A graphene sheet consists of a single layer of carbon atoms. It is effectively a

Question

A graphene sheet consists of a single layer of carbon atoms. It is effectively a two-dimensional object, having no height. It can conduct electricity and when placed in a magnetic field, will show Hall Effect phenomenon. To calculate the area density of charge carriers in graphene, you apply a 100 nA amp current in the longitudinal direction and place the graphene sheet in a magnetic field of 2 Tesla. A Hall voltage of 47 ?V is then measured across the terminals as shown. What is the density of charge carriers (electrons) per square centimeter in the graphene?

Explanation / Answer

we know, Hal voltage

Vh = B*I/(n*e*t)

here B is magnetic field

I is current

n is no of charge carriers per unit volume

e is charge of electron

t distance between probes

so, n*t = B*I/(e*Vh)

= 2*100*10^-9/(1.6*10^-19*47*10^-6)

= 2.67*10^16 electrons/m^2 <<<<<<<----------------------Answer

here, n represnts no of charge carriers per unit volume

but n*t represnts no of charge carriers per unit Area

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