Band Edge Thermometry

A relatively recent advance in non-contact thermometry of semiconductors uses the established temperature dependence of the band edge, given by the Varshni equation:

, (3.5) Reconstruction B In ci d e n t g ro u p V flu x Substrate temperature Reconstruction A

where Eg(T) denotes the band gap at temperature T, Eg(0) is the band gap at 0K and

and are constants specific to the sample.13 This equation shows that the reduction in band gap changes from being proportional to T2 atlow temperatures to a linear trend with T at higher temperature.14

The device is a wide band infrared spectrophotometer and software processing package, which scans a range of wavelengths in order to calculate a value for the onset of the band edge. Using known values α and β for the wafer under investigation, equation (3.5) is to determine the temperature. The values of α and β are obtained from temperature measurements with a thermocouple placed between wafers of the material subject to calibration.* While the technique may generally be referred to as band edge thermometry, it may also be named more specifically as diffuse reflectance spectroscopy or infrared transmission thermometry, depending on the mode in which it operates, as shown in Figure 3.4.15 For the former implementation, a light source irradiates the sample and the characteristic absorption profile is deduced from the reflected signal. In transmission mode, broadband radiation from behind the substrate (either from a fibre optic light-pipe, or the heater) is collected at the detector, permitting the spectral absorption of the sample to be obtained. In some respects, the reflection geometry is preferable to transmission measurements, as the signal cannot be attenuated by increasing deposition thickness and is more likely to provide a temperature value that has a lesser degree of coupling to the characteristics of the substrate. Where there are no viewports to allow illumination of the wafer face, a period of downtime is required, which means venting the growth chamber to atmospheric pressure, followed by time for baking

the system, as well as time to accommodate viewport installation. This procedure also introduces the risk of contamination to the growth chamber and material sources and is conducted as infrequently as possible.

Figure 3.4: A series of simplified schematic representations depicting the operating modes offered by use of a broadband spectrophotometer. Whether or not heater radiation is detected in any case, it is possible to restrict the bands detected to exclude undesirable signals.

In some circumstances, a band gap is not accessible within the dynamic range of the instrument, or it may be obscured by the absorption profile of a grown layer. The spectrophotometer can perform as a multi-colour pyrometer, by measuring the intensity of incident radiation and obtaining a value for the temperature as described by (3.4). Due to the large bandwidth of such equipment in comparison with pyrometer detection bands, the regions used to calculate the grey body curve characteristics can better defined, to give a more accurate determination of the

Sample Detector Infrared transmission thermometry Diffuse reflectance spectroscopy Pyrometry Heater Heater Heater

temperature. This method of operation is dependent upon a sufficient wavelength range of the grey body signal of the substrate falling within the spectral band of the spectrophotometer, but overcomes the problems suffered by single and dual colour pyrometers at low temperatures. It also allows the filtering out wavelength bands in which the sample is transparent to heater radiation and permits interpolation in these regions to calculate a more accurate temperature. Furthermore, with correct calibration, the contribution of stray light sources may be eliminated from calculation of the temperature, although care must be taken where sample rotation is employed, as there is the potential to induce a periodic variation in detected radiation.

Further details about how such systems calculate the temperature are difficult to ascertain, due to their proprietary nature. However, it is evident that in an accurate temperature determination system, there must be some compensation for emissivity, for example using the relationship between absorptivity and emissivity as given by Kirchhoff’s law:

A( ) = ( ), (3.6)

where A is the absorptivity with respect to incident radiation of frequency . There must also be a standard point of band edge determination, which is complicated by the presence of the band tail (Figure 3.5).

Figure 3.5: Representation of the absorption profile of a semiconductor in the region of the band edge. The band tail makes a definitive value for the band edge difficult to obtain, although a linear extrapolation (dashed line) may be employed to provide a more consistent value.

Using linear extrapolation of the above to zero absorption to obtain an energy value is one way in which this may be achieved, although literature reports indicate that first (and higher) order derivatives may also be employed.6,8

While such systems offer three methods by which temperature is determined, this flexibility is reflected in the cost and, due to the limitations described above, do not provide a universal solution to the issue of temperature determination.