[Paper Review] Precise Optical Measurement of Carrier Mobilities Using Z-scanning Laser Photoreflectance

Will Chism|arXiv (Cornell University)|Oct 30, 2017

Silicon and Solar Cell Technologies6 references3 citations

TL;DR

This paper presents a Z-scanning laser photoreflectance technique that enables precise, nondestructive measurement of carrier mobility in semiconductors by analyzing the Z-dependent modulated reflectance signal from a tightly focused Gaussian laser beam. By fitting the amplitude and phase of the signal to analytic expressions involving diffusion length and recombination lifetime, the Einstein relation yields mobility with sub-2% uncertainty, demonstrating high precision for process monitoring in semiconductor manufacturing.

ABSTRACT

A simple yet precise optical technique for measuring the ambipolar carrier mobility in semiconductors is presented. Using tightly focused Gaussian laser beams in a photo-reflectance system, the modulated reflectance signal is measured as a function of the Z (longitudinal) displacement of the sample from focus. The modulated component of the reflected probe beam is a Gaussian beam with its profile determined by the focal parameters and the complex diffusion length. The reflected probe beam is collected and input to the detector, thereby integrating over the radial profile of the beam. This results in analytic expressions for the Z dependence of the signal in terms of diffusion length and recombination lifetime. Best fit values for the diffusion length and recombination lifetime are obtained via an iterative fitting procedure. The output diffusion lengths and recombination lifetimes and their estimated uncertainties are combined according to the Einstein relation to yield the mobility and its uncertainty.

Motivation & Objective

• To develop a simple yet highly precise optical technique for measuring ambipolar carrier mobility in semiconductors without destructive testing.
• To enable in-line, nondestructive monitoring of carrier mobility during semiconductor processing steps.
• To simultaneously extract diffusion length and recombination lifetime from Z-scan photoreflectance data using analytical models.
• To achieve sub-2% uncertainty in mobility measurements via iterative fitting and error propagation.
• To validate the method using silicon samples with controlled process variations, including amorphizing implantation and flash annealing.

Proposed method

• The technique uses co-focused, tightly confined Gaussian laser beams for pump and probe in a photo-reflectance system.
• The sample is scanned along the Z-axis (longitudinal direction) through the beam focus, and the modulated reflectance signal is measured as a function of Z.
• The radial integration of the reflected probe beam yields analytic expressions for the Z-dependent amplitude and phase of the signal in terms of diffusion length and recombination lifetime.
• Nonlinear fitting of experimental Z-scan data to these expressions extracts diffusion length and recombination lifetime with statistical uncertainty estimates.
• Mobility is calculated from the Einstein relation μ = qD/kBT, where D = Ld²/τ, using the fitted Ld and τ values.
• Measurement uncertainty is propagated through the fitting and Einstein relation to yield uncertainty in mobility.

Experimental results

Research questions

• RQ1 Can Z-scanning laser photoreflectance provide a precise, nondestructive method for measuring carrier mobility in semiconductors?
• RQ2 To what extent can diffusion length and recombination lifetime be simultaneously extracted from Z-scan LPR data with high accuracy?
• RQ3 What is the achievable uncertainty in mobility measurements using this technique?
• RQ4 How do process variations such as amorphizing implantation and flash annealing affect the extracted carrier parameters?
• RQ5 Can the method reliably detect changes in carrier mobility due to process-induced damage and recovery?

Key findings

• The technique achieves a measurement uncertainty in carrier mobility of less than 2% across all tested samples, demonstrating high precision.
• Amorphizing implantation (AI) reduces the diffusion length from ~6.07 μm to ~5.06 μm and shortens the recombination lifetime, consistent with increased defect density.
• Repeating the 1300°C/550°C flash anneal increases the diffusion length by ~1.5× and boosts mobility from ~157 to ~382 cm²/V·s.
• Raising the flash anneal temperature to 600°C increases the recombination lifetime by ~10% and mobility by ~10%, indicating improved defect removal.
• The 1350°C/600°C flash anneal further increases mobility to 312 cm²/V·s, with a 11.68 μm diffusion length, showing near-complete recovery of carrier properties.
• Measured mobilities agree with values expected from activated doping levels, validating the method’s accuracy and reliability.