Virtual measuring device and method

A method of predicting a deposition thickness of amorphous silicon being deposited on a substrate, the method comprising:

• during a process of depositing the amorphous silicon to the substrate, predicting the deposition thickness by using a prediction model expressing a relationship between the deposition thickness and a plurality of process factors that are correlated with the deposition thickness of the amorphous silicon;
• and
• after measuring the deposition thickness, and comparing the predicted deposition thickness with the measured deposition thickness, adapting the prediction model to compensate the relationship between the deposition thickness and the plurality of process factors according to the comparison difference, wherein the adapted prediction model is used to predict a deposition thickness during a subsequent process of depositing amorphous silicon,
• wherein adapting the prediction model uses a Kalman filter
• wherein the plurality of process factors include a radio frequency power (RF power Vpp) of the deposition apparatus in depositing the amorphous silicon and manufacturing the substrate, a TUNE that is an impedance control factor of a power source that supplies power to the deposition apparatus during the deposition process, and a process time (PT) of the deposition process, and
• wherein the prediction model is modified by using a Kalman filter, such that
• {circumflex over (x)}k+1=Ak{circumflex over (x)}k+AkKk[{tilde over (y)}k−Ck{circumflex over (x)}k],
• where, {tilde over (y)}k denotes the measured deposited thickness, {circumflex over (x)}k denotes a statistical estimate value of the status xk=[β0 β1 β2]T, {circumflex over (x)}k+1 denote a statistical estimate value of Xk+1;
• C
• k
• =
• PT
• k
• ⁡
• [
• 1
• Vpp
• k
• TUNE
• k
• ]
• ,
• A
• k
• =
• [
• 1
• 0
• 0
• 0
• 1
• 0
• 0
• 0
• 1
• ]
• ;
• and Kk denotes a Kalman gain.

A virtual measuring device to predict a deposition thickness of amorphous silicon being deposited on a substrate, comprising:

• a prediction unit to predict the deposition thickness of the amorphous silicon being deposited to the substrate by using a prediction model expressing a relationship between the deposition thickness of the amorphous silicon and a plurality of process factors that are correlated with the deposition thickness of the amorphous silicon;
• and
• an adaptation unit to adapt the prediction model to compensate the relationship between the deposition thickness and the plurality of process factors according to the comparison difference, after comparing a measured deposition thickness with the predicted deposition thickness, wherein the adapted prediction model is used to predict a deposition thickness during a subsequent process of depositing amorphous silicon,
• wherein, in adapting the prediction model, the adaptation unit uses exponentially weighted moving averages (EWMA) in order to include a moving average of deviations that have occurred in the prediction model,
• wherein the plurality of process factors include a radio frequency power (RF power) of a deposition apparatus in a process of depositing the amorphous silicon and manufacturing the substrate, a TUNE that is an impedance control factor of a power source that supplies power to the deposition apparatus during the deposition process, and a process time (PT) of the deposition process, and
• wherein the prediction model is modified by using the exponentially weighted moving averages (EWMA), such that
• yk=THKk+ck|k−1+ek
• where, THKk=PTk[β0+β1(Vpp)+β2(TUNE)] denotes the estimated deposition thickness of a kth substrate;
• β0, β1, and β2 denote values that reflect a variation in the process factors over time, ck|k−1 denotes a deviation of the estimated deposition thickness of the k-th substrate based on deviations of the estimated deposition thickness, and a measured deposited thickness of a (k−1)-th substrate and the measured deposited thickness;
• ek denotes a theoretical error term of the equation;
• and yk denotes the modified estimated deposition thickness of the k-th substrate.

