All the probe systems we shall talk about rely on the same piezoelectric scanning, electronic feedback, and display techniques used in the STM that was discussed in the previous section. For example, when imaging a flat magnetic surface with a magnetic force microscope (MFM), the variations in the z-position signal can be related to variations in the magnetic interaction between tip and sample, in direct analogy to the variations in tunneling probability.
Figure 45. The Scanning Thermal Probe is schematically illustrated.The following is taken directly from reference [7, and references therein] unless otherwise noted.Electrical Extensions of STM
Several extensions of the STM have been demonstrated, both in relation to electrical measurements and optical measurements. The scanning noise microscope is an STM where no external bias voltage is applied to the tunnel junction. The rms noise voltage from the junction is measured in a broad bandwidth, and then maintained constant using a feedback loop that controls tip-sample spacing. Since the rms noise voltage is proportional to the gap resistance, this technique allows one to maintain a constant gap resistance as the tip is rastered across the sample. Beyond just being able to map the topography of the surface, this technique is also useful for providing an independent control of the gap while simultaneously making other measurements (for example, thermoelectric voltage) across the tunnel junction, in a band outside the bandwidth in which the noise is measured.
Another modification of the STM is the scanning tunneling potentiometer. In this technique, a bridge method is used to measure the spatial variation in potential across the sample as the tip is controlled and scanned so as to track the surface topography. An AC voltage (typically a few kHz) is applied between tip and sample which generates an AC tunnel current. The amplitude of this current is then used to control the tip-sample spacing. An independent control loop, whose band (DC to 1 kHz) is outside the band of the gap control loop, is used to maintain zero DC tunnel current by continuously causing the voltage on the tip to track the voltage on the sample as the tip is rastered across its surface. The tip voltage is then equal to the sample voltage at every point on the surface. This technique is useful for measuring nanometer scale potential variations on devices such as Schottky barriers and pn-junctions. The voltage resolution is typically on the order of a few millivolts. As we shall see later, these techniques have now been extended to scanning force microscopy allowing one to measure potential distributions on insulating surfaces as well.Optical Extensions
Important extensions of the STM have been demonstrated in the context of nonlinear optical mixing and inverse photoemission microscopy. Cat whisker diodes were used as far back as 1901 to rectify RF signals. Recently, the STM has been used for electrical rectification, optical rectification, and non- linear optical frequency mixing. Unlike the Cat's whisker diode, the STM allows one to have a well-defined and controllable junction. In the experiments dealing with nonlinear mixing at the STM junction, the STM tip acts as a receiving antenna for the incident electromagnetic radiation. The generated current is rectified due to the nonlinearity of the STM I-V response. These nonlinearities arise from material, geometrical, or thermal asymmetries between tip and sample. A power density of 108 W/cm2 can generate typical fields as high as 108 V/cm at the tip apex. Typically, the rectified tunnel current generated is on the order of 1 nA for a focussed 10 mm wavelength CO2 laser. An important application of nonlinear mixing at the STM junction is to microscopy. In the early experiments, a CO2 laser was directed at the STM junction and the rectified tunnel current was used to control tip-sample spacing in order to record the image. Atomic resolution has been achieved on graphite surfaces. In later experiments, two frequencies of the CO2 laser spaced by 9 GHz were directed at the STM junction and the mixed, re-radiated, signal at 9 GHz was used to control tip-sample spacing. In the latter experiments the microscope operated with no electrical connection to the tunnel junction. The experiments just described suggest several new possibilities. First, the photon-driven STM, where all electrical connections to the junction are removed, opens up the intriguing possibility of imaging insulators with the STM. Second, the very high frequency response (1014 Hz) of the tunnel junction should allow one to perform optical spectroscopy on a nanometer scale; the rectified DC junction current being monitored as a function of incident wavelength to record the spectrum. The stimulation of photon emission by tunneling electrons in an STM was first observed in 1988. This and further experiments have served to demonstrate the potential of inverse photoemission microscopy. Early experiments recorded isochromat spectra, where the emission at a fixed wavelength was monitored as a function of tip bias voltage. These spectra showed features that essentially followed the density-of-states features obtained from I-V spectra of the STM junction. In the case of metallic films, the emission wavelength has been shown to correspond to surface plasmon modes in the film that are inelastically excited by the tunneling electrons and then radiatively decay as light. These plasmon modes are thought to originate as charge oscillations between the tip and sample in the STM junction and then scatter into light waves through the same junction. In further experiments, the tunneling parameters were maintained constant while the emission output was analysed in a spectrometer. Such experiments have successfully mapped the bandgap luminescence spectrum of semiconductors such as GaAs and deep level states in CdS. As the STM experiments allow one to simultaneously record I-V spectra, it enables one to follow both the elastic and inelastic pathways of tunnel injection including the de-excitation processes.Near-Field Thermal Microscopy and Extensions
The scanning thermal probe was invented for profiling insulating surfaces. At that time, the atomic force microscope (AFM) which has since demonstrated the capability of profiling atomic features on both insulating and conducting crystals did not exist. The thermal probe consists of a thermal sensor (a thermocouple) built at the end of a fine tungsten tip (see Fig. 45). If a steady current is passed through this thermocouple junction, it heats up and comes to an equilibrium temperature above the ambient value. If the tip now approaches a sample surface (an insulator, conductor, or even a liquid), it cools down due to heat transfer from tip to sample. The tip temperature detected by the thermocouple can then be used to control tip-sample spacing (in much the same way as the tunnel current is used in an STM) as the tip is rastered across the surface. In operation, instead of measuring the DC thermoelectric voltage as described above, the tip is vibrated by a few tens of angstroms in the vertical direction, and the AC change in the thermoelectric voltage is used as a monitor of the tip-sample spacing. This renders the system immune to ambient temperature variations caused by room temperature fluctuations and air currents in the vicinity of the probe tip.
