Ultrafast Scanning Tunneling Microscopy. G. M. Steeves and M. R. Freeman

Transcription

1 Ultrafast Scanning Tunneling Microscopy G. M. Steeves and M. R. Freeman 2002

2 Contents 1 Ultrafast Scanning Tunneling Microscopy Introduction History Ultrafast Scanning Probe Microscopy Junction Mixing STM Distance Modulated STM Photo-Gated STM Ultrafast STM by direct optical coupling to the tunnel junction Conclusions References

3 Chapter 1 Ultrafast Scanning Tunneling Microscopy 1.1 Introduction Advances in nano-fabrication have allowed the creation of novel devices which operate in a unique regime where both classical and quantum theory govern their behavior. These developments have stimulated a wide interest in all aspects of nano-scale physical phenomena. To facilitate studies on nano-scale systems, efforts have been devoted to forging new techniques in microscopy. The scanning tunneling microscope (STM), forefather of all scanning probe microscopies, was a result of such efforts [1]. Scanning tunneling microscopes have been used to image surface topography with atomic resolution [2]. STM has been used to image the local densities of electron states on superconducting samples using scanning tunneling spectroscopy [3, 4]. Recently magnetic imaging capabilities have been added to the arsenal of powerful STM modalities through ballistic electron magnetic microscopy [5] and STM assisted electron spin resonance [6]. While STM is renowned for its imaging ability this ability has been limited to the study of static systems, however with the incorporation of ultrafast optical techniques a new probe has emerged. An aggregate probe allowing ultrafast dynamical imaging and atomic resolution [7]. There are many potential uses for such a probe. Electron transport could be studied in high-speed integrated circuits, single electron transistors, Coulomb blockade structures, carbon nano-wires or DNA. Electronic and magnetic transitions could be observed, it may even be possible to re- 2

4 solve the question of whether electronic or structural reordering occurs first in a phase transition. The main limitation on the speed of a conventional STM is caused by the relatively low bandwidth of STM electronics. STM electronics have been designed to measure very small currents typically in the range of pico to nanoamps. To accurately measure these small currents STM electronics operate at low bandwidths to maximize signal to noise. STM scan rates are determined by the mechanical response of an STM s scan mechanism (typically khz bandwidths) which also relates to STM electronic response characteristics. This response is adequate for static STM imaging but insufficient for ultrafast STM imaging. Efforts to speed up STM temporal response have achieved feedback response times in the microseconds [8]. The ultimate response of a real time STM measurement is governed by probabilistic tunneling rates, for typical tunneling currents this allows measurements at MHz frequencies as explored by Ochmann et al. [9]. To surpass these limitations it is necessary to switch to repetitive measurements. Using repetitive measurements allows the average dynamical response to be measured with far greater signal to noise than any single shot measurement. Repetitive measurements are easily facilitated by the availability of pulsed laser systems. Commercial Ti/Sapph laser systems, for example, can produce a train of 60 fs pulses of order 10 ns. A single pulse can be split with a beam splitter to produce two synchronous pulses for pump/probe experiments. Subsequent pulses repeatedly pump and probe the system allowing an average response to be determined. With repetitive pump/probe modulations of an STM s tunneling current the averaged dynamical tunneling current can be measured. The component of tunneling current from the dynamical pump/probe modulation can easily be separated from DC tunneling current by switching on and off the pump and probe beams using an optical chopper at a slow (khz) rate within the bandwidth of normal STM electronics. By varying the relative pump/probe delay time a convolved dynamical response can be measured, which can reveal the dynamics of the underlying system. This the the premise for ultrafast STM. 3

5 1.2 History With this approach in mind, we now consider the type of modulations which will allow stroboscopic ultrafast STM. The first approach suggesting pump/probe techniques was disclosed anonymously in 1989 [10]. Entitled Contactless, High-Speed Electronic Sampling Probe the disclosure entails using optical pulses, coupled to a vacuum tunneling probe to sample fast electrical transients propagating in an integrated circuit. An optical pulse incident on the metal-vacuum-metal tunnel junction is rectified by the non-linear current-voltage characteristic of the tunnel junction (non-linear optical rectification was investigated in metal-barrier-metal tunnel junctions by Faris, Gustafson et al. [11, 12, 13] as early as 1973, well before the invention of a STM). An electrical transient in the test circuit, coincident with the optical pulse will modify the tunnel junction response allowing cross correlation measurements between the electrical and optical pulses. Using the current-voltage rectification of an optical pulse the authors state that this technique should allow better than 5 fs temporal resolution. They also suggest that the tunneling probe could be scanned micrometer distances across the device surface to look for inhomogeneities and defects. They do not speculate on the ultimate spatial resolution of this technique. Direct optical coupling was later explored by Feldstein et al. [14] and Gerstner et al. [15] as will be discussed in a subsequent section. Due to the relative obscurity of the afore mentioned proposal, nothing was known of time resolved STM until the work of Hamers and Cahill [16, 17]. Here Hamers and Cahill successfully demonstrated the use of an STM tip to detect an ultrafast signal. The signal was generated using pump/probe laser pulses incident on a 7 7 reconstructed Si (111) surface. The laser pulses induced a surface photovoltage, which was detected capacitively using the STM tip. Capacitive detection was chosen over tunneling current detection as signal to noise was significantly enhanced. Tunneling current detection was proposed to achieve STM spatial resolution in an ultrafast pump/probe measurement, this had yet to be demonstrated. In 1993 four groups demonstrated ultrafast signal detection in which the ultrafast signal was extracted from the tunneling current of an STM. Within an eleven day period, the techniques of Photo-Gated STM (PG-STM), Dis- 4

