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Electrical characterization of gate oxides by scanning probe microscopies
Journal of Non-Crystalline Solids 303 (2002) 150–161 www.elsevier.com/locate/jnoncrysol
Section 8. Local structure of high k dielectrics and defect characterization
Electrical characterization of gate oxides by scanning probe microscopies R. Ludeke
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IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA
Abstract Ballistic electron emission microscopy (BEEM) and non-contact atomic force microscopy (NC-AFM) are used to characterize SiO2 and Al2 O3 layers grown on Si(1 0 0). The effective conduction band mass and its energy dispersion in SiO2 and an offset between Al2 O3 and Si conduction bands of 2.78 eV were obtained with BEEM. NC-AFM was used to image electrons, and in some instances holes, trapped in the oxide layers near the surface and in the bulk of the oxide. Modeling of the tip–surface interaction supports the interpretation of image features arising from a single electron occupying a trap. The polarity of the trapped charge was deduced from Kelvin (potential difference) images that were simultaneously recorded with the topographic images. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Scanning probe microscopies, analytical methods based on the scanning tunneling microscope (STM) and the atomic force microscope (AFM), are generally thought of as surface specific techniques. This is indeed the case for the vast majority of applications, and is due to the dominance of surface properties in controlling the interactions between the tip of the instrument and the surface. In the case of the STM the interactions affect the tunneling current, whereas for the AFM it is the mostly repulsive tip–surface interaction that determines the instrument’s response. However, in select cases the tip–surface interactions can be used as control to detect and measure phenomena as-
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Tel.: +1-914 945 2591; fax: +1-914 945 2536. E-mail address: [email protected] (R. Ludeke).
sociated with specific properties in the bulk of the sample. Specifically, two such techniques are ballistic electron emission microscopy (BEEM) and non-contact AFM (NC-AFM), both of which will be discussed here in terms of novel applications that address gate oxide issues previously deemed unsolvable by other known analytical techniques. BEEM, a STM based transport technique, is sensitive to the potentials in the gate oxides and can be used to determine barrier heights (band discontinuities) and transport dependent parameters, such as the effective electron mass in the conduction band of the oxide. BEEM, specifically the current component transmitted through the sample, is also very sensitive to local interface and bulk charges, but is generally unable to resolve these as isolated, individual charges. The NC-AFM and its variations are sensitive to these charges as well, but have the additional sensitivity to resolve individual electrons, to determine their polarity and, in
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 0 9 7 8 - X
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the case of interface charge, assess their binding energy relative to the band edges. In this paper we will first discuss some novel BEEM applications, and subsequently the imaging of oxide charge using NC-AFM and the determination of the charge polarity employing a Kelvin probe. The latter entails a modification in the conventional operating mode of the NC-AFM. Historically novel methods are first applied to well-understood material systems, an approach taken here as well. Therefore the analytical concepts will be demonstrated first for SiO2 , but applications of both techniques will also be shown for high-K materials, in the present case, Al2 O3 . The capabilities of BEEM will be illustrated by a unique determination of the conduction band mass of SiO2 , as well as by the determination of band offsets in the W/Al2 O3 /Si structure. Charge imaging and charge density determinations, including trapping–detrapping phenomena, will be illustrated for SiO2 and Al2 O3 gate oxides using NC-AFM and Kelvin methods.
2. Ballistic electron emission microscopy applications to gate oxides 2.1. Ballistic electron emission microscopy basics The first application of BEEM was the determination of the Schottky barrier height for Au–Si [1]. Subsequent applications to Schottky barriers and semiconductor heterostructures can be found in several reviews [2–4]. Applications to SiO2 metal– oxide-semiconductor (MOS) structures have been reported [5,6] and recently reviewed by the author [7]. The experimental methods have been described elsewhere [7] and only a brief description will be given here. The MOS structures were prepared in ultrahigh vacuum by evaporating a thin tungsten layer through a shadow mask and onto the devicequality oxides, which were grown ex situ on Si(1 0 0) substrates. In BEEM electrons are injected from the STM tip into the metal layer covering the oxide. The tip of the STM is biased relative to the metal film, rather than the substrate, as in a conventional STM. This is achieved for the present situation by manipulating and placing a metal wire at ground
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potential in contact with the W dot. The tip bias VT imparts the electrons injected by the tip into the W layer with a kinetic energy (KE) of eVT relative to the Fermi level EF of the metal. For thin metal layers (1.8–4 nm used here) the electrons traverse the metal ballistically and may enter the conduction band of the oxide for eVT > UB , the barrier height between EF and the conduction band edge of the oxide. Electrons that reach the Si substrate are detected as an emerging ‘collector’ current Ic . An energy band diagram corresponding to BEEM applied to a MOS structure is shown in Fig. 1(a). A bias Vb applied across the oxide can be adjusted to achieve a desired potential profile. The trapezoidal barrier, shown by the dashed line, represents the static barrier potential for a positive applied bias. The profile encountered by an electron is modified by screening effects (image force effects) from electrons in either metal or Si substrate, a situation that cannot be ignored in actual transport experiments [8]. The result of screening on the potential profile is shown by the solid line. Progressively decreasing Vb permits the attainment of the flat band position (dotted curve) and subsequently a raised potential peak near the Si interface for negative biases (dashdotted profile). The collector current becomes finite only when the tip bias exceeds the maximum barrier energy. In the spectroscopic mode of BEEM employed here the scanning of the STM tip is stopped temporarily and Ic is measured while the tip bias (i.e. the electron KE) is ramped from below UB /e to several volts above it. BEEM is thus a threshold technique, the threshold tip bias Vth corresponding to the maximum in the profile of the barrier potential between the metal and the Si substrate. Examples of BEEM spectra (Ic vs. VT ) are shown in Fig. 1(b) for SiO2 (dotted) and Al2 O3 -based MOS structures. The net transmitted current is larger for SiO2 because of lower electron scattering rates. A dominant scattering event in SiO2 arises from electron-acoustic phonon interactions, which causes the observed decrease in Ic for VT > 6 V [9]. 2.2. Quantum interference oscillation and the dispersion of the SiO2 conduction band mass For SiO2 -based MOS structures Ic may exhibit an oscillatory modulation arising from
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Fig. 1. (a) Energy band diagram of a BEEM experiment on a MOS structure for various biasing situations, (b) representative BEEM spectra of MOS structures composed of a W gate with a 8 nm Al2 O3 layer (solid curve) and a Pd gate with a 10 nm SiO2 layer (dotted curve) on Si(1 0 0). The gate is grounded and VT and Vb are referenced to it.
interference effects of the electron wave function in the oxide conduction band [10,11], analogous to the oscillations observed in Fowler–Nordheim transport [12,13]. In the simplest approximation for a rectangular barrier [14], peaks in the transmission function occur at energies E ¼ UB þ 2 ðnp h=dox Þ = 2mox , where dox is the oxide thickness, mox the effective conduction band mass, h is Planck’s constant divided by 2p and n ¼ 1; 2; 3 . . . An example is shown in Fig. 2 for a 1.8 nm W/3 nm SiO2 /p-Si(1 0 0) structure. An oscillatory structure in the spectrum is clearly observable [15].
The STM tip bias at threshold was 3.77 V. Flat band condition was achieved at Vb ¼ 0:3 V (substrate positive). An effective transmission function can be extracted from the raw data by subtracting a simulated incoherent component of Ic [15]. The resulting experimental transmission function is shown as a dotted curve in the upper part of Fig. 2(a), from which the interference maxima can be readily obtained. These cannot be indexed by simple theories that neglect image force effects and assume a constant effective mass. Instead the 1D Schr€ odinger equation was solved numerically and
Fig. 2. (a) BEEM spectrum, Ic vs. VT , for a 1.8 nm W/3.0 nm SiO2 /p-Si(1 0 0) MOS structure (dotted curve) with an estimated unmodulated collector current component shown by a dashed line. Their ratio yields an ‘experimental’ transmission coefficient, shown by the dotted curve in the upper left. The theoretical transmission calculated with a dispersive mass is shown as a solid curve. Vertical arrows mark interference maxima in the transmission coefficient calculated with a fixed mass mox ¼ 0:42mo , where mo represents the free electron mass. (b) Conduction band mass dispersion mox ðEÞ for SiO determined from quantum interference oscillations in BEEM spectra (top two curves), compared to a dispersion derived from MC simulations of experimentally determined electron mean free paths (lowest dashed curve).
