Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography - however, this potential can only be achieved through the accurate, quantitative reconstruction of the power spectral density of real-world surfaces.

/pdf/quantitative-characterization-of-surface-topography-using-1di6n32wn5.pdf

Quantitative characterization of surface topography using spectral analysis

Roughness determines many functional properties of surfaces, such as adhesion, friction, and (thermal and electrical) contact conductance. Recent analytical models and simulations enable quantitative prediction of these properties from knowledge of the power spectral density (PSD) of the surface topography. The utility of the PSD is that it contains statistical information that is unbiased by the particular scan size and pixel resolution chosen by the researcher. In this article, we first review the mathematical definition of the PSD, including the one- and two-dimensional cases, and common variations of each. We then discuss strategies for reconstructing an accurate PSD of a surface using topography measurements at different size scales. Finally, we discuss detecting and mitigating artifacts at the smallest scales, and computing upper/lower bounds on functional properties obtained from models. We accompany our discussion with virtual measurements on computer-generated surfaces. This discussion summarizes how to analyze topography measurements to reconstruct a reliable PSD. Analytical models demonstrate the potential for tuning functional properties by rationally tailoring surface topography—however, this potential can only be achieved through the accurate, quantitative reconstruction of the PSDs of real-world surfaces.

/pdf/quantitative-characterization-of-surface-topography-using-45kh8tzr33.pdf

An antenna covered with photoresist patterns having high-aspect-ratio openings caused charge damage to the gate oxide in various processing plasmas. This damage increased with the pattern's aspect ratio, and occurred even when the test wafer was cut into chips about 5 mm square and mounted on a wafer with insulation. These results prove the electron shading model: the photoresist patterns shade the antenna from electrons of oblique incidence, resulting in local charging occurring without a wafer-scale voltage difference, which is essential for conventional charging. The damaging current from this mechanism increased by a factor of more than ten with a decrease in the gate oxide thickness only from 8 nm to 6 nm, implying that the degree of shading depends on the gate charging voltage. An improved model is proposed to accommodate this strong dependence.

https://iopscience.iop.org/article/10.1143/JJAP.33.6013/pdf

Charge Damage Caused by Electron Shading Effect

The effect of antenna shape on charge damage has been examined using electron cyclotron resonance (ECR) plasma metal etching and test devices with an 8-nm-thick gate oxide. A dense-line antenna causes capacitor breakdown and the positive shift of the transistor's threshold voltage (Vt), while a sparse-line antenna does not. This positive Vt shift corresponds to a positive charge-up of the dense line, and is not dependent on overetching. Such damage is hardly observed when the antenna's top surface is exposed to the plasma, indicating that the plasma is uniform in terms of conventional charge damage. These new phenomena can be explained by a new mechanism consisting of electron shading with photoresist patterns. This shading leads to less neutralization of the ion charge impinging onto the transitory metal which remains between the antenna lines because of the microloading effect, and thus the excess positive charge causes the damage.

https://iopscience.iop.org/article/10.1143/JJAP.32.6109/pdf

New Phenomena of Charge Damage in Plasma Etching: Heavy Damage Only through Dense-Line Antenna

Various statistical quantities (such as average, peak-to-valley, and root-mean-square roughness) have been applied to characterize surface topography. However, they provide only vertical information. Because spectral analysis provides both lateral and longitudinal information, it is a more informative measurement than all these commonly used statistical quantities. Unfortunately, a standard method to calculate power spectral density (PSD) is not available. For example, the dimensions of PSD are often denoted as either (length)3 or (length)4. This may lead to confusion when utilizing spectral analysis to study surface morphology. In this paper, we will first compare the definitions of PSD commonly used by various authors. Using silicon surface roughness measurements as examples, we will demonstrate the advantages of spectral methods on atomic force microscopic (AFM) image analysis. In this context, we study the effects of typical AFM imaging distortions such as image bow, drift, tip-shape effects, and acou...

Analyzing atomic force microscopy images using spectral methods

Measurements of Si surface roughness by atomic force microscopy and ellipsometry have been performed over a wide range of conditions. Advanced methods of data analysis have been applied to both techniques leading to a quantitative comparison of root‐mean‐square (rms) roughness to the ellipsometric paramter Δ. Differences in Δ are observed for surfaces with the same rms roughness, but different roughness spectral densities, as expected from theory.

Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry

A model is developed to explain how plasma etching/ashing can damage gate covered oxides via plasma nonuniformity. In addition, the role of antenna structure parameters on this damage is examined. Plasma nonuniformity leads to a local imbalance between electron and ion currents from the plasma. This imbalance of local particle currents from the plasma leads to gate charging and subsequent thin oxide degradation. This article discusses a sheath model for this charging where measurements of plasma potential nonuniformity are used to calculate the peak surface charging potential and subsequent thin oxide tunneling current. It is this oxide tunneling current that generates the surface states at the Si/SiO2 interface and the trapped charge in the oxide that degrades oxide yield and reliability. This model is applied to analyze oxide damage in an O2 magnetron plasma, via the simulation program with integrated circuits emphasis, Langmuir probe measurements, and antenna capacitor breakdown measurements. The oxide current derived from this model shows good agreement with experimental damage data of antenna capacitors. Finally, oxide damage is shown to depend on antenna structure parameters and is explained by this model.

Charging damage to gate oxides in an O2 magnetron plasma

Charge damage is a consequence of plasma nonuniformity which leads to a local imbalance of ion and electron currents to the wafer surface. Damage during etching is found to occur near endpoint and to scale with gate electrode edge length. A model is proposed in which surface currents prevent charging during most of the time the gate is etching. Near endpoint, these currents are terminated while a temporary conductive halo still remains around the gate. During a brief period before it disappears, the halo can collect enough current to charge the thin oxide to the point of conduction and subsequent damage. This model is supported by plasma measurements, etching damage results, and simulations via the Simulation Program with Integrated Circuits Emphasis.

Model for oxide damage from gate charging during magnetron etching

Surface charging effects on etching profiles during silicon etching in a nonuniform plasma were investigated by scanning electron micrographs and plasma potential measurements. The distortion in ion trajectories caused by the surface charging was calculated by an ion lens simulator. A tilt in the etching profile was found in holes and trenches near a large etched area when an insulating mask such as photoresist or silicon dioxide was used. Ion trajectory calculations showed that this profile tilt was caused by the local electric field resulting from the potential difference between the charged mask surface and the electrically grounded silicon substrate. This profile result agrees well with gate oxide damage results which were also successfully explained by surface charging.

Ion trajectory distortion and profile tilt by surface charging in plasma etching

A new, physically-based model has been developed to successfully explain the roles of device structure and plasma nonuniformity on charge damage. The model includes an equivalent circuit for the charging of MOS antenna structures exposed to a nonuniform plasma, and the use of SPICE, a circuit simulator, to correlate plasma measurement to breakdown measurements. The model is applied to analyze thin oxide damage in an O 2 magnetron plasma asher. The simulation results show good agreement with experimental damage data of “antenna” capacitors using ramp voltage breakdown measurements.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S1946427400318942

Sychyi Fang

Papers

Comparison of Si surface roughness measured by atomic force microscopy and ellipsometry

Charging damage to gate oxides in an O2 magnetron plasma

Model for oxide damage from gate charging during magnetron etching

Ion trajectory distortion and profile tilt by surface charging in plasma etching

The Role of “Antenna” Structure on Thin Oxide Damage from Plasma Induced Wafer Charging