Characterization of Electrical Properties

     Main representatives among electricity-sensitive techniques based on SFM are Scanning Capacitance Microscopy (SCM), Scanning Kelvin Probe Microscopy (SKPM), Scanning Spreading Resistance Microscopy (SSRM) and Conductive AFM (C-AFM, which, in fact, is more general than SSRM).

     All these techniques involve using conductive tip and voltage bias applied between tip and sample. Therefore, one should not be extra generalization to consider Electric Force Microscopy (EFM) as a collective term for all mentioned techniques since all they utilize electric driving forces. Sometimes investigators use specific names for particular techniques such as mentioned above and sometimes not, using the common term "EFM". One should note at the same time, that this abbreviature often refers to Electrostatic Force Microscopy which can be also considered as a sort of Electric Force Microscopy. Let us take an overview on each backing on the real explorations.

     Scanning Capacitance Microscopy is used to measure capacitance differences between tip and sample while maintaining constant height of the tip (in noncontact mode) or constant force (in contact mode). The latter is used when nonconductive layer such as oxide covers the sample or when tip is intentionally oxidized beforehand.

     Difference in capacitance may witness for:

1) variations of surface potential of the sample;
2) changing media properties between tip and sample.

     Variations in surface potential may be caused by variation in carrier concentration that may reveal dopant level distribution on semiconductor surface, or, say, phase inhomogeneity in alloys (different work functions for different phase components) etc.

     As for media properties, capacitance is sensitive to

1) distance between tip and sample, hence variations in thickness of intermediate layer such as oxide can be measured;
2) dielectric properties of the intermediate layer, for example, various defects such as smallest pin-holes in etching mask, sources of current leakage in Metal-Oxide-Semiconductor (MOS) structures, surface conducting contaminants etc. can be readily visualized.

     Surface potential as well as capacitance variations can be measured also by means of Scanning Kelvin Force/Probe Microscopy (SKFM, SKPM or even SKM), which can be regarded as a sort of SCM. Classical vibrating Kelvin capacitor is known to be used for more than a century in determining of the surface potential. Periodical variation in the distance between plates of electrical capacitor made of a pair of conductors investigated leads to variation of its capacitance and appearance of alternate current which can be measured. The analogous oscillating capacitor is inherent to the system that consists of conducting cantilever operating in dynamic noncontact mode and conductive sample. This resemblance gave rise to the name of this technique. Though, capacitance of such system is very low and the current flows through it is extremely low either. Therefore, this technique does not measure current but exploit the extraordinary sensitivity of SFM to detect the smallest deflection or frequency shift of vibrating cantilever due to electrostatic interactions. In general it looks like the following: applying AC voltage of frequency w (which usually differs from the resonant frequency of the cantilever) between tip and sample it is necessary to minimize these interactions adjusting DC bias, which occurs to be equal to surface potential of the sample at every scan point.

     Karpov et al. [1401] describes application of EFM, and SKPM in particular, to quantitative measurements of voltages in metal interconnects and planar resistors, as well as to imaging pn junctions and trapped charges. Two-pass technique was implemented (so-called Liftmode™, registered by Digital Instruments) to acquire sequential topographic and electrostatic force data. On the first pass, the surface morphology is recorded along a scan line in tapping mode. On the second pass, the oscillating tip is raised 30-500 nm above the surface and scanned along the same scan line reproducing previously recorded topography but gathering electrostatic force data. Cantilevers with resonant frequencies f_o of 60 and 200 KHz were used. The frequency shift Df_o was measured by a frequency modulation technique with a typical resolution of 0,1 Hz. The frequency shift of the oscillating cantilever caused by presence of electrostatic force F can be estimated by the following equation:

assuming that the force derivative term does not significantly affect the vibration mode of the cantilever (dF/dz < k, were k - cantilever spring constant). Therefore, the more the resonant frequency of the cantilever and the less its spring constant, the more change in resonant frequency is reachable.

     When low frequency (w=1-200 Hz) AC voltages are applied to the cantilever, magnitude of frequency shift Df_o shows clear linear dependence of the AC amplitude. It can be shown that periodical alterations in resonant frequency consist of two counterparts D f_o= Df _o(w)+D f _o(2w) corresponding to a pair of electrostatic forces F₁ (w) and F₂(2w): at low AC amplitudes alterations occur mainly with frequency w, whereas at high AC amplitudes component D f_o (2w) dominates. Negative and positive frequency shifts were observed over p and n-regions of the junctions.

