3.1 Scanning tunneling microscopy and spectroscopy
3.1.1 STM operation modes
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Chapter 3
Instrumentation
Figure 3.1: Basic illustration of a scanning tunneling microscope: A sharp tip is brought close enough toward the surface of a voltage-biased sample so that a detectable quantum mechanical tunneling current may be detected. In the constant-current topography mode of STM operation, the tip is scanned across the surface and a constant current is maintained by a feedback loop. The tip-sample separation necessary to maintain a constant current is controlled by a piezoelectric tube scanner, discussed in more detail in Fig. 3.3. The topographic signal is given by the z-piezo voltage of the tube scanner, Vz, needed for the feedback loop to maintain a constant-current as the tip is scanned.
der fluctuations. Furthermore, studies of the vortex-state of cuprate superconductors require spatial resolution better than ξSC to adequately characterize the intra-vortex and inter-vortex electronic DOS, or the quasiparticle excitation spectra.
In order to perform STM experiments with atomic resolution, the STM tip must be brought within several angstroms of the sample surface and must then be moved laterally with sub-angstrom control. In addition, the small quantum tunneling currents (1pA–100nA) must be detected with a large signal-to-noise ratio. To meet these requirements, piezoelectric elements are employed to achieve fine motion control, and the STM instrumentation must be designed to achieve sufficiently small acoustic, vibrational, and electronic noises to resolve the small STM signals. Piezoelectrics typically provide control on the order of 1nm/V, and the typical electronic noise for a well designed STM system is on the order of a few pA.
There are three modes of STM operation that we concern ourselves with here: the constant- current imaging, the constant-height imaging, and the constant tip-junction resistance spectroscopy
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modes. All three modes require sophisticated instrumentation to perform experiments, which we discuss more fully below. Briefly, the block diagram of the STM and the electronics associated with the operation are shown in Fig. 3.2. Coarse-motion stages (XY-stage and Z-stage) initially position the tip near the sample, and then fine motion control is achieved by a piezoelectric (piezo) tube scanner. The STM controller1 controls the voltage bias between the tip and sample, measures the tunneling current after amplification, communicates with the feedback controller, and applies voltages to control the piezo tube scanner.
The constant-current imaging mode is an STM mode of operation that is used to measure the topography associated with a constant tunneling current between the tip and sample. This mode is commonly associated with the ability to resolve individuals atoms on a surface of interest, such as our measurements showing individual atoms on highly-oriented pyrolytic graphite (HOPG) shown in Fig. 3.4. A constant-current imaging scan is performed by engaging the STM controller feed- back circuit, which maintains a constant tunneling current between the sample and the tip, and scanning the tip across the sample by changing the high-voltage outputs to the piezo tube scanner.
Throughout this process a constant voltage bias is maintained between the tip and sample. The desired tunneling current for imaging may be selected by adjusting the set point current, Iset, of the feedback loop. The topography of the surface, z(x, y), is determined by the voltage applied to the z-piezo of the piezo tube scanner,Vz, in order to maintain a constant current between the tip and sample and the conversion relation between Vz andz(x, y). An illustration of scanning in the constant-current mode is shown in Fig. 3.1.
Ideally, each point in an image of the constant-current mode is obtained with a constant-current;
however, the feedback loop does not respond instantly to changes in topography. Therefore, the gain and time-constant,τ, of the STM feedback control on the STM controller must be adjusted such that the tip can follow the contours of the surface as accurately and quickly as possible. Rough surfaces require the feedback loop to respond to changes in topography quick enough to avoid a “crash”
between the tip and sample. The scanning speed and feedback parameters must be optimized in
1SPM 1000 Controller from RHK Technology
obtained by turning off the feedback loop and measuring the resulting tunneling current as the tip is scanned across the sample. The tip may be scanned more quickly in constant-height mode because the feedback loop response time is no longer a factor. The scan speed is limited by the response time of the current pre-amplifier, and the upper limit of scan speed is determined by the lowest mechanical resonance of the STM head. An advantage of scanning faster in constant-height mode is the fact that the effects of low frequency noises, such as building vibrations (f ∼1−20Hz), on topography images are reduced. The topography, z(x, y), in constant-height mode is obtained by assuming an exponential relation between the measured tunneling current and the distance between tip and sample, such as would be expected for Eqs. 2.10 and 2.11. However, the actual height between tip and sample requires knowledge of the local tunneling barrier height; thus the relative height is usually measured in constant-height topography mode. The surface must be relatively flat (nearly atomically flat) to avoid tip contact with the sample in constant-height mode and to maintain tunneling currents large enough to be measurable by the electronics.
