Techniques to extract MOS CAP parameters from C-V measurement.

Introduction: 

From the C-V measurement, we are able to extract the oxide thickness, flat and voltage, threshold voltage, effective oxide charges, and substrate doping concentration. The detailed techniques are discussed below:

Oxide thickness: 

From the measured C-V, and relation as shown in equation (1), we can estimate the oxide thickness is measured in the MOS structure. The Cox-accum is the strong accumulation capacitance value that is measured.

Figure 1: C-V curve 

Equation (1)

Flat capacitance and voltage:

In my previous discussion, I have clearly mentioned band bending and flat band, depletion conditions. It is difficult to get a flat band because all the surfaces have defects that are dangling bonds that create band bending so it is necessary the amount of bending in terms of voltage is effective for device operation considerations. Flat band condition in C-V measurement can be obtained. The gate voltage required to get a flat band is called flat band voltage(V_FB). The surface potential is zero in this condition because the band is flat. This voltage and its shift are widely used to judge device parameters, especially oxide charges. We can estimate flat band voltage through the C-V measurement of MOS CAP. First, flat band capacitance is calculated by oxide-capacitance and Debye length One important point is that the flat band capacitance is invalid if the interface trap is too large (over 10¹²). The C_ox means the value of the capacitance at a strong accumulation point. The Debye length is an indicator of the distance to which an electrical interaction can be sensed in the semiconductor. Once we know the flat band capacitance then from the position of the flat band capacitance, we can estimate the corresponding flat band voltage. By using equations (2) and (3) we can get the required information to estimate the flat band capacitance.

Equation (2)

Equation (3)

Effective oxide charge density:

The effective oxide charge (Qi) is a combination of fixed charge, oxide trapped charge, and mobile ionic charge. In C-V measurement, we cannot distinguish them. Temperature cycling can be a way to distinguish them. We only assume the charge is in between the semiconductor-oxide interface. Now, to estimate the flat effective oxide charge density simply calculate the difference of metal-semiconductor work function difference, and using equation (4) we have the relation of effective oxide charge. If we simply divide the charge by the electron’s charge (q) then we get the effective oxide-charge density. 

Equation (4)

Substrate doping concentration: Please check an example of it here. Please also find a detailed discussion about Magnetic phase transition, structural analysis, and crystallography understanding in the link.