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included image force effects and boundary conditions suitable for the materials used in the experiment. The details are discussed elsewhere [10,15]. The maxima in the transmission function calculated for a fixed electron mass, depicted at the top of the figure by arrows, show poor agreement with experiment. After matching the first low energy maximum, the effective mass value had to be progressively readjusted upwards to obtain a match for all remaining maxima. The resulting transmission function is shown by the solid curve in the top part of Fig. 2(a). The values of mox ðEÞ at each maximum are then used to obtain the dispersion curve represented by the connected filled circles in Fig. 2(b). The abscissa shows the KE of the conduction band electrons, obtained by subtracting the threshold energy. The curve of connected triangles represents the dispersion for a 2.3 nm SiO2 , which was thermally grown on p-Si(1 0 0) and was covered with 4 nm Pd metal layer. Its upward displacement relative to the 3 nm oxide cannot be accounted for by uncertainties in the parameters, but may be attributed to quantum size effects, such as an onset of band structure changes. The overall increase in mox ðEÞ for the thinner oxide is consistent with a narrowing of the bands due to the decreasing dimensionality [16]. Also shown in Fig. 2(b) is the mass dispersion obtained from the Monte Carlo (MC) simulations of the attenuation lengths in SiO2 , obtained by internal photoemission experiments [15]. Although the discrepancy with the BEEM-determined dispersion is appreciable, it is comforting to note that the changes in mass over comparable energy intervals are quite close. Agreement cannot be expected since the ‘reference’ mass for the MC calculations at 1.5 eV was assumed to be 0.5mo . The range of the dispersions in all three cases, which are comparable in magnitude, implies considerable non-parabolic behavior in the dispersion of the conduction bands of SiO2 . 2.3. Band offset and interface charge determination for W–Al2 O3 MOS structures The 8 nm thick Al2 O3 layers used in these experiments were grown by atomic layer chemical vapor deposition (ALCVD) on HF etched n- and
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p-Si(1 0 0) substrates (q 1–17 X cm). The amorphous films were stoichiometric with atomically flat and abrupt interfaces. Details of the deposition and the structural characterization of the layers can be found elsewhere [17]. The samples were annealed in forming gas to partly passivate the interface states. A typical BEEM spectrum is shown in Fig. 1(b). Spectra were taken for a broad range of biases Vb applied across the oxide. The thresholds Vth were obtained by fitting a model power law to the spectra [4]. For Vb J 0 the thresholds decreased, whereas for Vb K 0 they increased, in agreement with the expected raising of the barrier depicted by the topmost barrier profile in Fig. 1(a). The decrease in Vth , however, can only be attributed to image force effects, which lead to 1=2 a barrier lowering of dUB ¼ ðqVox =4peeif dox Þ , where e is the permittivity in vacuum and eif is a dynamic (image force) dielectric constant. This effect was already observed in SiO2 -based MOS structures [8]. The oxide potential Vox was obtained by solving the Poisson equation for the appropriate Si and oxide parameters [9,18]. Fig. 3(a) shows the dependencies of Vth on the oxide potential, plotted as a function of Vox1=2 , for both n- and ptype substrates. The linear behavior indicates that the threshold response is dominated by image force effects. Results for Vox > 0 are shown by filled symbols; the solid lines are least square linear fits to the data sets. Their zero field intercepts are within 10 meV, giving an average value of UB ¼ 3:90 0:03 eV. The uncertainty is based on the accuracy of determining the threshold voltages. The image dielectric constant is obtained from the slope of the linear fit and exhibits a value of eif ¼ 1:77 for the p-type sample (N). A value of eif ¼ 1:86 0:1 was obtained by averaging the fits for all data sets. It should be emphasized that eif is drastically lower than the static dielectric constant eo 8–9, a difference whose significance will be discussed below. For negative values of Vox the ordinate values are represented by (Vth jVox j) instead of Vth . This procedure cancels the contribution of Vox to the barrier height, which allows the observation of field induced changes, if any, at the Al2 O3 –Si interface (topmost barrier profile in Fig. 1(a)). The resulting curve for the n-type sample is shown in
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Fig. 3. (a) Threshold energies for 8 nm Al2 O3 layers on n- and p-Si(1 0 0) substrates plotted against the root of the oxide potential. The reduced threshold Vth jVox j is plotted for Vox < 0 (open symbols). The solid lines are least square fits, (b) flat band barrier profile for W/Al2 O3 /p-Si(1 0 0). The circles represent trap levels of density rif near the oxide–Si interface, which for the p-type substrate remained unfilled for Vox > 0.
Fig. 3(a) by connected open circles. A least square fit is again a straight line up to 1 V1=2 with a slope and intercept nearly identical to those for positive bias. This confirms, as well, the presence of image force effect at the oxide–Si interface. Beyond 1 V1=2 the thresholds, that is (Vth jVox j), decrease progressively with increasing Vox for the n-doped sample. This reduction is attributed to a decrease in negative charge near the interface. The discharging, which was reversible upon reducing Vb , probably occurs through field enhanced leakage across the oxide and into the gate. For other biases this charge was constant, which suggests that it was not generated by the experiment but rather pre-existed it. The location of the charge, or more precisely that of the centroid of its distribution, x, can be obtained from the slope of the Vth vs. Vox plot, which should be proportional to xVox =dox , with x measured from the W–Al2 O3 interface [6,19]. The centroid, which BEEM measures, is located at the maximum of the potential profile. For Vox < 0, a linear plot of Vth vs. Vox for the ntype sample (not shown) indicates a linear region of slope 0.89. Thus x ¼ 0:89 (a value that approaches unity after correcting for image forces), which indicates that the charge resides at or very near the Al2 O3 –Si interface [20]. For the p-type sample the threshold response for Vox < 0 is quite different. The results, specifically (Vth jVox j), are plotted as open triangles in
Fig. 3(a). For the bias range shown, (Vth jVox j) initially increases rapidly, reaches a maximum and then decreases more gradually. For this bias range the Fermi level at the Si interface moves from a position near the valence band (flat band) to the conduction band edge (inversion). It is therefore surmised that the increase in thresholds is caused by the charging of previously neutral electron traps near the interface, whose energy distribution is largely confined to an interval matching the band gap of Si. The saturation in the trapping indicates that few, if any, trap levels overlap the Si conduction band. Once the traps are filled, and in analogy to the n-type case, the subsequent decrease of the threshold energy at a linear rate with slope close to that of the other cases discussed implies that these trap states are also located near the oxide–Si interface. The results thus suggest that the trap states are of similar origin for both substrate types and that their occupancy is solely determined by the position of the Fermi level at the Si interface. The saturation of charge trapping for the p-type sample allows an estimation of the charge density rif . A value rif ¼ 2:5
1012 electrons/cm2 was calculated using a simple sheet charge model that includes image force corrections at both interfaces [21]. A determination is now possible of the Si– Al2 O3 band offsets because of the negligible trapping in the p-type Si for Vox P 0. For the known
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substrate doping and measured barrier energies, including a flat band voltage Vfb ¼ 0:25 V, the energy band relationship shown in Fig. 3(b) was obtained [22]. A Si–Al2 O3 conduction band offset dEcb ¼ 2:78 0:06 eV was deduced, which is within 0.2 eV of previously reported values obtained for thicker layers using internal photoemission [23,24]. It should be emphasize at this point that the indicated barrier heights only apply in the zero field limit. For other biases substantial lowering can be expected due to the strong image force effects, effects that cannot be ignored in predictions of direct and Fowler–Nordheim tunneling currents. It should be further noted that due to the low value of eif 1:86, image force effects in Al2 O3 are larger than in SiO2 , for which eif ¼ 2:69 [8]. This value is much larger than the optical dielectric constant of SiO2 (e1 2) because electron–optical phonon scattering still dominates electron transmission in SiO2 at energies near the thresholds [8]. The lower eif for Al2 O3 is consistent with estimates of a lower electron–LO phonon coupling compared to SiO2 [22].