     Sensitivity of EFM to map local surface charging effect of very smooth (RMS of merely 0,25 nm) silicon wafer after polishing was also demonstrated. The features corresponded to the direction of the polishing. The contrast of the features was found to depend on the tip potential indicating their electrostatic origin. Authors suggested that the features represent local charges trapped in the native oxide.

     Bresse and Blayac [1404] used EFM/AFM in liftmode for quantitative determination of sheet resistance of the epitaxial layer under ohmic contact. The authors used first harmonic force component F₁(w) for measurements. Corresponding amplitude of the tip vibration excited by applied voltage of frequency w is determined by the following equation:

were k is the spring constant of the cantilever and Q is its quality factor. For cantilever with k=2N/m, Q~200, excitation voltage amplitude V₁=2V and tip-sample bias V₀ of 1V as well as lifting height of 200 nm the amplitude amounts to 24 nm. The sensitivity of the potential measurements reported to be of ±10mV. Values of sheet resistance obtained by EFM and using traditional Transmission Line Model (TLM) structure was in excellent agreement of ±3%. It was found that experimental profile of the potential, measured using the EFM is fitted with two determined values for the epitaxial layer sheet resistance outside and under the ohmic contact. This allowed to conclude that the sheet resistance of the epilayer under the metal is not affected by the ohmic contact formation due to limited diffusion of the Au/Ti composition into the semiconductor.

     Qualitative studies of cross-section potential profile of microcrystalline silicon (µc-Si) solar cells by SKPM were performed by Breymesser et al. [866, 1227]. Quantitative description fails because grinding and polishing procedures led to formation of abundant surface states that influence the position of the Fermi level. Measurements and 1D-simulations revealed unappropriate effective charge distribution in the middle of the intrinsic layer resulting in reduced drift-field-assisted collection of photoinduced charge carriers. It was also found that reverse polarized p-Si/n-TCO (Transparent Conductive Oxide) diode sequenced with the p-i-n diode can be deduced from the data obtained. This diode possibly responsible for the low open-circuit voltages of the solar cells. Thus, SKPM can be successfully used for assessing the quality of the intrinsic µc-Si layer and to provide suggestions for further improvement of the deposition processes.

     Böhm [1403] describes electric force tester for submicron device characterization working at GHz frequencies. The tester is capable of measuring very fast voltage changes. As the mechanical response ability of the probe precludes the measurement of fast voltage changes a mixing scheme was considered where the probe is biased with either a sine wave or a sampling voltage pulse. In this way high measurement bandwidths exceeding 100 GHz in combination with a spatial resolution below 100 nm can be achieved. The author claims that the spatial resolution in the voltage contrast mode depends strongly on the probe-sample surface separation. For typical separations of 50 nm a spatial resolution below 100 nm can be attained. The voltage sensitivity is better than 1 mV. As an example a combined high resolution measurement of an electron-beam written meander waveguide was demonstrated. The exact position of the doped area (300 nm width) within waveguide of 800 nm in width cannot be estimated from the topography image. For the voltage contrast mapping the probe was lifted to a fixed height (50 nm) above the device surface and the local deflection of the probe caused by the electrical force interaction was gathered at every measurement point via computer and a voltage contrast image was generated. A 1 GHz, 5 dBm signal was fed onto the waveguide, the probe was biased with a sampling pulse with a repetition frequency of 1 GHz+10 KHz. The future improvement involves incorporation of integrated pulse generator into the probe itself. The prototype has been also demonstrated.

