What is Hall Effect?

If a specimen carrying a current is placed in transverse magnetic field an electric filed is induced in a direction perpendicular to both electric current and magnetic field. This phenomenon is known as Hall Effect. Let us consider a semiconductor bar of breadth ‘l’ in the in the direction of magnetic field and width ‘d’ carrying a uniform current ‘I’ travelling in X direction and placed in uniform magnetic field ‘B’ in Y direction. Assume the semiconductor current is composed of flow of charge carrier each carrying an electric charge ‘Q’, the Lorentz force on each charge carrier is Fl = BoQVo where Vo is velocity of charge carrier and is given by Vo = I/ (ldΦ), Φ is charge concentration (or) charge density, the force due to electric field produced by displaced charge is Fe= E*Q. At equilibrium these two forces balances each other

BoQVo = E*Q

Electric field produced by displaced charges is equal to E = VH/d, where VH is hall voltage. Hence VH = (Bo* I)/ (lΦ), VH = (BoI*RH)/ l where RH is hall coefficient given by RH = (1/ Φ).