A virtual measuring device to predict a deposition thickness of amorphous silicon being deposited on a substrate, comprising:

• a prediction unit to predict the deposition thickness of the amorphous silicon being deposited to the substrate by using a prediction model expressing a relationship between the deposition thickness of the amorphous silicon and a plurality of process factors that are correlated with the deposition thickness of the amorphous silicon;
• and
• an adaptation unit to adapt the prediction model to compensate the relationship between the deposition thickness and the plurality of process factors according to the comparison difference, after comparing a measured deposition thickness with the predicted deposition thickness, wherein the adapted prediction model is used to predict a deposition thickness during a subsequent process of depositing amorphous silicon,
• wherein the adaptation unit uses a Kalman filter in adapting the prediction model, and
• wherein the plurality of process factors include a radio frequency power (RF power Vpp) of the deposition apparatus in depositing the amorphous silicon and manufacturing the substrate, a TUNE that is an impedance control factor of a power source that supplies power to the deposition apparatus during the deposition process, and a process time (PT) of the deposition process, and
• wherein prediction model is modified by using a Kalman filter, such that
• {circumflex over (x)}k+1=Ak{circumflex over (x)}k+AkKk[{tilde over (y)}k−Ck{circumflex over (x)}k],
• where, {tilde over (y)}k denotes the measured deposited thickness, {circumflex over (x)}k denotes a statistical estimate value of the status xk=[β0 β1 β2]T, {circumflex over (x)}k+1 denote a statistical estimate value of XK+1;
• C
• k
• =
• PT
• k
• ⁡
• [
• 1
• Vpp
• k
• TUNE
• k
• ]
• ,
• A
• k
• =
• [
• 1
• 0
• 0
• 0
• 1
• 0
• 0
• 0
• 1
• ]
• ;
• and Kk denotes a Kalman gain.

A method of modeling a deposition thickness of amorphous silicon being deposited on a substrate in real time, the method comprising:

• estimating a deposition thickness of the amorphous silicon being deposited on the substrate by using an equation expressing a relationship between the deposition thickness and a plurality of process factors of a deposition apparatus used during the deposition of the amorphous silicon;
• measuring a deposited thickness of the amorphous silicon over a designated sheet interval and comparing the measured deposited thickness with the estimated deposition thickness to generate a difference data;
• and
• modifying the equation with additional terms for the equation based on the generated difference data so that subsequent difference data is within a predetermined range, wherein:
• the plurality of process factors include a radio frequency power (RF power Vpp) of the deposition apparatus in depositing the amorphous silicon and manufacturing the substrate, a TUNE that is an impedance control factor of a power source that supplies power to the deposition apparatus during the deposition process, and a process time (PT) of the deposition process, and
• the equation is modified by using exponentially weighted moving averages (EWMA), such that
• yk=THKk+ck|k−1+ek,
• where, THKk=PTk[β0+β1(Vpp)+β2(TUNE)] denotes the estimated deposition thickness of a kth substrate;
• β0, β1, and β2 denote values that reflect a variation in the process factors over time, ck|k−1 denotes a deviation of the estimated deposition thickness of the k-th substrate based on deviations of the estimated deposition thickness, and a measured deposited thickness of a (k−1)-th substrate and the measured deposited thickness;
• ek denotes a theoretical error term of the equation;
• and yk denotes the modified estimated deposition thickness of the k-th substrate.

A method of modeling a deposition thickness of amorphous silicon being deposited on a substrate in real time, the method comprising:

• estimating a deposition thickness of the amorphous silicon being deposited on the substrate by using an equation expressing a relationship between the deposition thickness and a plurality of process factors of a deposition apparatus used during the deposition of the amorphous silicon;
• measuring a deposited thickness of the amorphous silicon over a designated sheet interval and comparing the measured deposited thickness with the estimated deposition thickness to generate a difference data;
• and
• modifying the equation with additional terms for the equation based on the generated difference data so that subsequent difference data is within a predetermined range, wherein:
• the plurality of process factors include a radio frequency power (RF power Vpp) of the deposition apparatus in depositing the amorphous silicon and manufacturing the substrate, a TUNE that is an impedance control factor of a power source that supplies power to the deposition apparatus during the deposition process, and a process time (PT) of the deposition process, and
• the equation is modified by using a Kalman filter, such that
• {circumflex over (x)}k+1=Ak{circumflex over (x)}k+AkKk[{tilde over (y)}k−Ck{circumflex over (x)}k],
• where, {tilde over (y)}k denotes the measured deposited thickness, {circumflex over (x)}k denotes a statistical estimate value of the status xk=[β0 β1 β2]T, {circumflex over (x)}k+1 denote a statistical estimate value of XK+1;
• C
• k
• =
• PT
• k
• ⁡
• [
• 1
• Vpp
• k
• TUNE
• k
• ]
• ,
• A
• k
• =
• [
• 1
• 0
• 0
• 0
• 1
• 0
• 0
• 0
• 1
• ]
• ;
• and Kk denotes a Kalman gain.

