MEMS Scaling Laws

The Ganz-Griesser whiteness index is a linear formula widely used, particularly in the textile industry. It is derived from CIE tristimulus values and is defined as \(W_{GG} = Y - Px - Qy + C\), where P, Q, and C are constants specific to the illuminant and observer. For the D65/10° condition, the formula is \(W_{GG} = Y - 1868.322x - 3695.690y + 1809.441\).

Lithium-ion batteries function via an intercalation mechanism, a reversible insertion of ions into a layered host material. During discharge, lithium ions (\(Li^+\)) de-intercalate from a negative electrode (anode), typically graphite, and move through a non-aqueous electrolyte to intercalate into a positive electrode (cathode), typically a metal oxide. Electrons travel through the external circuit, creating current.

Depth of Discharge (DoD) indicates the percentage of a battery's capacity that has been discharged. It is the inverse of State of Charge (SoC), where 100% DoD means the battery is empty. A battery's cycle life is highly dependent on its average DoD; lower DoD cycles (e.g., discharging to only 80% capacity) significantly increase the number of cycles a battery can endure.

Neodymium magnets are the strongest type of permanent magnet commercially available. They are a ternary alloy of neodymium, iron, and boron, with the stoichiometric formula Nd2Fe14B. Their immense magnetic strength results from the material's high magnetic anisotropy and saturation magnetization, derived from its tetragonal crystal structure. However, they are brittle, susceptible to corrosion, and have a low curie temperature.

A Single-Electron Transistor (SET) is a switching device that uses controlled electron tunneling to manipulate the flow of single electrons. It consists of a quantum dot (the 'island') coupled to source and drain leads via tunnel junctions, and capacitively coupled to a gate electrode. Its operation relies on the Coulomb blockade effect, enabling extreme sensitivity and low power consumption.

In 1986, Georg Bednorz and K. Alex Müller discovered superconductivity in a ceramic material, a lanthanum-based cuprate perovskite, at a critical temperature of ~35 K. This was significantly higher than the ~23 K record for conventional superconductors at the time and shattered the belief that superconductivity was restricted to much lower temperatures, opening the field of high-temperature superconductivity.

Molecular electronics explores using individual molecules or nanoscale molecular collections as fundamental electronic components. This approach aims to build circuits at the ultimate limit of miniaturization, far beyond traditional silicon-based technology. Key components include molecular wires, switches, and rectifiers, leveraging quantum mechanical properties like electron tunneling through molecular orbitals for their function.

Physics of Failure (PoF) is a reliability engineering approach that uses knowledge of materials science and physics to understand and model the root-cause mechanisms of failure. Instead of relying purely on statistical data from past failures, it focuses on predicting failure by analyzing the physical processes (e.g., fatigue, corrosion, creep) that lead to degradation and breakdown.

The Quantum Size Effect describes the phenomenon where the electronic and optical properties of a material change as its size approaches the nanoscale. When the dimensions of a material become comparable to the electron's de Broglie wavelength, quantum confinement occurs. This quantizes the electron energy levels, leading to a size-dependent band gap, \(E_g(R) \approx E_{g,\b\u\lk} + \frac{\hbar^2\pi^2}{2R^2}(\frac{1}{m_e^*} + \frac{1}{m_h^*})\).

The equilibrium vapor pressure of water over a liquid surface in moist air (\(p^*_{H_2O,a}\)) is slightly greater than the equilibrium vapor pressure over a pure water surface (\(p^*_{H_2O}\)). This difference is quantified by the water vapor enhancement factor, \(f_w\), which depends on temperature and the pressure of the moist air. The relationship is \(p^*_{H_2O,a} = f_w(T, p_{ms}) \cdot p^*_{H_2O}\).

Rare-earth magnets are strong permanent magnets made from alloys of rare-earth elements. Developed in the 1970s and 1980s, the most common types are neodymium magnets (NdFeB) and samarium–cobalt magnets (SmCo). They are the strongest type of permanent magnets made, producing significantly stronger magnetic fields than ferrite or alnico magnets, enabling miniaturization and improved performance in many technologies. Note: the term 'rare-earth element' is a historical misnomer. These elements are not exceptionally rare in the Earth's crust. Cerium, the most abundant, is the 25th most abundant element, similar to copper. Even the least abundant stable rare earth, lutetium, is nearly 200 times more common than gold. The 'rare' label arose because they were difficult to separate.

A lithium-ion (Li-ion) battery is a rechargeable battery where lithium ions move from the negative electrode (anode) through an electrolyte to the positive electrode (cathode) during discharge, and back when charging. It utilizes an intercalated lithium compound as the cathode material and typically graphite as the anode. The high reactivity of lithium allows for high energy density.

The CIE Whiteness Index is a standardized formula by the International Commission on Illumination to quantify the perception of whiteness. It is calculated from CIE tristimulus values (X, Y, Z) and the chromaticity coordinates (x, y) of the sample and a reference illuminant. The primary formula is \(W_{CIE} = Y + 800(x_n - x) + 1700(y_n - y)\).

Molecular self-assembly is a 'bottom-up' process where molecules spontaneously organize into ordered structures without external guidance. This phenomenon, driven by non-covalent interactions like hydrogen bonds, hydrophobic effects, and van der Waals forces, is fundamental in biology (e.g., protein folding, lipid bilayer formation). In biomaterials, it is harnessed to create complex, nanostructured materials like hydrogels and nanofibers for biomedical applications.