Ja. Harley et Tw. Kenny, 1/F noise considerations for the design and process optimization of piezoresistive cantilevers, J MICROEL S, 9(2), 2000, pp. 226-235
Piezoresistive cantilevers are limited by two major noise sources: Johnson
noise, which is independent of frequency, and conductance fluctuation noise
, which has a 1/f spectrum. The 1/f fluctuations of piezoresistive cantilev
ers are shown to vary inversely with the total number of carriers in the pi
ezoresistor, as formulated by Hooge in 1969, Therefore, while 1/f noise is
reduced for large heavily doped cantilevers, sensitivity considerations fav
or thin lightly doped cantilevers. Balancing these conflicting constraints
produces optima for many design and processing parameters. For a cantilever
with specified spring constant and bandwidth requirements, optima are iden
tified far the beam thickness and Length, and it is shown that the legs sho
uld be between 1/3 and 2/3 of the total length with a doping depth that is
1/3 of the beam thickness. Additionally, an optimal doping concentration is
identified as a function of the cantilever volume and the measurement band
width. Annealing reduces 1/f noise, but causes a loss in sensitivity due to
dopant diffusion, and an optimal anneal is computed with a typical diffusi
on length 10(-6) cm, The analysis, methods, and some of the conclusions of
this paper are also applicable to other types of piezoresistive sensors.