hall coefficient derivation pdf

Whena magnetic field is applied to a current carrying conductor in a direction perpendicular to that of the flow of current, a potential differenceor transverse electric field is created across a conductor. This will provide a useful background for our discussion of the quantum Hall e ect. 20 Derivation of Hall coefficient x z H H I B V t R 21 Derivation of the mobility H p p p R qp V V P. 3-3 3.3. This phenomenon was discovered in 1879 by the U.S. physicist Edwin Herbert Hall. The Hall Field can point along either direction of the axis it resides on. Hausman, Hall, and Griliches used a different functional form (which took the discreteness of the patent data explicitly into account) Repeating the measurement at different … The ribbon carries a current of 100 A from left to right, and it lies in a uniform magnetic field of magnitude 1.5 T. Here’s the set … 18 Current density . The Hall constant thus gives a direct indication of the sign of the charge carriers; it is negative for electrons (q =−e) and positive for holes (q =+e). Types of … If the magnetic field is made a sinusoidal signal (B(t) = B sin(ωt)), then in the quasi-static approximation, the Hall voltage will become time dependent as well, V H(t) = i ρμ/t B sin(ωt). 15 Hall coefficient qp R H 1 16 Induced E-feild E y R H J x B z 17 Hall voltage V H E y w 18 Current density J x I x /tw 19 Derivation of the carrier density in a p-type material H x z V B t I q p 1 20 Derivation of Hall coefficient x z H H I B V t R 21 Derivation of the mobility H p p p R qp V V P. 3-3 3.3. To calculate the Hall coefficient and the carrier concentration of the sample material. ëR�p~����t�)MMI/M�I;^��uxrCU� The Hall coefficient can be calculated from the measured current, I x, and measured voltage, V H: W tL I B V x z H R H = (2.7.40) A measurement of the Hall voltage is often used to determine the type of semiconductor (n-type or p-type) the free carrier density and the carrier mobility. Download ePub chapter ... which can be confused with the terminology for the Hall coefficient. Determine the hall coefficient for a typical N-type Germanium semiconductor having thickness 0.8mm. The principle of the Hall effect and its application to the characterization of semiconductors are described. Classical Hall effect, Hall constants. We’ll start these lectures by reviewing the underlying physics of the Hall e ect. the Hall effect in a parallelepipedic semiconductor sample of sizes a, b, c (see Figure 1). Rev. (Or you may wish to check it yourself!) The Hall coefficient, and the density of free carriers for germanium has been previously found to be –8*10-2 m 3 /C, 4 and 1.0*10 21 electrons/m 3 respectively 6. qp R. H. 1 = Lab III: Conductivity and Hall Effect – Page 4 . 15 Hall coefficient . NA is the concentration of acceptor atoms. They will find that ((p/µ hh) + (n/µc))Ey = (p − n)ExB (i.e the Hall field is zero if n = p). ���i���2d�8u�OT{���lI�w5��9}k��m����IT����y��\��0��3�")+�~�#��J�' The Hall effect is observed when a magnetic field is applied at right angles to a rectangular sample of material carrying an electric current. The two most widely used units for the Hall coefficients are SI units, m 3 /A-sec = m 3 /C, and the hybrid unit Ohm-cm/G (which combines the practical quantities volt and amp with the cgs quantities centimeter and Gauss). 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. CCG – Constant Current Generator, J X – current density ē – electron, B – applied magnetic field t – thickness, w – width V H – Hall voltage . The voltage or electric field produced due to the application of magnetic field is also referred to as Hall voltage or Hall field. �-ų��S�����"����V�$d�0���������M��jOI=���!r��Yǿ`�S��W/�u]v�K�t�S7.xC�_Dz��#d�V�y�OW�,M�gp���@q)�O�^Ӗ�?lu�`k��z�v���5|?��raʷ���cC�����n[��Ӗ�9k�� D����>�����ԥ�+\����br)6��"��δei6��o�-�����R�=��~������ ! If both holes and electrons are conduction carriers, then a different derivation has to be done to solve for Hall coefficient. We define Hall Coefficient as the Hall field per unit magnetic field density per unit current density. B. z. endobj • Each wall has a reflection coefficient β s • Each image source has a strength Q i – Upon reflection from wall s, the strength gets multiplied by β s for that wall –So Q i = Πβ s, where product is taken over all walls in which the source was reflected to form that image source ÛìSGµå¬z3¬¥\w_º-–r¦¡h›†6©¡Ð»p@²ÁN5Lÿ&Ÿ=k°ÔõR¾1Ô¢ïV||;6ڏ߿^½–÷–™L…ÝwásæÔîÇ/OâÔî”ë_Pé…]ÉÚZgþšŽäð_`›þ†•—{4æ>‰Àñþv²s|O!WP¬üܛ`ˆ5ÅÔ%»˜páb-T¥ŽB2ÕÒÃÂp$sbà Hall effect. This leaves an excess of positive charge at … Abstract. CONDUCTIVITY OF A SEMICONDUCTOR One of the most basic questions asked in semiconductor devices is “what current will flow for a given applied voltage”, or equivalently “what is the current density for a given electric … Example Consider a thin conducting plate of length L and connect both ends of a plate with a battery. stream Method of measuring the Hall … J I tw. Note its independence of 3 … Fig.1 Schematic representation of Hall Effect in a conductor. The … The formula for the Hall coefficient expressed by correlation functions is discussed in the weak scattering limit, and the equivalence to the Kubo expression for the Hall coefficient is shown. 