Characterization of the Temperature Dependence of the Piezoresistive Coefficients of Silicon From ${-}150\,^{\circ}$C to ${+}125\,^{\circ}$C

Abstract

Stress sensing test chips are widely utilized to investigate integrated circuit die stresses arising from assembly and packaging operations. In order to utilize these test chips to measure stresses over a wide range of temperatures, one must have values of six piezoresistive coefficients for n-and p-type silicon over the temperature range of interest. However, the literature provides limited data over the desired range, and even the data at room temperature exhibit wide discrepancies in magnitude as well as sign. Thus, this work focuses on an extensive experimental study of the temperature dependence of the fundamental piezoresistive coefficients, 11 12 , and 44 , for both p-and n-type silicon from 150 C to +125 C, as well as a number of useful combined coefficients.Measurements were performed using stress sensors fabricated on (001) silicon. In order to minimize errors associated with misalignment with the crystallographic axes on (001) silicon wafers, anisotropic wet etching was used to accurately locate the axes. Four-point bending (4PB) was used to generate the required stress in strip-on-beam samples, and finite-element simulations were used to determine the states of stress in the silicon material.

Bending induced electrical response variations in ultra-thin flexible chips and device modeling

“…Biaxial flexural tests on plates, which have been used to evaluate the strength of ceramics for more than 40 years in various configurations such as ball-on-ring, 111,112 uniform pressure, 113 ring-on-ring, 114 or piston-on-threeballs, 115 have been adapted to investigate the biaxial strain effects in UTCs. 116,117,150 Properties such as phonon or electronic deformation potentials 118,119 are measured through these tests to find the fracture strength 96,[120][121][122] or to investigate the 2D strain effects on the electrical behavior of MOSFETs. 123,124 In the case of thin samples, the fracture strength is influenced by the roughness and morphology of the surface, 125 which in turn are affected by the surface defects introduced through backside grinding, polishing, chemical etching, and edge defects caused by wafer sawing or dicing.…”

“…Further, the value of shear piezoresistive coefficients varies linearly with the compressive biaxial strain but is highly nonlinear in the case of tensile strain. 17 The value of the shear piezoresistive coefficients also varies with temperature 150 -decreasing linearly and monotonically with the increase in temperature from À150…”

Nanoelectromechanical resonant narrow-band amplifiers

“…Aside from the overall significance of a desired low-power consumption for any electronic device, a high DC power consumption typically leads to excessive heating and reliability issues, a reduction of the piezoresistive coefficient [11][12][13] , and higher levels of thermal and mechanical noise. Therefore, optimization is required for such devices to maintain high levels of gain while lowering the required DC power.…”

Partially integrated cantilever-based airborne nanoparticle detector for continuous carbon aerosol mass concentration monitoring

“…For the implanted and diffused wafers, the standard deviations of the measured resistivity from the desired value were ∼ 0.6 and ∼ 4.1 % in proportion to their lateral doping distribution, respectively. Typical values of the junction depth and the surface doping concentration amounted to ∼ 4.5 µm and 1.5-3.0 × 10 18 cm −3 , respectively, representing a tradeoff between a large piezoresistive coefficient π 44 ≈ 1 GPa −1 and a low temperature coefficient around −3 × 10 −3 • C −1 (Cho et al, 2008;Peiner et al, 2008). 4.…”