Achieving < ±25 ppb Frequency Stability With a ±0.125 °C Oven Control on a Si Interposer for an AlScN-on-Si Shear-BAW Resonator

A major challenge of long-term clock stability is frequency drift due to temperature variations. This paper describes the design of a proportional, integral, derivative (PID) control system for external ovenization of an AlScN-on-Si Shear-BAW Resonator (S<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">3</sup>R), which has a fixed turnover temperature where the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$1{^{\text {st}}}$</tex-math> </inline-formula> order temperature coefficient of frequency is <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\approx 0$</tex-math> </inline-formula> ppm/°C. The control system provides <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm ~0.125^{\circ }$</tex-math> </inline-formula>C temperature stability and assists in achieving better than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\pm ~25$</tex-math> </inline-formula>ppb frequency stability over a temperature range of 15-40°C by maintaining resonator operation near the turnover temperature, where the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$2{^{\text {nd}}}$</tex-math> </inline-formula> order temperature coefficient of frequency drift is -62.71ppb/°C<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup>. The robust and adaptive PID algorithm (programmed on an external microcontroller unit connected to the interposer) ensures continuous ovenization by configuring the duty cycle of a compact heat actuator (powerMOS) that is placed in <3.5mm proximity of the 2mm<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times 2$</tex-math> </inline-formula>mm resonator and a complementary to absolute temperature sensor (implemented as a 1mm<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times 1$</tex-math> </inline-formula>mm, 65nm integrated circuit), that are all held on a thermally conductive 7mm<inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\times$</tex-math> </inline-formula>7mm Si interposer.