Dielectric Constant, k


The dielectric properties of the various materials used in semiconductor fabrication and packaging play an important role in achieving the desired performance of integrated circuits. A basic understanding of dielectric properties is therefore needed by most engineers working in the semiconductor industry. 


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One important property of a dielectric material is its permittivity.  Permittivity (ε) is a measure of the ability of a material to be polarized by an electric field. 


It is, however, easier to grasp the concept of permittivity by first discussing a closely related property, capacitance (C). Capacitance is a measure of the ability of a material to hold charge if a voltage is applied across it, and is best modeled by a dielectric layer that's sandwiched between two parallel conductive plates. 


If a voltage V is applied across a capacitor of capacitance C, then the charge Q that it can hold is directly proportional to the applied voltage V, with the capacitance C as the proportionality constant.  Thus, Q = CV, or C = Q/V.  The unit of measurement for capacitance is the farad (coulomb per volt).


The capacitance of a capacitor depends on the permittivity ε of the dielectric layer, as well as the area A of the capacitor and the separation distance d between the two conductive plates.  Permittivity and capacitance are mathematically related as follows:  C = ε (A/d).


When the dielectric used is vacuum, then the capacitance Co = εo (A/d), where εo is the permittivity of vacuum (8.85 x 10-12 F/m).


The dielectric constant (k) of a material is the ratio of its permittivity ε to the permittivity of vacuum εo, so k = ε/εo The dielectric constant is therefore also known as the relative permittivity of the material. Since the dielectric constant is just a ratio of two similar quantities, it is dimensionless. 


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Given its definition, the dielectric constant of vacuum is 1. Any material is able to polarize more than vacuum, so the k of a material is always > 1. Note that the dielectric constant is also a function of frequency in some materials, e.g., polymers, primarily because polarization is affected by frequency. 


A low-k dielectric is a dielectric that has a low permittivity, or low ability to polarize and hold charge.  Low-k dielectrics are very good insulators for isolating signal-carrying conductors from each other.  Thus, low-k dielectrics are a necessity in very dense multi-layered IC's, wherein coupling between very close metal lines need to be suppressed to prevent a degradation in device performance.


A high-k dielectric, on the other hand, has a high permittivity.  Because high-k dielectrics are good at holding charge, they are the preferred dielectric for capacitors.  High-k dielectrics are also used in memory cells that store digital data in the form of charge.


See also:  Dielectric




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