6 tance Modulated STM (DM-STM) and Junction Mixing STM (JM-STM) were introduced. The essential feature of the PG-STM technique, developed by Weiss et al., is a photo-conductive switch in series with a tunneling STM tip. DC tunneling with an unilluminated tip is still possible in this configuration since the dark resistance of the switch is typically comparable to tunnel junction impedances. If a PG-STM is set to tunnel into a dynamically evolving sample, the switch on the STM tip can be briefly opened to gate the instantaneous state of the sample. The STM will only be sensitive to dynamics which are manifest in one of its usual acquisition modes such as topography or differential conductivity. Photo-gating acts in much the same way that a photographers flash capture instantaneous motion. Extremely fast 900 fs time resolution has been demonstrated with PG-STM [18] using silicon-onsapphire switches implanted with O 2+ which possesses extremely fast carrier recombination times. Unfortunately, though conceptually simple, this technique was found to be limited in spatial resolution. This limitation is directly related to the geometrical capacitance from the segment of the STM tip between photo-switch and sample. Geometrical capacitance is thought to hamper spatial resolution in PG-STM to the tens of nanometers. Distance modulated STM, developed by Freeman and Nunes, provides an alternate means for detecting ultrafast sample dynamics. Here the tip sample separation is modulated on an ultrafast time-scale to enhance the transient current contribution from the sample. In this implementation the time-resolved tunneling current originates at the tunnel junction so there should be no loss in spatial resolution, though this has yet to be demonstrated. The only drawback to this technique is the need to mechanically alter the elevation of the STM tip high above a sample on fast time scales. This modulation has been demonstrated on nanosecond time-scales using a magnetostrictive STM tip driven by a current coil. There the response is limited by the sound propagation time across the excited volume of the tip. Using an electronic pulsed current source allows a greater degree of flexibility in the pulse amplitude and repetition rate, over optically generated pulses. Picosecond and femtosecond speeds have yet to be shown but are probably needed, to compel adoption of this technique. Photoacoustic pulse generation seems a feasible route to this goal. 5

7 To overcome the speed limitations of the distance modulated technique Nunes and Freeman developed junction mixing STM. This technique relied on a fast electrical pulse which is launched into the STM tunnel junction. The inherent electrical non-linearities of a tunnel junction allow the pulse to mix with the electronic state of the sample. If the electronic state of the sample is dynamical, then the arrival time of the input pulse will evoke a series of responses. By deconvolving this signal with the shape of the electrical pulse, the evolution of the electronic state of the sample can be determined. It is worth noting that this technique should be capable of imaging any dynamical process which affects the tunneling current of an STM. To this date the junction mixing technique has been used to demonstrate combined 20 ps, 1 nm spatio-temporal resolution. The ultimate spatial resolution of JM- STM is thought to correspond to that of an ordinary STM and calculations suggest that sub-picosecond temporal resolution can be achieved. To explore the boundaries of ultrafast STM time resolution, even the fastest electronic pulses are too slow. If ultrafast STM is to approach temporal resolution of tens of femtoseconds then optical pulses must be directly coupled to the STM tunnel junction. For this idea to be demonstrated a number of experimental challenges must be met, but direct junction coupling stands as the grail in ultrafast STM. 1.3 Ultrafast Scanning Probe Microscopy Shortly after the 1989 anonymous disclosure was published, a more widely cited idea for ultrafast STM was put forward by Hamers and Cahill [16, 17]. This paper was the first experimental attempt to combine laser methods for ultrafast time resolution with a scanning probe microscope(an STM tip was used outside the tunneling regime to detect a change in capacitance between tip and sample). In addition to this experimental demonstration the authors outlined a technique and requirements to add ultrafast time resolution to other types of scanning probe microscopes (their original motivation had been to attempt a time-resolved detection of surface photovoltage using a scanning tunneling microscope, but signal to noise requirements mandated the scanning capacitance scheme). The process that the authors studied was the decay of photoexcited carriers at a Si (111) (7 7) surface. Their experimental setup is shown in Figure

8 UHV STM Chopper Lens PP EOM Mode locked YAG Laser Dye Laser N Figure 1.1: Schematic diagram of experimental apparatus. N = Cavity dumper, EOM = electro-optic modulator, PP = polarizing prism. Reproduced with permission from R. J. Hamers and David G. Cahill, J. Vac. Sci. Technol. B, 9, 514 (1991). In this scheme, they proposed that, Using the SXM 1 probe tip as a local detector of a deviation from equilibrium which is a nonlinear function of an externally controlled stimulus (such as an optical pulse), it is possible to achieve unprecedented time resolution which is limited only by the inherent time scale of the underlying physical process. In their experiment a scanning capacitance microscope was used as the local probe, and optical pulses from a dye laser were used to create a transient surface photo-voltage (SPV) which was detected by the probe. Using a capacitive probe allows the tip sample separation to be large minimizing the effects of photothermal expansion of sample and tip due to laser intensity fluctuations. Under continuous illumination the magnitude of the SPV varies as: SP V A ln(1 + CδQ/Q) (1.1) where A and C are constants and δq is the photoexcited carrier density [19]. Under pulsed illumination using 1 ps pulses every 13.1 ns the SPV can be fit with this same equation (with modified values of A and C) as shown in Figure 1.2. The fitting curve was generated with A=28 mv which is almost identical to the value A=31 mv found under continuous illumination 1 Where SXM refers to a generic scanning probe microscopy 7

