In 1985 Klaus von Klitzing won the Nobel Prize for discovery of
the quantised Hall effect. The previous Nobel prize awarded in
the area of semiconductor physics was to Bardeen, Shockley and
Brattain for invention of the transistor. Everyone knows how
important transistors are in all walks of life, but why is a
quantised Hall effect significant? 100 years ago E.H. Hall
discovered that when a magnetic field is applied perpendicular
to the direction of a current flowing through a metal a voltage
is developed in the third perpendicular direction. This is well
understood and is due to the charge carriers within the current
being deflected towards the edge of the sample by the magentic
field. Equilibrium is achieved when the magnetic force is
balanced by the electrostatic force from the build up of charge
at the edge. This happens when Ey = vxBz .The Hall coefficient
is defined as RH = and since the current density is jx = vxNq ,
RH =1/Nq in the case of a single species of charge carrier. RH
can thus be measured to