If the magnetic field is applied along negative z-axis, the Lorentz force moves the charge carriers (say electrons) toward the y-direction. When averaged, the single-particle velocity v is replaced by the average V. When averaged, the single-particle velocity v is replaced by the average V. The Hall voltage and the sample resistance may be therefore measured as functions of the temperature using an interface connected to a Personal Computer. The contacts 7 and 5 are used to measure the voltage V R =RI across the sample, to obtain the resistance R. The Hall Coefficient (or Constant) RH is officially defined as this proportionality constant: Ey =RH JB. VHallq w (5) Finally, substituting for the magnetic force yields VHall = 1 nq IB d (6) where d is the thickness of the sheet. (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. Hall effect is a very useful phenomenon and helps to Determine the Type of Semiconductor By knowing the direction of the Hall Voltage, one can determine that the given sample is whether n-type semiconductor or p-type semiconductor. 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. 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 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. The Hall Effect where: n is the number of electrons per unit volume A is the cross-sectional area of the conductor. 20.9 and 20.10 the resistance R is given by: R = V I = El neA„E R = l neA„ (20.11) 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. Note its independence of 3 Remember that V is not the velocity of any given particle, but an average. As expected from the two-band model, the Hall coefficient shows its peak at 50 K at which σ ib … If the electron and hole motilities are 0.38 and 0.18 m 2 V 1 S 1 respectively, calculate the resistivity. (a) Electrons move to the left in this flat conductor (conventional current to the right). 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. Fig.1 Schematic representation of Hall Effect in a conductor. 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. Note its independence of 3 Remember that V is not the velocity of any given particle, but an average. The Hall Coefficient (or Constant) RH is officially defined as this proportionality constant: Ey =RH JB. Figure 1. Seven wires are soldered to the sample with the geometry shown in figure 2. Hence using Eq. Note that F is a velocity-dependant force. (Ans : 0471 m) 5. The conductivity the Hall coefficient is (–8.4 × 10 –11)m 3 / coulomb. 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 field” for Figure 1: Illustration of the Hall effect in a bar of conducting material. CCG – Constant Current Generator, J X – current density ē – electron, B – applied magnetic field t – thickness, w – width V H – Hall voltage . Experiment20. 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. Hall Co-efficient: The hall coefficient can be defined as the Hall’s field per unit current density per unit magnetic field. 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 motivation for compiling this table is the existence of conflicting values in the " popular" literature in which tables of Hall coefficients are given. The Hall effect. Electrons per unit volume a is the cross-sectional area of the conductor z-axis, Hall... Magnetic field is applied along negative z-axis, the Hall Effect where: n is cross-sectional! 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