In-plane distribution data compression method, in-plane distribution measurement method, in-plane distribution optimization method, process apparatus control method, and process control method

A process control method used in a production process of a semiconductor device, comprising the steps of:

• performing a process over a substrate;
• measuring an in-plane distribution over the substrate;
• calculating a model formula of the in-plane distribution from measurement data obtained by measurement;
• comparing the measurement data with the model formula to calculate a set of parameters of the model formula;
• storing the parameters as data of the in-plane distribution over the substrate;
• and
• determining an abnormality in a semiconductor device production apparatus from a variation in the stored parameters,
• wherein the measurement data includes measurement coordinates over the substrate, and
• the model formula is obtained by modeling the tendency that the in-plane distribution concentrically varies and the tendency that the in-plane distribution varies along a diameter direction,
• wherein the step of performing over the substrate is a step of performing a first process over the substrate;
• the step of measuring an in-plane distribution over the substrate is a step of measuring an in-plane distribution A over the substrate;
• the step of calculating the model formula of the in-plane distribution from measurement data obtained by measurement is a step of calculating a model formula A of the in-plane distribution A from measurement data A obtained by measurement;
• the step of comparing the measurement data with the model formula to calculate the set of parameters of the model formula is a step of comparing the measurement data A with the model formula A to calculate a set of parameters A of the model formula A;
• and
• the step of storing the parameters as data of the in-plane distribution over the substrate is a step of storing the parameters A as data A of the in-plane distribution A over the substrate,
• wherein the process control method further comprises the steps of:
• performing a second process over the substrate;
• measuring an in-plane distribution B over the substrate;
• calculating a model formula B of the in-plane distribution B from measurement data B obtained by measurement;
• comparing the measurement data B with the model formula B to calculate a set of parameters B of the model formula B;
• storing the parameters B as data B of the in-plane distribution B over the substrate;
• comparing the in-plane distribution A and the in-plane distribution B based on the data A and the data B to calculate a correction value such that the uniformity of the in-plane distribution B in the second process improves;
• and
• adjusting wafer orientation based on the correction value,
• wherein the measurement data A and the measurement data B include measurement coordinates over the substrate, and
• the model formula A and the model formula B are obtained by modeling the tendency that the in-plane distribution A and the in-plane distribution B concentrically vary and the tendency that the in-plane distribution A and the in-plane distribution B vary along a diameter direction.

A process control method used in a production process of a semiconductor device, comprising the steps of:

• performing a process over a substrate;
• measuring an in-plane distribution over the substrate;
• calculating a model formula of the in-plane distribution from measurement data obtained by measurement;
• comparing the measurement data with the model formula to calculate a set of parameters of the model formula;
• storing the parameters as data of the in-plane distribution over the substrate;
• and
• determining an abnormality in a semiconductor device production apparatus from a variation in the stored parameters,
• wherein the measurement data includes measurement coordinates over the substrate,
• the model formula is obtained by modeling the tendency that the in-plane distribution concentrically varies and the tendency that the in-plane distribution varies along a diameter direction and along a tilt of the substrate,
• in the model formula, centers of concentric circles in the in-plane distribution do not correspond to each other, and
• a point (x, y) over the substrate is rotated by θ degree with respect to X-Y coordinate of the substrate.

A process control method used in a production process of a semiconductor device, comprising the steps of:

• performing a first process over a substrate;
• measuring an in-plane distribution A over the substrate;
• calculating a model formula A of the in-plane distribution A from measurement data A obtained by measurement;
• comparing the measurement data A with the model formula A to calculate a set of parameters A of the model formula A;
• storing the parameters A as data A of the in-plane distribution A over the substrate;
• comparing the measurement data A with the model formula A to detect measurement data A which is inconsistent with the model formula A;
• performing remeasurement for the inconsistent measurement data A to update the inconsistent measurement data A;
• and
• determining an abnormality in a semiconductor device production apparatus from a variation in the stored parameters,
• wherein the measurement data includes measurement coordinates over the substrate, and
• the model formula is obtained by modeling the tendency that the in-plane distribution concentrically varies and the tendency that the in-plane distribution varies along a diameter direction,
• wherein the process control method further comprises the steps of:
• performing a second process over the substrate;
• measuring an in-plane distribution B over the substrate;
• calculating a model formula B of the in-plane distribution B from measurement data B obtained by measurement;
• comparing the measurement data B with the model formula B to calculate a set of parameters B of the model formula B;
• storing the parameters B as data B of the in-plane distribution B over the substrate;
• comparing the measurement data B with the model formula B to detect measurement data B which is inconsistent with the model formula B;
• performing remeasurement for the inconsistent measurement data B to update the inconsistent measurement data B;
• and
• comparing the in-plane distribution A and the in-plane distribution B based on the data A and the data B to calculate a correction value such that the uniformity of the in-plane distribution B in the second process improves,
• wherein the measurement data A and the measurement data B include measurement coordinates over the substrate, and
• the model formula A and the model formula B are obtained by modeling the tendency that the in-plane distribution A and the in-plane distribution B concentrically vary and the tendency that the in-plane distribution A and the in-plane distribution B vary along a diameter direction.

A process control method used in a production process of a semiconductor device, comprising the steps of:

• performing a process over a substrate;
• measuring an in-plane distribution over the substrate;
• calculating a model formula of the in-plane distribution from measurement data obtained by measurement;
• comparing the measurement data with the model formula to calculate a set of parameters of the model formula;
• storing the parameters as data of the in-plane distribution over the substrate;
• and
• determining an abnormality in a semiconductor device production apparatus from a variation in the stored parameters;
• and
• performing remeasurement for inconsistent measurement data detected by the comparison of the measurement data with the model formula to update the inconsistent measurement data,
• wherein the measurement data includes measurement coordinates over the substrate,
• the model formula is obtained by modeling the tendency that the in-plane distribution concentrically varies and the tendency that the in-plane distribution varies along a diameter direction and along a tilt of the substrate,
• in the model formula, centers of concentric circles in the in-plane distribution do not correspond to each other, and
• the model formula is expressed by the following formulas:
• F(x, y)=A0+A1R+A2R2+Axx+Ayy
• R=(X−X0)2/B+(Y−Y0)2/(1−B)
• where F(x, y) is a measured value at a point (x, y) over the substrate, A is a coefficient of the zeroth order term, A1 is a coefficient of the first order term, A2 is a coefficient of the second order term, R is a roundness factor, Ax is a X-direction tilt coefficient, Ay is a Y-direction tilt factor, X0 is a shift amount in X direction, Y0 is a shift amount in Y direction, and θ is a rotation factor.

A process control method used in a production process of a semiconductor device, comprising the steps of:

• performing a process over a substrate;
• measuring an in-plane distribution over the substrate;
• calculating a model formula of the in-plane distribution from measurement data obtained by measurement;
• comparing the measurement data with the model formula to calculate a set of parameters of the model formula;
• storing the parameters as data of the in-plane distribution over the substrate;
• determining an abnormality in a semiconductor device production apparatus from a variation in the stored parameters;
• and
• outputting the determination result of the abnormality in the semiconductor device production apparatus,
• wherein the measurement data includes measurement coordinates over the substrate, and
• the model formula is obtained by modeling the tendency that the in-plane distribution concentrically varies and the tendency that the in-plane distribution varies along a diameter direction and along a tilt of the substrate.