3. Imaging of oxide charge In this section we discuss the detection of captured charges of as little as a single electron or hole trapped in SiO2 and Al2 O3 gate oxides. Evidence of charge appears in the images of the oxide surfaces obtained with an AFM operating in the noncontact (NC) mode in ultrahigh vacuum. Although the observation of surface charge by NC-AFM has recently been reported on single crystal surfaces of semiconductors [25] and TiO2 [26], the direct imaging of individual charges buried below the surface has not been reported. In a NC-AFM topograph the presence of charge takes on the form of a ‘hole’ in the layer. This is illustrated in Fig. 4(a), which is an image for a 2.8 nm thermal oxide grown on an n-Si(1 0 0) wafer at IBM’s Advanced Silicon Technology Laboratory. The oxide is of gate oxide quality, yet the dark depressions are comparable to or may even exceed the oxide thickness. Fig. 4(d) shows a depth profile in the area of the dashed square in Fig. 4(a), specifically along the dashed line in the enlarged
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image of Fig. 4(c). Clearly the depths of the holes are incompatible with the device grade quality of the oxide. The holes, therefore, do not represent physical depressions, but are virtual holes generated by surface–AFM tip interactions other than the strongly repulsive hard sphere interaction between the two materials that leads to the classical image of the surface topography. As will be shown, the interaction that results in the virtual holes arises from the attractive forces, specifically the force gradients, between a charge embedded in the oxide and its image charge of opposite polarity in the AFM tip. Since the interaction is always attractive, the polarity of the charge cannot be obtained from the topographic image. Instead we have developed a methodology based on the simultaneously recorded potential difference or Kelvin image that allows an unequivocal determination of the polarity of the charge. 3.1. Concepts of charge imaging and polarity determination with the NC-AFM In the NC mode the cantilever of the AFM vibrates near its natural resonance frequency (xo =2p) given by x2o ¼ k/m, where k is the cantilever stiffness and m its mass, k is essentially the intrinsic force gradient of the cantilever, which can be affected by other force gradients arising from the proximity of the tip to the surface. Examples of such modifying force gradients arise mainly from the interaction between tip and surface atoms (the classical ‘contact’ situation), as well as from electrostatic, magnetic, Van der Waals and capillary forces. Only the first two are of significance here. Operation of the NC-AFM is based on the detection of a small frequency change in the cantilever resonance, given by dx ¼ dF 0 xo =2k. dF 0 is the change in the force gradient normal to the surface, effectively a change in the net stiffness of the cantilever, arising from changes in the tip– surface interaction [27]. dx is thus a direct measure of dF 0 . The AFM operates in the constant dx mode, with changes detected by frequency demodulation methods [27]. The feedback directs the piezoelectric z-driver (motion normal to the surface) to move the cantilever in or out to maintain a constant dx; the driving signal is used to generate
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Fig. 4. Topography (a), with gray scale range of 6 nm, and Kelvin image (b) for a 2.8 nm SiO2 layer on n-Si(1 0 0). A magnified region (dashed square) in (a) is shown in (c), with the depth profile along the dashed cut shown in (d).
the topographic image. The cantilevers used here had a stiffness in the range of 5–14 N/m and resonance frequencies in the range of 180–380 kHz. Experimental values of dx=2p were in the range of 100–200 Hz, for which slopes of 20 to 30 Hz/ nm were obtained from measured z vs. dx plots (not shown). This slope, which is a measure of the net cantilever stiffness, increases as the tip approaches the surface (increased repulsive F 0 ). Thus, an excursion of the scanner of 1 nm in the z-direction (surface normal), a value that is equivalent to the depth of a virtual hole in the topography (Fig. 4), corresponds to a change in the local force gradient of dF 0 103 N/m. It will be shown next that modeling of the interaction of an electron embedded in a dielectric and its image charge in the metallic AFM tip leads to force gradients F 0 ¼ oFz =oz of comparable size. The tip is represented by a conductive sphere of radius r at a distance a above the surface. The charge q is
located a distance dq below the surface and laterally a distance l from the projected point of contact of the tip on the surface. The solution is [28] " # " # 2 2 2 2 2 2 q r 3z þ r l qV r l 2z b F0 ¼ : 4pee2eff ðz2 þ l2 r2 Þ3 eeff ðz2 þ l2 Þ5=2 ð1Þ
Here z ¼ r þ a þ dq , eeff ¼ ðeox þ 1Þ=2 is the effective dielectric constant arising from screening of the charge in an oxide of dielectric constant eox (¼3.9 for SiO2 , 8–9 for Al2 O3 ), e is the permittivity and Vb the applied substrate bias. Fig. 5 shows curves calculated with Eq. (1) for Vb ¼ 0 and for some realistic values for r, a and dq . For charges near the surface F 0 1 103 N/m, a value consistent with that necessary to account for an image force induced ‘hole’ of 1 nm depth. F 0 is quite sensitive on the depth of the charge, as well as on the dielectric constant of the oxide. In SiO2 ,
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Fig. 5. Vertical force gradients on conductive AFM tip arising from image charge effects.
a charge 1 nm below the surface is reduced by a factor of 3 from one near the surface, but by factor of 7 when the material has the dielectric constant of amorphous Al2 O3 . The maximum in F 0 ðlÞ (at l ¼ 0) is independent of r, but not so its width at half maximum, as can be observed by comparing the two topmost curves in Fig. 5, which differ only in the assumed value of the tip radii. A full width at half maximum of 6–8 nm is obtained for tip radii in 5–10 nm range. The calculated widths are consistent with observation in most cases [29]. The imaging of a virtual hole can now be understood as follows: as the tip scans over the surface towards a charge, the increasing attractive force will counteract the repulsive tip–surface interaction, thereby decreasing dx. Since a constant dx is maintained by the AFM feedback, the piezoelectric z-driver responds by pushing the cantilever towards the sample, thus creating the appearance of a hole in the image. Further evidence that the virtual holes are associated with trapped charge is obtained from Kelvin images [30]. These are acquired simultaneously with the topographs. The images are generated by adding a small low frequency modulation voltage Vm sinðxm tÞ to the tip–substrate bias V b , which represents the net sum of the applied bias Vb and a local surface potential. This subjects the cantilever to an additional attractive force gradient given by F 0 ¼ 0:5V 2 o2 C=oz2 , where V ¼ V b þ Vm sinðxm tÞ, and C is an effective
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capacitance of the tip–surface system. The demodulated output of the AFM has superimposed on it a signal proportional to V b Vm sinðxm tÞ, which is fed into a lock-in amplifier. Its output in turn is fed into a second imaging channel of the AFM to generate the Kelvin image. The magnitude of the lock-in output is proportional to V b Vm , and its phase depends on the sign of V b , that is, on which side of the F 0 ðV Þ parabola the bias is set. As an aside, the value of Vb for which V b ¼ 0 corresponds to contact potential difference (CPD). Thus contrast in the Kelvin image reflects the polarity of V b and its local variations, which allows a determination of the polarity of the local chargeinduced potential, and hence that of the charge itself. The sign of the phase is arbitrary. The convention was adopted here that an increasingly negative local potential lowered (darkened) the Kelvin image brightness for negative V b . This convention results in a darkened image for increasing positive potentials under positive bias. That is, under positive bias electrons image as protrusions (bright areas) and positive charge as holes (dark areas), with the reverse contrast occurring for negative bias. 3.2. Imaging of charge in SiO2 gate oxides The oxides used were thermally grown ex situ on 200 mm£ Si(1 0 0) wafers. Samples of suitable size for the AFM experiments (2 7 mm2 ) were then cleaved and introduced into the preparation chamber of a JEOL SPM4500A, an ultrahigh vacuum, multi-chamber AFM/STM. The samples were outgassed near 300 °C to remove volatile surface contaminants, including water, and subsequently transferred into the AFM analysis chamber for the measurements. The topographic image covering a 500 500 nm2 area of a 2.8 nm SiO2 layer on n-type Si(1 0 0) is shown in Fig. 4(a). The corresponding Kelvin image is shown in Fig. 4(b). It shows a one-to-one correspondence between the virtual holes in the topograph and similar dark holes in the Kelvin image. The tip bias was Vb ¼ 0:037 V, which was sufficiently negative to ensure that for the phase convention discussed in the previous section the dark features in the Kelvin image correspond to areas of negative
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potential relative to the lighter features and are therefore associated with negative charge. The irregular shape of some of the larger and darker features in the topograph, one of which was profiled as shown in Fig. 4(d), indicates that it is composed of a cluster of several charges. The intensity indicates that these charges are in the near surface region of the oxide. Clustering of charges has also been observed for SiO2 films grown on Si(1 1 1) substrates [29]. The broad range of depths of the virtual holes indicates a random distribution of trapped charge throughout the thickness of the oxide. The smallest depressions in the profile of Fig. 4(d) are 2–3 nm from the surface according to best estimates obtained with Eq. (1), which would place the charges near the SiO2 –Si interface. The overall density of trapped charges for this forming gas annealed oxide layer was estimated to be 1:5 1011 cm2 , a factor 5 higher than for simultaneously grown thermal oxide layers on p-Si(1 0 0) substrates. These values are consistent with estimates obtained by electrical characterization. Thus far, mostly negative charges have been observed on thermally grown SiO2 /Si(1 0 0) using
the NC-AFM/Kelvin imaging methods. However, a notable exception was the observation of positive charge (holes) trapped at interface Pb centers of vacuum annealed, thin (1.8 nm) SiO2 layers grown on p-type Si(1 1 1) [29]. 3.3. Imaging of charge in Al2 O3 gate oxides The Al2 O3 samples were taken from the same wafer of ALCVD-grown and forming gas annealed material as those used in the BEEM experiments discussed in Section 2.3. Sample size and pre-analysis treatment were similar to those used for the SiO2 samples. Fig. 6(a) depicts a 200 200 nm2 topographic image of the oxide surface taken at a bias Vb ¼ 0:7 V. This bias value is more positive than the CPD value of about 1 V, so that negative charge should image as bright areas in the Kelvin image. This is indeed the case, as can be seen in Fig. 6(b). The darker areas in this image are regions that exhibit a surface potential that is more positive than that of the negative charges. As for SiO2 , a one-to-one correspondence is observed between virtual holes in the topograph and fea-
Fig. 6. Topography (a), with gray scale range of 3 nm, and Kelvin image (b) for an 8 nm Al2 O3 layer on n-Si(1 0 0). The depth profile along the dashed cut in (a) is shown in (c).
