The Hall effect finds important application in the...

The Hall effect finds important application in the electronics industry. It is used to find the sign and density of the carriers of electric current in semiconductor chips. The arrangement is shown in Figure $\mathrm{P} 22.66 .$ A semiconducting block of thickness $t$ and width $d$ carries a current $I$ in the $x$ direction. A uniform magnetic field $B$ is applied in the $y$ direction. If the charge carriers are positive, the magnetic force deflects them in the $z$ direction. Positive charge accumulates on the top surface of the sample and negative charge on the bottom surface, creating a downward electric field. In equilibrium, the downward electric force on the charge carriers balances the upward magnetic force and the carriers move through the sample without deflection. The Hall voltage $\Delta V_{\mathrm{H}}=V_{c}-V_{a}$ between the top and bottom surfaces is measured, and the density of the charge carriers can be calculated from it. (a) Demonstrate that if the charge carriers are negative the Hall voltage will be negative. Hence, the Hall effect reveals the sign of the charge carriers, so the sample can be classified as $p$ -type (with positive majority charge carriers) or $n$ -type (with negative). (b) Determine the number of charge carriers per unit volume $n$ in terms of $I, t, B$ $\Delta V_{\mathrm{H}},$ and the magnitude $q$ of the carrier charge.

Key Concepts

Equilibrium Condition in the Hall Effect

The equilibrium condition occurs when the transverse electric force induced by the Hall voltage balances the magnetic Lorentz force acting on the moving charge carriers. At equilibrium, the net force on the charge carriers is zero, and they continue to flow without further deflection. This balance is crucial for accurately determining the Hall voltage and, by extension, the sign and density of the charge carriers.

Charge Carrier Density

Charge carrier density refers to the number of charge carriers (electrons or holes) per unit volume within a semiconductor. In the Hall effect, the relationship between the measured Hall voltage, the applied magnetic field, and the current through the sample is used to derive an expression for the carrier density. This calculation is central to understanding the electrical characteristics of the semiconductor material.

Lorentz Force

The Lorentz force is the force experienced by a moving charge in the presence of electric and magnetic fields. Specifically, in the context of the Hall effect, the magnetic component of the Lorentz force acts perpendicular to both the velocity of the charge carriers and the applied magnetic field, causing the deflection of the charge carriers and the accumulation of opposite charges on the surfaces of the electrical sample.

Hall Effect

The Hall effect is a phenomenon observed in conductors and semiconductors when a current-carrying material is placed in a perpendicular magnetic field, leading to the development of a transverse voltage (Hall voltage) across the material. This effect is used to determine both the type (positive or negative) and density of charge carriers in the material, making it an important diagnostic tool in the electronics industry and semiconductor physics.

Semiconductor Doping (p-type and n-type)

Semiconductor doping involves introducing impurities into a semiconductor to change its electrical properties. A p-type semiconductor has positive majority charge carriers (holes) while an n-type semiconductor has negative majority charge carriers (electrons). The Hall effect reveals the sign of these carriers by showing the polarity of the induced Hall voltage, thus helping to classify the semiconductor as either p-type or n-type.

Transcript

00:02 As we know that positive charge carriers move in the direction of conventional current and electrons move in the opposite direction of conventional current.

00:22 So we can write direction of electrons, direction of electrons is opposite to the conventional current.

00:44 From the figure the direction of conventional current is from left to right so the direction of electrons that is a direction of negative charge will be from right to left when the electrons move from right to left in the specimen then we can find the direction of magnetic on electrons by using the right hand rule.

01:45 So the negative charge accumulates on the top surface of the specimen and positive charge will accumulate at the lower surface of specimen.

02:26 This will cause an awathe electric field and this will produce.

02:41 Produce a negative hull voltage.

02:57 Thus, if the direction of field and current are known, then the sign of charged carriers can be determined from the whole effect.

03:24 So nature of charge carriers can be determined from hall effect.

03:39 In equilibrium we can write the electrostatic force equal to the magnetic force as electrostatic force is equal to charge times electric intensity and magnetic force equal to the charge into the speed of charge carriers that is drift velocity strength of magnetic field into the sign of angle between velocity of charge carriers and magnetic field here theta is equal to 90 degree that is the direction the angle between velocity of charge carriers and magnetic field is perpendicular this gives us electric intensity equal to drift velocity of charge carriers times the strength of magnetic field.

05:19 Q will be cancelled from both sides.

05:31 As we can write elective intensity as whole voltage divided by d...

Please give Ace some feedback