Chapter 2

Q. 2.2

Consider the transistor shown in Fig. 2.18, where the total width of the four parallel transistors is 80λ, its length is 2λ, and λ = 0.2 μm. Assuming node 2 is the source, node 1 is the drain, and the device is in the active region, find the source-bulk and drain-bulk capacitances given the parameters C_j=0.24  \mathrm{fF} / \mu \mathrm{m}^2 \text { and } C_{j-\mathrm{sw}}=0.2  \mathrm{fF} / \mu \mathrm{m}. Also find the equivalent capacitances if the transistor were realized as a single device with source and drain contacts still evenly placed.



Verified Solution

Starting with node 1, the drain, we find that the areas of the junctions are equal to

\mathrm{A}_{\mathrm{J} 2}=\mathrm{A}_{\mathrm{J} 4}=6 \lambda \times 20 \lambda=120 \lambda^2=4.8  \mu \mathrm{m}^2

Ignoring the gate side, the perimeters are given by

\mathrm{P}_{\mathrm{J} 2}=\mathrm{P}_{\mathrm{J} 4}=6 \lambda+6 \lambda=12 \lambda=2.4  \mu \mathrm{m}

As a result, \mathrm{C}_{\mathrm{db}} can be estimated to be

\mathrm{C}_{\mathrm{db}}=2\left(\mathrm{~A}_{\mathrm{J} 2} \mathrm{C}_{\mathrm{j}}+\mathrm{P}_{\mathrm{J} 2} \mathrm{C}_{\mathrm{j}-\mathrm{sw}}\right)=3.3  \mathrm{fF}

For node 2, the source, we have

\mathrm{A}_{\mathrm{J} 1}=\mathrm{A}_{\mathrm{J} 5}=5 \lambda \times 20 \lambda=100 \lambda^2=4  \mu \mathrm{m}^2


\mathrm{A}_{\mathrm{J} 3}=\mathrm{A}_{\mathrm{J} 2}=4.8  \mu \mathrm{m}^2

The perimeters are found to be

\mathrm{P}_{\mathrm{J} 1}=\mathrm{P}_{\mathrm{J} 5}=5 \lambda+5 \lambda+20 \lambda=30 \lambda=6  \mu \mathrm{m}


P_{\mathrm{J} 3}=P_{\mathrm{J} 2}=2.4  \mu \mathrm{m}

resulting in an estimate for \mathrm{C}_{\mathrm{sb}} of

C_{s b}=\left(A_{J 1}+A_{J 3}+A_{J 5}+W L\right) C_j+\left(P_{J 1}+P_{J 3}+P_{J 5}\right) C_{j-s w}

=\left(19.2  \mu \mathrm{m}^2\right) 0.24  \mathrm{fF} / \mu \mathrm{m}^2+(14.4  \mu \mathrm{m}) 0.2  \mathrm{fF} / \mu \mathrm{m}

=7.5  \mathrm{fF}

It should be noted that, even without the additional capacitance due to the WL gate area, node 1 has less capacitance than node 2 since it has less area and perimeter.

In the case where the transistor is a single wide device, rather than four transistors in parallel, we find

A_J=5 \lambda \times 80 \lambda=400 \lambda^2=16  \mu \mathrm{m}^2


P_{\mathrm{J}}=5 \lambda+5 \lambda+80 \lambda=90 \lambda=18  \mu \mathrm{m}

resulting in \mathrm{C}_{\mathrm{db}}=7.4  \mathrm{fF} \text { and } \mathrm{C}_{\mathrm{sb}}=9.0  \mathrm{fF} \text {. } Note that in this case, C_{\mathrm{db}} is nearly twice what it is when four parallel transistors are used.