The threshold voltage expression given by (1.1) can be applied to n-channel as well as p-channel transistors. However, some of the parameters have opposite polarities for the pMOS and the nMOS transistors. For example, the substrate bias voltage V_SB is positive in nMOS and negative in pMOS devices. Also, the substrate potential difference is negative in nMOS, and positive in pMOS. Whereas, the body-effect coefficient is positive in nMOS and negative in pMOS. Typically, the threshold voltage of an enhancement mode n-channel transistor is positive, while that of a p-channel transistor is negative.

Example 2.1 Given the following parameters, namely the acceptor concentration of p-substrate N_A =10¹⁶ cm^-3 , polysilicon gate doping concentration N_D =10¹⁶ cm^-3 , intrinsic concentration of Si, n_i =1.45 X 10¹⁰ cm^-3, gate oxide thickness t_ox =500 Å and oxide-interface fixed charge density N_OX =4 X 10¹⁰cm^-2 , calculate the threshold voltage V_TO at V_SB=0.

Ans : The potential difference between E_I and E_F for the p-substrate is