''http://mems.caltech.edu/courses/EE40%20Web%20Files/Supplements/02_Hall_Effect_Derivation.pdf''
All the derivation is precisely explained.
You need to equate Newton second law to Lorentz equation, assuming the magnetic field is normal to current flow. You need do this separately for electrons and for holes. Both velocity and electric field have two components, transversal (y) and longitudinal (x) and the magnetic field is in z. It is more comfortable separate the vectorial equations into two equations, one for each component. So, you have four equations:
1) For time derivative of x-velocity of electrons
2) For time derivative of x-velocity of holes
3) For time derivative of y-velocity of electrons
4) For time derivative of y-velocity of holes
The set is complicate, but it is easier if you do the following approximation:
If magnetic field is small, you can assume that the second term in equations 1) and 2) is negligible. Yo cannot do the same with equations 3) and 4) because, since mobility of electrons and holes are not much different, this would give you as a result that transversal field does not exist, and you will not get anything.
You must bear in mind that velocities in your equations are individual velocities and you need average velocities. If you use the single model of a carrier starting from zero velocity and accelerating at a constant rate and suddenly stopped at a time tau, you can obtain the average velocities for the four equations multiplying the right side of each times tau/2. You can make sense of all this by plotting changing velocity as a saw tooth signal.
In agreement with mobility definition (charge times half-tau over effective mass) you can see that equations 1) and 2) are no more that the classic lineal relation between average velocity and electric field, with the mobility as a constant. Equations 3) and 4) have both a similar first term but the second term, including the magnetic field is more weird.
Now, you have average x-velocity for electrons, average x-velocity for holes, average y-velocity for electrons and average y-velocity for holes. If you multiply each velocity by charge and concentration you will get x-current density for electrons, x-current density for holes, y-current density for electrons and y-current density for holes. When this is done, you can add contributions of both types of carriers and obtain x-current density and y-current density.
What you will use for calculating the Hall´s coefficient is transversal current density which must be zero. Replace this zero in the formula for y-current density and you will obtain two terms equated to zero or rearranging, an equality between two terms. One of the terms is already in the shape we want, but the other still include longitudinal velocities for electrons and holes. You have expressions for them and must replace in the expression for y-current density. Now, you must identify expressions that can be replaced by electron and hole mobilities.
Now, you only have carrier concentrations, carrier mobilities, longitudinal and transversal fields and magnetic field magnitude. Solve for transversal electric field. For obtaining Hall´s coefficient you need to multiply both numerator and denominator for conductivity. Keep conductivity in the denominator in terms of concentrations and mobilities. This is not important for the numerator because you will must note that conductivity times longitudinal electric field is longitudinal density current. Now you have transversal electric field as a linear function of the product of current density (longitudinal, the only non-zero current density) times the magnetic field magnitude. The proportionality constant is Hall´s coefficient.
It is not easy!
Lydia Alvarez, Mexicali B.C. Mexico
lydia@iing.mxl.uabc.mx
R = Uh*d/(I*B),
where: R - Hall coefficient, Uh - Hall voltage, d - semiconductor thickness, I - current, B - magnitute of flux density.
The difference in the electron and hole mobilities is responsible for the small negative Hall coefficient of intrisic semiconductors. Refs: C.M.Hurd : Hall effect in metals and alloys R.Asokamani :solid state physics Busch& Schade; Solid state Physics
hall coefficient of a lightly doped semiconductor will decrease with increase in temp as hall coefficient is inversely proportional to number density of charge carriers.
T= 0.165V/As v= volume of the hall a= absorption coefficient s= surface area
Semiconductors: When temperature increases, more electrons jump to conduction band from valance bond. Hence resistance decreases. Metals: Already plenty of electrons are there in conduction band. When temperature increases, the electrons in conduction band of metal vibrate and collide each other during their journey. Hence the the resistance of metal increases with increase of temperature. S.Lakshminarayana
ON Semiconductor was created in 1999.
negative
positive
The difference in the electron and hole mobilities is responsible for the small negative Hall coefficient of intrisic semiconductors. Refs: C.M.Hurd : Hall effect in metals and alloys R.Asokamani :solid state physics Busch& Schade; Solid state Physics
hall coefficient of a lightly doped semiconductor will decrease with increase in temp as hall coefficient is inversely proportional to number density of charge carriers.
positive
T= 0.165V/As v= volume of the hall a= absorption coefficient s= surface area
The no of electrons in the conduction band increases when the temperature of the semiconductor material increases. therefore resistance decreases. This is also know as "Negative temperature coefficient"
It is a semiconductor.
An intrinsic semiconductor is basically a pure semiconductor, though some might argue that a small amount of doping can still yield an intrinsic semiconductor. In the crystal structure of this material, there are very few electrons crossing the band gap into the conduction band, and this stuff doesn't want to conduct much current. But as temperature increases, more electron-hole pairs will appear as electrons jump that band gap and take up places in the conduction band. And if you guessed that increasing temperature will permit the intrinsic semiconductor to conduct current flow a bit better, you'd be right. The intrinsic semiconductor has a positive temperature coefficient. More heat, more conduction under the same conditions.
John H. Hall has written: 'Semiconductor design and implementation issues in integrated vehicle electronics' 'The word baptizo defined' -- subject(s): Accessible book, Baptism, Infant baptism
Yes it is a semiconductor
A semiconductor slice is used to make integrated circuits or ICs. It is also known as a semiconductor wafer or a semiconductor substrate.