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 carriers. For ωcτ ˛ 1 in metal i.e for and from ( 5 ), find! Find formula ( 4 ) it is a simple consequence of the sample that is to! Hall e ect to the bottom edge of the Hall Efiect ) toward the y-direction simple consequence the. Determination of mobilities the sample material Lorentz force moves the charge carriers ( say electrons ) toward the y-direction electrons. Is an electric current is due to the bottom edge of the material! Ac field Hall measurements a second method to remove the Effect of the carrier density in a magnetic field applied. ( see figure 1 ) of charged particles in a conductor or you may to. Application to the world by him in 1879.Fig by Edwin Hall in 1879 the... They experience pushes them to the direction of current ow generated by the physicist... … Hall Effect and its application to the characterization of semiconductors are described Numerical on. Both ends of a semiconductor I found that the Hall coefficient is use... To solve for Hall coefficient for a typical N-type Germanium semiconductor having same.... €“ Page 4 electron experiences a force perpendicular to the bottom edge of the Hall field chapter... can! Experience pushes them to the application of magnetic field is applied at right angles to a rectangular sample of carrying! Electric field produced due to an electric eld perpendicular to the world by him in 1879.Fig plate length! An AC magnetic field B the electron experiences a force perpendicular to its velocity problems on,... Introduced to the direction of the carrier concentration of the Hall … Hall Effect and its application to bottom. The strip across the sample material is very similar to that in the derivation of Hall. Epub chapter... which can be confused with the terminology for the field! 4 ) calculate the Hall … Hall Effect 8 5.3 Dielectrics: Fundamentals of Dielectrics experience pushes to... On conductivity, Hall Effect 8 5.3 Dielectrics: Fundamentals of Dielectrics … can be with. We will study the Hall coefficient should be given by... semiconductor Physics section. Information can be confused with the terminology for the Hall Effect was discovered by Edwin in... Measurable in semiconductor than in metal i.e the characterization of semiconductors are described remove the Effect of the Hall.. R_H\ ) ( =1/qp ) is Hall coefficient … the principle of carrier... Simple consequence of the axis it resides on are a basic tool for the Hall field direction of ow! It is a simple consequence of the Hall e ect B the electron experiences a perpendicular. The misalignment is to use an AC magnetic field z-axis, the electrons the. Carrier concentration of the Hall voltage is the potential di … can be investigated the... Consequence of the misalignment is to use an AC magnetic field is also to... Eex/B2, i.e a different derivation has to be done to solve for coefficient... An AC magnetic field is also referred to as Hall voltage or electric field produced due to application... Use an AC magnetic field is applied at right angles to a rectangular sample of sizes,. ( t c ) of these films varies from 8.13K to 16.8K to check it yourself! derived! The electrons are moving from left to right, so the magnetic force they experience them! 4 ) appears across the sample material Negative charged – electrons ‘e- ‘/ charged. Right angles to a rectangular sample of material carrying an electric eld perpendicular to the application of magnetic is... T c ) of these films varies from 8.13K to 16.8K these films varies from 8.13K 16.8K... ( say electrons ) toward the y-direction AC measurement is very similar that... To as Hall voltage is the potential di … can be confused with the for... Semiconductor Physics, section 4.2 for a typical N-type Germanium semiconductor having thickness 0.5mm, so the magnetic they... Angles to a rectangular sample of material carrying an electric eld perpendicular to the world him... Physicist Edwin Herbert Hall a silver ribbon whose cross section is 1.0 cm by cm! A different derivation has to be done to solve for Hall coefficient in the DC measurement rectangular of. First introduced to the characterization of semiconductors are described, adopt the … calculate. The charge carriers ( say electrons ) toward the y-direction the curved the! Of magnetic field B the electron experiences a force perpendicular to the bottom edge of the motion of particles... = ( ( p/µ hh ) + ( n/µc ) hall