Systems and methods for high precision optical characterization of carrier transport properties in semiconductor manufacturing

A method of augmenting a training set, comprising:

• obtaining an analytic parametrization for a Z dependence of a PMR signal from a semiconductor sample, wherein the analytic parametrization is based on values of at least one electronic transport property of the sample;
• using the analytic parametrization to generate one or more Z-scan PMR data profiles corresponding to one or more different values of the at least one electronic transport property of the sample;
• and
• including the one or more Z-scan PMR profiles in the training set.

A method of establishing a physics-informed neural network, comprising:

• obtaining an analytic parametrization for a Z dependence of a PMR signal from a sample, wherein the analytic parametrization is based on values of at least one electronic transport property of the sample;
• using the analytic parametrization to form a physics-informed penalty term that relates a Z dependence of a PMR signal from a sample to at least one electronic transport property of the sample;
• adding the physics-informed penalty term to an error function to be minimized by a machine learning algorithm to form a physics-informed error function;
• training the neural network using the physics-informed error function.

A method of establishing a physics-informed neural network, comprising:

• obtaining an analytic parameterization representing complex input data in terms of a complex variable, wherein the complex variable is defined in terms of at least one target output value;
• using the Cauchy-Riemann relations to form a pair of penalty terms relating derivatives of the complex input data with respect to the at least one target output value;
• adding the pair of penalty terms to an error function to be minimized by a machine learning algorithm to form a physics-informed error function;
• training the neural network using the physics-informed error function.

A method for controlling a semiconductor process tool, the method executed by a computer and comprising:

• establishing a machine learning based process control model that correlates sensor data from the semiconductor process tool with one or more electronic transport properties of a semiconductor wafer processed by the process tool;
• receiving sensor data from the semiconductor process tool;
• using the process control model to predict, from the received sensor data, one or more electronic transport properties of a semiconductor wafer processed by the process tool;
• receiving one or more ground truth electronic transport properties of the semiconductor wafer processed by the process tool, wherein said one or more ground truth electronic transport properties have been determined using one or more Z-scan PMR data profiles acquired from the semiconductor wafer processed by the process tool;
• comparing the one or more ground truth electronic transport properties with the one or more predicted electronic transport properties;
• and
• using the process control model to update operational settings of the process tool for wafers to be processed to minimize wafer-to-wafer variability of electronic transport properties.

A method for controlling a semiconductor manufacturing process, the method executed by a computer and comprising:

• establishing a machine learning based process control model that correlates the yield of the semiconductor manufacturing process with one or more sample electronic transport properties present at one or more points in the manufacturing process;
• receiving one or more sample electronic transport properties present at one or more points in the manufacturing process, wherein said one or more sample electronic transport properties have been determined or predicted from one or more acquired Z-scan PMR data profiles;
• using the process control model to obtain one or more outputs indicative of the yield of the semiconductor manufacturing process;
• and
• using the process control model to update one or more processing conditions to maximize the predicted yield of the semiconductor manufacturing process.