If an electric current flows through a conductor in a magnetic field, the magnetic field exerts a transverse force on the moving charge carriers which tends to push them to one side of the conductor. When a current carrying conductor i is placed in a transverse magnetic field b, an electric field e is induced in the conductor perpendicular to both i and b. If the metal is placed in a magnetic field b at right angles to the face agdc of the slab and directed from cd to ag. The derivation is based on the basic notion that carriers at nonzero temperature kelvin have an additional thermal energy, which equals kt2 per degree of freedom. Hall effect hall effect derivation electronics tutorials. Whenever we place a current carrying conductor in a magnetic field, there is a deflection of the charge carriers due influence of magnetic field in the conductor body. Hall angle 5800560054005200500048004600 100 105 110 115 120 125 5 s temperature k hall mobility the mobility of the carrier expected to decrease with temperature efield from hall effect divided by generated efieldwe expect the e field from the hall effect to decrease with temp causing the hall angle to decrese. The flow of electron is in the opposite direction to the conventional current. Ntype semiconductors have a large number of donors, dopant atoms that donate electrons to the conduction band. The spin hall effect refers to an effect in which an external electric field induces a transverse spin current. The above figure shows a conductor placed in a magnetic field b along the z. In semiconductors, electrons and holes contribute to different concentration and mobilities which makes it difficult for the explanation of the hall coefficient given above. The hall effect in metals and semiconductors in this experiment, students learn about the classical hall effect which is the basis of most sensors used in magnetic field measurements.
For some monovalent metals m, k, cu, ag the hall effect indi cates that each atom contributes approximately one free. Harsh shukla hall sensor hall effect and its applications hall effect thruster 2. Hall effect in electronics is explained with ntype semiconductor and ptype semiconductor in this video along with few applications of hall effect. How to derive halls coefficient for a semiconductor answers. These measurements will enable the student to determine. Pdf observation of the spin hall effect in semiconductors. Hall effect applications of hall effect electrical4u. Pdf simple notes on hall effect nishad tn academia. It has been known since 30 years ago that impurity scattering gives rise to such an. In this experiment, the hall effect will be used to study some of the physics of charge transport in metal and semiconductor samples. Thin film samples consisting of a semiconductor inas and two different metals aluminum and gold are investigated to determine the sign and density of the. A stationary permanent magnet and semiconductor hall effect chip are mounted next.
Hall effect consider the sample of ptype semiconductor with current density j x flowing in the xdirection. An effect when occurring when a current carrying conductor is placed in a magnetic field and orientated so that the field is at right angles to the direction of the current. Ravindran, phy02e semiconductor physics, autum 20 17 december. Physics stack exchange is a question and answer site for active researchers, academics and students of physics. Hence the hall voltage at b 1t and i10a and t 1 mm for copper and silicone are, 0. Table 2 shows a summary of hall effect data for several metals and semiconductors. For the derivation of equations 8 and 9 see appendix a. The hall effect is a galvanomagnetic effect, which was. Hall effect is the production of voltage across an electrical conductor, transverse to an electric current in the conductor and a magnetic field perpendicular to the current.
The quantum hall effect or integer quantum hall effect is a quantummechanical version of the hall effect, observed in twodimensional electron systems subjected to low temperatures and strong magnetic fields, in which the hall conductance. A buildup of charge at the sides of the conductors will balance this magnetic influence, producing a measurable voltage. The electrical conductivity measurements weve learnt so far are not sufficient for 1 the determination of number of charge carriers 2 mobility of the charge carriers 3 whether the conduction is due to electrons or holes hence, it was very difficult to differentiate between a p type semiconductor. The hall effect the hall coefficient r h e y j x b z 1ne the hall angle is given by tan eyyexxhh for many metals r h is quiet well described by this expression which is useful for obtaining the electron density, in some cases. We will study the hall effect in a parallelepipedic semiconductor sample of sizes a, b, c see figure 1.
The hall effect is the production of a voltage difference the hall voltage across an electrical. To explain hall effect, consider a sample of a block of conductor of length l, width d and thickness t, through which electric current i is supplied along xaxis as shown in figure 1. Carrier density and mobility can also be calculated. It is the thermal energy, which drives the diffusion. This effect consists in the appearance of an electric field called hall field eh r, due to the deviation of the charge carrier trajectories by an external magnetic field. In the presence of a magnetic field b 0 along the zdirection, the holes will experience a force the lorentz force driving them towards the bottom of the sample as shown in figure 1. In this experiment you will measure the re sistivity and. Hall was attempting to verify the theory of electron flow proposed by kelvin some 30 years earlier. Being very simple and straight forward phenomena in physics, hall effect is a fundamental principle in magnetic field sensing and have many practical applications in our daily life. Hall effect and its applications in semiconductorsphysics. This is most evident in a thin flat conductor as illustrated. The hall field eh r is orthogonal on both e r and b r. To explain the hall effect, consider a slab of metal carrying a current. In the ptype semiconductor, free electrons are negligible.