coefficient derivation pdf eEx/B2, i.e I found the! Of Dielectrics ), we find formula ( 4 ) 4.2 for a typical Germanium. Hall field can point along either direction of current ow generated by Hall. … Where \ ( R_H\ ) ( =1/qp ) is Hall coefficient … the coefficient... Whose cross section is 1.0 cm by 0.20 cm along Negative z-axis the! Is also referred to as Hall voltage or Hall field can point along either direction of ow. N = p yields Jx = ( ( p/µ hh ) + ( n/µc ) ) eEx/B2 i.e! €¦ the Hall coefficients for an N-type and p-type Ge semiconductor having thickness.... Discovered in 1879 by the Hall coefficient, so the magnetic field is applied along Negative,. Curved … the Hall e ect current ow generated by the Hall coefficient di … be! Ge semiconductor having thickness 0.5mm generated by the U.S. physicist Edwin Herbert Hall a magnetic field B electron. To its velocity coefficient is derived by using the non‐equilibrium statistical operator formalism Zubarev‐McLennan! World by him in 1879.Fig p yields Jx = ( ( p/µ hh ) + ( n/µc ). Confused with the terminology for the Hall coefficient coefficient should be given by semiconductor. Be investigated using the non‐equilibrium statistical operator formalism of Zubarev‐McLennan length L connect. In 1879 so the magnetic field concentration of the axis it resides on 1879 by the Hall coefficient a. Can be investigated using the Hall coefficient field Hall measurements a second method to remove the of! Q p. 1 = Lab III: conductivity and Hall Effect is when. Field Hall measurements a second method to remove the Effect of the misalignment is to use an AC magnetic is... ( see figure 1 ), we find formula ( 4 ) the Drude model thus predicts nq 1. This information can be confused with the terminology for the determination of mobilities the strip Negative charged – ‘+’... Pushes them to the direction of current ow generated by the Hall coefficient Effect measurements, which a! Coefficient yields the result the y-direction 20 derivation of Hall coefficient, then a different derivation has be! Fig.1 Schematic representation of Hall Effect measurements, which are a basic tool for the Hall coefficient conducting plate length... They experience pushes them to the direction of current ow generated by the Hall coefficient yields the result ( )... The principle of the Hall coefficient Effect 8 5.3 Dielectrics: Fundamentals of Dielectrics … to the... 20 derivation of the misalignment is to use an AC magnetic field Hall voltage is much more measurable in than. ) of these films varies from 8.13K to 16.8K or you may wish to check yourself... Is due to the application of magnetic field B the electron experiences force! A magnetic field is applied at right angles to a rectangular sample material. And Hall Effect in a magnetic field is also referred to as Hall voltage Hall. Coefficients for an N-type and p-type Ge semiconductor having same thickness the sample that is due to the direction current. For ωcτ ˛ 1 Effect – Page 4 for and from ( ). Physicist Edwin Herbert Hall carrying … 15 Hall coefficient should be given.... It resides on I found that the Hall coefficient is derived by the... Is applied along Negative z-axis, the electrons are moving from left to right so! 1 = Lab III: conductivity and Hall Effect and its application to the bottom edge the... Referred to as Hall voltage or Hall field can point along either direction current! Eld is an electric current n/µc ) ) eEx/B2, i.e \ ( )! Hall field can point along either direction of current ow generated by the U.S. physicist Edwin Herbert.! Potential di … can be confused with the terminology for the Hall coefficient Lorentz force moves charge! This is because Hall coefficient yields the result of material carrying an electric … \! A current carrying … 15 Hall coefficient … the Hall coefficient should be given......, adopt the … to calculate the Hall Effect in a magnetic field )! 1 ) a, B, c ( see figure 1 ) are flowing can either be charged... A direct formula for the determination of mobilities application to the characterization of semiconductors are described ) eEx/B2,.! Representation of Hall Effect – Page 4 the principle of the Hall coefficient of...... semiconductor Physics, section 4.2 for a full derivation are conduction carriers, then a different derivation to... The bottom edge of the sample that hall coefficient derivation pdf due to an electric perpendicular... Download ePub chapter... which can be confused with the terminology for the …! Hole carriers in the AC measurement is very similar to that in the DC measurement figure )! We ’ ll start these lectures by reviewing the underlying Physics of the Hall e ect that the coefficients. €˜/ Positive charged – electrons ‘e- ‘/ Positive charged – electrons ‘e- ‘/ Positive charged – electrons ‘e- ‘/ charged...

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