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tures in the Kelvin image (this time hillocks), which strongly supports the notion that their origin is electrostatic. The darker (deeper) virtual holes are again attributed to electrons trapped near the surface. Considerable clustering occurs for these traps, which aggregate into a wavy pattern that extends across the field of view. The cause or implication of this behavior is not known. A depth profile along the dashed line in Fig. 6(a) is shown in Fig. 6(c). Even in parts of the profile that goes through relatively featureless areas of the image, considerable weak structure is observed, which is evidence of charge buried deeper into the sample. Based on Eq. (1), the depth of the weakest image features corresponds to electrons located 2:5 0:5 nm below the surface. A density of trapped electrons of 9 1012 cm2 was estimated from the images for negatively biased samples. If one conjectures that the traps are randomly distributed throughout the oxide, that would place potentially 3–4 1012 cm2 charges within 1 nm of the interface. Perhaps coincidentally, this number is close to the 2:5 1012 cm2 value for the trapped interface charge obtained for the same material with BEEM (Section 2.3). The role of substrate bias on the charge and its effect on the topographic features is illustrated in the images of Fig. 7 for the same 60 60 nm2 area of an 8 nm Al2 O3 /n-Si(1 0 0) sample. Fig. 7(a) was taken with Vb ¼ 1:5 V, which is near the CPD; that is, only a small potential difference exists between tip and surface. When the bias was changed by 2 V to Vb ¼ 3:5 V, the image, shown in Fig. 7(b), changed noticeably. For negative bias electrons are pushed towards the interface, while leaving a positive charge on the tip. Many of the features once seen in Fig. 7(a) are no longer observable or are very weak in Fig. 7(b). This is attributed to neutralization of the trap levels: electrons trapped near the surface with trap levels that rise above the Fermi level of the tip upon increasing the bias can now be transferred to the tip, neutralizing the level. That this effect is not due to a weakening of the cantilever stiffness can be ruled out by comparing the intensities of the remaining virtual holes. Profiles taken at identical locations are shown in Fig. 7(d). Clearly the depths of the virtual holes present for both biases remain comparable, which indicates that their trap levels
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remain below the tip’s Fermi level. The situation for a change in bias of roughly comparable magnitude as before, but in the opposite direction (Vb ¼ þ1:0 V) is shown in Fig. 7(c). For this case most of the charge has leaked out to the substrate, leaving a generally featureless image. The depth of one of the remaining holes, compared to depths at the other biases, is much smaller, as can be seen in the dotted curve of Fig. 7(d). The weakness can be attributed to partial occupancy of the trap level, with charge that slowly leaks out being replenished by new charge from the tip. It should be noted here that the images are reproducible when the bias is returned to the appropriate value. Unlike SiO2 , positive bulk oxide charge has been observed in Al2 O3 . An example of this is shown in Fig. 8. The images were taken with Vb ¼ 0:5 V within the area marked by the dashed rectangle in Fig. 7(a). The bias is slightly more positive than that of Fig. 6, so that negative charge should image as bright features (hillocks) in the Kelvin image and positive charge as dark spots or holes. This is indeed observed in the accompanying Kelvin image in Fig. 8(b). Both hillocks and holes in the Kelvin image correspond to virtual holes in the topograph, as befits their origin of image charges whose attractive forces are polarity insensitive. The circled virtual holes in the topograph represent positive charge, as deduced from their dark features in the Kelvin image. Profiles along the same location in both images are shown in Fig. 8(c). These intersect charges of both polarities. The topographic profile (solid line) only exhibits the depressions, whereas that of the Kelvin image (dashed line) shows a positive relative potential for the dark spots and a negative potential for the bright features in the Kelvin image.
4. Summary and conclusions Illustrative samples highlighting two quite different scanning probe methods were presented. Each has strengths that are based on their operational characteristics and the nature of their physical interaction between sample and probe. BEEM is essentially a transport technique capable of probing material or sample properties that
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Fig. 7. Topographic images of an 8 nm Al2 O3 layer on n-Si(1 0 0) of the same 60 60 nm2 area for biases of (a) Vb ¼ 1:5 V; (b) Vb ¼ 3:5 V and (c) Vb ¼ þ1 V. The depth profiles along identical cuts are shown in (d). Gray scale ranges are for (a) 2 nm, (b) 1 nm, (c) 0.8 nm.
Fig. 8. Topograph (a), and Kelvin image (b), of square area outlined in Fig. 7(a), but for Vb ¼ 0:5 V. Profiles along the marked cuts are shown in (c). The circled features in (a) correspond to positive charges imaged as dark features in the Kelvin image.
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affect electron transmission. These need not to be ‘intrinsic’ properties; on the contrary, the role of BEEM in elucidating defect and breakdown characteristics in oxides has been amply demonstrated elsewhere [7]. The NC-AFM is essentially a potential profiler, sensitive to all surface and nearsurface charges. The complimentary relationship of the two methods has only been intimated, primarily because of the very novelty of the charge imaging technique. Its role and possible future applications appear to be extensive, particularly in relation to dielectric stressing and defect generation, and its extension beyond dielectrics to other material systems, including semiconductors and organic systems, is quite obvious.
Acknowledgements I wish to thank the many co-authors and coworkers who through the years were essential in helping me define and implement the directions of this research. In alphabetical order they are Doug Buchanan, Ed Cartier, Maria Teresa Cuberes, Chris D’Emic, Evgeny Gusev, Andreas Schenk and Huajun Wen.
References [1] W.J. Kaiser, L.D. Bell, Phys. Rev. Lett. 60 (1988) 1406. [2] M. Prietsch, Phys. Rep. 253 (1995) 163. [3] L.D. Bell, V. Narayanamurti, Curr. Opin. Solid State Mater. Sci. 3 (1998) 39. [4] R. Ludeke, in: K. Horn, M. Scheffler (Eds.), Handbook of Surface Science, vol. 2, Elsevier, Amsterdam, 2000, p. 799. [5] R. Ludeke, A. Bauer, E. Cartier, Appl. Phys. Lett. 66 (1995) 730. [6] B. Kaczer, Z. Meng, J.P. Pelz, Phys. Rev. Lett. 77 (1996) 91; B. Kaczer, P.J. Pelz, J. Vac. Sci. Technol. B 14 (1996) 2864.