     Ferroelectric thin films are of growing importance due to possible use in non-volatile random access memories. Materials with high permittivity (so-called "high-k materials" [928, 1046]) offer advantages in building low-sized capacitors being the active elements in such memory devices. Further shrinking of their dimensions imposes insurmountable restrictions on use of "usual-k materials" in this field. Electric Force Microscopy is a valuable tool for investigating such objects. But ferroelectrics are much more complicated materials as compared, for example, with metals or even semiconductors and their quantitative description by means of EFM should take into account nonlinearity of their properties during measurement due to piezoelectric effect and electrostriction. Franke et al. [1406] describe the procedure of extracting spontaneous polarization information from experimental EFM data. The authors emphasize that the first harmonic EFM-signal coincides with the polarization signal only for materials in which the permittivity is constant in the measured area. Therefore they consider a contribution of mentioned above electromechanically induced forces besides electrostatic ones (also called "Maxwell stress"). It was shown mathematically and experimentally that spontaneous polarization can be separated from the first harmonic EFM signal by dividing the latter by a permittivity-dependent function. This conclusion is valid only for contact mode. Estimations gave rise to assert that in the case of thin films with a high permittivity, a gap of air only a few nanometers thick would dominate the second harmonic signal and prevent an accurate determination of the film permittivity. Therefore, the noncontact mode is not applicable for the separation of polarization.

     For studying of piezoelectric and ferroelectric materials so-called piezoresponse mode SFM (PFM) is also used [843]. The technique is based on the detection of electromechanical surface oscillations due to the inverse piezoelectric effect induced by tip AC bias. Spectroscopic variant of PFM allows local electromechanical hysteresis loops to be obtained. PFM can also be used to modify local domain structure on the nanometer level by applying dc bias to the tip. Relatively soft (0.03-0.3 N/m) cantilevers are optimal for high lateral resolution (~7-10 nm), while stiff cantilevers (1-50 N/m) are required for quantitative measurements.

     Similar technique was used by Franke et al. [1408], who report the experiments on EFM induced repolarization of lead zirconate titanate (PZT) films. It is known that remanent polarization degrades under applied external stress or due to internal stress peculiar to thin films. To diminish this unwanted process better understanding and qualitative description of stress-induced repolarization effects are necessary. It has been found that the depolarization is set off at 93 MPa going on until 260 MPa and originated from Maxwell stress caused by electrostatic interaction between the EFM tip and the dielectric sample. Authors believe that results remain to be true even if the domains cannot be resolved because of their small dimensions. Thus, stress dependent polarization measurements significantly extend the efficiency of Electric Force Microscopy.

     Resolution and problems of quantitative measurements by means of Kelvin Probe Microscopy are discussed in details by Jacobs et al. [1231]. A model, which correlates the measured potential with the actual surface potential distribution, is introduced in this paper. It was demonstrated that the observed potential is a locally weighted average over all potentials present on the sample surface. From the comparison of numerical simulations based on the model proposed with experimental data from test structures follows that the good resolution in potential maps is obtained by long and slender but slightly blunt tips on cantilevers of minimal width and surface area. Authors specially stress that special attention must be paid to the geometry of the tip and cantilever because the cantilever surface predominates the local electrostatic interaction when the tip apex size is too small. Here again, conducting carbon nanotube tips seem to be the best choice [1247, 1611].

     Thorough overview of the existing probes for various EFM techniques has been done by Trenkler et al. [1266]. The authors emphasized on applications on Si at high contact forces. Two classes of probes were examined geometrically and electrically: Si sensors with a conductive coating and integrated pyramidal tips made of metal or diamond. Swift and nondestructive procedures to characterize the geometrical and electrical properties of the probes prior to the actual AFM experiment have been developed.

     Robin et al. [1229] measured the cross-sectional electric field and potential distribution of a cleaved A^IIIB^V-based p-i-n laser diode using SKPM with a lateral resolution as high as 50 nm. The data obtained occur to be in a good agreement with 2D-simulations despite some discrepancies in absolute values. The understated measured value as compared to the simulated one was attributed to presence of surface traps due to the exposure of the sample to the air as well as consequences of incomplete ionization of dopant impurities.

     The phenomenon of understated measured values has been mentioned also by Simpkins et al. [1232] who studied variations of surface potential in epitaxial GaN (0001) by means of SKPM. The measurements confirmed that, as reported in other studies, surface potential variations amount ~0,1-0,2 V in magnitude, and that variations are associated to a large degree with threading dislocations present at the GaN surface. Their density apparently decreases as the film goes thicker. It was stated that the finite size of the probe tip will cause the measured value of a highly localized variation in surface potential to be smaller in magnitude than the actual value, particularly for features that are comparable in size to or smaller than the probe tip radius. Therefore actual surface potential variations in the vicinity of a threading dislocation at the GaN film may be considerably larger than those measured by SKPM. Sophisticated simulations proved this assumption. Authors emphasize that this decrease should be taken into consideration for any studies of highly localized features in surface electronic structure using this and related techniques. Thus, recommendations of Jacobs et al. [1231] concerning the statement that the tips are to be slightly blunted is inapplicable to explorations of the structures with subnanometer electrically active features.