9 suggesting that carrier relaxation occurred on time scales slower than 13.1 ns. To probe carrier relaxation on longer time scales a cavity dumper was used to vary the repetition rate of laser pulses at the sample surface. One picosecond duration excitation pulses would arrive with a spacing (in time) in increments of τ ML = 13.1 ns. The authors measured the average photovoltage as they varied the repetition rate of their excitation pulses from τ ML to 40 τ ML while maintaining a constant time averaged illumination intensity. In this way they could look for deviations from Equation 1.1. When the cavity dumper repetition rate was high with respect to the carrier relaxation time, a large carrier density would be established producing a saturated SPV and measured displacement current signal (through repeated pumping of the sample). For a long repetition rate (compared to the recombination time) most photo-carriers recombined diminishing the SPV before the next excitation pulse resulting in a diminished current signal. The excitation pulse train was optically chopped at 4 khz so that a lock-in amplifier could be used for detecting and discriminating the time resolved signal. An averaging transient recorder measured the displacement current induced in the tip at 4 khz. Integrating the displacement current over the on time of the chopper gave an averaged value proportional to the time-averaged SPV. A SPV plot with respect to the pulse separation time is shown in Figure 1.3. This curve was fit and a 1µs carrier decay time was deduced in the limit of small photovoltages. This experiment was the first to use a scanning probe to detect a signal with fast transient origins. The authors did not report on the effect of scanning the detector over the silicon surface so combined spatio-temporal resolution was not demonstrated. The technique used to achieve time-resolution in this case relied solely on properties of the sample under investigation. The saturation of the SPV at different pump powers and pump repetition rates allowed the authors to deduce the carrier recombination time for the Si (111) surface, but this technique is not generalizable for time-resolved studies of other material properties. Nonetheless the authors demonstrated the first use of a local probe to investigate the 1µs photoexcited carrier recombination time of a Si (111)-(7 7) surface. Two years after the work by Hamers and Cahill, the group of Hou, Ho and Bloom published results demonstrating picosecond time resolution using a scanning electrostatic force microscope (SFM) [20]. Atomic force microscopes (AFM) had only been invented about 6 years earlier by Binnig, Quate and Gerber [21] and were already acquiring a great number of indus- 8

10 80 70 SPV=A log (1 + BP) A=28 mv, B=0.49 mw 1 60 Photovoltage (mv) Laser power (mw) Figure 1.2: Dependence of SPV on incident power using 1 ps pulses separated by 13.1 ns. Reproduced with permission from R. J. Hamers and David G. Cahill, J. Vac. Sci. Technol. B, 9, 514 (1991). 9

11 100 Average Photovoltage (mv) τ 0 5 µ s 2 µ s 1 µ s 500 ns 200 ns 50 ns Pulse Separation (units of 13.1 ns) Figure 1.3: Time dependence of surface photovoltage, obtained by measuring the displacement current induced in the tip as a function of delay time between optical pulses, at constant average illumination intensity. Individual points were measured in random order. Reproduced with permission from R. J. Hamers and David G. Cahill, J. Vac. Sci. Technol. B, 9, 514 (1991). 10

12 trial applications due to their flexibility and ease of use. Adding ultrafast time resolution to a modified AFM would prove to be not only interesting, but quite practical. In the Hou, Ho, Bloom scheme the nonlinear force F = ɛ 0AV 2 between SFM tip and the sample would serve to mix the excitation response of the system with a time varying probe signal. This differed 2z 2 from the Hamers and Cahill experiment where they used repetitive pumping at differing time intervals to build a measurable signal (there was only a pumping stimulus and the frequency of this stimulus was varied). In the Hou, Ho, Bloom configuration two different signals, a pump and a probe signal at different frequencies were mixed in the force nonlinearity to produce a difference frequency signal within the bandwidth of the SFM cantilever and electronics. In demonstrating this technique the authors combined the 1 Volt outputs of two synthesized sinusoidal signals at frequencies f and f + f, and launched the combined signal down a transmission line (TRL). The fundamental frequency f=1ghz was used and f was varied from 0 25 khz. The deflection amplitude of the cantilever is shown in Figure 1.4. The 19 khz peak corresponds to the mechanical resonance frequency of the cantilever. By characterizing the mechanical resonances of the SFM tip, the mixing signal can be obtained. Similar mixing experiments were successful up to 20 GHz, limited by the quality of the experimenters high speed electronics. This group also performed experiments in the time domain using a pair of step-recovery-diode (SRD) comb generators, which produced 110 ps pulses at 500 MHz and 500 MHz + 10 Hz respectively. These pulse trains were combined and launched onto a co-planar waveguide structure patterned onto a GaAs substrate. The beat pattern from the two pulse trains is shown in Figure 1.5, where a 130 ps correlation between pulse trains is shown. In their concluding remarks, the authors contend that this technique should be capable of measuring voltage signals with picosecond time resolution and submicron lateral resolution. This technique should be quite useful especially when excitation and probe pulses are close enough in frequency that the mechanical cantilever will respond with sufficient amplitude to be detected. One questions the ultimate resolution of this technique as it relies on a tip sample force which is capacitive in origin, yet the technique should provide the submicron resolution the authors suppose. 11