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[7] R. Ludeke, IBM J. Res. Develop. 44 (2000) 517. [8] H.J. Wen, R. Ludeke, D.M. Newns, S.X. Lo, J. Vac. Sci. Technol. A 15 (1997) 784. [9] R. Ludeke, A. Bauer, E. Cartier, J. Vac. Sci. Technol. B 13 (1995) 1830. [10] H.J. Wen, R. Ludeke, A. Schenk, J. Vac. Sci. Technol. B 16 (1998) 2296; R. Ludeke, H.J. Wen, A. Schenk, Appl. Phys. Lett. 73 (1998) 1221. [11] B. Kaczer, H.-J. Im, J.P. Pelz, J. Vac. Sci. Technol. B 16 (1998) 2302. [12] J. Maserjian, J. Vac. Sci. Technol. 11 (1974) 996. [13] S. Zafar, K. Conrad, Q. Liu, E.A. Irene, G. Hames, R. Kuehn, J.J. Wortman, Appl. Phys. Lett. 67 (1995) 1031. [14] K.H. Gundlach, Solid State Electron. 9 (1966) 949. [15] R. Ludeke, E. Cartier, A. Schenk, Appl. Phys. Lett. 75 (1999) 1407. [16] F. Bassani, G. Pastori Parravicini, Electronic States and Optical Transitions in Solids, Pergamon, New York, 1975. [17] E.P. Gusev, M. Copel, E. Cartier, I.J.R. Baumvol, C. Krug, M.A. Gribelyuk, Appl. Phys. Lett. 76 (2000) 176. [18] E.H. Nicollian, J.R. Brews, MOS Physics and Technology, Wiley, New York, 1982. [19] D.J. DiMaria, J. Appl. Phys. 47 (1976) 4073. [20] R. Ludeke, M.T. Cuberes, E. Cartier, J. Vac. Sci. Technol. B 18 (2000) 2153. [21] R. Ludeke, H.J. Wen, Appl. Phys. Lett. 71 (1997) 3123. [22] R. Ludeke, M.T. Cuberes, E. Cartier, Appl. Phys. Lett. 76 (2000) 2886. [23] N. Szydlo, R. Poirier, J. Appl. Phys. 42 (1971) 4880. [24] D.J. DiMaria, J. Appl. Phys. 45 (1974) 5454. [25] S. Morita, M. Abe, K. Yokoyama, Y. Sugawara, J. Cryst. Growth 210 (2000) 408. [26] K. Fukui, H. Onishi, Y. Iwasawa, Appl. Surf. Sci. 140 (2000) 259. [27] T.R. Albrecht, P. Gr€ utter, D. Horne, D. Rugar, J. Appl. Phys. 69 (1991) 668. [28] J.D. Jackson, Classical Electrodynamics, Wiley, New York, 1962. [29] R. Ludeke, E. Cartier, Appl. Phys. Lett. 78 (2001) 3998. Because of strong, tip induced band bending ‘shallow’ traps may only be occupied in the immediate area of the tip apex, thereby effectively reducing the distance of interaction, and hence the width of the virtual hole in the image. [30] S. Kitamura, M. Iwatsuki, Appl. Phys. Lett. 72 (1998) 3154.
Section 8. Local structure of high k dielectrics and defect characterization
Electrical characterization of gate oxides by scanning probe microscopies R. Ludeke
*
IBM T.J. Watson Research Center, P.O. Box 218, Yorktown Heights, NY 10598, USA
Abstract Ballistic electron emission microscopy (BEEM) and non-contact atomic force microscopy (NC-AFM) are used to characterize SiO2 and Al2 O3 layers grown on Si(1 0 0). The effective conduction band mass and its energy dispersion in SiO2 and an offset between Al2 O3 and Si conduction bands of 2.78 eV were obtained with BEEM. NC-AFM was used to image electrons, and in some instances holes, trapped in the oxide layers near the surface and in the bulk of the oxide. Modeling of the tip–surface interaction supports the interpretation of image features arising from a single electron occupying a trap. The polarity of the trapped charge was deduced from Kelvin (potential difference) images that were simultaneously recorded with the topographic images. Ó 2002 Elsevier Science B.V. All rights reserved.
1. Introduction Scanning probe microscopies, analytical methods based on the scanning tunneling microscope (STM) and the atomic force microscope (AFM), are generally thought of as surface specific techniques. This is indeed the case for the vast majority of applications, and is due to the dominance of surface properties in controlling the interactions between the tip of the instrument and the surface. In the case of the STM the interactions affect the tunneling current, whereas for the AFM it is the mostly repulsive tip–surface interaction that determines the instrument’s response. However, in select cases the tip–surface interactions can be used as control to detect and measure phenomena as-
*
Tel.: +1-914 945 2591; fax: +1-914 945 2536. E-mail address: [email protected] (R. Ludeke).
sociated with specific properties in the bulk of the sample. Specifically, two such techniques are ballistic electron emission microscopy (BEEM) and non-contact AFM (NC-AFM), both of which will be discussed here in terms of novel applications that address gate oxide issues previously deemed unsolvable by other known analytical techniques. BEEM, a STM based transport technique, is sensitive to the potentials in the gate oxides and can be used to determine barrier heights (band discontinuities) and transport dependent parameters, such as the effective electron mass in the conduction band of the oxide. BEEM, specifically the current component transmitted through the sample, is also very sensitive to local interface and bulk charges, but is generally unable to resolve these as isolated, individual charges. The NC-AFM and its variations are sensitive to these charges as well, but have the additional sensitivity to resolve individual electrons, to determine their polarity and, in
0022-3093/02/$ - see front matter Ó 2002 Elsevier Science B.V. All rights reserved. PII: S 0 0 2 2 - 3 0 9 3 ( 0 2 ) 0 0 9 7 8 - X
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the case of interface charge, assess their binding energy relative to the band edges. In this paper we will first discuss some novel BEEM applications, and subsequently the imaging of oxide charge using NC-AFM and the determination of the charge polarity employing a Kelvin probe. The latter entails a modification in the conventional operating mode of the NC-AFM. Historically novel methods are first applied to well-understood material systems, an approach taken here as well. Therefore the analytical concepts will be demonstrated first for SiO2 , but applications of both techniques will also be shown for high-K materials, in the present case, Al2 O3 . The capabilities of BEEM will be illustrated by a unique determination of the conduction band mass of SiO2 , as well as by the determination of band offsets in the W/Al2 O3 /Si structure. Charge imaging and charge density determinations, including trapping–detrapping phenomena, will be illustrated for SiO2 and Al2 O3 gate oxides using NC-AFM and Kelvin methods.
2. Ballistic electron emission microscopy applications to gate oxides 2.1. Ballistic electron emission microscopy basics The first application of BEEM was the determination of the Schottky barrier height for Au–Si [1]. Subsequent applications to Schottky barriers and semiconductor heterostructures can be found in several reviews [2–4]. Applications to SiO2 metal– oxide-semiconductor (MOS) structures have been reported [5,6] and recently reviewed by the author [7]. The experimental methods have been described elsewhere [7] and only a brief description will be given here. The MOS structures were prepared in ultrahigh vacuum by evaporating a thin tungsten layer through a shadow mask and onto the devicequality oxides, which were grown ex situ on Si(1 0 0) substrates. In BEEM electrons are injected from the STM tip into the metal layer covering the oxide. The tip of the STM is biased relative to the metal film, rather than the substrate, as in a conventional STM. This is achieved for the present situation by manipulating and placing a metal wire at ground
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potential in contact with the W dot. The tip bias VT imparts the electrons injected by the tip into the W layer with a kinetic energy (KE) of eVT relative to the Fermi level EF of the metal. For thin metal layers (1.8–4 nm used here) the electrons traverse the metal ballistically and may enter the conduction band of the oxide for eVT > UB , the barrier height between EF and the conduction band edge of the oxide. Electrons that reach the Si substrate are detected as an emerging ‘collector’ current Ic . An energy band diagram corresponding to BEEM applied to a MOS structure is shown in Fig. 1(a). A bias Vb applied across the oxide can be adjusted to achieve a desired potential profile. The trapezoidal barrier, shown by the dashed line, represents the static barrier potential for a positive applied bias. The profile encountered by an electron is modified by screening effects (image force effects) from electrons in either metal or Si substrate, a situation that cannot be ignored in actual transport experiments [8]. The result of screening on the potential profile is shown by the solid line. Progressively decreasing Vb permits the attainment of the flat band position (dotted curve) and subsequently a raised potential peak near the Si interface for negative biases (dashdotted profile). The collector current becomes finite only when the tip bias exceeds the maximum barrier energy. In the spectroscopic mode of BEEM employed here the scanning of the STM tip is stopped temporarily and Ic is measured while the tip bias (i.e. the electron KE) is ramped from below UB /e to several volts above it. BEEM is thus a threshold technique, the threshold tip bias Vth corresponding to the maximum in the profile of the barrier potential between the metal and the Si substrate. Examples of BEEM spectra (Ic vs. VT ) are shown in Fig. 1(b) for SiO2 (dotted) and Al2 O3 -based MOS structures. The net transmitted current is larger for SiO2 because of lower electron scattering rates. A dominant scattering event in SiO2 arises from electron-acoustic phonon interactions, which causes the observed decrease in Ic for VT > 6 V [9]. 2.2. Quantum interference oscillation and the dispersion of the SiO2 conduction band mass For SiO2 -based MOS structures Ic may exhibit an oscillatory modulation arising from
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Fig. 1. (a) Energy band diagram of a BEEM experiment on a MOS structure for various biasing situations, (b) representative BEEM spectra of MOS structures composed of a W gate with a 8 nm Al2 O3 layer (solid curve) and a Pd gate with a 10 nm SiO2 layer (dotted curve) on Si(1 0 0). The gate is grounded and VT and Vb are referenced to it.
interference effects of the electron wave function in the oxide conduction band [10,11], analogous to the oscillations observed in Fowler–Nordheim transport [12,13]. In the simplest approximation for a rectangular barrier [14], peaks in the transmission function occur at energies E ¼ UB þ 2 ðnp h=dox Þ = 2mox , where dox is the oxide thickness, mox the effective conduction band mass, h is Planck’s constant divided by 2p and n ¼ 1; 2; 3 . . . An example is shown in Fig. 2 for a 1.8 nm W/3 nm SiO2 /p-Si(1 0 0) structure. An oscillatory structure in the spectrum is clearly observable [15].
