Equation icon  Black's equation

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Resource type: Equation
Description: 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 {A} = material/geometry dependent constant
w {w} = width of metal wire, sometimes included with the constant A (m) {m}
j {j} = current density (A.m-2) {A.m^{-2}}
n {n} = material/geometry dependent consant (typically = 2)
Q {Q} = activation energy for electromigration (eV) {eV}
k {k} = Boltzmann's constant (8.617 eV.K-1) {8.617 eV.K^{-1}}
T {T} = temperature (K) {K}

Keywords: Black's • failure • time • IC • integrated circuits • transistors • MOSFET
Categories: Science approaches
Science approaches > Modelling & simulation
Applications > Electronics
Properties > Electrical, magnetic & optical
Testing, analysis & experimentation
Created by: The University of Liverpool
License: This resource is released under the Creative Commons Attribution license (2.0 UK: England & Wales).
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Date created: 18 August 2010
Date added: 14 September 2010
Resource ID: 3199