system without dis-connecting the preamplifier. IV. AMPLIFIER DESIGN
Figure 4(a) shows the details of our amplifier circuit. Theoperational amplifier of Fig. 1 is replaced by three stages, with +– C c +– OP3LTC6090-5 +– OP2OP37 orTHS46311k 10k 10k 8k2 R f
1G 10k10k LM4040-10,100n each ±10 V output
All diodes: 1N4448Transistors:MMBT2222A (npn)MMBT2907A (pnp)+10 V−10 VV+V−1k1k 20k5+20k5 bandwidth R c main compensationmid-f compensation*input (a) (b) +– ½ AD8676 +– ½ AD867610n100k +– triangle output±1.25 V (with ±5 V supply)1 kHz (5 V/ms) triangle generator FIG. 4. (a) Schematics of the transimpedance amplifier circuit. See the text for components marked with an asterisk. (b) The trianglegenerator for adjustment (see section III) is a simple integrator-comparator design with an additional buffer to reduce influencing the integratorby transients from the comparator. gains of 10 and 5 for the 2nd and 3rd stage, respectively. Sincethe feedback resistor is connected to the output of the 3rdstage, the 2nd and 3rd stage do not increase the overall trans-impedance, only the open-loop gain of the circuit. We usea 1 G Ω feedback resistor and a nominal output voltage rangeof ±
50 V for the last stage, which provides a current rangeof ±
50 nA. Together with the low thermal noise of the feed-back resistor and the low input bias current of the first-stageamplifier (AD8615, 0.2 pA typ.), this ensures a very large dy-namic range as desired for a general-purpose STM preampli-fier (see introduction). This dynamic range is achieved with-out the need of switching the feedback resistor, which wouldbe difficult especially when putting the first stage into vacuum.The first stage (OP1 and R f ) can be placed in vacuum ifdesired. The AD8615 works well at liquid-nitrogen (LN2)temperatures. For operation at liquid-helium temperaturesslight counterheating by its power dissipation is needed, thusit should be mounted with high thermal resistance to thecryostat.
27 29
In our experience, standard RuO -based G Ω re-sistors have no substantial temperature coefficient down toLN2 temperature; at LHe temperature the resistance increases(in our case, by ≈ f and from OP1 output); we have not no-ticed any influence of 120 pF capacitance from these lines toground. We found that the cable shields must not be used asthe only ground connections, however: Due to their induc-tance with respect to ground and the current due to the ca-pacitance between shield and inner conductor, a voltage dropwould occur along the cable shields. A “solid” ground con-nection via the cooling tubes of the cryostat or other mas-sive parts in UHV is required to ensure stable operation ofthe amplifier. If the first stage is outside vacuum, next to therest of the circuit, it is important to take into account that thecombined gain-bandwidth product of the first three stages is 1.2 GHz (24 MHz for the AD8615 in the first stage, gain 50 for2nd and 3rd stage). Together with the high input impedance,this makes it clear that any stray capacitance between the in-put and the later stages must be intercepted by an electrostaticshield.Independent of whether the first stage is in UHV or out-side vacuum, it is important to avoid a ground plane below thefeedback resistor. The capacitance between the resistive trackand ground would lead to a large negative phase shift (delay)of the feedback signal, which is difficult to compensate andlikely to cause oscillations. A further important considerationfor the first stage is reducing the noise of its supply voltage.We found that the noise levels of standard voltage regulatorslead to increased noise of the amplifier; we therefore use volt-age dividers and large electrolytic capacitors (1000 µF, with470 nF ceramic multi-layer capacitors in parallel) to provide a + . − . ± ±
10 V. It uses a fast operational amplifier,either OP37 (gain bandwidth product 63 MHz) or THS4631(210 MHz). With the latter also higher gains would be possi-ble without introducing any sizable phase shift, i.e., withoutreducing the overall phase margin (for a gain of 10, the OP37has the advantage of better DC accuracy due to a lower volt-age offset). This stage also includes a voltage limiter, to avoidsaturation of OP2 or OP3. The third stage, with ±
60 V sup-ply voltage, provides the output voltage of nominally ±
50 V,to obtain a large dynamic range. The LTC6090-5 used forthis stage offers a good compromise between speed (gain-bandwidth product 24 MHz, slew rate 37 V / µs typ.) and volt-age range (supply max. ±
70 V). Since the output of the am-plifier (to the STM controller) should be ±
10 V, not ±
50 V,we use the output of the second stage as the ±