13 60 Cantilever deflection amplitude (Å) Intermediate(beat) frequency (khz) Figure 1.4: SFM electrical mixing at 1 GHz. Reproduced with permission from A. S. Hou, F. Ho and D. M. Bloom, Electron. Lett., 28, 2302 (1992) c 1992 IEEE. 12

14 Amplitude (arbitrary units) 130 ps Time (ns) Figure 1.5: Equivalent-time correlation trace of two 110 ps pulse trains. Reproduced with permission from A. S. Hou, F. Ho and D. M. Bloom, Electron. Lett., 28, 2302 (1992) c 1992 IEEE. 13

15 The absolute magnitude of the mixed signal is a convolution of the force exerted on the cantilever, due to the voltage pulses being measured, and the mechanical response of the cantilever. This complication was later addressed using a nulling method developed by Bridges, Said and Thompson [22] in their time-resolved AFM system. In the work by Bridges et al. the electrostatic force between a flexible tip and sample is monitored and used to demodulate an ultrafast signal. The sample under investigation is repetitively pumped and probed and by cleverly modulating the amplitude of the repetitive probe signal while adding a variable AC dither the sample response can be accurately mapped, irrespective of the cantilever displacement. The force between cantilever tip and sample can be written as: F Z = 1 2 z C(x, y, z) [v p(t) v c (x, y, t)] 2 (1.2) where v c is the voltage on the circuit element being tested, v p is the voltage on the scanned probe, and C(x, y, z) is dependent on the probe tip/circuit geometry and position. To measure v c one could use a series of probe pulses similar to the technique of Hou et al., calibrating the response of the cantilever would still be a problem though. The trick that Bridges, Said and Thompson used was to use a modulated pulse train to probe the circuit voltage. The initial sampling voltage train was given as v s (t) = G δ (t τ) (where G δ (t τ) is a step function at time τ with width δ) but this was modified, giving v p (t) = [A + K cos(ω r t)]v s (t) where w r is the resonant frequency of the cantilever. In the previous equation the variables A, K and v s (t) are all user controlled parameters. Using v p (t) in equation 1.2, gives a number of terms in the force equation. Most of these terms will appear as DC contributions but there will be a term at the modulation frequency ω r, which a lock-in amplifier can detect. This term is expressed as: F z ω ωr = z C(x, y, z) [A v s(t), v s (t) v s (t), v c (x, y, t) ] K cos(ω r t) (1.3) where a, b = 1 T T a(t)b(t)dt is the inner product over the period T. Using v s (t) in equation 1.3 and evaluating the inner product v s (t), v s (t) noting that δ is the width of the impulse G δ (t τ), we rewrite F z as: F z ω ωr = [ z C(x, y, z) A δ ] T G δ(t τ), v c (x, y, t) K cos(ω r t) (1.4) Under the condition that the width of the impulse approaches zero, we note that G δ (t τ), v c (x, y, t) v c (x, y, t = τ) δ T. Recalling that v c(x, y, t) 14

16 is the function we are trying to determine, we see that by adjusting the modulating parameter A to null the force F z, one can easily determine v c. This approach only works when the response of the detection system is very slow compared to the speed of the sampling pulses. The work by Hou, Ho and Bloom was quite illustrative for early proposals for time-resolving STM operation, especially the junction mixing techniques. In the Bloom work, a pump/probe configuration was used, where pump and probe signals were mixed in the squared voltage nonlinearity exerting a force on the AFM tip. The technique of Greg Bridges et al., employed this same nonlinearity, but by using a single excitation source for pump and probe pulses, the electronics required were greatly simplified. The nulling procedure overcomes the problems of calibrating cantilever response and allows the determination of the response of a sample to electrical excitation. These techniques offer fast time resolution, demonstrated into the picosecond range, but the spatial resolution of this technique will be limited by the range of the geometrical capacitance between tip and sample. For time-resolved microscopies where atomic scale spatial resolution is necessary one must look past other scanning probe microscopes to the grandfather of the field, the STM. 1.4 Junction Mixing STM The most successful technique in ultrafast STM has been junction mixing. In this technique a sample is repetitively stimulated (or pumped) where this stimulus will, in some way, affect the tunneling current of the STM. The effect could be to change the tunneling I/V characteristic, through some local surface modification, or to change the bias voltage within the original I/V characteristic. I/V characteristics for metal insulator metal tunneling are typically given by a form of the Simmons equation [23]: I = β(v + γv 3 ) + O(V 5 ), (1.5) showing a cubic non-linearity. The probe pulse, in the junction mixing technique is launched either from the tip or the sample towards the tunnel junction, mixing with the pump pulse at the junction itself. This leads to a time-resolved current contribution which varies with the time delay between pump and probe pulses as they arrive at the tunnel junction. This technique was first demonstrated by Nunes and Freeman [7]. The experimental setup is shown in Figure 1.6. In order to distinguish the time-resolved current 15