Operation of the STM in constant tip-junction resistance spectroscopy mode allows measurements of the tunneling current-(I-)vs.-voltage bias (Vbias) or measurements of the tunneling differential conductance-(dI/dV-)vs.-Vbiasto be made. The dI/dV-vs.-Vbiasmay also be computed numerically from I-vs.-Vbias measurements. As was discussed in Chapter 2, measurements of the tunneling differential conductance for superconducting samples provide a measurement of the quasiparticle excitation spectra. Initially constant tip-junction resistance spectroscopy is performed similar to the constant-current imaging mode of operation in that a constant voltage bias is applied to the sample while the feedback loop adjusts the tip height to maintain a constant tunneling current at
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each pixel. After establishing the desired tip-junction resistance at each pixel in a spectroscopy map, the feedback loop is disabled in order to perform spectroscopy. This mode is referred to as constant tip-junction resistance spectroscopy mode because the tip junction resistance is given by Rjunction =Vbias/I, and the tip-sample junction resistance is the same at each pixel of the spectroscopy map.
The surface topography of the sample is approximately eliminated from measurements of spatially resolved differential conductance maps in constant tip-junction resistance spectroscopy mode for a homogeneous surface. This fact arises for a homogeneous surface because constant tip-sample junction resistance ensures approximately constant tip-sample height separation at each pixel in this scenario. For the general case of examining cuprate superconductors, which are known to have varying local density of states on the order of a few nanometers in some cases [68], the voltage bias must be set to exceed the energy scale over which variations are observed to maintain an approximately constant height. For Y-123 and La-112 considered here, we do not observe such inhomogeneity in zero-field spectra, and variations in quasiparticle spectra in a finite magnetic field occur up toω=±∆ef f =∼ ±40meV. Therefore, we apply Vbias=-80meV and expect that constant- junction resistance spectroscopy mode eliminates surface topography roughness from measurements of spectroscopy to a first approximation in Y-123 and La-112. Additional electrical cross-talk between the high-voltages on the tube scanner and the signal at the tunneling tip are also minimized by our instrumentation to eliminate the effect of topography roughness on dI/dV-vs.-Vbiasmaps in constant tip-junction resistance spectroscopy mode.
The majority of measurements performed in Chapters 4 and 5 are measurements of constant tip-junction resistance spectroscopy measurements. Typical resistances used were 1GΩ, with Iset=- 80pA, Vbias=-80meV. At each pixel in a spatially resolved scanning tunneling spectroscopy (STS) map, an I-vs.-Vbias curve was taken. The differential conductance, dI/dV, was then numerically computed from the I-vs.-Vbias curves to determine the local quasiparticle DOS from dI/dV-vs.- Vbias. We now describe the instrumentation of our STM for performing these measurements.
