Normatividad de los protocolos de comunicación en los vehículos ligeros y

An optical pyrometer detects incident radiation within one or more wavelength bands. Pyrometry as a means of non-contact temperature measurement is based upon the Stefan-Boltzmann law, which states that the energy flux density, j*, emitted by an object is related to the temperature, T, by the relationship

j*= T4, (3.1)

where is the Stefan-Boltzmann constant. The frequency distribution of radiation of j* is given by Planck’s law of black-body radiation:

(3.2)

where is the frequency of emitted radiation, T is the temperature of the black body, h denotes Planck’s constant, c represents the speed of light and kB is the Boltzmann

Figure 3.1: Simulations of the energy distributions of a black body at 300 K, 500 K and 1000 K. The maximum of each peak decreases in both intensity and energy, shifting to shorter wavelengths as the temperature increases.

Eq. (3.1) applies only to perfect black-bodies. The factor differentiating the theoretical behaviour of a black body from the emission characteristics of a real entity is the emissivity. Defined as the ratio of energy emitted by an object compared to that emitted by a black body at the same temperature, the emissivity is given as

(3.3)

where and denote the energy flux densities at a frequency and temperature T, for an object and black-body respectively. Since the black-body is a theoretical construct that exhibits perfect emission ( = 1), values for the emissivity of real objects necessarily fall within the range 0 < < 1. For practical applications,

0 5000 10000 15000 20000 25000 300 K 500 K 1000 K Int ens ity [ arb. unit s] Wavelength [nm]

the grey body case may be used, with insertion of the fractional emissivity coefficient into eq. (3.1):

j*= T4 (3.4)

On this basis, pyrometers may be used to calculate the temperature from the intensity of the radiation measured over a narrow range of wavelengths (such as the single colour pyrometer), or take ratios of intensities measured over two or more bands, allowing the radiation profile to be better established.

Figure 3.2: Viewing the simulations from Figure 3.1 with a log y-axis for clarity, the difference in intensities emitted by a black body at a selection of temperatures in the spectral range of the pyrometer (hatched) is evident.

Due to the combination of the fixed wavelength band(s) used by these instruments and the profile of Planck’s distribution, there are finite ranges of temperature that may be evaluated with any degree of accuracy. For the Modline 3V pyrometer used in this study ( = 0.91-0.97 m), the intensity of radiation emitted in the detected region decreases by approximately six orders of magnitude as the temperature decreases from 1000 K to 500 K (Figure 3.2).

It is evident that a single colour pyrometer operating in this region will be adversely affected, if the incident radiation in this region falls sufficiently low that instrument sensitivity or signal-to-noise ratio become limiting factors. Readings from instruments using two bands will also be affected, should either band coincide with a region where this is the case.

The Modline 3V pyrometer was selected for use on the GEN II apparatus, as its spectral range was designed to permit temperature measurements on GaAs substrates. GaAs is transparent to infrared radiation in the 0.91-0.97 µm range at room temperature, but the energy of the GaAs band edge decreases sufficiently with an increase in temperature that it becomes opaque in the operating wavelength range above ca. 400°C. This is discussed further in section (3.1.1.4). In addition, given the lower band gaps of both GaSb and InSb in comparison to GaAs, the Modline 3V apparatus was considered a suitable choice of instrument for this investigation.

Even within the ideal operating range, these modes of operation can both be greatly affected by a number of factors, including variation of window transmittance over the spectral ranges sampled, variation of emissivity as a function of time, which occurs during epitaxial growth and deposited species on the pyrometer viewport.

The last factor has been observed in the GEN II instrument, with differences in temperatures found to be caused by the absorption of radiation in the region measured by the pyrometer.7

Additional issues may arise from assuming is constant, rather than a function of thickness, wavelength, angle of emission, structural morphology, chemical composition and temperature.8

Problems may also occur if the pyrometer operates in a region in which the substrate is not optically opaque. This is caused by the band gap of a semiconductor wafer being at a shorter wavelength than one or both of the pyrometer bands, and results in the transmission of a proportion of the radiation from the substrate heater, or from the sample platen.7 This occurs more frequently in long-wavelength pyrometers, which have a larger intensity signal at low photon energies and permit lower temperatures to be determined. The detection of radiation not originating from the sample also means that reflections emanating from the cell heaters, for example, cause variations in the measured temperature.9

Despite these problems, pyrometry is a technique that is simple to set up, allows rapid acquisition of a temperature value, allows a “hot-swap” capability for changing detectors, and permits real-time monitoring of the infrared signal received. In addition, where adverse factors may be systematically eliminated or remain constant, it is possible to achieve reproducible growth even if the temperatures recorded may not be readily transferred between experimental equipment.