The cross section of the DG MOSFET considered in this paper is shown in Fig.. Region 1 of length Lo represents the nondamaged region, and region 2 represents the damaged region of length Ld with the interface charge of density Nis per square area. Referring to Fig., the potential distributions ϕ1(x, y) and ϕ2(x, y) in regions 1 and 2. the boundary condition and the cross-sectional diagram of the device are attached in fig.

From the fig, the first derivative of the potential w.r.t y is the normal field component at the boundary. But the normal component should not be equal in the presence of charge density.

REF: Effect of Localized Interface Charge on the Threshold Voltage of Short-Channel Undoped Symmetrical Double-Gate MOSFETs, IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 58, NO. 2, FEBRUARY 2011