Doped silicon

Infrared analysis of charge carriers in doped semiconductors

A classical example of optical product control is the determination of carrier concentrations in doped semiconductors. In case of high doping levels the wafers to be inspected can be considered as optically thick (halfspace model). In this case the infrared reflectivity depends on the concentration and damping of the charge carriers only:

A simple Drude model with two parameters (plasma freqency and damping constant) to adjust will do an excellent job in most cases. The follwing picture shows the simulation in blue and the measured data (doped silicon wafer) in red:

The dielectric function obtained from the parameter fit looks like this (blue: real part, red: imaginary part):

From the dielectric function parameters plasma frequency and damping constant that are obtained by the fit one can calculate the carrier concentration and the resistivity. The values for the given example are 1.06×10²⁰ cm^-3 and 1.74 mWcm, respectively.

SCOUT_98 users: This example is available as configuration file that you can download

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