Epitaxial Si Sensors at Low Temperatures: Non-Linear Effects

Abstract

Cryogenic bolometric sensors made from epitaxially grown Si:As have been tested down to 40 mK. The sensors were grown by chemical vapour deposition with a doped layer 8.4 µm thick. The dopant concentration was measured using SIMS and was constant, ±1%, with an excellent box profile. Arsenic concentrations up to 7.5 × 1018 cm−3 were achieved. Above 100 mK the low power resistance R(T) followed the variable range hopping law, or Efros-Shklovskii law for a Coulomb gap, R(T) = R0 exp(T0/T)1/2 with T0 ≈ 25 K, typically. A double sensor arrangement was used to measure the electron-phonon coupling in the sensors and the phonon coupling to the heat sink. As the dc current bias through a sensor was increased, spontaneous voltage oscillations were observed across the sensor below 100 mK, which limited the sensitivity of the sensors in this region. These are circuit-limited oscillations between high and low resistance states. A phase diagram was established for the spatio-temporal coexistence of the two states, with a critical temperature Tc = 115 mK. We show that this is an intrinsic phase transition within a thermal model of the electron-phonon coupling. For a resistance-temperature characteristic given by the Efros-Shklovskii law we find Tc = 0.00512 T0, independent of R0 and the coupling strength. This predicts Tc = 115 ± 4 mK in this case. The model gives excellent agreement for the critical voltage and current, by assuming that the breakdown occurred via the formation of a filamentary region of high current density and high electron temperature. At higher currents, the response was temperature independent and given by I(E) = I(0) exp{−(E0/E)1/2} where E is the average applied electric field and E0 ≈ 380 V/cm, in agreement with a thermal model which includes the phonon-phonon coupling to the heat sink.