17 Figure 1.6: Experimental layout for junction mixing STM. 16

18 contribution, an optical chopper was used to chop pump and probe beams at different frequencies and a lock-in amplifier was used to detect at the sum frequency. As a proof of principle experiment, photo-conductively generated electrical pulses were sent down a transmission line, with one pulse acting as pump and one as probe. The pulses were generated by a single laser pulse train, split into a pump and probe pulse train. Each pulse train was optically chopped at a different frequency and a phase sensitive detector was used to monitor the tunneling current at the sum of the two chopping frequencies. A variable delay between pump and probe was the result of an optical delay line. When the electrical pulses are not coincident at the tunnel junction each pulse causes a slight increase in the tunneling current acquired by the STM electronics. The STM feedback electronics compensates for this increase by withdrawing the STM tip, but the effect is negligible since the duration of the pulses is four orders of magnitude smaller than their repetition rate of the pulses and their magnitude is comparable to the DC bias voltage. If the optical chopping frequencies are above the bandwidth of the STM feedback electronics, the STM tip position will not be effected by a change in tunneling current at this frequency. When pump and probe pulses are not coincident there will be no time-resolved signal at the sum frequency as the feedback will have compensated for the additional current at each of the constituent frequencies. When the pulses are coincident, the non-linearity of the tunnel junction will produce an excess tunneling current contribution as V (I 1 + I 2 ) > V (I 1 ) + V (I 2 ). Because this excess current is only manifest at the sum of the chopping frequencies the feedback electronics will not be fast enough to compensate for it, allowing its detection. To use this scheme one must ensure that the sum frequency falls within the bandwidth of the STM current preamplifier.when these electrical pulses arrived simultaneously at the tunnel junction of the STM, the sum voltage leads to a non-linear increase in tunneling current which can be seen in Figure 1.7. Because the mixing between pump and probe pulse is occurring in the tunnel junction, this technique should maintain the spatial resolution of the STM. This method is non-contact and essentially non-perturbative, considering that the current leaking from the circuit under test is on the order of picoamps. There are limitations to the junction mixing technique; for the signal to mix in the tunnel junction the stimulated sample must offer I/V contrast with the unstimulated sample. In the experiment by Nunes and Freeman both pump and probe pulses were sent down a transmission line to 17

19 Figure 1.7: Time-resolved current using JM-STM indicated by the solid line. Dashed line is a fit assuming an exponentially decaying optically launched voltage pulse. Reprinted with permission from Geoff Nunes, Jr. and M. R. Freeman, Science, 262, 1029 (1993). Copyright 1993 American Association for the Advancement of Science. 18

20 Patterned Gold contacts. Indium contact to Photoconductive switch Indium contact to tip Cleaved GaAs Tip Figure 1.8: An integrated STM tip with photo-conductive switch for JM- STM modeled after a similar design by Groeneveld et al. [24]. In this design there is a direct path from STM tip to the STM current electronics, and there is a photo-conductive switch which can be biased with respect to the tip line, so that electrical pulses can be launched into the tunnel junction from the tip. Though fabricated this tip design has not been tested. the tunnel junction. This is not a requirement of the technique. The sample can be pumped in any manner which will affect the tunneling current, and can be probed using a voltage pulse sent from the tip or sample into the tunnel junction. If the voltage pulse is to be sent down the tip into the tunnel junction there must already be a fixed conduction channel between the junction and the STM current preamp which the pulse is coupled onto as shown if Figure 1.8. This eliminates the possibility that capacitive charging of the tip could lead to a time-resolved signal and is one of the essential differences between the junction mixing technique and the photo-gated STM (PG-STM) technique which will be discussed later. In the initial junction mixing experiments of Nunes and Freeman the authors demonstrated the detection of a transient voltage pulse on a transmission line with 130 ps time resolution. When the STM tip was withdrawn from the tunneling regime the time resolved signal also diminished at the 19

21 same rate as the quasi-dc tunneling current. This suggested that the tunnel junction was indeed the origin of the time resolved signal. Further work by Steeves, Elezzabi and Freeman confirmed the origin of the time-resolved signal by launching electrical pulses from either side of a transmission line into the tunnel junction [25]. The detection of 10 ps electrical transients in this junction mixing experiment confirmed that the non-linear mixing of pump and probe pulses was occurring at the tunnel junction since timing arguments ruled out mixing at any other location. Up till this point it had been shown that the junction mixing STM technique was capable of detecting fast electrical transients traveling along a transmission line which an STM was tunneling into. Since the tunnel junction of the STM had been shown to be the origin of the time-resolved current it was assumed that the junction mixing technique would preserve the excellent spatial resolution inherent in scanning tunneling microscopy. To confirm this fact and to begin measurements of the spatio-temporal resolution limitations of the junction mixing technique another experiment was devised by Steeves, Elezzabi and Freeman [26]. To clearly demonstrate combined spatio-temporal resolution they designed a gold transmission line structure which had 3 µm titanium dots patterned onto it. The characteristic I/V curve tunneling into the gold surface contrasted sharply with that of the titanium as shown in Figure 1.9. A time resolved signal originating because of the I/V nonlinearity of the tunnel junction should also show this contrast as an STM tip is scanned from one material to the other. The transmission line structures used in this experiment were made from 100 nm thick, 200 µm wide gold lines, deposited onto a H + ion-implanted ( cm 2 ion dose at 200 ke)) GaAs substrate. Titanium dots, 20 nm thick, with a 3 µm diameter were patterned onto regions of the gold transmission line using sputtering and lift-off. A schematic of the structure is shown here in Figure With this structure a time-resolved STM experiment was performed where initially a dot was found on the transmission line, and then synchronous pump/probe pulses were used to establish a time-resolved current. Once the time resolved signal was detected through a lock-in amplifier an STM image was taken of the titanium dot and its gold transmission line host. Acquire time for these images was quite lengthy, 21 minutes for a pixel scan as a long 300 ms lock-in time constant was necessary to detect 20

