April_AMP_Digital

A D V A N C E D M A T E R I A L S & P R O C E S S E S | A P R I L 2 0 2 0 1 9 pre-defined in Comsol and are applied to resolve the electrical properties in the stationary study [9] . ∇ •j = Qj,v (Eq 1) J = σ+Je (Eq 2) E = - ∇ V (Eq 3) ANALYSIS After defining the boundary con- ditions for terminal and ground in the direction of W M , (see Fig. 6), the study was executed to derive the global re- sistance R W between the ground and Fig. 2 — Example hexagonal pattern. Fig. 3 — Full foil segment model. Fig. 4 — Repeating unitary-cell model. Fig. 5 — Repeating multi-cell model. BOUNDARY CONDITIONS Before a solution can be attempt- ed, boundary conditions must be ap- plied. Current conservation and the initial electrical potential of equation (4) were applied to the solid. All boundar- ies were identified as insulating except those identified as “ground” and “terminal.” V = 0 Volts (Eq 4) Before assigning ground and terminal designations to boundaries, an orientation must be chosen. If it is desired to de- termine the conductivity in the direction of W M , the terminal and ground boundaries must be as- signed along the edges of sym- metry which are orthogonal to the W M measurement as shown in Fig, 6. If it is desired to determine the con- ductivity in the direction of L M , the ter- minal and ground boundaries must be assigned along the edges of symmetry, which are orthogonal to the L M mea- surement as shown in Fig. 7. The ground boundaries were as- signed the stationary value of Equa- tion (4). The terminal boundaries were designated as current type boundaries and assigned a non-zero value of Equa- tion (5). I 0 = 1 A (Eq 5) The amount of current used for the evaluation must be appropriate to the size of the model, the thickness of the foil, the amount of open-hole area, and the foil material. A large amount of current can cause significant ohm- ic heating. This may or may not be desired depending upon the goals of the evaluation. For this determination, heating was not desired; however, too lit- tle current will cause the poten- tial drop between terminal and ground to be too low for a robust determination of resistance. A sensitivity study is easy to per- form to identify a range of cur- rents that yield stable results. For studies of this configura- tion and objective, 1 A is a use- ful value. Fig. 6 — Boundary conditions for determination along W M . Fig. 7 — Boundary conditions for determination along L M .