The Design of Fast Thermopiles and the Ultimate Sensitivity of Thermal Detectors

Abstract

The design criteria for fast thermopiles of maximum sensitivity are obtained, with particular reference to their use with interrupted radiation in infra‐red spectroscopy. It is shown that since the heat capacity of short, fine wires can be made small compared to that of the receiver, the conventional construction has certain advantages over evaporated thermopiles. Sources of noise are discussed and it is shown that in the cases treated the noise caused by the temperature fluctuations of the receiver is somewhat less than that resulting from Johnson noise. If Johnson noise is the chief factor, the minimum detectable power in the form of incident radiation is inversely proportional to a quantity S=E/R ½ (E=voltage sensitivity; R=thermopile resistance) defined as the absolute sensitivity. The optimum design of d.c. thermopiles is derived and a factor of merit for thermoelectric materials, Q/(κρ)½ (Q=thermoelectric power; κ=thermal conductivity; ρ=electrical resistivity) is obtained. Physical constants and factors of merit for various materials are tabulated. Cd–Sb and Te alloys have the highest factor of merit but it is concluded that their irreproducibility outweighs their slight advantages. General relations for the time constant are given in terms of the construction and it is shown that response times of less than 0.02 second are practicable. By using these relations the optimum design of thermopiles for use with interrupted radiation is obtained. Several concrete designs for use at a 5 c.p.s. interruption frequency are given. With a receiver area of 0.005 cm2 the incident radiation, interrupted at 5 c.p.s., equal to the Johnson noise in a 1 c.p.s. frequency range is 5×10−5 μwatts. At this frequency the response is 90 percent of the equilibrium value. Approximately the same performance may be obtained at 10 c.p.s. Using the best available materials this sensitivity may be almost doubled. If ideal materials should ever be found there is still an ultimate limit to the sensitivity of any detector, thermopile or bolometer, which measurestemperature, set by the temperature fluctuations. At 300°K this limit of detection is 4×10−6 μwatt for a detector of 0.005 cm2 area and a measurement in a 1 c.p.s. frequency band.