22 75 Tunnel Current (na) Au, γ =1.3 Ti, γ = Bias Voltage (V) Figure 1.9: I/V curves tunneling into titanium and gold surfaces. Reproduced with permission from G. M. Steeves, A. Y. Elezzabi and M. R. Freeman, Appl. Phys. Lett., 72, 504 (1998). 21

23 Figure 1.10: Schematic, showing the gold transmission line structure with titanium dots patterned on top. Reproduced with permission from G. M. Steeves, A. Y. Elezzabi and M. R. Freeman, Appl. Phys. Lett., 72, 504 (1998). 22

24 the time-resolved tunneling signal. In this configuration, time-resolved and topographic images are acquired simultaneously by monitoring the STM feedback signal and the time-resolved signal at the chopping frequency as was done in the original Nunes and Freeman junction mixing experiment. By subsequently varying the relative timing between pump and probe pulses the transit of an electrical pulse across the titanium dot can be recorded using ultrafast STM as shown in Figure 1.11 from Steeves Ph. D. thesis [27]. To analyze the combined spatio-temporal resolution of the microscope junction mixing STM was performed on the edge of a titanium dot. As the STM tip passed from the gold transmission line to encounter the titanium surface the time-resolved STM signal was carefully monitored. It was found that the time-resolved signal changed dramatically in amplitude just as the STM began tunneling into titanium and the resolution of the titanium gold interface established an upper limit on the spatial resolution of junction mixing STM. The temporal resolution in this experiment was determined by the pulse width of the electrical pulses which were created on the gold transmission line, 20 ps. In this way Steeves et al. demonstrated combined 20 nm 20 ps spatio-temporal resolution using junction mixing STM. Continuing this work with an ultrahigh vacuum Omicron STM, Khusnatdinov, Nagle and Nunes [28] were able to demonstrate a factor of 20 improvement in spatial resolution, showing combined spatio-temporal resolution of 1 nm and 20 ps. A line scan showing the topographic and time-resolved STM signals at the edge of a titanium dot is shown in Figure Junction mixing STM has been shown to achieve the goals of ultrafast STM. Combined picosecond time-resolution and single nanometer spatial resolution are the result of a time-resolved signal originating at the STM tunnel junction. Ultimately sub-angstrom spatial resolution should be possible using this technique. The ultimate time-resolution of this technique has been investigated by Steeves, Elezzabi, Teshima, Said and Freeman through modeling the JM-STM tunnel junction using a simple lumped parameter circuit model [29]. The geometry of the model is shown in Figure The circuit elements consist of a transmission line impedance Z and the tunnel junction elements are a non-linear resistance R t (V ) and the geometrical tip/sample capacitance C t. The form of the non-linear tunnel junction resistance is derived 23

25 Figure 1.11: Time-resolved STM image scans, colour contrast represents contrast in time-resolved current between titanium and gold. Each image corresponds to a pump/probe delay time as follows: A = 0 ps, B = 40 ps, C = 45 ps, D = 50 ps, E = 52.5 ps, F = 55 ps, G = 60 ps, H = 80 ps, I = 100 ps. Reproduced with permission from G. M. Steeves s Ph. D. thesis, Junction Mixing Scanning Tunneling Microscopy c

26 Figure 1.12: Topography and time-resolved current of the Au/Ti interface. Time-resolved current(open circles) uses left axis, topography(solid line) uses right axis. Reproduced with permission from N. N. Khusnatdinov, T. J. Nagle, and G. Nunes, Jr., Appl. Phys. Lett., 77, 4434 (2000). 25

27 Figure 1.13: Equivalent lumped element model of STM and transmission line. Reproduced with permission from G. M. Steeves s Ph. D. thesis, Junction Mixing Scanning Tunneling Microscopy c from the Simmons equation [23]: R t (V ) = 1 β(1 + γ(v (t) I(t)Z) 2 ) (1.6) Voltage pulses are expressed as the integrated charge produced by a convolution of the laser pulse shape competing with carrier relaxation processes: t t0 ( ) ( ) τ τ (t V (t t 0 ) = V 0 sec h 2 t0 ) exp dτ (1.7) t p The time t 0 is adjusted for each voltage pulse to simulate the varying delay times between pump and probe optical pulses in junction mixing experiments. It is convenient to note that the integral can be expressed as a hypergeometrical function which in the case of t 0 = 0, can be expressed as: 2F 1 {1, 2; } 1 ; t p e t sec h2 t (1.8) t p 26 t c

