R. Johnson, M. Beaudoin, M. Boonzaayer, E. Grassi, and Y.-H. Zhang
Center for Solid State Electronics Research
Department of Electrical Engineering
Arizona State University
Tempe, AZ 85287-6206
Figure 1. The position of the spectrum and hence substrate temperature is given by the intersection of the asymptotes of the knee region of the spectrum. The knee region is shown by the solid dots.
The sensitivity of material properties to growth temperature means that an accurate and reliable method for measuring substrate temperature is essential during epitaxial growth. Recently, optical methods have been developed that overcome some of the limitations of thermocouples and pyrometers [1-3]. Pyrometry for example, does not work at low temperatures, is affected by surface roughness, window coating, and substrate emissivity changes during growth. Since both rotating and radiatively heated substrates are preferred during epitaxial growth, physical contact between the substrate and the temperature sensor is not practical. Therefore, thermocouples are radiatively coupled to the substrate and typically have a large temperature offset compared to the substrate. This offset depends on the substrate and heater temperatures, the substrate doping level and type, the back surface texture of the substrate, and the changing absorptance and emittance of the epilayer during growth.
In these new optical methods, substrate temperature is inferred from the onset of transparency of the substrate itself. The band edge of III-V semiconductors (which cuts off exponentially) broadens and shifts to lower energies with temperature . In practice, substrate temperature is inferred from the spectral position of various points in the diffuse reflectance spectrum  or transmission spectrum [2,3]. The onset of transparency of a 350 µm thick InP:Fe substrate is shown in Figure 1. Here, the onset of transparency (or position of the spectrum) is defined as the intersection of the background signal with a linear extrapolation through the steepest part of the spectrum.
Figure 2. Schematic of the nested proportional-integral-derivative (PID) control loop used to control substrate temperature.
The nested loop shown in Figure 2 is a convenient way to add an accurate external temperature sensor to the conventional Eurotherm-thermocouple control loop found in molecular beam epitaxy systems. In this case, the outer control loop updates the Eurotherm (thermocouple) setpoint based on the difference between the user setpoint and the value measured by the external sensor, using a proportional-integral-derivative (PID) algorithm implemented in the control software. This method has the advantage that the Eurotherm-thermocouple control system is left intact.
The Eurotherm-thermocouple (inner) loop primarily controls the heating element and is limited in its ability to detect and control true temperature of the substrate. This inability also means that the Eurotherm-thermocouple control loop only partially rejects external disturbances, such as the thermal-shutter transients that occur at the substrate when effusion cell shutters are toggled. In this control scheme, the outer loop periodically updates the thermocouple setpoint, causing the Eurotherm control loop to bring substrate temperature back in line with its target value. For example, during the growth of absorbing overlayers, radiatively heated substrates are known to heat up dramatically. This occurs under either constant heater power or constant thermocouple temperature. Under these growth conditions, it is imperative that one has an alternative non- contact method of determining substrate temperature, such as, diffuse reflectance spectroscopy (DRS).
Figure 3. Real-time control of substrate temperature during the growth of lattice-matched InGaAs on semi-insulating InP, using diffuse reflectance spectroscopy (DRS). The substrate setpoint is 435 °C.
Thermocouple temperature, substrate (DRS) temperature, and heater voltage recorded during the growth of lattice-matched InGaAs on InP are shown in Figure 3. The supervisory computer samples the DRS temperature every 30 s, if the DRS temperature has deviated more than ± 1 °C from the substrate setpoint of 435 °C, the outer PID loop updates the Eurotherm (inner) setpoint. Throughout most of the growth of the InGaAs layer, the substrate temperature is about 1 °C above its setpoint. Decreasing the update time would bring the substrate temperature closer to the setpoint during the first part of the growth. As can be seen in Fig. 3, each time the thermocouple setpoint is updated, there is a sharp drop in the heater voltage and the thermocouple temperature quickly moves to its new setpoint. The thermal response of the thermocouple-heater system is fast (4 s time constant) compared to the thermal response of the substrate (60 s time constant). This allows appropriate control action.
The thermocouple is insensitive to the substrate temperature increase caused by the strong absorption of heater radiation in the InGaAs overlayer. The small-bandgap epilayer absorbs a larger part of the heater radiation spectrum than the InP substrate, which is transparent to most of the blackbody spectrum at these temperatures. Therefore, as the InGaAs layer thickens, the transmission losses of heater radiation are reduced. In order to maintain constant substrate temperature, the control system continually reduces the heater power by decreasing the thermocouple setpoint (52 °C in total) during the growth.
The small oscillations in the substrate temperature at the start and stop points are caused by the abrupt changes in the thermal load on the substrate when the In and Ga cells are togged. At the start of growth the thermocouple setpoint is reduced by 6 °C in an effort to correct for the thermal disturbance caused by additional radiant heat load of the In and Ga effusion cells. At the end of the growth, no shutter disturbance rejection is used and the substrate momentarily drops 4 °C below the setpoint.
 S. R. Johnson, T. Tiedje, J. Crystal Growth, 175/176, 38 (1997).
 J. A. Roth, T. J. DeLyon, M. E. Adel, Mat. Res. Soc. Symp. Proc. 324, 353 (1994).
 E. S. Hellman, J. S. Harris, J. Crystal Growth, 81, 38 (1987).
 S. R. Johnson, T. Tiedje, J. Appl. Phys. 78, 5609 (1995).
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