An apparatus to model a deposition thickness of amorphous silicon being deposited on a substrate in real time, the apparatus comprising:

• a predictor to estimate a deposition thickness of the amorphous silicon being deposited on the substrate by using an equation expressing a relationship between the deposition thickness and a plurality of process factors of a deposition apparatus used during the deposition of the amorphous silicon;
• a measurer to measure a deposited thickness of the amorphous silicon over a designated sheet interval for use in comparing the measured deposited thickness with the estimated deposition thickness to generate a difference data;
• and
• an adapter to modify the equation with additional terms for the equation based on the generated difference data so that subsequent difference data is within a predetermined range, wherein:
• the plurality of process factors include a radio frequency power (RF power Vpp) of the deposition apparatus in depositing the amorphous silicon and manufacturing the substrate, a TUNE that is an impedance control factor of a power source that supplies power to the deposition apparatus during the deposition process, and a process time (PT) of the deposition process, and
• the equation is modified by using exponentially weighted moving averages (EWMA), such that
• yk=THKk+ck|k−1+ek,
• where, THKk=PTk[β0+β1(Vpp)+β2(TUNE)] denotes the estimated deposition thickness of a kth substrate;
• β0, β1, and β2 denote values that reflect a variation in the process factors over time, ck|k−1 denotes a deviation of the estimated deposition thickness of the k-th substrate based on deviations of the estimated deposition thickness, and a measured deposited thickness of a (k−1)-th substrate and the measured deposited thickness;
• ek denotes a theoretical error term of the equation;
• and yk denotes the modified estimated deposition thickness of the k-th substrate.

An apparatus to model a deposition thickness of amorphous silicon being deposited on a substrate in real time, the apparatus comprising:

• a predictor to estimate a deposition thickness of the amorphous silicon being deposited on the substrate by using an equation expressing a relationship between the deposition thickness and a plurality of process factors of a deposition apparatus used during the deposition of the amorphous silicon;
• a measurer to measure a deposited thickness of the amorphous silicon over a designated sheet interval for use in comparing the measured deposited thickness with the estimated deposition thickness to generate a difference data;
• and
• an adapter to modify the equation with additional terms for the equation based on the generated difference data so that subsequent difference data is within a predetermined range, wherein:
• the plurality of process factors include a radio frequency power (RF power Vpp) of the deposition apparatus in depositing the amorphous silicon and manufacturing the substrate, a TUNE that is an impedance control factor of a power source that supplies power to the deposition apparatus during the deposition process, and a process time (PT) of the deposition process, and
• the equation is modified by using a Kalman filter, such that
• {circumflex over (x)}k+1=Ak{circumflex over (x)}k+AkKk[{tilde over (y)}k−Ck{circumflex over (x)}k],
• where, {tilde over (y)}k denotes the measured deposited thickness, {circumflex over (x)}k denotes a statistical estimate value of the status xk=[β0 β1 β2]T, {circumflex over (x)}k+1 denote a statistical estimate value of XK+1;
• C
• k
• =
• PT
• k
• ⁡
• [
• 1
• Vpp
• k
• TUNE
• k
• ]
• ,
• A
• k
• =
• [
• 1
• 0
• 0
• 0
• 1
• 0
• 0
• 0
• 1
• ]
• ;
• and Kk denotes a Kalman gain.