28 From these equations t c is the electro-optic switch carrier recombination time and t p is the laser excitation pulse width. A value for the tip sample capacitance was still needed to begin calculations. Accurate modeling of STM tip sample capacitance was investigated by Kurokawa and Sakai [30] but in this work a simply method of images calculation was used [31]. It is worthy to note that on nanoscopic scales additional non-linear capacitive effects may contribute additionally to the circuit model presented here. The low frequency admittance, of a quantum point contact was derived by Christen and Büttiker [32]. Complementing this analysis, was the work of Wang, Zhao, Wang and Guo who examined the density of states induced non-linear capacitance for a parallel plate system, and propose a quantum scanning capacitance microscope [33]. The finite element model used by Steeves et al., gave a nominal value for C t = 33 ff. The equation for the time-resolved tunneling current was given as: di(t) = 1 ( dv (t) 1 I(t) + 1 ) + V (t) (1.9) dt Z dt ZC t R t C t R t ZC t where V (t) is the sum of both voltage pulses delivered by the two ultrafast photoconductive switches and different values of t 0. Solving for I(t) numerically using a fourth order Runge-Kutta solver gave results which were compared with experimental data as shown if Figure The panel on the left shows calculations using the parameters V 0 = 0.49V, β = 5.1 ns, γ = 0.75V 2, Z = 68Ω, C t =33 ff, t c = 10 ps, and t p = 2.8 ps. All the values used in calculation were measured experimentally with the exception of the amplitude V 0 which was used to fit calculation to experiment. Parameters for the right hand panel were quite different since the time-resolved current in this panel was acquired from a faster transmission line structure. Measured values of β = 23 ns, γ = 1.3V 2, t c = 4.5 ps and t p = 2.8 ps were used with a voltage pulse amplitude of V 0 = V, impedance Z = 68Ω and capacitance C t = 33 ff. For both panels the amplitude of the calculated current pulse had to be scaled over the duty cycle of the laser to achieve proper fits with data. Good agreement is seen between experimental results and calculations, though there is some disagreement between the tails of the experimental pulse on the right panel. The authors attribute this to pulse dispersion and reflections in their transmission line structure. Investigating variations of tip sample capacitance on the time-resolved STM signal resulted curves displayed in Figure A time-resolved signal 27

29 25 Time-Resolved Current (pa) Time-Resolved Current (pa) Delay Time (ps) Delay Time (ps) Figure 1.14: Time-resolved tunneling currents. Experimental data is indicated by dashed lines, model calculations are represented by solid lines. (a) Data for a 10 ps voltage pulse. (b) Data from a faster 4 ps pulse. Reproduced with permission from G. M. Steeves, A. Y. Elezzabi, R. Teshima, R. A. Said, and M. R. Freeman, IEEE J. Quantum Electron., 34, 1415 (1998) c 1998 IEEE. 28

30 was not affected by a varying capacitance for values of C t < 1 ff. For values greater than 1 ff the width and amplitude of the time-resolved signal is effected in a roughly linear manner as the signal broadens and diminishes for increasing values of capacitance, shown in the inset. Intuitively this result seems reasonable, current from a fast voltage pulse encountering a resistor and capacitor in parallel will preferentially couple its high frequency components across the capacitor. This leads to a broader, smaller timeresolved tunneling signal when tip sample capacitance is large. For a fixed tip sample capacitance of 33 ff the speed of the junction mixing technique is then evaluated by examining the calculated time-resolved current as a function of transmission line pulse widths governed by t c. Figure 1.16 shows calculated time-resolved currents for carrier recombination times ranging from 1 ps down to 300 fs. The inset shows that for carrier recombination times under 1 ps, the correlation pulse width falls off slowly implying that femtosecond time-resolution will be difficult to achieve without reducing tip sample capacitance below 33 ff. 1.5 Distance Modulated STM Around the same time that the junction mixing technique was first proposed Freeman and Nunes [34] reported a completely different technique for time-resolving an STM, the distance modulation technique. In this work a sample is repetitively stimulated while the distance between tip and sample is varied on a nanosecond time scale. Recall that STM tunneling current varies exponentially with tip/sample separation. Varying this separation on a short time scale allows the gating (or fast sampling) of a signal. This is a technique to mechanically switch the tunneling conductance of the STM without the inherent capacitance problems associated with having an electrical switch on the STM tip. The experimental setup is shown in Figure 1.17 where the STM tip was electro-chemically etched nickel wire (125 µm diameter). Nickel is magnetostrictive, changing its structure by constricting or elongating with applied magnetic field. A pulsed magnetic field can cause an acoustic pulse to be launched along the magnetostrictive nickel tip, modulating STM tip/sample separation on nanosecond time scales. When biased to the steepest part of its magnetization curve the maximum reversible magnetostriction was 0.1 ppm/oe. Using a static bias field of 30 Oe and applying a 80 ns, 20 Oe pulse resulted in a maximum absolute tip displacement of 5 Å (measured through time-resolved fiber-optic interferometry). The direc- 29

31 Pulse Induced Current (na) Correlation Pulse Width (ps) Capacitance (ff) 1 ff 2 ff 10 ff 20 ff 30 ff 40 ff 50 ff 70 ff Pulse Separation Time (ps) Figure 1.15: Tunneling junction current time-resolved signals for different tip-transmission line capacitances. Inset shows the width of the correlation pulses as the capacitance is varied. Model parameters are:β =23 ns, γ =1.3 V 2, V 0 =1 V, t c =1 ps, and t p =200 fs. Reproduced with permission from G. M. Steeves, A. Y. Elezzabi, R. Teshima, R. A. Said, and M. R. Freeman, IEEE J. Quantum Electron., 34, 1415 (1998) c 1998 IEEE. 30

32 Pulse Induced Current (na) Correlation Pulse Width (ps) Carrier lifetime (ps) 1 ps 700 fs 500 fs 300 fs Pulse Separation Time (ps) Figure 1.16: Calculated time-resolved tunneling current for various electrical excitation pulses. Inset shows the width of the correlation pulses as the width of the voltage pulse along the transmission line is varied. Model parameters are : β=23 ns, γ=1.3 V 2, V 0 =1 V, C t =33 ff, and t p =200 fs. Reproduced with permission from G. M. Steeves, A. Y. Elezzabi, R. Teshima, R. A. Said, and M. R. Freeman, IEEE J. Quantum Electron., 34, 1415 (1998) c 1998 IEEE. 31

