Analysis of Lorentz Force in Semiconductor

[Petar Mali]

I have a few questions about this effect. If I have some semiconductor of N type in which I have electrical field in x direction, and magnetic field in z direction

$$\vec{E}=E\vec{e}_x$$

$$\vec{B}=B\vec{e}_z$$

Then Lorence force is in the -y direction because in N type of semiconductor $$n>>p$$ so

$$F_l=-e\vec{\upsilon_D}x\vec{B}$$

And for this case Hall constant $$R_H=-\frac{1}{ne}$$ is negative. Am I right?

And in same case but for P type Lorentz force will be

$$F_l=e\vec{\upsilon_D}x\vec{B}$$

so in y direction, and Hall constant

$$R_H=\frac{1}{pe}$$?

 

[vin300]

All clear.

 

[charng]

Yes, your understanding of the Lorentz force in semiconductors is correct. The Lorentz force is the force experienced by a charged particle moving in an electric and magnetic field, and it is given by the equation F_l=q(\vec{E}+\vec{v}\times\vec{B}), where q is the charge of the particle, \vec{E} is the electric field, \vec{v} is the velocity of the particle, and \vec{B} is the magnetic field. In a semiconductor, the majority carriers (electrons or holes) experience this force due to their motion in the electric and magnetic fields.

In the case of an N-type semiconductor, the majority carriers are electrons, which have a negative charge. So, in the presence of an electric and magnetic field in the directions you mentioned, the Lorentz force on these electrons will be in the -y direction, as you correctly stated. This is because the electrons will experience a force in the opposite direction of their velocity, which is in the +x direction.

The Hall constant, which is a measure of the strength of the Lorentz force, is indeed negative for N-type semiconductors. This is because the Lorentz force is in the opposite direction of the electric current, which is defined as the direction of positive charge flow. Since the majority carriers in an N-type semiconductor are negative charges, the current and the Lorentz force are in opposite directions, resulting in a negative Hall coefficient.

Similarly, for a P-type semiconductor, the majority carriers are holes, which have a positive charge. So, in the presence of the same electric and magnetic fields, the Lorentz force on these holes will be in the +y direction, as you correctly stated. And the Hall constant will be positive, as the Lorentz force and the current are in the same direction.

I hope this helps clarify your understanding of the Lorentz force in semiconductors. Please let me know if you have any further questions.