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At increasingly higher frequencies, even in the absence of the substrate, the current distribution in the metal layers changes due to eddy currents in the metallization, also known as skin and proximity effects, current constriction, and current crowding. At any given frequency, alternating currents take the path of least impedance. Currents tend to accumulate at the outer layer or skin of conductors since magnetic fields of the device penetrate the conductors and produce opposing electric fields within the volume of conductors.

7 nH multi-level inductor with a Q = 3. Incidentally, this proposal was also put forward in 1989 at the GaAs symposium by Geen et al. , 1989]. Geen further proposed offsetting or staggering the spirals to reduce the interwinding capacitance. Kim et al. 2 GHz for a 10 nH inductor. 45 nH achieving a Q = 24. 8 were demonstrated utilizing series and shunt connections of multiple metal layers. , 1996]. 5 GHz. 8 nH device at 1 GHz. The work of [Yue and Wong, 1997] [Yue and Wong, 1998] demonstrated electrostatic shielding of inductors from the substrate by utilizing a patterned layer of polysilicon or metal under the device.

For such a thin, moderately conductive grounded substrate, one must take into account ground “image” currents which can reduce the inductance value and serve as a further loss mechanism [Krafcsik and Dawson, 1986]. If the substrate is sufficiently conductive such that the skin depth is much less than the substrate thickness, then image currents will be confined to flow at the substrate surface. 3. DEVICE LAYOUT In this section we will discuss various ways to lay out inductors using the planar metallization layers of a typical IC process.