     Earlier Hansen et al. [1236] studied the same material by combination of AFM and Scanning Capacitance Microscopy. The points where screw dislocations exit the surface have been clearly observed by tapping mode AFM. Their sizes was estimated to be within 30-55 nm range which less than those from the work of Simpkins et al. [1232] who reported of 100 nm average diameters. From the simple comparison of SPKM and SCM images one can conclude that resolution power and contrast of SPKM was much more perfect. Nonetheless, nowadays Scanning Capacitance Microscopy has also become a powerful characterization tool, which meets rigid requirements in resolution, time efficiency and implementability for practical industrial use. SCM is a quite real candidate for 2D carrier probing not only passive but also active electronic devices in both research and manufacturing phase [1239].

     In general, SCM unit consists of the tip being in contact with oxidized surface usually forming Metal-Insulator-Semiconductor structure. Data are acquired under various DC biases V_DC with superimposed AC sinusoidal signal, which is needed to get the dC/dV derivatives at every V_DC value. Changing in capacitance is related to (major) carrier concentration. For accurate measurements of dC specific RF module with sensor working at about 1GHz is commonly used.

     It should be noted that the problem of quantitative determining of 3D dopant profiles in semiconductor devices is very complicated since carrier concentration usually does not coincide with real dopant concentration especially in compensated semiconductors. This problem can be solved through sophisticated simulations and development of more complicated procedures. In this sense, Scanning Capacitance Microscopy itself is not entirely new technique; it is rather implementation of C-V methods at micro- and nanoscale. Development of special simulation software packages and accounting of probe tip size and shape is now the best way to improve resolution and make an interpretation of the data received more relevant and quantitative. The examples of such simulation endeavours are modification of TSUPREM-4 and MEDICI packages by Kang et al. [1235], direct inversion method by Marchiando et al. [1220] and SCaMsim simulation package described by Ciampolini et al. [1237, 1238].

     Direct inversion or calibration curve method (CCM) now is widely used to calculate theoretical C-V curves for a series of model samples with uniform dopant levels in order to built SCM-signal-to-doping conversion curves for further mapping of the measured signals into doping levels. Various tip curvature radii and oxide thicknesses are also taken into account. In some particular situations, for example, for slowly changing dopant profiles this method gives good approximation. Later the authors reported the limitations of this method [1265] and showed that without correction for relative steep profile gradients, SCM leads to the underestimation and displacement of dopant peak. Concentration of the impurities occurred to be 50% of actual one.

     SCaMsim program is based on the DESSIS_ISE package for electronic device simulation by finite element method and also involves MATLAB™ sessions. Authors extended calibration curve method and built more excessive C-V database, which data calculated for a wide set of tip-sample geometries. It was shown that Signal to Noise Ratio (SNR) highly depends upon dopant level and surface oxide thickness. The higher is dopant level the noisy becomes signal.

     Systematic analysis of noise sources during Scanning Capacitance Microscopy measurements is performed by Zavyalov et al. [1267]. The authors suppose that the main noise sources are capacitance sensor noise and oxide-semiconductor surface induced noise. For adequate tip size, the dominant noise in SCM measurements is caused by variations in the quality of surface due to variations in the densitiy of oxide traps (nonstationary noise) and in oxide layer thickness (stationary noise). Heat treatment under ultraviolet irradiation or in a hydrogen ambient is found to be an effective way to reduce or even eliminate the former type of SCM noise. And reducing the topographic roughness one can make stationary noise much lower. It is shown that the capacitance sensor noise depends on the capacitance sensor tuning parameters and under proper conditions can be reduced to a negligible level for standard probe tips used in SCM measurements.

