Bond wires in Integrated Circuits

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An integrated circuit on a die is connected to external world through bond wires. Depending on the packaging or assembly technique we use, the bond wire length changes. The self or mutual inductance of the bond wire is directly proportional to length and have a great impact on the performance of RFICs.

Self inductance of a wire with rectangular cross-section is given by [?]

(1)   \begin{equation*} L_{s} = {\mu_o l \over 2\pi}\left[\ln\left({2l\over w+t}\right)+{1\over2}+\left(\frac{w+t}{3l}\right) \right] \end{equation*}

where l is length of the wire, w and t are width and thickness of the cross-section of the conductor.

The self inductance of a wire with circular cross-section is given by

(2)   \begin{equation*} L_{s} = {\mu_o l \over 2\pi}\left[\ln\left({l\over \rho}+\sqrt{1+\left({l\over \rho}\right)^2}\right) - \sqrt{1+\left({\rho\over l}\right)^2} + {1\over 4} +{\rho\over l} \right] \end{equation*}

where \rho is cross-section radius of the conductor.

Mutual inductance between two wires is given by

(3)   \begin{equation*} M_{12} = {\mu_o l \over 2\pi}\left[\ln\left({l\over d}+\sqrt{1+\left({l\over d}\right)^2}\right) - \sqrt{1+\left({d\over l}\right)^2} + {d\over l} \right] \end{equation*}

where d is the distance between two wires.

If L_1 and L_2 are the self inductances of wires \textcircled{\small 1} and \textcircled{\small 2}, then mutual inductance between two wires is given by M_{12}=k\sqrt{L_1L_2}
where, k is magnetic coupling factor

Rules of thumb for design calculations:
self inductance of lead frame ~\approx 0.9nH/mm
self inductance of a bondwire is ~\approx 1nH/mm

Typical values of bond-wire inductance, capacitance and resistance can be found here[?]

At very high frequencies skin effect comes into effect, and resistance at high frequencies is much higher than DC resistance. The following slides[?] show the modeling results of self and mutual inductance and capacitance along with DC and AC resistance of a 1-mil bondwire.

In a multi-segment bond wire, the self-inductance of entire wire is sum of self-inductance of each segment and mutual-inductance among the segments

(4)   \begin{equation*} L_{s}= \sum\limit_{i=1}^{N}L_i + \sum\limit_{i=1}^{N}\sum\limit_{j=i+1}^{N}2k_{ij}M_{ij} \end{equation*}

where L_i is the self-inductance of segment i, M_{ij} and k_{ij} are the mutual inductance and coupling coefficient between i and j segments.

k_{ij}=0, currents in i and j segments are orthogonal
k_{ij}=1, currents in i and j segments are in same direction
k_{ij}=-1, currents in i and j segments are in opposite direction

Bond wire modeling guidelines[?]

Bonding methods[?]

Fusing currents [?]
The current carrying capability of a bond wire changes with size of the wire and material used for it. The bond pad requirement also changes with the selection bond wire size. Here is a reference with some numerical info to select bond wire size, material and bond pad[?]

Characteristic Impedance of Integrated Circuit Bond Wires [?]


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