The STM tip bias at threshold was 3.77 V. Flat band condition was achieved at Vb ¼ 0:3 V (substrate positive). An effective transmission function can be extracted from the raw data by subtracting a simulated incoherent component of Ic [15]. The resulting experimental transmission function is shown as a dotted curve in the upper part of Fig. 2(a), from which the interference maxima can be readily obtained. These cannot be indexed by simple theories that neglect image force effects and assume a constant effective mass. Instead the 1D Schr€ odinger equation was solved numerically and
Fig. 2. (a) BEEM spectrum, Ic vs. VT , for a 1.8 nm W/3.0 nm SiO2 /p-Si(1 0 0) MOS structure (dotted curve) with an estimated unmodulated collector current component shown by a dashed line. Their ratio yields an ‘experimental’ transmission coefficient, shown by the dotted curve in the upper left. The theoretical transmission calculated with a dispersive mass is shown as a solid curve. Vertical arrows mark interference maxima in the transmission coefficient calculated with a fixed mass mox ¼ 0:42mo , where mo represents the free electron mass. (b) Conduction band mass dispersion mox ðEÞ for SiO determined from quantum interference oscillations in BEEM spectra (top two curves), compared to a dispersion derived from MC simulations of experimentally determined electron mean free paths (lowest dashed curve).
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included image force effects and boundary conditions suitable for the materials used in the experiment. The details are discussed elsewhere [10,15]. The maxima in the transmission function calculated for a fixed electron mass, depicted at the top of the figure by arrows, show poor agreement with experiment. After matching the first low energy maximum, the effective mass value had to be progressively readjusted upwards to obtain a match for all remaining maxima. The resulting transmission function is shown by the solid curve in the top part of Fig. 2(a). The values of mox ðEÞ at each maximum are then used to obtain the dispersion curve represented by the connected filled circles in Fig. 2(b). The abscissa shows the KE of the conduction band electrons, obtained by subtracting the threshold energy. The curve of connected triangles represents the dispersion for a 2.3 nm SiO2 , which was thermally grown on p-Si(1 0 0) and was covered with 4 nm Pd metal layer. Its upward displacement relative to the 3 nm oxide cannot be accounted for by uncertainties in the parameters, but may be attributed to quantum size effects, such as an onset of band structure changes. The overall increase in mox ðEÞ for the thinner oxide is consistent with a narrowing of the bands due to the decreasing dimensionality [16]. Also shown in Fig. 2(b) is the mass dispersion obtained from the Monte Carlo (MC) simulations of the attenuation lengths in SiO2 , obtained by internal photoemission experiments [15]. Although the discrepancy with the BEEM-determined dispersion is appreciable, it is comforting to note that the changes in mass over comparable energy intervals are quite close. Agreement cannot be expected since the ‘reference’ mass for the MC calculations at 1.5 eV was assumed to be 0.5mo . The range of the dispersions in all three cases, which are comparable in magnitude, implies considerable non-parabolic behavior in the dispersion of the conduction bands of SiO2 . 2.3. Band offset and interface charge determination for W–Al2 O3 MOS structures The 8 nm thick Al2 O3 layers used in these experiments were grown by atomic layer chemical vapor deposition (ALCVD) on HF etched n- and
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p-Si(1 0 0) substrates (q 1–17 X cm). The amorphous films were stoichiometric with atomically flat and abrupt interfaces. Details of the deposition and the structural characterization of the layers can be found elsewhere [17]. The samples were annealed in forming gas to partly passivate the interface states. A typical BEEM spectrum is shown in Fig. 1(b). Spectra were taken for a broad range of biases Vb applied across the oxide. The thresholds Vth were obtained by fitting a model power law to the spectra [4]. For Vb J 0 the thresholds decreased, whereas for Vb K 0 they increased, in agreement with the expected raising of the barrier depicted by the topmost barrier profile in Fig. 1(a). The decrease in Vth , however, can only be attributed to image force effects, which lead to 1=2 a barrier lowering of dUB ¼ ðqVox =4peeif dox Þ , where e is the permittivity in vacuum and eif is a dynamic (image force) dielectric constant. This effect was already observed in SiO2 -based MOS structures [8]. The oxide potential Vox was obtained by solving the Poisson equation for the appropriate Si and oxide parameters [9,18]. Fig. 3(a) shows the dependencies of Vth on the oxide potential, plotted as a function of Vox1=2 , for both n- and ptype substrates. The linear behavior indicates that the threshold response is dominated by image force effects. Results for Vox > 0 are shown by filled symbols; the solid lines are least square linear fits to the data sets. Their zero field intercepts are within 10 meV, giving an average value of UB ¼ 3:90 0:03 eV. The uncertainty is based on the accuracy of determining the threshold voltages. The image dielectric constant is obtained from the slope of the linear fit and exhibits a value of eif ¼ 1:77 for the p-type sample (N). A value of eif ¼ 1:86 0:1 was obtained by averaging the fits for all data sets. It should be emphasized that eif is drastically lower than the static dielectric constant eo 8–9, a difference whose significance will be discussed below. For negative values of Vox the ordinate values are represented by (Vth jVox j) instead of Vth . This procedure cancels the contribution of Vox to the barrier height, which allows the observation of field induced changes, if any, at the Al2 O3 –Si interface (topmost barrier profile in Fig. 1(a)). The resulting curve for the n-type sample is shown in
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Fig. 3. (a) Threshold energies for 8 nm Al2 O3 layers on n- and p-Si(1 0 0) substrates plotted against the root of the oxide potential. The reduced threshold Vth jVox j is plotted for Vox < 0 (open symbols). The solid lines are least square fits, (b) flat band barrier profile for W/Al2 O3 /p-Si(1 0 0). The circles represent trap levels of density rif near the oxide–Si interface, which for the p-type substrate remained unfilled for Vox > 0.
Fig. 3(a) by connected open circles. A least square fit is again a straight line up to 1 V1=2 with a slope and intercept nearly identical to those for positive bias. This confirms, as well, the presence of image force effect at the oxide–Si interface. Beyond 1 V1=2 the thresholds, that is (Vth jVox j), decrease progressively with increasing Vox for the n-doped sample. This reduction is attributed to a decrease in negative charge near the interface. The discharging, which was reversible upon reducing Vb , probably occurs through field enhanced leakage across the oxide and into the gate. For other biases this charge was constant, which suggests that it was not generated by the experiment but rather pre-existed it. The location of the charge, or more precisely that of the centroid of its distribution, x, can be obtained from the slope of the Vth vs. Vox plot, which should be proportional to xVox =dox , with x measured from the W–Al2 O3 interface [6,19]. The centroid, which BEEM measures, is located at the maximum of the potential profile. For Vox < 0, a linear plot of Vth vs. Vox for the ntype sample (not shown) indicates a linear region of slope 0.89. Thus x ¼ 0:89 (a value that approaches unity after correcting for image forces), which indicates that the charge resides at or very near the Al2 O3 –Si interface [20]. For the p-type sample the threshold response for Vox < 0 is quite different. The results, specifically (Vth jVox j), are plotted as open triangles in
Fig. 3(a). For the bias range shown, (Vth jVox j) initially increases rapidly, reaches a maximum and then decreases more gradually. For this bias range the Fermi level at the Si interface moves from a position near the valence band (flat band) to the conduction band edge (inversion). It is therefore surmised that the increase in thresholds is caused by the charging of previously neutral electron traps near the interface, whose energy distribution is largely confined to an interval matching the band gap of Si. The saturation in the trapping indicates that few, if any, trap levels overlap the Si conduction band. Once the traps are filled, and in analogy to the n-type case, the subsequent decrease of the threshold energy at a linear rate with slope close to that of the other cases discussed implies that these trap states are also located near the oxide–Si interface. The results thus suggest that the trap states are of similar origin for both substrate types and that their occupancy is solely determined by the position of the Fermi level at the Si interface. The saturation of charge trapping for the p-type sample allows an estimation of the charge density rif . A value rif ¼ 2:5
1012 electrons/cm2 was calculated using a simple sheet charge model that includes image force corrections at both interfaces [21]. A determination is now possible of the Si– Al2 O3 band offsets because of the negligible trapping in the p-type Si for Vox P 0. For the known
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substrate doping and measured barrier energies, including a flat band voltage Vfb ¼ 0:25 V, the energy band relationship shown in Fig. 3(b) was obtained [22]. A Si–Al2 O3 conduction band offset dEcb ¼ 2:78 0:06 eV was deduced, which is within 0.2 eV of previously reported values obtained for thicker layers using internal photoemission [23,24]. It should be emphasize at this point that the indicated barrier heights only apply in the zero field limit. For other biases substantial lowering can be expected due to the strong image force effects, effects that cannot be ignored in predictions of direct and Fowler–Nordheim tunneling currents. It should be further noted that due to the low value of eif 1:86, image force effects in Al2 O3 are larger than in SiO2 , for which eif ¼ 2:69 [8]. This value is much larger than the optical dielectric constant of SiO2 (e1 2) because electron–optical phonon scattering still dominates electron transmission in SiO2 at energies near the thresholds [8]. The lower eif for Al2 O3 is consistent with estimates of a lower electron–LO phonon coupling compared to SiO2 [22].