Figure 3.2: Overview illustration of the STM head. (a) Schematic drawing of the STM and the connections to the STM controller and the coarse approach motor controller. The STM controller controls the piezoelectric tube scanner movement, measures the quantum tunneling current, applies the voltage bias, Vbias, for imaging and spectroscopy, provides the feedback loop to control tip height, and records all data to the computer. Each of the voltages necessary to manipulate the piezoelectric tube scanner (Vz, Vx, Vy,V−x, V−y), which are shown in Fig. 3.3, can be varied from -215V to 215V to provide fine motion control. In addition, the coarse approach motor controller applies a high-voltage waveform (amplitude up to 300V), shown in Fig. 3.5e, to the piezoelectric shear stacks in order to move the XY- or Z-stages in coarse steps. The coarse step process is illustrated more fully in Fig. 3.5. (b) Schematic illustration of the location of the XY- and Z-coarse stages, as well as the tip holder. (c) A more detailed map of the STM head. The piezoelectric tube scanner is controlled by the STM to provide fine (atomic-resolution) motion. An electrically insulating Macor spacer attaches to the end of the tube scanner to prevent electrical shorts between the tip isolation ground and the tube scanner connections. (Macor is a machineable ceramic made by Corning, Inc.) The tip isolation ground helps to decouple the high voltage piezo tube scanner signals from the tunneling current detected at the STM tip. Another Macor space separates the tip isolation ground from the STM tip to prevent an electrical short between the two. The STM tip, oxygen-free high thermal conductivity (OFHC) copper sample stage, and the sample are shown in the figure. The shear piezoelectric (piezo) stacks, the sapphire plates, the sapphire prism, and the copper-beryllium (Cu-Be) springs that comprise the XY- and Z-stages for coarse motion are also shown. The Z-stage coarse motion parts are discussed in more detail in Fig. 3.5. A resistive heater is mounted directly to the top sapphire plate of the XY coarse-motion stage in order to raise the temperature of the STM above the temperature of the cryogenic bath. A Cernox temperature sensor (purchased from Lakeshore Cryotronics, Inc.) was located on the OFHC sample stage. (d) A picture of the actual STM head without the XY-stage attached. The design of the STM head combines elements of design from Refs. [103, 104].
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Figure 3.3: Schematic illustration of the functionality of the piezoelectric tube scanner: (a) Schematic illustration of the piezoelectric tube scanner. The tube scanner used was a hollow cylinder with dimensions of: O.D. = 0.125”, I.D = 0.085”, length = 0.600”. It is divided into four quadrants of shear piezos to provide scanning motion in the x- and y-directions. The piezoelectric tube scanner showing the connections to the four quadrants (Vx, Vy,V−x,V−y), as well as the shared connection to the inner surface of the piezoelectric tube (Vz), are shown in the figure. (b) By applying an equal positive and negative voltage to opposite quadrants relative to Vz, the piezoelectric tube scanner will shear oppositely on the two quadrants and provide a displacement for scanning. A representative displacement (∆x) along the x-direction is shown. The value of ∆x = 0.9dd31V L2
mt , where d31 is the shear piezo contast, V is the voltage applied, L is the length of the tube scanner,dm= (O.D.+I.D)/2, and t is the wall thickness of the tube scanner. The value ofd31 at T = 293K for an EBL#2 piezo is −0.173nm/V on average. However, the actual value is gained by calibrating each tube scanner.
(c) If an equal voltage is applied to all four quadrants relative to Vz, the tube scanner will extend by an amount, ∆L= d31tV L. For simplicity, it can be considered that the quadrant voltages, (Vx, Vy,V−x,V−y), control the motion in the x- and y-directions, while Vzcontrols the height of the tube scanner. Other configurations to control motion are possible, but a full discussion is beyond the scope of this work. (d) A picture of an actual piezoelectric tube scanner. Actual tube scanners used in this work were calibrated on highly-oriented pyrolytic graphite (HOPG) to determine the calibrated voltage dependence of ∆x, ∆y, and ∆L. A representative calibration of a piezoelectric tube scanner on graphite showing atomic resolution topography, from the constant-current topography mode of STM operation, is shown in Fig. 3.4.
Figure 3.4: A representative topographic image measured on HOPG using a piezo tube scanner.
The image shows atomic resolution topography obtained using the constant-current topography mode of STM operation. The image was used to calibrate the piezo tube scanner motion, and the carbon-carbon separations were found to be∼0.142nm upon proper calibration, as expected.