B Ideal MOS Capacitor

Appendix B
Ideal MOS Capacitor

The band diagrams of an ideal MOS structure consisting of a gate electrode (metal or polysilicon), a dielectric (oxide), and a semiconductor (nMOS or pMOS) are shown in Fig. B.1 under different operating conditions for both nMOS and pMOS. For the most simple case it is assumed that (i) there are no charges in the oxide, (ii) the resistivity of the oxide is infinite, and (iii) the work function difference between the metal and the semiconductor, $ϕms$ , is zero [10]. The operating conditions depend on the applied voltage $V$ on the metal contact with respect to the Fermi level of the grounded semiconductor and are called accumulation (a), flatband (b), depletion (c), and inversion (d).

In the following the pMOSFET with n-substrate will be explained:

(a) When a positive voltage is applied at the contact the conduction band $Ec$ bends down towards the Fermi level $Ef$ that is set constant in the semiconductor where no current flows. This bending yields an accumulation of the majority carriers (electrons) near the interface.

(b) For $V = 0$ all bands remain flat and the semiconductor and its majority and minority carriers are in thermal equilibrium.

(c) Under a small negative voltage the majority carriers are repelled from the interface, involving that the bands are bend up. The intrinsic energy $Ei$ gets closer to $Ef$ .

(d) When further increasing the negative voltage this bending continues and once $Ei$ crosses $Ef$ the minority carriers (holes) exceed the majority carriers at the interface. Hence, this case is called inversion, as the interface is inverted.

For the p-type structure with holes as majority carriers and electrons as minority carriers only the polarity of the voltage has to be changed.

Figure B.1: The energy band diagrams for ideal MOS-capacitors under different bias conditions: (a) accumulation, (b) flatband, (c) depletion, and (d) inversion. The resulting charges bend the bands upwards near the interface of the oxide/substrate (insulator/semiconductor) if $V < 0$ and downwards if $V > 0$ . The energy levels and potentials are marked for the flatband condition ( $V = 0$ ), with $ϕ ms$ denoting the Fermi potential with respect to the vacuum level, $χi$ and $χ$ , as electron affinity for the oxide and the substrate, and $Eg$ as bandgap in the substrate. Top: For a p-semiconductor (nMOS) it holds that $ϕms ≡ ϕm − (χ + Eg∕q − ϕp) = 0$ , where $ψBp$ and $ϕp$ represent the Fermi potentials with respect to the intrinsic energy $Ei$ and valence band $Ev$ . Bottom: For an n-semiconductor (pMOS) one obtains $ϕms ≡ ϕm − (χ+ ϕn ) = 0$ with $ϕn$ and $ψ Bn$ as the Fermi potentials with respect to the conduction band $E c$ and intrinsic energy $Ei$ .

Appendix BIdeal MOS Capacitor

Appendix B
Ideal MOS Capacitor