MOSFET Depletion Region Capacitance

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${C_D}={varepsilon_S}/{x_D}$

Substitute for depletion region width from identity table:

${C_D}={varepsilon_S}/{sqrt { {2 phi_s } / {Phi_s} }}$

Now breaking down the identities to show the same form as the book:

${C_D}={varepsilon_S}/{sqrt { {2 phi_s } / {qN_a / varepsilon_s} }}$

${C_D}={sqrt{{varepsilon_S qN_a}/{2 phi_s}}}$ ….this is almost the same as equation 2.1.27 of CMOS Analog Design Using All Region MOSFET Modeling

If you want to include the linear term of depletion region electric field then substitute ${(phi_s - phi_t)}$ for ${phi_s}$

${C_D}={sqrt{{varepsilon_S qN_a}/{2 (phi_s - phi_t)}}}$

And the phrase now exactly matches the book.

Identity Table

$Phi = {qN_a / varepsilon_s}$	$E_surface = sqrt { {2 phi_s Phi_s} }$
$x_d = sqrt { {2 phi_s } / {Phi_s} }$
${C_D/C_ox}={varepsilon_S}/{t_D} {/} {varepsilon_ox}/{t_ox}$	$gamma = {varepsilon_s}/{1} {/} {varepsilon_ox}/{t_ox} {sqrt{2 Phi_s }}$

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