Carrier-resolved hall measurement with multi-harmonic magnetoresistance analysis

A system for semiconductor characterization, comprising:

• a memory;
• and
• a processor communicatively coupled to the memory, wherein the processor is configured to perform a method comprising:
• directing a testing module to adjust orientations of dipole line magnets to apply a magnetic field parallel to a sample comprising a first channel and a second channel;
• receiving, from the testing module, first longitudinal and transverse magnetoresistance measurements of the sample in the magnetic field parallel to the sample;
• directing the testing module to adjust the orientations of the dipole line magnets to apply a magnetic field perpendicular to the sample;
• receiving, from the testing module, second longitudinal and transverse magnetoresistance measurements of the sample in the magnetic field perpendicular to the sample;
• subtracting the first longitudinal and transverse magnetoresistance measurements from the second longitudinal and transverse magnetoresistance measurements, respectively, to obtain a longitudinal magnetoresistance value Rxx and a transverse magnetoresistance value Rxy, wherein the longitudinal magnetoresistance value Rxx and the transverse magnetoresistance value Rxy are measures of magnetoresistance due to Lorentz force;
• and
• determining, based on the longitudinal magnetoresistance value Rxx and the transverse magnetoresistance value Rxy, harmonic magnetoresistance coefficients a0, a2, b1, and b3.

A computer program product for semiconductor characterization, the computer program product comprising a computer readable storage medium having program instructions embodied therewith, the program instructions executable by a processor to cause a device to perform a method comprising:

• directing a testing module to adjust orientations of dipole line magnets to generate a magnetic field parallel to a sample comprising a first channel and a second channel;
• receiving, from the testing module, first longitudinal and transverse magnetoresistance measurements of the sample in the magnetic field parallel to;
• receiving, from the testing module, second longitudinal and transverse magnetoresistance measurements of the sample in the magnetic field perpendicular to the sample;
• subtracting the first longitudinal and transverse magnetoresistance measurements from the second longitudinal and transverse magnetoresistance measurements, respectively, to obtain a longitudinal magnetoresistance value Rxx and a transverse magnetoresistance value Rxy, wherein the longitudinal magnetoresistance value Rxx and the transverse magnetoresistance value Rxy are measures of magnetoresistance due to Lorentz force;
• and
• determining, based on the longitudinal magnetoresistance value Rxx and the transverse magnetoresistance value Rxy, harmonic magnetoresistance coefficients a0, a2, b1, and b3 of charge carriers in the sample.

A method of semiconductor testing and characterization, comprising:

• obtaining a sample comprising a first channel and a second channel;
• directing a testing module to adjust orientations of dipole line magnets to apply a magnetic field parallel to a sample comprising a first channel and a second channel;
• measuring, in a magnetic field parallel to the sample, a first longitudinal magnetoresistance and a first transverse magnetoresistance of the sample;
• directing the testing module to adjust the orientations of the dipole line magnets to apply a magnetic field perpendicular to the sample;
• measuring, in a magnetic field perpendicular to the sample, a second longitudinal magnetoresistance and a second transverse magnetoresistance of the sample;
• calculating, by a processor communicatively coupled to a memory, longitudinal and transverse magnetoresistance values Rxx and Rxy, wherein the calculating comprises subtracting the first longitudinal magnetoresistance and the first transverse magnetoresistance from the second longitudinal magnetoresistance and the second transverse magnetoresistance, and wherein the longitudinal magnetoresistance value Rxx and the transverse magnetoresistance value Rx are measures of magnetoresistance due to Lorentz force;
• and
• determining, based on the longitudinal magnetoresistance value Rx and the transverse magnetoresistance value Rxy, harmonic magnetoresistance coefficients ao, as, bi, and b3.

A system for semiconductor testing and characterization, comprising:

• a testing module, the testing module comprising dipole-line magnets;
• and
• a processor communicatively coupled to a memory, wherein the processor is configured to carry out a method comprising:
• applying, using the dipole-line magnets, a magnetic field parallel to a sample in the testing module;
• measuring, by the testing module and in the magnetic field parallel to the sample, a first longitudinal magnetoresistance and a first transverse magnetoresistance of the sample;
• applying, using the dipole-line magnets, a magnetic field perpendicular to the sample in the testing module;
• measuring, by the testing module and in the magnetic field perpendicular to the sample, a second longitudinal magnetoresistance and a second transverse magnetoresistance of the sample;
• subtracting the first longitudinal magnetoresistance and the first transverse magnetoresistance from the second longitudinal magnetoresistance and the second transverse magnetoresistance to obtain longitudinal and transverse magnetoresistance values Rxx and Rxy, wherein the longitudinal magnetoresistance value Rxx and the transverse magnetoresistance value Rxy are measures of magnetoresistance due to Lorentz force;
• and
• determining, based on the longitudinal magnetoresistance value Rxx and the transverse magnetoresistance value Rxy, harmonic magnetoresistance coefficients a0, a2, b1, and b3.