Four point bending setup for characterization of semiconductor piezoresistance

Abstract

We present a four point bending setup suitable for high precision characterization of piezoresistance in semiconductors. The compact setup has a total size of 635cm3. Thermal stability is ensured by an aluminum housing wherein the actual four point bending fixture is located. The four point bending fixture is manufactured in polyetheretherketon and a dedicated silicon chip with embedded piezoresistors fits in the fixture. The fixture is actuated by a microstepper actuator and a high sensitivity force sensor measures the applied force on the fixture and chip. The setup includes heaters embedded in the housing and controlled by a thermocouple feedback loop to ensure characterization at different temperature settings. We present three-dimensional finite element modeling simulations of the fixture and discuss the possible contributions to the uncertainty of the piezoresistance characterization. As a proof of concept, we show measurements of the piezocoefficient π44 in p-type silicon at three different doping concentrations in the temperature range from T=30°CtoT=80°C. The extracted piezocoefficients are determined with an uncertainty of 1.8%.

Piezoresistance in p-type silicon revisited

“…The piezoresistance characterization is done in an automated four point bending fixture. This fixture applies a uniaxial, uniform stress to the resistors in the center region of the chip 33 in steps of approximately 5 to a maximum value of 70 MPa, which corresponds to a strain of ⑀ xx Ϸ 0.0004.…”

Medium doped non-suspended silicon nanowire piezoresistor using SIMOX substrate

“…In this work, four point bending (4PB) apparatus is employed to produce uniform and uniaxial stress along the <110> direction of the piezoresistors [15], [16], [21]- [23]. Figure 5 illustrates the apparatus used.…”

“…Linear bearings are employed to minimize friction as the top block moves downwards. The stress (σ) at the centre is derived as [15], [16], [21]- [23] where F is force, a is inner separation, w is width and t is the thickness of the silicon beam. Deflection is given by [15], [16], [21]- [23]   where L is the length of the beam, and E is the Young's modulus of silicon.…”

“…Applying a uniaxial stress along the <110> direction, the relative resistance change for a piezoresistor can be simplified to [15], [16], [21]- [23] …”

“…The thickness and width of the chip are defined based on the dimension of the Zero Insertion Force connector (ZIF) which creates a simple plug and measure method [15], [16]. Flat flexible cable is employed to establish electrical connections to the test chip to minimize measurement error.…”