10 V amplifieroutput.As mentioned in the introduction, a flat frequency responseis obtained using a compensation network based on Fig. 1(c).The potentiometer in series to C c can be used to reduce thebandwidth if desired (reducing the overall noise); especiallyfor fast STMs this is not needed because of the integrating (I)controller usually employed for constant-current STM imag-ing, which suppresses high-frequency noise. The resistor inseries to the potentiometer should be chosen such that strongovershoot or oscillations cannot occur at the minimum settingof the bandwidth potentiometer; for an input capacitance of35 pF we found 470 Ω a suitable value. The additional RCseries circuit labelled “mid-f compensation” can be used forslightly tweaking the frequency response in the region be-tween the R f C f pole (1–2 kHz) and the bandwidth limit. Suit-able values for the mid-f-compensation components dependon details of the environment of the feedback resistor; for dif-ferent geometries (breadboard, printed circuit board) we havefound capacitors in the 100 pF–1 nF range useful (for valuesnear the lower end, the trim potentiometer in series shouldhave a higher value than shown, 200–500 k Ω ).Setting the compensation network to obtain a flat frequencyresponse ensures also a low phase shift of the feedback net-work and, hence, stability in the linear regime. Nevertheless,the circuit may oscillate when it enters the nonlinear regime;this is caused by additional delays in the feedback loop whenan operational amplifier recovers from saturation or reaches itsslew rate limit. Thus, without any additional measures, largesignals or spikes at the input (which often occur in STM appli-cations) could drive the circuit into oscillations. To suppresssaturation of the 2nd and 3rd stages, the second stage includesa voltage limiter. As soon as the second stage reaches an out-put voltage slightly above 11 V (either polarity), one of thetwo transistors (acting as common-base amplifier) will startconducting and provide an additional negative-feedback pathstrongly reducing the gain of the 2nd stage. The two antiparal-lel diodes suppress the influence of transistor leakage currentsor parasitic capacitances on the input of OP2; these currentsinstead find their way via a 10 k Ω resistor to ground. Oscilla-tions in the nonlinear regime can also occur without saturationof OP2 and OP3: The time delay of recovery from saturationof OP1 and the time for full output swing of OP3 limited by itsslew rate are comparable; this situation is similar to two stagesintroducing a phase shift of − ◦ each, which will render thecircuit unstable. This can be avoided by limiting the slew rateof OP3 for large voltage excursions. This is done by a high-pass circuit with a voltage divider at the output: If the outputswing is large with a high slew rate, the output voltage of thevoltage divider will be high enough to overcome the forwardthreshold of one of the two diodes. This additional negative-feedback path will reduce the slew rate. For “normal” signals,including high-frequency noise, this limiter remains inactiveand does not introduce nonlinearity. V. FURTHER CONSIDERATIONS FOR AN STMPREAMPLIFIER
As for all sensitive measurements, where the signal source(here, the STM) and the signal processing (STM control elec-tronics) are separated by some distance and/or have separateground connections, it is essential to avoid ground loops. ForSTMs in ultrahigh vacuum (UHV), this cannot be done byrunning the transimpedance amplifier at the ground voltageof the STM control electronics, since the unavoidable capac-itance from the current input to ground of the UHV cham-ber would then cause capacitive pickup of the difference ofthe ground potentials. This means that the transimpedanceamplifier must use the ground of the UHV chamber and theSTM controller should have a differential input for the out-put of the transimpedance amplifier. If this is not the case,the output of the transimpedance amplifier should be fed intoan instrumentation amplifier (INA) taking its reference (out-put ground) from the STM controller. Essentially the same istrue for the bias voltage, which must be supplied with respectto the ground potential of the transimpedance amplifier, i.e.,with respect to UHV ground. For this purpose, it is best tohave an instrumentation amplifier as a driver for the bias volt-age (we use an AD8421, which is placed on the circuit boardof the transimpedance amplifier). In addition, to avoid groundloops, the transimpedance amplifier (and the INA for drivingthe bias) should have its own power supply, with the groundconnected to the UHV chamber, not to mains ground.The usual bias voltage range of an STM is ±
