Electrode tuning method and apparatus for a layered heater structure
A layered heater structure including an electrode layer and a localized tuning method for tuning the electrode layer of a layered heater structure with high precision is provided. The localized tuning method tunes the electrode layer to its proper local resistance to minimize temperature offsets on the heater surface and thus provide a desired thermal profile that is in marked contrast to conventional, non-localized resistance tuning approaches based on thickness trimming practices, such as grinding or blasting, or resistivity adjustment, such as local heat treatment.
1. A method for performing a precise localized resistance tuning of an electrode layer of a layered heater structure, the method comprising:
virtually partitioning a pre-determined pattern of the electrode layer into at least one segment;
(ii) computing, for each virtually partitioned segment, a local target segment resistance based on segment geometry;
(iii) measuring, for each virtually partitioned segment, a local segment resistance;
(iv) computing, for each virtually partitioned segment a difference value between said local target segment resistance and said local measured segment resistance;
(v) computing, for each virtually partitioned segment, the number of through-thickness perforations with selected size and shape needed to increase the local segment resistance to meet the target segment resistance; and
(vi) introducing at least one through-thickness perforation, based on the above calculation, into each of the identified partitioned segments to sufficiently modify the electrical resistance of the identified partitioned segments such that the modified electrical local segment resistance does not deviate from said target segment resistance by an amount exceeding a absolute value of an pre-determined threshold.
2. A method according to claim 1 , wherein said introduced perforation alters an electrical current flow of the identified partitioned segments.
3. A method according to claim 1 , wherein said introduced perforation reduces an effective cross-section of the identified partitioned segments.
4. A method according to claim 1 , wherein said at least one perforation is selected from the group comprising: a circular void, an oval void, a square void, a curved line cut, a straight line cut, and an isolation loop.
5. A method according to claim 1 , further comprising: repeating steps (ii) through (vi) for all partitioned segments identified at said step (ii) until no further identified virtually partitioned segments remain having a local segment resistance that deviates from said target segment resistance by an amount exceeding said absolute value of said pre-determined deviation threshold.
6. A method according to claim 1 , wherein said step of computing a local target segment resistance for each virtually partitioned segment is a numerical computation.
7. A method according to claim 6 , wherein said numerical computation comprises: utilizing finite element analysis based on an electrostatic model of the electrode.
8. A method according to claim 1 , wherein said step of computing a local target segment resistance for each virtually partitioned segment is an analytical computation.
9. A method according to claim 8 , wherein said analytical computation further comprises: utilizing electrical and geometrical properties of the electrode to calculate a segment resistance based on the relation, R=ρ·L/A, where ρ is the resistivity of the electrode material, L is the length of the electrode segment and A is the cross section area of the electrode.
10. A method according to claim 1 , wherein said measuring step further comprises measuring the local segment resistance using a measurement technique selected from the group comprising: a 4-point probe measurement, thermal mapping, thickness measurement, and Ohm meter measurement.
11. A method according to claim 1 , wherein said pre-determined threshold is substantially +/−1% of said target segment resistance.
12. A method according to claim 1 , wherein the number of virtually partitioned segments is a function of segment size and an electrode pattern design.
13. A method according to claim 12 , wherein a segment size of each of said segment is substantially in the range of 1 mm to 1000 mm per segment.
14. A method according to claim 1 , wherein a total number of virtually partitioned segments is arbitrarily selected.