3. Imaging of oxide charge In this section we discuss the detection of captured charges of as little as a single electron or hole trapped in SiO2 and Al2 O3 gate oxides. Evidence of charge appears in the images of the oxide surfaces obtained with an AFM operating in the noncontact (NC) mode in ultrahigh vacuum. Although the observation of surface charge by NC-AFM has recently been reported on single crystal surfaces of semiconductors [25] and TiO2 [26], the direct imaging of individual charges buried below the surface has not been reported. In a NC-AFM topograph the presence of charge takes on the form of a ‘hole’ in the layer. This is illustrated in Fig. 4(a), which is an image for a 2.8 nm thermal oxide grown on an n-Si(1 0 0) wafer at IBM’s Advanced Silicon Technology Laboratory. The oxide is of gate oxide quality, yet the dark depressions are comparable to or may even exceed the oxide thickness. Fig. 4(d) shows a depth profile in the area of the dashed square in Fig. 4(a), specifically along the dashed line in the enlarged
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image of Fig. 4(c). Clearly the depths of the holes are incompatible with the device grade quality of the oxide. The holes, therefore, do not represent physical depressions, but are virtual holes generated by surface–AFM tip interactions other than the strongly repulsive hard sphere interaction between the two materials that leads to the classical image of the surface topography. As will be shown, the interaction that results in the virtual holes arises from the attractive forces, specifically the force gradients, between a charge embedded in the oxide and its image charge of opposite polarity in the AFM tip. Since the interaction is always attractive, the polarity of the charge cannot be obtained from the topographic image. Instead we have developed a methodology based on the simultaneously recorded potential difference or Kelvin image that allows an unequivocal determination of the polarity of the charge. 3.1. Concepts of charge imaging and polarity determination with the NC-AFM In the NC mode the cantilever of the AFM vibrates near its natural resonance frequency (xo =2p) given by x2o ¼ k/m, where k is the cantilever stiffness and m its mass, k is essentially the intrinsic force gradient of the cantilever, which can be affected by other force gradients arising from the proximity of the tip to the surface. Examples of such modifying force gradients arise mainly from the interaction between tip and surface atoms (the classical ‘contact’ situation), as well as from electrostatic, magnetic, Van der Waals and capillary forces. Only the first two are of significance here. Operation of the NC-AFM is based on the detection of a small frequency change in the cantilever resonance, given by dx ¼ dF 0 xo =2k. dF 0 is the change in the force gradient normal to the surface, effectively a change in the net stiffness of the cantilever, arising from changes in the tip– surface interaction [27]. dx is thus a direct measure of dF 0 . The AFM operates in the constant dx mode, with changes detected by frequency demodulation methods [27]. The feedback directs the piezoelectric z-driver (motion normal to the surface) to move the cantilever in or out to maintain a constant dx; the driving signal is used to generate
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Fig. 4. Topography (a), with gray scale range of 6 nm, and Kelvin image (b) for a 2.8 nm SiO2 layer on n-Si(1 0 0). A magnified region (dashed square) in (a) is shown in (c), with the depth profile along the dashed cut shown in (d).
the topographic image. The cantilevers used here had a stiffness in the range of 5–14 N/m and resonance frequencies in the range of 180–380 kHz. Experimental values of dx=2p were in the range of 100–200 Hz, for which slopes of 20 to 30 Hz/ nm were obtained from measured z vs. dx plots (not shown). This slope, which is a measure of the net cantilever stiffness, increases as the tip approaches the surface (increased repulsive F 0 ). Thus, an excursion of the scanner of 1 nm in the z-direction (surface normal), a value that is equivalent to the depth of a virtual hole in the topography (Fig. 4), corresponds to a change in the local force gradient of dF 0 103 N/m. It will be shown next that modeling of the interaction of an electron embedded in a dielectric and its image charge in the metallic AFM tip leads to force gradients F 0 ¼ oFz =oz of comparable size. The tip is represented by a conductive sphere of radius r at a distance a above the surface. The charge q is
located a distance dq below the surface and laterally a distance l from the projected point of contact of the tip on the surface. The solution is [28] " # " # 2 2 2 2 2 2 q r 3z þ r l qV r l 2z b F0 ¼ : 4pee2eff ðz2 þ l2 r2 Þ3 eeff ðz2 þ l2 Þ5=2 ð1Þ
Here z ¼ r þ a þ dq , eeff ¼ ðeox þ 1Þ=2 is the effective dielectric constant arising from screening of the charge in an oxide of dielectric constant eox (¼3.9 for SiO2 , 8–9 for Al2 O3 ), e is the permittivity and Vb the applied substrate bias. Fig. 5 shows curves calculated with Eq. (1) for Vb ¼ 0 and for some realistic values for r, a and dq . For charges near the surface F 0 1 103 N/m, a value consistent with that necessary to account for an image force induced ‘hole’ of 1 nm depth. F 0 is quite sensitive on the depth of the charge, as well as on the dielectric constant of the oxide. In SiO2 ,
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Fig. 5. Vertical force gradients on conductive AFM tip arising from image charge effects.