Figure 46. A scanning thermal probe is used to scan a seven micron photoresist step on Si.
Figure 47. A "tunneling thermometer" makes thermoelectric measurements.
The temperature differential can be due to either the absorption of incident light or by direct heating of the sample
Figure 48. Part (a) The Atomic Force Microscope is illustrated schematically.
Part (b) The displacement of the cantilever is detected by the deflection of a laser beam into a four quadrant photodetector.
(a)
(b)
Figure 49. The Scanning Force Microscope.
(a)
We can obtain an expression for the minimum detectable value for the force gradient F' in the following way. The force gradient F' between tip and sample causes a change in cantilever stiffness Dk = F'. We can relate the fractional change in cantilever resonance frequency w to the fractional change in cantilever stiffness k by the expression
For k = 10 N/m, w/2p = 500 kHz, A = 1 nm, and Q = 500, Fm' = 8.4 x 10-5 N/m, and N = 5 x 10-3 angstroms. The minimum vibration amplitude change that can be detected using the laser probe is 5 x 10-5 angstroms. This suggests that the full potential of the laser probe will only be realised by cooling the microscope to liquid helium temperatures thereby reducing the thermally excited vibration amplitude N towards its detection limit. 
The attractive mode force microscope has been used to demonstrate a number of novel measurements ranging from non-contact profiling of surfaces to magnetic imaging and electrostatic imaging.In magnetic force microscopy (MFM), the tip is replaced by a magnetic one--typically iron or nickel and a magnetic interaction force between tip and sample is detected. The "apparent" topography measured over a flat magnetic surface can be directly related to its magnetic features. Both hard and soft magnetic materials have been imaged and resolutions of less than 100 angstroms have been achieved. One problem with the technique is that there is a perturbing interaction between the tip and the sample.
In the electrostatic force microscope, an AC voltage is applied between tip and sample and the induced force is measured. The force is proportional to the square of the applied voltage V2 times the rate of change of tip-sample capacitance with spacing. In early experiments, a regular surface profile was compared with a capacitive force image of a resist step on silicon. The capacitive force image showed a decrease in the force over the resist as compared with the bare silicon, as expected, because the electric field is largely dropped in the resist layer (as opposed to the gap) when the tip is over the resist. The effective change in capacitance that can be measured in this way is in the range of 10-21 F. The capacitance measurement technique can be used to map dopant profiles in semiconductors by measuring the change in tip-sample capacitance versus voltage at different sample bias voltages.
Figure 50. The atomic scale periodicity of the friction force as measured using an FFM. We might ask ourselves what the meaning of friction is at the atomic scale since frictional forces were originally defined in macroscopic interactions. Blau [10] discusses the possibility of defining a "frictomic" force, f(x) to decribe nanocontacts that are functions of the atomic periodicity as f(x) = Pmnano where P is the applied load. The force f(x) is periodic in sliding distance and may be approximated as The FFM produces an image of an area whose brightness and contrast vary directly with localized variations in friction force. Two methods are used as illustrated in Figure 51. In one case, bidirectional movements are monitored using two sensors (such as capacitance gap or tunneling); and in the other case, one sensor (laser and four quadrant photodetector).
The electrostatic force microscope has also been applied to measure voltages on Circuits. In this case, the tip is usually connected to ground potential and a small ac voltage is superimposed onto the bias voltage. The induced vibration of the tip can then be used to determine the voltage on the circuit being probed. A map the voltage distribution across circuit lines can be mapped in this way.
The Friction Force Microscope (FFM) [8]
An instrument was developed by McClellan et al. in which a tungsten wire with a fine tip was brought down on the surface of HOPG. The specimen was oscillated at a freqeuncy of 10 Hz. The spring constant of the cantilevered wire was 2500 N/m. The normal force was measured using the measured deflection of the cantilever. As the normal force was decreased (in the range 6 - 75 mN), contributions of individual atoms to the apparent tangential force became apparent. At the same time, the motion of the tip became less smooth, a behavior reminiscent of stick-slip phenomena. Figure 50 shows the results of that experiment. The estimated friction coefficient from these experiments is 0.01, about 10% of the value reported on the large scale for a variety of metals sliding on HOPG and on itself. 
f(x) = Fmax(cos wx -f) + C
Figure 52 shows an example of the output from a commercial FFM. The image on the left is a topographical image of a patterned organic monolayer on a gold substrate. The image on the right is a friction force map of the same area. In these kinds of measurements the results must be viewed in terms of the specific tips used and samples studied. The results of such experiments may not correlate well with what is observed on a larger scale.
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