Thermal Grating NDE
Thermal Diffusivity Measurement of Semiconductors using Transient Surface Grating
Management and Computer Sciences,
ABSTRACT
Remote sensing optical techniques are finding increasing applications in material characterization and non-destructive evaluation (NDE). This paper describes a new laser induced transient surface grating (TSG) technique specifically designed for thermal diffusivity measurements of condensed materials. Thermal diffusivity measurements of Ge and Si using this technique are reported for the first time in this paper.
Keywords: NDE, TSG, LIG, Reflecting geometry, Thermal diffusivity.
1. INTRODUCTION
Laser Induced Grating (LIG) techniques have been used to study material properties, especially semiconductor charge carrier recombination dynamics, including thermal and acoustic parameters since mid 1970's1. Until recently, however; such experiments used transmission geometries, which restricted their application to transparent samples of high optical quality. The innovation of surface reflecting sensing from opaque samples2-5 obviates the need for high optical quality and allows measurements to be made without access to both sides of the sample, thus widening very considerably the range of materials and sample geometries that can be studied. The surface specificity of this approach6 makes the technique potentially suitable for studying thin films and near surface phenomena in isolated slabs, thus addressing important industrial material evaluation needs.
2. THEORY
TSG technique uses two pulsed, intersecting, coherent pump beams to produce interference bands of low and high irradiance on the surface of the sample. This causes a diffraction grating pattern of thermal expansion as shown in Figure 1, and modulated reflectance to be produced. The line spacing L, depends on the wavelength lex of the excitation laser and the semi-angle of inclination q, between the interfering beams7:
(1)
The decay of the grating is sensed by measuring the intensity of a CW He-Ne laser beam. The Intensity I of the 1st order diffracted signal which is proportional to the square of the grating amplitude is given by8:
(2)
Where t is the characteristic decay time,
(3)
From which the thermal diffusivity D can be calculated.
Figure 1. Thermo-elastically deform surface.
3. EXPERIMENTAL ARRANGEMENTS
Schematic diagram of experimental set-up is shown in Figure 2. A Spectron Q-switched Nd:YAG pump laser, with pulses of »15 ns duration at a wavelength of 532 nm and with a repetition frequency of 3 Hz is used. The output of Nd:YAG laser is split and recombined onto the sample surface using a Mach-Zehnder interferometer, consisting of two beam splitters BSI and BS2 and two mirrors Ml and M2. An apertured pump beam of » 6rnrn diameter is used without focusing, in order to minimize the risk of surface damage. The use of beam splitter BS2 for recombining the excitation beam, in place of conventionally used mirror or prism, allows very small beam inclinations to be produced in a compact optical geometry. The grating spacing L can be varied between 5mm to I00 mm by precisely controlled adjustments of the positions and inclinations of mirrors M1 and M2. TSG is probed by diffraction of a CW He-Ne laser beam of »3rnrn diameter and 633nrn wavelength.
The area probed is wholly within the area pumped by the Nd: YAG laser, in order to reduce measurement errors arising from surface temperature gradients other than those associated with the transient grating itself. Its expanded diameter gives a high sensitivity and angular resolution by diffracting from a large number of grating lines. Diffracted light (signal) is collected by means of a telescope of 30 rnm focal length, fitted with 633 nm interference filter, to reject excitation radiation and ambient light, and focused on to a 200mm diameter optical fiber of 8m length, which guides the signal to a photomultiplier tube. This arrangement provides excellent rejection of light scattered from less than optically perfect sample surfaces, whilst substantially reducing signal distortion due to electromagnetic (RF) interference from the YAG laser by separating it from the photomultiplier.
The telescope is mounted on a sturdy radius arm fitted to a precision rotational stage designed to give rapid alignment of the detector with the 1st order diffracted probe beam. Transient signals are finally captured in a digital oscilloscope (HP54510A) interfaced with a PC via IEEE-488 link, for real time signal averaging, analysis and display.