33 Figure 1.17: A schematic diagram of the distance modulated STM apparatus. 32

34 tion of tip deflection can be changed by reversing the polarity of the field pulse. For the experiment described, the effective tunneling work function φ=0.45 ev gives a characteristic tunneling range (2k ) 1 =1.45Åwhich is less than the 5 Ådisplacement of the tip, indicating that the acoustic pulse will have a very significant effect on the tunneling current signal over its duration. Using the distance modulation technique to sample an electrical pulse sent down a gold transmission line, as shown in Figure 1.17 gives the curves shown below in Figure The fact that the time-resolved signal reversed polarity as the pulse field polarity was reversed illustrated the fact that the time-resolved current contribution decreases as the tip is withdrawn. It does not represent a negative current, just a lowering of current relative to the average since the y-axis zero corresponds to a DC current of 1 na. This apparent bipolar signal is evidence that tip magnetostriction is responsible for the time-resolved current observed. This technique is quite general in its applications. It poses few restrictions on the type of samples which can be studied. So long as the samples can be stimulated repetitively in a way that the STM can detect, distance modulated STM can be used. The primary hindrance of the technique is the inertia of the tip (limiting distance modulated STM to the nanosecond time domain). A technique with no moving parts would enable superior time-resolution. Motivated by this criterion the junction mixing STM technique was developed. 1.6 Photo-Gated STM 1993 was a banner year for experiments demonstrating the time-resolved operation of the scanning tunneling microscope. Four papers, published over a two month span by three different groups, brought three competing methods to add ultrafast time resolution to STM operation. The third of the competing methods is photo-gated STM. In PG-STM [35] an optical pulse train is split into a pump/probe configuration, the pump beam repetitively stimulates the sample under investigation while the probe beam is directed to an optical switch embedded in series with the tip of the STM. In this work the photoconductive switch had a finite dark resistance of 30MΩ (small compared to a typical STM tunnel junction resistance of 100MΩ or more) so that the STM operated without the necessity of illuminating the switch. The idea with this configuration is 33

35 Figure 1.18: Measured time-resolved tunneling current obtained using the tunnel distance modulation technique to sample the presence of a voltage pulse on the transmission line sample. Data are shown for both directions of current flow through the magnetic field pulse coil, and are compared with a model calculation based on the data of Fig. 2 of Ref [34]. Note that the vertical scale for the lower curve has been expanded by a factor of 5. DC tunneling parameters used to stabilize the quiescent tip position are 1 na, 50 mv. Reproduced with permission from M. R. Freeman and Geoff Nunes, Jr. Appl. Phys. Lett., 63, 2633, (1993). 34

36 to use the pump beam to stimulate the sample such that the tunneling current between tip and sample will be modified. Without the probe beam the additional current will be small, the electronics of the STM will integrate this additional current contribution and the feedback system of the STM will compensate by adjusting the STM tip height. When the probe pulse is implemented, the current contribution from coincidence between pump excitation and probe gating will be enhanced. Under these circumstances, the STM electronics will again integrate the excess current and the STM feedback electronics will adjust the tip height accordingly. To avoid this, the pump and probe beams are optically chopped at different frequencies, where the chopped frequencies are outside the response time of the feedback system, but within the bandwidth of the STM current pre-amp. A lock-in amplifier is used to detect the excess current at the chopping sum or difference frequency (beating). By shifting the phase between pump and probe pulse trains, a cross-correlation between the response of the sample (to the pump pulse), and the response of the photo-conducting switch (to the probe pulse), can be created. If one characterizes the response of the photo-conductive switch, the response of the sample can be extracted by deconvolution. The experimental setup used by Weiss et al. is shown in Figure The cross-correlated current measured by this device is shown in Figures 1.20 and In Figure 1.20 each trace is at a different tunneling resistance. Figure 1.21 shows the time-resolved current measured through tunneling and across a tip in contact with the transmission line. In their results Weiss et al. noted that the time resolved signal is proportional to the average tunnel currents, from which they concluded that there is no geometrical capacitive contribution to the time resolved signal. By extracting the tunneling tip 50 Å from the surface, the DC and time-resolved currents drop to zero. The authors used this evidence to conclude that the PG-STM technique has spatial resolution of at least 50 Å. This conclusion is not valid. Even in ordinary STM I/Z sensitivity and lateral resolution are essentially unrelated. Another interesting observation was that the time-resolved correlation pulse width increases with increasing gap resistance. This the authors attribute to an RC time for the tunnel junction, where R is the gap resistance and C is a quantum capacitance between tip and sample. One perplexing question about this work, is the role of tip/sample geometrical capacitance. According to Weiss et al., a quantum tip/sample capacitance ( F) played a significant role in the shape of the timeresolved current. This was supported by the evidence that the shape of the 35

37 Figure 1.19: Photo-gated STM. One laser pulse excites a voltage pulse on a transmission line. The second pulse photoconductively samples the tunneling current on the tip assembly. 36

38 150 AC tunnel current (pa) MΩ 64 MΩ 256 MΩ Time delay (ps) Figure 1.20: The tunneling current I( t) for different gap resistances (16, 64, and 256 MΩ from top to bottom). Reproduced with permission from S. Weiss, D. F. Ogletree, D. Botkin, M. Salmeron, and D. S. Chemla, Appl. Phys. Lett., 63, 2567 (1993). 37