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For which one of the following materials, is the Hall coefficient closest to zero?
Hall coefficient is defined as:
ρ_{c} = charge density
σ_{n} = nμ_{n}q and σ_{p} = Pμ_{p}q
Hall coefficient depends on the hole and electron concentration, and also on the mobility of carriers.
In a metal, the gap between the conduction band and the valence band is very low.
The concentration of ions (n) is very high in metals.
So, the Hall coefficient will be zero almost for the metal as the Hall coefficient is inversely proportional to the concentration (n).
In Hall effect, a difference voltage is produced _______ to electric current in the conductor, and to an applied _____ field perpendicular to the current.
The following diagram resembles an experimental setup for the observation of the Hall effect
Here we could observe that
Hall effect finds major applications in
Hall Effect is basically the production of voltage (known as hall voltage) across conductor transverse to an electric current and to an applied magnetic field perpendicular to the current.
Application of Hall Effect:
From Hall Effect we have:
Where the hall coefficient is given as:
Hall Effect can be used to measure the carrier concentration and type of semiconductor.
Calculate the hall voltage when the magnetic field is 8 A/m, current is 4 A, width is 5 m and the concentration of carrier is 100000.
The hall voltage V_{A} is given by:
ρ_{c}: Charge density = ne
R_{H}: Hall coefficient
W is the side across which the magnetic field is applied.
n is the carrier concentration
e is the electron charge
Calculation:
W = Thickness = 5 m, I = 4 A, B = 8 A/m, n = 100000
ρ_{c} = ne
ρ_{c} = 100000 × 1.6 × 10^{19}
ρ_{c} = 1.6 × 1014
For an ntype Ge specimen, width = 4 mm, length = 1 mm, current (along the length of specimen) = 1 mA, magnetic field (perpendicular to the current flow direction) = 0.1 Wb/m^{2}^{ }and Hall voltage magnitude = 0.005 V. Calculate the majority carriers density.
Concept:
The hall voltage VA is given by:
ρ_{c}: Charge density
R_{H}: Hall coefficient
W is the side across which the magnetic field is applied.
Calculation:
W = Thickness = 4 mm, I = 1 mA, VH = 0.005 V, B = 0.1 Wb/m^{2}
Since hall voltage is positive, the majority charge carriers will be holes, with the concentration calculated as:
p ≈ 3 × 10^{19} m^{3}
For a particular material, the Hall coefficient is found to be zero. The material is
Hall coefficient is defined as:
We can find the electron concentration as:
ρc = charge density
σ_{n} = nμ_{n}q and σ_{p} = pμ_{p}q
Hall Effect Transducers:
Which of the following quantities cannot be measured/determined using Hall Effect?
Hall Effect: It states that if a “specimen (meta or semiconductor) carrying the current I is placed in traverse magnetic field B, then Electric field Intensity E is induced in a direction perpendicular to both I and B”.
Hall Voltage is given by:
The hall coefficient is given as:
Where,
ρ = charge density = σ / μ
n = charge concentration
σ = conductivity
μ = mobility constant
Hence Hall coefficient becomes
From Hall Experiment, we can determine the following properties:
Note: Diffusion constant is found from electron mobility using Einstein's relationship.
Hall Effect: It states that if a “specimen (meta or semiconductor) carrying the current I is placed in traverse magnetic field B, then Electric field Intensity E is induced in a direction perpendicular to both I and B”.
From Hall Experiment, we can determine the following properties:
From the above properties, we can say that, Option (b) is correct.
The Hall Effect may be used to
1. Determine whether the semiconductor is ptype or n  type.
2. Determine the carrier concentration.
3. Calculate the mobilty.
Which of the above statements are correct?
Hall Effect:
It states that if a specimen (metal or semiconductor) carrying a current (I) is placed in a transverse magnetic field (B), an electric field is induced in the direction perpendicular to both I and B.
Hall Voltage is given by:
The hall coefficient is given as:
Where,
ρ = charge density = σ / μ
n = charge concentration
σ = conductivity
μ = mobility constant
Hence Hall coefficient becomes
Applications of Halleffect:
Hall effect can be used to find:
1. Carrier concentration
2. Type of semiconductor
3. Conductivity
4. Mobility
It cannot be used to find a magnetic field.
Common Confusion Point:
Looking at the formula one can think that the magnetic field can be calculated but in HALL Experiment, perpendicular MAGNETIC field and electric field are applied on the material and other parameters are measured.
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