a charge 1 nm below the surface is reduced by a factor of 3 from one near the surface, but by factor of 7 when the material has the dielectric constant of amorphous Al2 O3 . The maximum in F 0 ðlÞ (at l ¼ 0) is independent of r, but not so its width at half maximum, as can be observed by comparing the two topmost curves in Fig. 5, which differ only in the assumed value of the tip radii. A full width at half maximum of 6–8 nm is obtained for tip radii in 5–10 nm range. The calculated widths are consistent with observation in most cases [29]. The imaging of a virtual hole can now be understood as follows: as the tip scans over the surface towards a charge, the increasing attractive force will counteract the repulsive tip–surface interaction, thereby decreasing dx. Since a constant dx is maintained by the AFM feedback, the piezoelectric z-driver responds by pushing the cantilever towards the sample, thus creating the appearance of a hole in the image. Further evidence that the virtual holes are associated with trapped charge is obtained from Kelvin images [30]. These are acquired simultaneously with the topographs. The images are generated by adding a small low frequency modulation voltage Vm sinðxm tÞ to the tip–substrate bias V b , which represents the net sum of the applied bias Vb and a local surface potential. This subjects the cantilever to an additional attractive force gradient given by F 0 ¼ 0:5V 2 o2 C=oz2 , where V ¼ V b þ Vm sinðxm tÞ, and C is an effective
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capacitance of the tip–surface system. The demodulated output of the AFM has superimposed on it a signal proportional to V b Vm sinðxm tÞ, which is fed into a lock-in amplifier. Its output in turn is fed into a second imaging channel of the AFM to generate the Kelvin image. The magnitude of the lock-in output is proportional to V b Vm , and its phase depends on the sign of V b , that is, on which side of the F 0 ðV Þ parabola the bias is set. As an aside, the value of Vb for which V b ¼ 0 corresponds to contact potential difference (CPD). Thus contrast in the Kelvin image reflects the polarity of V b and its local variations, which allows a determination of the polarity of the local chargeinduced potential, and hence that of the charge itself. The sign of the phase is arbitrary. The convention was adopted here that an increasingly negative local potential lowered (darkened) the Kelvin image brightness for negative V b . This convention results in a darkened image for increasing positive potentials under positive bias. That is, under positive bias electrons image as protrusions (bright areas) and positive charge as holes (dark areas), with the reverse contrast occurring for negative bias. 3.2. Imaging of charge in SiO2 gate oxides The oxides used were thermally grown ex situ on 200 mm£ Si(1 0 0) wafers. Samples of suitable size for the AFM experiments (2 7 mm2 ) were then cleaved and introduced into the preparation chamber of a JEOL SPM4500A, an ultrahigh vacuum, multi-chamber AFM/STM. The samples were outgassed near 300 °C to remove volatile surface contaminants, including water, and subsequently transferred into the AFM analysis chamber for the measurements. The topographic image covering a 500 500 nm2 area of a 2.8 nm SiO2 layer on n-type Si(1 0 0) is shown in Fig. 4(a). The corresponding Kelvin image is shown in Fig. 4(b). It shows a one-to-one correspondence between the virtual holes in the topograph and similar dark holes in the Kelvin image. The tip bias was Vb ¼ 0:037 V, which was sufficiently negative to ensure that for the phase convention discussed in the previous section the dark features in the Kelvin image correspond to areas of negative
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potential relative to the lighter features and are therefore associated with negative charge. The irregular shape of some of the larger and darker features in the topograph, one of which was profiled as shown in Fig. 4(d), indicates that it is composed of a cluster of several charges. The intensity indicates that these charges are in the near surface region of the oxide. Clustering of charges has also been observed for SiO2 films grown on Si(1 1 1) substrates [29]. The broad range of depths of the virtual holes indicates a random distribution of trapped charge throughout the thickness of the oxide. The smallest depressions in the profile of Fig. 4(d) are 2–3 nm from the surface according to best estimates obtained with Eq. (1), which would place the charges near the SiO2 –Si interface. The overall density of trapped charges for this forming gas annealed oxide layer was estimated to be 1:5 1011 cm2 , a factor 5 higher than for simultaneously grown thermal oxide layers on p-Si(1 0 0) substrates. These values are consistent with estimates obtained by electrical characterization. Thus far, mostly negative charges have been observed on thermally grown SiO2 /Si(1 0 0) using
the NC-AFM/Kelvin imaging methods. However, a notable exception was the observation of positive charge (holes) trapped at interface Pb centers of vacuum annealed, thin (1.8 nm) SiO2 layers grown on p-type Si(1 1 1) [29]. 3.3. Imaging of charge in Al2 O3 gate oxides The Al2 O3 samples were taken from the same wafer of ALCVD-grown and forming gas annealed material as those used in the BEEM experiments discussed in Section 2.3. Sample size and pre-analysis treatment were similar to those used for the SiO2 samples. Fig. 6(a) depicts a 200 200 nm2 topographic image of the oxide surface taken at a bias Vb ¼ 0:7 V. This bias value is more positive than the CPD value of about 1 V, so that negative charge should image as bright areas in the Kelvin image. This is indeed the case, as can be seen in Fig. 6(b). The darker areas in this image are regions that exhibit a surface potential that is more positive than that of the negative charges. As for SiO2 , a one-to-one correspondence is observed between virtual holes in the topograph and fea-
Fig. 6. Topography (a), with gray scale range of 3 nm, and Kelvin image (b) for an 8 nm Al2 O3 layer on n-Si(1 0 0). The depth profile along the dashed cut in (a) is shown in (c).
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tures in the Kelvin image (this time hillocks), which strongly supports the notion that their origin is electrostatic. The darker (deeper) virtual holes are again attributed to electrons trapped near the surface. Considerable clustering occurs for these traps, which aggregate into a wavy pattern that extends across the field of view. The cause or implication of this behavior is not known. A depth profile along the dashed line in Fig. 6(a) is shown in Fig. 6(c). Even in parts of the profile that goes through relatively featureless areas of the image, considerable weak structure is observed, which is evidence of charge buried deeper into the sample. Based on Eq. (1), the depth of the weakest image features corresponds to electrons located 2:5 0:5 nm below the surface. A density of trapped electrons of 9 1012 cm2 was estimated from the images for negatively biased samples. If one conjectures that the traps are randomly distributed throughout the oxide, that would place potentially 3–4 1012 cm2 charges within 1 nm of the interface. Perhaps coincidentally, this number is close to the 2:5 1012 cm2 value for the trapped interface charge obtained for the same material with BEEM (Section 2.3). The role of substrate bias on the charge and its effect on the topographic features is illustrated in the images of Fig. 7 for the same 60 60 nm2 area of an 8 nm Al2 O3 /n-Si(1 0 0) sample. Fig. 7(a) was taken with Vb ¼ 1:5 V, which is near the CPD; that is, only a small potential difference exists between tip and surface. When the bias was changed by 2 V to Vb ¼ 3:5 V, the image, shown in Fig. 7(b), changed noticeably. For negative bias electrons are pushed towards the interface, while leaving a positive charge on the tip. Many of the features once seen in Fig. 7(a) are no longer observable or are very weak in Fig. 7(b). This is attributed to neutralization of the trap levels: electrons trapped near the surface with trap levels that rise above the Fermi level of the tip upon increasing the bias can now be transferred to the tip, neutralizing the level. That this effect is not due to a weakening of the cantilever stiffness can be ruled out by comparing the intensities of the remaining virtual holes. Profiles taken at identical locations are shown in Fig. 7(d). Clearly the depths of the virtual holes present for both biases remain comparable, which indicates that their trap levels
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remain below the tip’s Fermi level. The situation for a change in bias of roughly comparable magnitude as before, but in the opposite direction (Vb ¼ þ1:0 V) is shown in Fig. 7(c). For this case most of the charge has leaked out to the substrate, leaving a generally featureless image. The depth of one of the remaining holes, compared to depths at the other biases, is much smaller, as can be seen in the dotted curve of Fig. 7(d). The weakness can be attributed to partial occupancy of the trap level, with charge that slowly leaks out being replenished by new charge from the tip. It should be noted here that the images are reproducible when the bias is returned to the appropriate value. Unlike SiO2 , positive bulk oxide charge has been observed in Al2 O3 . An example of this is shown in Fig. 8. The images were taken with Vb ¼ 0:5 V within the area marked by the dashed rectangle in Fig. 7(a). The bias is slightly more positive than that of Fig. 6, so that negative charge should image as bright features (hillocks) in the Kelvin image and positive charge as dark spots or holes. This is indeed observed in the accompanying Kelvin image in Fig. 8(b). Both hillocks and holes in the Kelvin image correspond to virtual holes in the topograph, as befits their origin of image charges whose attractive forces are polarity insensitive. The circled virtual holes in the topograph represent positive charge, as deduced from their dark features in the Kelvin image. Profiles along the same location in both images are shown in Fig. 8(c). These intersect charges of both polarities. The topographic profile (solid line) only exhibits the depressions, whereas that of the Kelvin image (dashed line) shows a positive relative potential for the dark spots and a negative potential for the bright features in the Kelvin image.
4. Summary and conclusions Illustrative samples highlighting two quite different scanning probe methods were presented. Each has strengths that are based on their operational characteristics and the nature of their physical interaction between sample and probe. BEEM is essentially a transport technique capable of probing material or sample properties that
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Fig. 7. Topographic images of an 8 nm Al2 O3 layer on n-Si(1 0 0) of the same 60 60 nm2 area for biases of (a) Vb ¼ 1:5 V; (b) Vb ¼ 3:5 V and (c) Vb ¼ þ1 V. The depth profiles along identical cuts are shown in (d). Gray scale ranges are for (a) 2 nm, (b) 1 nm, (c) 0.8 nm.
Fig. 8. Topograph (a), and Kelvin image (b), of square area outlined in Fig. 7(a), but for Vb ¼ 0:5 V. Profiles along the marked cuts are shown in (c). The circled features in (a) correspond to positive charges imaged as dark features in the Kelvin image.
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affect electron transmission. These need not to be ‘intrinsic’ properties; on the contrary, the role of BEEM in elucidating defect and breakdown characteristics in oxides has been amply demonstrated elsewhere [7]. The NC-AFM is essentially a potential profiler, sensitive to all surface and nearsurface charges. The complimentary relationship of the two methods has only been intimated, primarily because of the very novelty of the charge imaging technique. Its role and possible future applications appear to be extensive, particularly in relation to dielectric stressing and defect generation, and its extension beyond dielectrics to other material systems, including semiconductors and organic systems, is quite obvious.
Acknowledgements I wish to thank the many co-authors and coworkers who through the years were essential in helping me define and implement the directions of this research. In alphabetical order they are Doug Buchanan, Ed Cartier, Maria Teresa Cuberes, Chris D’Emic, Evgeny Gusev, Andreas Schenk and Huajun Wen.
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