Browse Prior Art Database

Flexible Cantilevers for Torque Magnetometry with Piezoresistive and Capacitive Readout

IP.com Disclosure Number: IPCOM000119153D
Original Publication Date: 1997-Dec-01
Included in the Prior Art Database: 2005-Apr-01
Document File: 6 page(s) / 238K

Publishing Venue

IBM

Related People

Rossel, C: AUTHOR [+2]

Abstract

Disclosed are new micromachined silicon cantilevers which are specially designed for torque magnetometry.

This text was extracted from an ASCII text file.
This is the abbreviated version, containing approximately 35% of the total text.

Flexible Cantilevers for Torque Magnetometry with Piezoresistive
and Capacitive Readout

      Disclosed are new micromachined silicon cantilevers which are
specially designed for torque magnetometry.

      The principle is to measure the magnetization M of a small
anisotropic, magnetic or superconducting sample fixed on a flexible
cantilever, through the torque generated on it by an homogeneous
external magnetic field B.  The torque is defined by tau vector = m
vector multiply B vector where  m vector is the magnetic moment of
the sample  of volume V (m vector = V multiply M vector).  The design
of the lever  is made to measure with high sensitivity the torque in
flexion (tau sub f), as well as in torsion (tau sub t) mode.  Two
different readouts  are proposed: a) piezoresistive and b)
capacitive.

I.  Piezoresistive Technique

      The relative change in piezoresistance at the surface of a
plain lever or beam bent by the action of a torque is given by Delta
R/R = beta pi sub L sigma bar sup sub p where pi sub L is the
longitudinal piezoresistive coefficient and  sigma bar sup sub sub p
the maximal average elastic stress at the surface of the
piezoresistive path.  In order to derive the piezoresistive
sensitivity, Delta R/R, sigma bar sup  sub p must be calculated for
each lever geometry, relative dimensions and shape of its
piezoresistive path.
  a) Two-leg cantilever
     Such cantilevers are widely used for Atomic Force Microscopy
      (AFM) (1-3) and are known for high-sensitivity torque
      magnetometry (4).  In Fig. 1, a new two-axes torquemeter
      lever is depicted, which is designed in such a way as to
      get the highest ratio of its sensitivity to torque-induced
      torsion over its sensitivity to flexion: S sub t / S sub f.

      The dimensions (i.e., leg length l, leg width w, hole width p,
total width b, and thickness t) are calculated to optimize the lever
sensitivity.  In case of flexion, the max stress produced by the
flexion on the piezoresistive path is:
  sigma bar sup sup f sub sub p = <3 tau sub f> over (w - p)t sup 2

In case of torsion around the x-axis, this max stress becomes:
  sigma bar sup t sub sub p = 3 over 2 %% tau sub t
   over < < b(w - p) t sup 2 > over l + G over 'Eb' <
   (w sup 3 - p sup 3) + (w - p)t sup 2 > over 3 >
  where E = Young's modulus and G = shear modulus of  Si.

      The condition for equal sensitivity in both modes is S sub f =
<sigma sup f max > over <tau sub f> identical S sub t = < sigma sup t
max > over < tau sub t > and leads to a complex condition with no
real solution.  The sensitivity in torsion is always less than the
sensitivity in flexion.  Nevertheless, the optimized ratio can be
found to be S sub f / S sub t = 4.6.

      The optimization is achieved through the presence of the two
sets of holes (A and B) etched in the two legs and the geometry of
the piezoresistive paths.  Hole A defines...