Question

In order to determine oxide thickness and lateral diffusion, two MOSFET structures are fabricated. These structures have the same width, but different drawn gate lengths. The oxide capacitance Cₒₓ of each structure is measured.

a) Find a method by which tₒₓ​ and ​LD can be determined from the two measured capacitance values.

Answer 1

To determine the oxide thickness (tox) and lateral diffusion (LD), use the capacitance formula for parallel plate capacitors in conjunction with measurements from two MOSFETs with different gate lengths. Solve the resultant equations to find the differences caused by LD and calculate the values of tox and LD.

Step-by-step explanation:

To determine the oxide thickness (tox) and lateral diffusion (LD) from the measured capacitance values of two MOSFET structures, one can employ a method involving the capacitance of a parallel plate capacitor given by the formula C = ε0εrA/d. Here, ε0 is the permittivity of free space, εr is the relative permittivity of the oxide material, A is the area of the gate, and d is the separation between the plates, which, in the case of the MOSFET, is the oxide thickness (tox).

By having two MOSFETs with differences only in gate lengths but with measured capacitance, one could solve for tox by setting up two equations based on the respective measurements and then solve them simultaneously. The given capacitance values can help in finding the area differences due to lateral diffusion and subsequently LD. Careful measurements and calculations are required to compensate for the changes in capacitance due to differences in the effective gate length.

The strategy for the calculation is also used in scenarios such as estimating a tunneling probability between conductors using quantum mechanical models, where parameters like the rest mass of the electron and Planck's constant are key factors in the calculation.