     SCM seems to be very attractive technique for pn-junction delineation [1240, 1241, 1244, 1264], imaging of active and passive devices under operation that gives valuable information for better understanding of physical processes in them, failure analysis and in-line testing equipment [1234, 1242, 1268, 1269].

     Similar technique has been used even for studying of very complicated structures such as metal-filled anodic alumina with the cantilevers of MikroMasch produce [1405].

     Just the same as for SCM, Scanning Spreading Resistance Microscopy could be regarded as an implementation of well-established Spreading Resistance Profiling (SRP) method for use at micro- and nanoscale. But generic SRP is dual probe technique, therefore the difference is remarkable. SSRM is another promising tool for determination of dopants distribution in semiconductor materials as well as for exact pn-junction delineation [1243, 1270, 1271, 1273, 1278]. Results of cross-sectional profiling of semiconductor devises are in good agreement with Second Ion Mass Spectrometry (SIMS) data. Development of commercial AFM equipped with SSRM unit (e.g. manufactured by Digital Instruments) greatly facilitates the process of data acquisition.

     Historically, first target for SSRM measurements was silicon, whereas during last two-three years researchers focused mainly on A^IIIB^V semiconductors (see corresponding references in [1274, 1275, 1276, 1277]).

     To improve the depth resolution, the samples for the conventional dual probe SRP require preparation of beveled surfaces, which quality has been found to affect significantly the measured contact resistance. Moreover, certain corrections are needed to account for junction shifts from carrier diffusion due to the beveled surface. In contrast, SSRM offers a much higher spatial resolution (several times less than a tip radius) and eliminates the need for surface beveling. SRP tips curvature radius is usually 10 µm tungsten alloy stylus as opposed to 50-100 nm (or even better) for diamond like carbon coated (DLC) SSRM tip. A voltage biases used for SRP are in order of magnitude higher than those for SSRM. Dynamic range for carrier concentrations in both n- and p-type Si covers five orders of magnitude 10¹⁵-10²⁰ cm^-3 [1274].

     The effects of the applied tip voltage, scanning rate, surface preparatlon and tip choice in SSRM measurements are discussed by Kline et al. [1272]. It was found that the active region of the laser structure, where the band gap is lowest, could be identified in the voltage dependence of the SSRM images.

     Conductive Atomic Force Microscopy uses conductive cantilevers in "full-contact" mode similar to SSRM. C-AFM is less sensitive and possesses lower lateral resolution as compared with STM. Nonetheless it still shows very attractive parameters sufficient to address a number of scientific and industrial problems. Furthermore, in contrast to STM, it does not require delicate sample preparation and maintaining the proper measurements conditions.

     Objects investigated by means of C-AFM vary widely. These are SiO₂ layers in MOS devices [141, 461], high-temperature superconductors [422], CoSi₂ precipitates in cobalt-implanted silicon [488], microcrystalline silicon [584], an Anopore™ ultrafiltration membrane [1359] and many others.

     None of the techniques mentioned so far is capable of direct measurement of surface potential. Nanopotentiometry or Scanning Voltage Microscopy (SVM) is another relatively novel EFM technique, which makes this possible [2004, 2009, 2032, 2038, 2804, 2805, 2806, 2807]. In nanopotentiometry, a conductive SPM tip is used in contact mode as a voltage probe in order to measure the distribution of electrical potential on the crossection of an operating device. The macroscopic quantity of voltage can be related to the microscopic quantity of internal potential in an operating device. The determination of internal potential distribution is pertinent to many other local properties, such as carrier concentration, band positions, quasi-Fermi level position, etc. This information is of use for the calibration of device simulations. In contrast to the other EFM techniques, measuring tip does not significantly perturb the device under test because state-of-the-art voltmeters offer very high input impedance (>10¹⁴ Ohm). Resolving power of nanopotentiometry is comparable or higher than that of SCM or SKPM, being of the order of AFM tip radius. But since contact mode is used, special probes are required combining both hardness and good conductivity.

     Nanopotentiometry has been successfully used for the characterization of Si-based MOSFET [2004, 2009], a buried heterostructure laser [2032] and an InP p-n junction depletion region [2038].

     There are a number of another EFM techniques not observed above such as Voltage-Modulated AFM (VM-AFM) [935] or "pure" Electrostatic Force Microscopy [1407], and their quantity extends year by year.