A simplified technique for measuring fast surface states

A technique is presented which measures the number of fast states (/cm²) between (flat band) φ_s = 0 and φ_s = 2φ_B using a high frequency C ? V and d.c. ramp I ? V tracing of any MIS capacitor. For cases where fast state densities near flat band are insignificant, the true flat band point V(φ_s = 0) is obtained from the high frequency C ? V curve. Then from the (I ? V) curve the V(φ_s = 2φ_B) point is obtained by graphically measuring off an area = I_max (2kT/q) ln (N_B/ni) between V = V_FB, V = V₁, I = Imax, and I ? V curve. Then the fast state density (N_FS(/cm²)), is obtained from the expression: $\text{Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 2φ}{}_{\mathrm{B}}\text{? Vφ}{}_{\mathrm{<mtext>s</mtext>}}\text{= 0 = 2φ}{}_{\mathrm{B}}\text{+}\text{q}\text{C}{}_{\mathrm{<mtext>ins</mtext>}}\text{N}{}_{\mathrm{si}}\text{+ N}{}_{\mathrm{FS}}\text{]}$ where all values are known. For cases where significant fast states exist near flat band, the true flat band point can be obtained graphically from the I ? V tracing using any value of surface potential near mid gap calculated from the high frequency capacitance.