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The Hall effect turned out to be out observable in a semi-condutor whos conduction electron mobility was eta= 2.0 times that of the hole mobility. Find the ratio of hole and conduction electron concetration in that semiconductor. |
Answer» Solution : When the sample contains unequal number of carries of both types whose mobilites are DIFFERENT, static equilibrium (i.e no transvese movement of either ELECTRON or holes) is impossible in a magnetic field. The trnasverse electric field acts DIFFERENTLY on electrons and holes. If the `E_(y)` that is set up is a shown, the net Lorentz force per unit charge (effective transverse electric field) on electron is `E_(y)-v_(x)^(-)B` and on holes `E_(y)+v_(x)^(+)B` (we are assuming `B=B_(Ƶ)`). There is then a transverse drift of electrons and holes and the net transverse current must vanish in equilibrium. Using MOBILITY `u_(0)^(-)N_(e)e(E_(y)-u_(0)^(-)E_(x)B)+N_(k)eu_(0)^(+)(E_(y)+u_(0)^(+)E_(x)B)=0` or `E_(y)=(N_(e)u_(0)^(-2)-Nu_(0)^(+2))/(N_(e )u_(0)^(-)+N_(h)u_(0)^(+))E_(x)B` On the other hand `j_(x)=(N_(e )u_(0)^(-)+N_(h)u_(0)^(+))eE_(x)` Thus, the Hall coefficient is `R_(H)=(E_(y))/(j_(x)B)=(1)/(e )(N_(e )u_(0)^(-2)-N_(h)u_(0)^(+2))/(e(N_(e )u_(0)^(-1)+N_(h)u_(0)^(+))^(2))` We see that `R_(H)=0` when `(N_(e ))/(N_(h))=(u_(0)/(u_(0)^(-)))^(2)=(1)/(eta^(2))=(1)/(4)` |
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