10 V, whichis higher than the permissible supply voltage of the first-stageOP1 (6 V between the positive and negative supply rails forthe AD8615). Since a short between the tip and sample of anSTM cannot be ruled out, it is therefore necessary to limit theoutput current of the bias driver to the maximum current ofthe protection diodes of OP1 (5 mA for the AD8615).For scanning tunneling spectroscopy (STS) with a lock-inamplifier, the choice of a good modulation frequency is diffi-cult: On the one hand, it is desirable to use a high frequency,to escape the 1 / f noise of the tunneling junction and haveshort settling times. On the other hand, at high frequencies thecapacitance between tip and sample will lead to a large capac-itive current, which can be much larger than the actual (mod-ulated) tunneling current. This will make lock-in measure-ments very sensitive to the phase and also increase shot noise.Another problem caused by the tip-sample capacitance is theoccurrence of current spikes when changing the bias voltage.The spikes have a large bandwidth and therefore disturb lockin-amplifiers, increasing the settling time required before ameasurement can be taken. The spikes can be also detrimentalfor normal STM operation in constant-current mode, as lower-ing the magnitude of the bias will lead to a spike with a polar-ity opposite to that of the tunneling current, which can causethe STM controller to push the tip into the surface. All theseproblems can be avoided by compensation of the capacitivecurrent at the input of the transimpedance amplifier, as shownin Fig. 5: We feed the inverted bias signal (with variable gain)into a capacitor with a similar capacitance as the tip-samplecapacitance. As the bias can be a few volts, it is important to +– ½ AD867610k bias inverted bias printedcircuit boardcapacitor electrodegrounded guard ringPTFE mm Ø 2.2 mmsolder terminalfor input current Ø 1.3 mm FIG. 5. Circuit for capacitance compensation and physical realiza-tion of a 1 pF capacitor built into the solder terminal for the amplifierinput. avoid any leakage current either through this capacitor or at itssurface, since even a T Ω leakage will result in an input cur-rent of a few pA. For the amplifier with the first stage outsidevacuum, we therefore use a homemade cylindrical capacitorbuilt into the PTFE-supported input terminal of the amplifier,with grounded guard electrodes between the input and the in-verted bias (Fig. 5). While this compensation works well, wedo not have sufficient experience with STS measurements tojudge whether it can come close to the performance of highlyoptimized radio-frequency methods. VI. PERFORMANCE OF THE AMPLIFIER
Depending on the exact layout of the environment of thefeedback resistor, the bandwidth of the amplifier in Fig. 4 isabout 100 kHz with zero input capacitance and 50 kHz with35 pF input capacitance (Fig. 6). These values can be in-creased by increasing the gain of the second stage (we couldobtain up to 200 kHz at an input capacitance of ≈ This would requirethe first stage to work with a fixed, positive gain, which isproblematic due to the proximity of the noninverting inputpin and the negative supply of most operational amplifiers,as mentioned in the introduction. Another possibility to in-crease the bandwidth is compensation at the output as shownin Fig. 1(b); for the curve in Fig. 6, this could easily increasethe bandwidth to 125 kHz. For our application, a bandwidthof 50 kHz is sufficient, however.Concerning the noise performance, we have tried our circuitwith different operational amplifier types, with and without anadditional 100 pF capacitance at the input, to simulate the am-plifier being connected to the STM by long cable (as for cryo-genic STMs with the amplifier outside vacuum) or very closeto the STM (cable capacitance negligible). We have measuredthe bandwidth-integrated noise with a 1st-order high-pass fil- ga i n ( d B ) pha s e ( ° ) FIG. 6. Frequency response of the circuit in Fig. 4 with 35 pF inputcapacitance. The data were measured with an AC voltage applied tothe tip-sample capacitance and division by j ω as explained in sectionIII. 0 dB corresponds to the DC transimpedance of the circuit (1 G Ω at the output of the 3rd stage, 1/5 G Ω at the ±
10 V output of stage2). The inset shows the oscilloscope trace with a 1.07 kHz trianglewave connected to the sample, using the capacitive coupling to theSTM tip to operate the amplifier as a differentiator and check thefrequency response (The oscilloscope was in × ter (7 Hz, to suppress the DC component) and a 10 kHz 4th-order low-pass filter. For comparison, we have also calculatedthe noise as expected from the Johnson noise of the feedbackresistor, as well as values from the datasheet for the input volt-age noise v n and input capacitance of each operational ampli-fier type, using eq. (1). The noise powers of these two con-tributions have been multiplied by the frequency response ofthe low-pass filter and integrated over the frequency. Figure7 shows these values, together with the values for the inputvoltage noise and input capacitance used for the calculation .Especially for the data without additional input capacitance(black data points in Fig. 7), it is obvious that the calcula-tions (open circles) strongly underestimate the noise in mostcases; as explained in section II we attribute this to capacitivecoupling of voltage noise at the source terminals of the inputFETs to their gate. According to eq. (4), this additional noisecontribution has similar consequences as an additional inputcapacitance, and its influence should vanish if a large exter-nal input capacitance is added. Indeed, this can be seen inFig. 