ABSTRACT
Figure 6.1 p Model of an on-chip inductor.The ac electrical resistivity of copper can be predicted by Drude model [11]:0( )= (1+ ),jr r t (6.1)where r0 is dc resistivity and t is the momentum relaxation time.The relation between ac electrical conductivity of CNT and frequency is given by [12], 0 ,= 1+ iss t (6.2)where s0 = 1/RS, t = lmfp/vF is electron relaxation time in CNT, vF is the Fermi velocity, and lmfp is mean-free path.At high frequencies, the Eddy currents induced in the substrate will significantly decrease the performance of the inductor. Approximate expression for Reddy is given by [3], eddy 8 ,= lR tWs (6.3)where l, t, and W are length, thickness and width of the interconnect,
In Fig. 6.1, capacitance (CS), oxide layer capacitance (Cox), substrate resistance (Rsub) and substrate capacitance (Csub) are calculated by using the modeling techniques presented in [10] based on the total length of the inductor. Table 6.1 summarizes the calculated values of p model parameters of Fig. 6.1, which are used in simulations. In Table 6.1, LS = 6 nH is the designed value for the LC VCO for both the metallic carbon nanotubes (MWCNT and SWCNT bundle) and copper wire inductors. The model parameters except RS are same for both metallic carbon nanotubes and copper because these are dependent on the geometry of the spiral inductor and independent on the metal materials. Here, b is the probability factor characterizing an SWCNT being metallic in a bundle or a shell being metallic in an MWCNT. Table 6.1 Inductor p model parameters Parameter
because of the lower resistance of CNTs but also because the skin effect in CNT interconnects is negligible [13]. The Q factors of CNT bundle wire inductors are much higher than that of the MWCNT wire inductor because there are more conductance channels in a bundle compared with a same size MWCNT wire, which means the resistance of an SWCNT bundle wire is smaller than that of a same size MWCNT wire.