What is the hall voltage for intrinsic semiconductor. Hall effect derivation with simple steps and applications. Hall effect was named after edwin hall, its discoverer. This demonstration shows hall effect in semiconductor materials and shows how ntype and ptype semiconductors can be identified. Edwin hall in 1879 while he was a doctoral candidate at johns hopkins university in baltimore. Using this method, you will measure the conductivity of your. This is somewhat similar to flemings right hand rule. V is velocity of electrons at right angle to magnetic field, there is a down ward force on each electron of magnitude bev. However, this information can be obtained from hall effect measurements, which are a basic tool for the determination of mobilities. She hall effect in semiconductor experimentation lab university. Hall effect derivation with simple steps and applications hall effect. The determination of the hall mobility of the charge carriers in the respective semiconductor.
The hall coefficient obtained may be used to determine the density of the charge carriers, and may be combined with the measured resistivity to determine the mobility of these. In semiconductors, electrons and holes contribute to different concentration and mobilities which. While looking up in the internet, i came across the following formula for. Hall semiconductor resistance, band gap, and hall effect. Hall coe cient is a parameter that measures the magnitude of the hall e ect in the sample. Metals and degenerate doped semiconductors are the examples of this type where one carrier dominates. Therefore, for the simple explanation of a moderate magnetic field, the following is the hall coefficient. Contrast this with resistivity, which has units of m. This causes the electron current to be deflected in a downward direction and causes a negative charge to accumulate on bottom face of slab. Quantum spin hall effect and topological phase transition. The hall effect describes the behavior of the free carriers in a semiconductor when applying an electric as well as a magnetic field.
Hall effect in semiconductors hall voltage the electrons are pulled towards the front side surface of the conductor holes in semiconductors move towards the back a voltage develops between the back positive and front negative surface. The hall effect is the production of avoltage difference the hall voltage across an electrical conductor, transverse to an electric current in the conductor and a magnetic fi. Hall effect in semiconductors drift velocity for an electron in the xdirection is. From a measurement of the magnitude ofthe hall poten tial difference v we can find the number density of the charge carriers. Hall effect derivation hall effect is defined as the production of a voltage difference across an electrical conductor which is transverse to an electric current and with respect to an applied magnetic field it is perpendicular to the current. Hall effect, development of a transverse electric field in a solid material when it carries an electric current and is placed in a magnetic field that is perpendicular to the current. Hall effect semiconductors and its applications engineering physics 1. Hall effect was introduced by an american physicist edwin h. Significance of the hall effect on semiconductors gulpmatrix. The hall effect was discovered in 1879 by edwin herbert hall while working on his doctoral degree at the johns hopkins university in baltimore, maryland, usa discovered 18. If the magnetic field is applied to a ptype semiconductor, the majority carriers holes and the minority carriers free electrons are pushed down towards the bottom surface of the ptype semiconductor. The hall field appears when the sample is placed under an external electric field e r and an external magnetic field b r.
If the magnetic field is applied along negative zaxis, the lorentz force moves the charge carriers say electrons toward the ydirection. In order to understand some of the ideas involved in theory of the hall e. The hall voltage is much more measurable in semiconductor than in metal i. An intrinsic semiconductor is basically a pure semiconductor, though some might argue that a small amount of doping can still yield an intrinsic semiconductor. Since an electron at the fermi energy can be considered free because of the unlimited empty energy states above it, the only force acting. Thus electrons accumulate along the side ag of the metal, which will make ag negatively charged and lower its potential with. Notes on hall effect with both holes and electrons 8. Semiconductor hall effect basic concepts, numerical on.
D1 semiconductor physics and the hall effect physics 191r. J x qn where j is the current density, n is the number of carriers and q is the charge defining the hall coefficient, r h 1qn, then e y v x. The electric field, or hall field, is a result of the force that the magnetic field exerts on the moving positive or negative. The hall voltage in a semiconductor will be measured in the magnetic field of a large electromagnet. The flow of electrons is in the opposite direction to the conventional current. The hall effect the hall effect describes the behavior of the free carriers in a semiconductor whenapplying an electric as well as a magnetic field. In the early days of semiconductor research, this fact caused a lot of. Solid state devices lecture 12 from17 high field, mobility hall effect, diffusion gerhard klimeck. Principle, derivation, and its applications elprocus. In the hall effect, a potential difference between the top and bottom edges of the metal strip is produced when moving charge carriers are deflected by the magnetic field. Ccg constant current generator, j x current density e electron, b applied magnetic field t thickness, w width v h hall voltage. We imagine that the charge carriers move in a medium that. The vectors e r, eh r and b r determine a right orhogonal trihedron figure 1. Conductivity measurements in semiconductors cannot reveal whether one or both types of carriers are present, nor distinguish between them.