HALL Effect in intrinsic semiconductors


In last post HALL EFFECT IN n TYPE SEMICONDUCTOR and HALL EFFECT IN p-TYPE SEMICONDUCTORS ,we have studied HALL effect in n-type and p-type semiconductors 

In this article we will familiar with hall effect in Intrinsic semiconductors 


HALL effect

Since mobility of electrons is higher than that of mobility of holes so more number of electron will accumulate at surface (2) in compare to that of number of holes ,

NOTE: So behavior of HALL effect in intrinsic Semiconductors is same as in case of HALL effect in n-type semiconductors 

HALL COEFFICIENT (chart?cht=tx&chl=R %7B%7BH%7D%7D): 

chart?cht=tx&chl=R %7B%7BH%7D%7D = -(chart?cht=tx&chl=%5Cfrac%7B1%7D%7Bnq%7D)   HALL coefficient is negative for  n-type semiconductors , metals , intrinsic semiconductors 

chart?cht=tx&chl=R %7B%7BH%7D%7D =  (chart?cht=tx&chl=%5Cfrac%7B1%7D%7Bpq%7D)  HALL coefficient is positive for p-type semiconductors 


(1) It can determine type of semiconductor materials , whether it is p-type or n-type semiconductor materials 

(2) If HALL coefficient(chart?cht=tx&chl=R %7B%7BH%7D%7D) for a semiconductor material is given , by use of this we can calculate the concentration of charge carriers in semiconductor material

chart?cht=tx&chl=R %7B%7BH%7D%7D = -(chart?cht=tx&chl=%5Cfrac%7B1%7D%7Bnq%7D

chart?cht=tx&chl=n = concentration of charge carriers =-(1/chart?cht=tx&chl=R %7B%7BH%7D%7D chart?cht=tx&chl=q)

(3) With the help of HALL coefficient chart?cht=tx&chl=R %7B%7BH%7D%7D ,we can determine mobility chart?cht=tx&chl=%5Cmu of charge carriers ( mobility of electron and holes) in a semiconductor material  

we know that 

chart?cht=tx&chl=R %7B%7BH%7D%7D = (chart?cht=tx&chl=%5Cfrac%7B1%7D%7Bnq%7D)                                               (1)  

chart?cht=tx&chl=%5Csigma%20%3D%20nq%5Cmu %7B%7Be%7D%7D                                                 (2)  

from equation (1) and (2) 

chart?cht=tx&chl=%5Cmu %7B%7Be%7D%7D = chart?cht=tx&chl=%5Csigmachart?cht=tx&chl=R %7B%7BH%7D%7D                                              (3)

by use of equation (3) one can calculate mobility of electrons chart?cht=tx&chl=%5Cmu %7B%7Be%7D%7D  , if conductivity due to electrons (chart?cht=tx&chl=%5Csigma) in semiconductors and Hall coefficients chart?cht=tx&chl=R %7B%7BH%7D%7D is given 

(4) Hall effect in semiconductor materials can used as multiplier , known as “HALL EFFECT MULTIPLIER”

we know that hall voltage chart?cht=tx&chl=V %7B%7BH%7D = chart?cht=tx&chl=%5Cfrac%7BBI%7D%7Bnqw%7D

let chart?cht=tx&chl=I=chart?cht=tx&chl=I %7B%7B1%7D%7D is first input to multiplier 

                                               chart?cht=tx&chl=V %7B%7BH%7D%7D = chart?cht=tx&chl=BI %7B%7B1%7D%7D%2Fnqw

let chart?cht=tx&chl=B∝ chart?cht=tx&chl=I %7B%7B2%7D%7D ( since a magnetic field an be produced by current ) 

 this will give                      chart?cht=tx&chl=V %7B%7BH%7D%7D = (chart?cht=tx&chl=I %7B%7B1%7D%7DI %7B%7B2%7D%7D%20%2Fnqw

So output voltage( chart?cht=tx&chl=V %7B%7BH%7D%7D)  of  multiplier is directly proportional to the product of these two input current chart?cht=tx&chl=I %7B%7B1%7D%7D%20 and chart?cht=tx&chl=I %7B%7B2%7D%7D%20 so outcomes of Hall effect can be used as multiplier