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• Package: Equations in Materials Science ( resources)
• The set of physical laws and mathematical equations commonly used in Materials Science and Engineering. All units and prefixes are given in accordance with in the SI standard (The International System of Units)....
• Creator: The University of Liverpool
• Keywords:
• Date added: 01 July 2010
• Corrected beam theory method for composite testing
• This modified beam theory equation assumes that the crack is effectively longer than that measured during the Double Cantilever Beam (DCB) test. The additional crack length is calculated from the sample's compliance (C=δ / P). Plotting C1/3 against a yields a linear graph in which the line of best fit crosses the x-axis at some negative value of a. The magnitude of this value is the additional crack length, ΔTeX format; {G_{Ic} = \frac{3 P \delta}{2B(a+\Delta)}}GIc {G_{Ic}} = mode I...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Beam theory method for composite testing
• The Double Cantilever Beam (DCB) test is used to assess the mode I failure strength of a composite sample. This equation gives a rough value for the mode I fracture energy, as it assumes that the beam is perfectly built in at the crack tip.TeX format: {G_{Ic} = \frac{3 P \delta}{2Ba}}GIc {G_{Ic}} = mode I fracture energy (J.m-2) {J.m^{-2}}P {P} = force (N) {N}δ {\delta} = displacement at point of force (m) {m}B {B} = sample width (m) {m}a {a} = distance from P to crack tip (m) {m}...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Resistor-capacitor (RC) delay
• As integrated circuits decrease in size and more transistors are squeezed into the same amount of space, the interconnecting wires remain at roughly the same overall length, whilst the width of dielectric layers between them is reduced. This introduces a capacitance and resistance which must be overcome for a signal to pass.TeX format: {RC delay \approx \rho \varepsilon \frac{L^2}{w^2}}RC delay {RC delay} = time take for a signal to pass through an interconnect wire (s) {s}ρ {\rho} = resisti...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Black's equation
• In integrated circuit manufacture, the Mean Time To Failure (MTTF) equation is used to predict the lifetime of nano-scale connections between components such as transistors. By running short experiments at elevated temperatures the constants in the equation can be calculated, allowing the time to failure (defined as the failure of 50% of interconnect lines) at normal operating temperatures to be predicted.TeX format {MTTF = Awj^{-n}exp^{\frac{Q}{kT}}}MTTF {MTTF} = mean time to failure (s) {s}A {...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Scheil equations
• The Scheil equations describe the concentration of a solute in the solid and liquid phases during solidification. This equation is commonly used in metallurgy, during the solidification of alloys and in semiconductor wafer manufacture for the solidification of single crystals of semiconductor materials.TeX format: {C_L=C_0(f_L)^{k-1}}TeX format: {C_S=kC_0(1-f_S)^{k-1}}CL {C_L} = concentration of solute in the liquid phase (mol.m-3) {mol.m^{-3}}CS {C_S} = concentration of solute in the solid phas...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Avrami equation
• The Avrami equation describes the change of matter from one state to another at a constant temperature. A graph of y against log(t) is characterized by an initially slow rate of change (corresponding to nucleation of the new phase) followed by a faster, steady rate (growth of the new phase), and finally a decrease in rate (as the driving force behind the phase change reduces).TeX format: {y = 1 - \exp^{- kt^{n}}}y {y} = fraction of material changedk {k} = material dependant constantn {n} = mater...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Equivalent oxide thickness
• As integrated circuits are miniaturised, quantum tunnelling of electrons between adjacent interconnects and transistors becomes a problem, causing signal loss and the generation of heat. To combat this, replacement dielectrics can be used, for example HfO2, which has a k ≅ 21 F.m-1. This allows a thicker dielectric layer to be used to give the same performance as SiO2 with a reduced likelihood of quantum tunnelling.TeX format: {EOT = t_{high-k} \left(\frac{k_{SiO_2}}{k_{high-k}}\right)}EOT...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
• Critical thickness for strained oxide deposition
• One method of increasing the speed of a microprocessor is to deposit strained channel material between gates in MOSFETs. This effectively reduces the delay in and between transistors. Electrons passing from one gate to another encounter less material and as such undergo less scattering, increasing their apparent velocity. The thickness of the strained material is limited by the strain field associated with the lattice mismatch between the channel and substrate material, and at a critical thickne...
• Creator: The University of Liverpool
• Keywords:
• Date added: 14 September 2010
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