Figure 2. Schematic diagram of TSG experimental set-up.
PC
Digital
Oscilloscope
Photo-
multiplier
Laser Power Supply
Q-Swithed
Nd:YAG Laser
Telescope
Sample
BD
HeNe Laser
Optical Fiber Link
BS2
BS1
M1
M2
4. RESULTS
Two samples of semiconductors selected for thermal diffusivity measurement were 99.99% pure Germanium and 99.95% pure Silicon. The Germanium sample was in the form of a circular disk of 20 mm diameter with a thickness of 1.1mm. Whereas the sample of Silicon was also in the form of a circular wafer having diameter and thickness of »30 mm and » 0.3 mm respectively. Each sample had one polished face with a high quality mirror finish and flatness » l/2. Both the samples were excited at 532 nm pump wavelength using average fluences 89 J/m2 and 110 J/m2 respectively. Transients were recorded using six values of grating spacing L » 20 - 65 mm and »15 - 50 mm for Germanium and Silicon respectively.
Thermal diffusivity measurements were performed at room temperature by observing transient grating decays over a range of grating spacing. Grating spacing were measured using microscopic examination of sacrificial samples of floppy disk, onto which grating patterns had been ablated at high excitation fluence. Fig. 3 shows a similar grating pattern ablated on Silicon wafer.
Figure 3. Photograph of permanent grating etched in Si using a single shot of excitation laser beam with l = 532 nm and fluence = 229J/m2.
A typical analysis is illustrated in Fig. 4. The overall fit was judged satisfactory. The deviation in the residuals near the peak of the signal is thought to be caused by the finite response speed of the apparatus, principally the laser pulse. Thermal diffusivities were measured from the gradients of the best fit straight lines shown in Fig. 5 using the non linear least squares method, to yield characteristic decay times and a test of appropriateness of the exponential model.
Figure 4. Analysis of data of Ge using non-linear least square fitting. Random distribution of the residual verifies the exponential decay.
Figure 6. Analysis of data obtained from 99.99% pure Ge using the single exponential model to illustrate the precision of measurement achieved and the excellence of the model through the direct proportionality between the fitted time and the square of the grating spacing. (Solid line best fit for our results and dotted line for recommended values)
Figure 5. Analysis of data obtained from Ge and Si using the single exponential model. (Solid line for Si and dotted line for Ge)
Thermal diffusivities thus determined are compared with recommended values9 in table-1. Both Ge and Si show pronounced oscillations superimposed on the underlying exponential decay. A typical measurement in Germanium illustrating these oscillations is shown in Figure 7.
Table-1
Sample |
|
Germanium |
0.32±0.01 |
0.35 |
Silicon |
0.8±0.01 |
0.88 |
5. CONCLUSIONS
Observations on semiconductors (Ge & Si) and the results presented here show that the pump beam energy is predominantly converted to heat with evidence of an acoustic effect not previously reported, namely the excitation of coherent standing acoustic waves in the air above the probed surface manifested as oscillations superimposed on the thermal decay10. However, the measured results of thermal diffusivities for Ge and Si were found within 6 to 8% less than the recommended values and illustrate the potential of the technique for precision thermal diffusivity measurements.
Figure 7. A typical response of Ge at L = 47.6 mm showing a pronounced oscillation superimposed on the exponential decay.
REFERENCES
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[7] Smith F.G. 1. and Thomson H., Optics, 1. Wiley & Sons Ltd. London 55, (1971).
[8] Vaitkus Yu, Gaubas E. and Yrashyunas K., Sov, Phys. Solid state 20(10), 1824, (1978)
[9] Touloukian Y. S., Powell R. W., Ho C. Y., and Nicolaou M. C. Thermal Diffusivity, Thermophysical properties of matter 10 (1973)
[10] Alam M., PhD thesis, University of Strathclyde Glasgow, Scotland (1994)
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