Current peak spreading schemes for multiplexed heated array

1. A method of operating a heating plate for a substrate support assembly used to support a semiconductor substrate in a semiconductor processing apparatus, wherein the heating plate includes a first electrically insulating layer, M electrically conductive power supply lines, N electrically conductive power return lines, an array of multiple planar heater zones wherein a respective planar heater zone Z ij is connected to an i-th power supply line and a j-th power return line wherein 1≦i≦M, 1≦j≦N, i and j are integers, and the planar heater zone Z ij comprises one or more heater elements, and a diode serially connected to planar heater zone Z ij between the i-th power supply line and the j-th power return line such that the diode does not allow reverse electrical current flow in a direction from the j-th power return line through the planar heater zone Z ij to the i-th power supply line, and wherein the planar heater zones are laterally distributed across the first electrically insulating layer and operable to tune a spatial temperature profile on the semiconductor substrate, and wherein no two planar heater zones are connected to the same pair of i-th power supply line and j-th power return line; the method comprising:

(a) calculating a time duration T ij for planar heater zone Z ij in the array of multiple heater zones, based on a difference between an actual temperature or an estimated temperature and a setpoint temperature of the planar heater zone Z ij , such that the planar heater zone Z ij reaches its setpoint temperature after being powered by a power supply for the time duration T ij ,

(b) maintaining a connection between the i-th power supply line and the power supply for a controller time duration T i ; and

(c) during the controller time duration T i , powering the planar heater zone Z ij connected to the i-th power supply line by maintaining a connection between the j-th power return line and an electrical ground for the heater zone time duration τ ij ;

(d) repeating step (c) for all integer values of j wherein 1≦j≦N such that not all time durations T ij begin at the same time;

(e) repeating steps (c) and (d) for all integer values of i wherein 1≦i≦M.

2. The method of claim 1 , wherein N is an integer between 2and 100inclusive, and M is an integer between 2 and 100 inclusive.

3. The method of claim 1 , wherein

∑

j

=

1

N

⁢

⁢

τ

ij

≤

T

i

,

and wherein step (d) further comprises, powering each planar heater zone Z ij connected to the i-th power supply line sequentially such that no more than one of planar heater zones Z ij is powered at any given time during T i .

4. The method of claim 1 , wherein

∑

j

=

1

N

⁢

⁢

τ

ij

>

T

i

,

and the time duration τ ij begins at time point α ij and ends at time point β ij relative to the beginning of the time duration T i , in step (d), determining α ij and β ij according to the following rules:

(i) α i1 =0; (ii) α i(j+1) =β ij and β i(j+1) =(α i(j+1) +τ i(j+1) ) if (α i(j+1) +τ i(j+1) )≦T i ; (iii) spliting T i(j+1) into one duration between α i(j+1) and T i and another duration between 0 and (α i(j+1) +τ i(j+1) −T i ) if (α i(j+1) +τ i(j+1) )≦T i .

5. The method of claim 1 , wherein step (d) further comprises moving one or more τ ij from one duration T i to a next duration T i .

6. The method of claim 1 , wherein in step (c) further comprises adjusting T i such that

T

i

=

∑

j

=

1

N

⁢

⁢

τ

ij

and wherein step (d) further comprises powering each planar heater zone Z ij connected to the i-th power supply line sequentially such that one and only one of the planar heater zones Z ij is powered at any given time during T i .

7. The method of claim 1 , wherein the estimated temperature of the heater zone Z ij is calculated in a model based fashion based on real time feedback of the heater zone Z ij .

8. The method of claim 1 , wherein the estimated temperature of the heater zone Z ij is based on previously measured calibration data.

9. The method of claim 1 , wherein the estimated temperature of the heater zone Z ij is calculated in an interpolated fashion based on a result of a model derived from prior calibrations so that the calculation of the time duration T ij for the each heater zone Z ij takes feed forward effects of prior substrate treatment processes into consideration.

10. The method of claim 1 , wherein the estimated temperature of the heater zone Z ij is calculated in an interpolated fashion based on a result of a model derived from prior calibrations so that the calculation of the time duration T ij for the each heater zone Z ij takes feed forward effects of subsequent substrate treatment processes into consideration.