7: When adding 100 pF input capacitance, the spread be-tween the experimental and calculated noise values becomessmaller in most cases, and sometimes the experimental val-ues are even better than the calculated ones (indicating thatthe particular operational amplifier used by us performs betterthan stated in the datasheet). The additional noise contribu-tion according to eq. (3) means that selecting operational am-plifiers according to input voltage noise and input capacitancedoes not guarantee good noise performance in a transimped-ance amplifier, as clearly seen in Fig. 7. Among the ampli-fiers examined by us, at low additional input capacitance, theAD8615 and AD8616 (dual version of the AD8615) performbest, even if they do not offer exceptionally low input voltagenoise according to the datasheet. This type also excels when AD795OPA657TLC071OPA827OPA637MAX4477LTC6240AD8616AD8615 C i (pF) + V n (nV/√Hz) ● I n (pA) 0.007–10 kHz C i + 100 pF C i + 0 pFcalc. exp. FIG. 7. Comparison of different operational amplifiers. The leftpanel shows the input voltage noise at 10 kHz (filled blue circles) andthe input capacitance (red crosses), both according to the datasheets.The right panel shows the total noise measured with a 7 Hz high-passfilter and a 10 kHz 4th-order low-pass filter (filled circles) as well asthe noise calculated for this frequency range (open circles), with andwithout an additional input capacitance of 100 pF (red and black, re-spectively). Except for the AD8615/8616, where very similar resultswere found for several chips, only one specimen was tested for eachoperational amplifier type.
100 1000 10000 frequency (Hz)05152010 i npu t c u rr en t no i s e ( f A / √ H z ) K 2 pF K 35 pF K 35 pF FIG. 8. Noise spectra of two amplifiers according to Fig. 4, with thefirst stage at T =
80 K and C in ≈
35 pF (cable capacitance), as well asan amplifier with all stages at room temperature and two different in-put capacitance values ( C in = ≈
10 pFinput capacitance of the AD8615 operational amplifier). The peaksbelow 500 Hz are due to insufficient shielding (line frequency over-tones; for the room-temperature amplifier at C in =
35 pF also includ-ing magnetic induction up to ≈ used for pickup of tiny signals from a high-impedance quartzcrystal in non-contact AFM . With 100 pF additional inputcapacitance, reasoning according to eq. (1) holds and the bestperformance is delivered by operational amplifiers with verylow input voltage noise.Fig. 8 shows exemplary noise spectra of our amplifier, withthe first stage at room temperature (2 and 35 pF input capac-itance, red and brown respectively), as well as with the firststage in a liquid-nitrogen cooled STM head, with ≈
35 pF ca-pacitance of the cable to the tunneling junction (blue). It is obvious that the noise floor at low frequencies decreases asthe feedback resistor is cooled (dotted lines mark the calcu-lated Johnson noise), whereas the noise at higher frequenciesstrongly increases with increasing input capacitance. The ex-tra noise of the room-temperature amplifier with C in =
35 pFat low frequencies ( (cid:46) T = ≈ ≈ ≈
35 pF cable capacitance) is shown in Fig. 9. With the first stage of the amplifier mounted to the STM op-erating at ≈ ∆ z RMS = . ) are stillvisible.Finally, Figure 10 shows a comparison of the present workwith several transimpedance amplifiers described in the liter-ature. We show the maximum − ±
12 V for operationalamplifiers that can be operated with ±
15 V supplies. With oneexception noted below, all data are for zero or very low inputcapacitance (data for input capacitance values typical for a ca-ble between a UHV STM and an atmospheric-side amplifierwere not available for most designs). In Fig. 10, better perfor-mance is indicated by a position of the bar further to the lowerright and a taller bar. While there are a few amplifiers thatare on the “better” side from ours, we note that all these havesubstantial limitations not present in our design. The ampli-fier labelled Ferrari 2009 is a specially designed CMOS chipwith nonlinear elements (FETs) replacing R f . It is uncertainwhether these will cause crossover distortions and other prob-lems due to nonlinearity; furthermore, without special precau-tions CMOS amplifiers tend to have rather high input voltagenoise, which would cause additional noise according to eq.