MOS Capacitors

The ICS Instructions contain the basic procedures for making measurements. This screen is intended to point out things unique to using the MOSC model file.

Device Selection

There are five types of capacitors in the mask set:

• metal over field oxide with guard rings (A),
• metal over gate oxide (B),
• metal over field oxide (C),
• metal over diffusion 1 (D) and
• metal over diffusion 2 (E).

Each type has been implemented with three different geometries:

• The square capacitor is 300 x 300 μm
• The round capacitor radius equals 150 μm
• The finger capacitor has a center region of 100 x 100 μm and twelve 20 x 100 μm fingers.

• Make the measurements on the round "B" capacitors.

You will determine the doping level of the silicon from the capacitance measurements in the report. You will also determine the oxide thickness (Gate Oxide in the case of the "B" capacitors.)

Probe Assignments

• SMU1 and CM(H) → probe1 → Round "B Capacitor" pad
• SMU2 and CM(L) → probe2 → Substrate (small square under the "B")

Theory

These are metal oxide semiconductor capacitors (MOSC), and the ece440 textbook has a description of what the capacitance vs. voltage curves should look like, as well as some of the information that can be determined from them.

Here are some brief highlights:

The capacitance of the oxide is given by:

C_ox = εA/d

where:

• ε = dielectric constant of insulator = ε₀ε_r
• A = area of the device
• d = distance between the plates (dielectric thickness)

Under a particular bias polarity, a depletion layer will form in the silicon below the oxide, adding another capacitor in series with the oxide capacitor. The differential capacitance, C_d, of the semiconductor-space charge region is

C_d = (dielectric constant of silicon)*(Area)/(Thickness of depletion region)

The total capacitance is

C_tot = (C_ox * C_d)/(C_ox+C_d)

Here is a typical C-V curve for a MOS capacitor on a grounded n-type substrate with ±10V applied to the aluminum contact on top of the oxide. The flat regions corresponding to the oxide capacitance and the total capacitance at maximum depletion width are evident.

It is possible to model the capacitors by separating the capacitance into center and edge effects. The equations are similar to those used for modeling the p-n junction capacitance.

The total capacitance per area is

C_total = P * C_edge + A * C_area,

where P equals the perimeter and A equals the area. Note that the units of C_edge and C_area are pF/μm and pF/μm², respectively. By using two of the capacitors, it is possible to solve for P and A.