The Hall Coefficient (or Constant) RH is officially defined as this proportionality constant: Ey =RH JB. Mathematically it can be given as:-In extrinsic semiconductor the current carrying charge carriers are of one type either electrons or hole, like in N-type semiconductor the charge carriers are electrons and in P-type semiconductor the charge carriers are holes. CCG – Constant Current Generator, J X – current density ē – electron, B – applied magnetic field t – thickness, w – width V H – Hall voltage . The Hall voltage and the sample resistance may be therefore measured as functions of the temperature using an interface connected to a Personal Computer. Note its independence of 3 Remember that V is not the velocity of any given particle, but an average. (a) Electrons move to the left in this flat conductor (conventional current to the right). Seven wires are soldered to the sample with the geometry shown in figure 2. As expected from the two-band model, the Hall coefficient shows its peak at 50 K at which σ ib … Note that F is a velocity-dependant force. In particular, the steep increase of the Hall mobility with increasing temperature around 50 K is attributed to the transition from ES-VRH conduction to free-hole conduction. The Hall Effect where: n is the number of electrons per unit volume A is the cross-sectional area of the conductor. If the magnetic field is applied along negative z-axis, the Lorentz force moves the charge carriers (say electrons) toward the y-direction. Note that F is a velocity-dependant force. Fig.1 Schematic representation of Hall Effect in a conductor. This equation shows that the Hall voltage, VHall, is proportional to a parameter β = IB d (7) with a constant of proportionality equal to the Hall constant RH = 1 nq (8) Procedure (Ans : 29.4 V and 57.7 × 10 –4 m 2 V –1) The intrinsic carrier density at room temperature in Ge is 2.37 × 10 19 m 3. VHallq w (5) Finally, substituting for the magnetic force yields VHall = 1 nq IB d (6) where d is the thickness of the sheet. The conductivity the Hall coefficient is (–8.4 × 10 –11)m 3 / coulomb. This transverse voltage is the Hall voltage V H and its magnitude is equal to IB/qnd, where I is the current, B is the magnetic field, d is the sample thickness, and q (1.602 x 10-19 C) is the elementary charge. Figure 1. The magnetic field is directly out of the page, represented by circled dots; it exerts a force on the moving charges, causing a voltage ε, the Hall emf, across the conductor. The Hall coefficient, R H, is in units of 10-4 cm 3 /C = 10-10 m 3 /C = 10-12 V.cm/A/Oe = 10-12. ohm.cm/G. The Hall Coefficient (or Constant) RH is officially defined as this proportionality constant: Ey =RH JB. The contacts 7 and 5 are used to measure the voltage V R =RI across the sample, to obtain the resistance R. The Hall effect. 20.7: I = neA„E (20.9) If l is the length of the conductor, the voltage across it is: V = El (20.10) From Ohm’s law and Eqs. 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. When averaged, the single-particle velocity v is replaced by the average V. Figure 1: Illustration of the Hall effect in a bar of conducting material. (Ans : 0471 m) 5. The motivation for compiling this table is the existence of conflicting values in the " popular" literature in which tables of Hall coefficients are given. If the electron and hole motilities are 0.38 and 0.18 m 2 V 1 S 1 respectively, calculate the resistivity. Hence using Eq. 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