Reflectometry


Reflectometry is a technique which relies on the local change of reflection coefficient in a heated sample. In such, requirements on sample surface finish place conditions on what pretreatment may be required. The technique is more complex than direct IR radiometry in that in addition to a modulated source it requires a probe beam, which is reflected off of the sample surface. The relative change of the sample reflectance due to the temperature change in the typical linear case is given by
Delta R/R=(1/R)(dR/dT)Delta T
The temperature coefficient dR/dT depends on probe wavelength and the sample material. By comparing with known values, and measuring Delta R/R, typically on the order of 10-6, we can deduce Delta T , the temperature variation, which is on the order of 10-2. This carries information about the local temperature parameters of the sample such as the thermal diffusivity D. This heated interaction volume can vary with pulsation variation, and is shown right.

With this method we may draw a temperature map on a micronic scale, and so analyze complicated samples such as laser diode facets and electronic devices. We may also measure thermal diffusivity on a microscopic scale in granulated samples such as AlN and Al2O3 or thermal barriers in Fe sintered samples. Our experimental setup is built up under an optical microscope, with a dichroic mirror inserted to direct the incoming pump laser (typically an Ar+) down onto the sample, which is mounted on a computerized translation stage. The probe beam, typically a visible diode laser, traverses the microscope optical chain, and is reflected back through the microscope, and directed by a beam splitter onto a photodiode. In order to optimize thermal map resolution, modulation frequencies upto a few MHz are used. A diagram of the experimental setup is shown on the left.

Thermal properties may be mapped out by carrying out the measurement over a grid of points on the sample surface. As the optical characteristics of the sample are important for the reflection of the probe beam, the geometry may be changed slightly to provide scanning of the pump beam. In this way, the sample surface need be prepared only at the probe location.









A measurement on a gold sample with a scratch is shown below. On the left, the scratch is clearly visible in the the reflectance values. On the right, the phase pattern, related to the spherical shape of the heating spot is shown as a contour plot, with equally spaced circles corresponding to equal phase increments. The graduations, visible on the edges of the plots, are in micrometers.

Furthermore, nonlinear effects such as temperature dependance of the thermal diffusivity or additional effects such as free photocreated carrier diffusion may be studied by including their influence in the reflectance equation. For instance, should we wish to study the influence of carriers (electron or hole) in silicon samples, we include a term for the change of carrier density vis:


Delta R/R=(1/R)(dR/dT)Delta T+(1/R)(dR/dN)Delta N
The carrier density, inferred from the carrier diffusion equation, which can be solved in the same way as the thermal diffusion equation, acts as a source term in the heat diffusion equation. Typical values of the contributions are dR/dT=10-4 and dR/dN=10-7 and we note that a 180° phase difference is to be expected in the contribution of these two terms. With this method, the level of implantation has been determined in different samples, and electronic diffusivity coefficients determined unambiguously.
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