(1) as soon as any input capacitance is added. As mentionedin the introduction, the amplifier labelled Michel 1992 hasthe problem of large input voltage offset, and the Ferrari 2007design is in this form not directly usable for STM becauseit essentially consists of two separate amplifiers for the ACand DC components of the signal. The data labelled le Sueur2006 are not directly comparable with the others because (a) (b) p m , , (c) n × 50 Hz removed (d) FIG. 9. Constant-current STM images of water dissociatively adsorbed at the the stoichiometric In O (111) surface acquired at T = b a nd w i d t h ( H z ) − − − − − no i se (f A / √ H z ) d y n a m i c r a n g e Eckel 2012Carlà 2004Petersen 2017 le Sueur 2006Ciofi 2007 Ferrari 2007Paul 2006Ferrari 2009Giusi 2015 Michel1992Demming1998 this work
FIG. 10. Comparison of transimpedance amplifiers described in theliterature. Except for “le Sueur 2006”, data are for small or zero in-put capacitance and room-temperature operation. The input currentnoise is given at 1 kHz and the dynamic range is based on a lowerlimit given by a signal-to-noise ratio of 10 dB at 1 kHz bandwidth.The orange bar stands for the amplifier presented in this work (witha second-stage gain of ≈ , Ciofi 2007 , Demming 1998 , Eckel 2012 (three-range amplifier, data for range 2), Ferrari 2007 , Ferrari 2009 ,Giusi 2015 , le Sueur 2006 , Michel 1992 , Paul 2006 , Petersen2017 . they are for a room-temperature amplifier with the feedbackresistor (14 M Ω ) in a millikelvin cryostat, which strongly re-duces the Johnson noise; on the other hand these data includethe influence of a cable between the STM and amplifier. VII. NOTES ON FURTHER APPLICATIONS
While our amplifier was developed for STMs, it is well-suited for many other applications. Its large bandwidthmakes it useful for specimen current imaging and electron-beam-induced conductivity (EBIC) in scanning electron mi-croscopy (SEM). At sufficiently low data rates and high beamcurrent, if the specimen noise is dominated by shot noise (c.f.Fig. 2), we can argue that specimen current measurement caneven lead to less noise than a conventional secondary elec-tron (SE) detector (Everhart-Thornley detector): The speci-men current is the difference between the incoming and thesecondary electron current. If the SE yield is close to unity(at low beam voltages), this difference is small compared tothe SE current, therefore its shot noise (which is proportionalto the square root of the current) is also smaller. In that case,also any fluctuations of the primary beam current will affectthe specimen current less than the SE current. Specimen cur-rent imaging should be also of advantage for environmentalSEM of low-Z materials, which have low backscattering yieldand therefore low gas-ionisation signal.For photodiode applications, where only one polarity is rel-evant, our amplifier could be modified using an asymmetricsupply for OP3 (e.g., −
10 and +
110 V), which would give it adynamic range up to 100 nA with a 1 G Ω resistor. This wouldrequire either a gain of 10 for the 3rd stage or an asymmetricsupply, e.g., −
25 and + Ω feedback resistor and 3 pF photodiode capacitance ;our circuit offers a larger bandwidth and ten times lower John-son noise (which is especially relevant at low frequencies andlow input currents).0 VIII. CONCLUSIONS
We have presented a transimpedance amplifier designed forscanning tunneling microscopy. The amplifier is based oncommercially available standard operational amplifiers andprovides a larger bandwidth than most previous designs, com-bined with very low noise. In addition, our amplifier providesan exceptionally large dynamic range without range switch-ing. The first stage of the amplifier, including the feedbackresistor, can be placed in UHV and also works at cryogenictemperatures, which makes it well-suited for low-temperatureSTM. We have described a fast and simple way to judge thefrequency response of a transimpedance amplifier, and wehave provided evidence for a source of noise that was pre-viously not discussed in the design of transimpedance ampli-fiers and is caused by a similar mechanism as the induced gatenoise of FETs. We have also discussed various additional con-siderations for the use of the amplifier for STM applications.Although the amplifier presented was designed for STMs itmay find many other applications.
ACKNOWLEDGMENTS
This work was supported by the Austrian Science Fund(FWF) projects F4505 (Functional Oxide Surfaces and Inter-faces “FOSXI”) and Wittgenstein Prize Z 250.The data that support the findings of this study are availablefrom the corresponding author upon reasonable request. E. Säckinger,
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