Additionally, the density of the charge carriers was. Although a wellrecognized phenomenon, there is still debate about its origins in the various materials. Instrument manuals this lab will be graded 30% on theory, 20% on technique, and 50% on analysis. The difference in the electron and hole mobilities is responsible for the small negative hall coefficient of intrisic semiconductors. Several manufacturers make hall effect sensors in which a sensitive comparator detects the hall voltage and provides a logic output. The hall effect studies also assumed importance because of an anomaly observed between the sign of the charge carriers indicated by hall coefficient and s in amorphous semiconductors. The hall effect which is used to measure the carrier concentration in semiconductors can be applied in a hall probe to measure the magnetic field. In the intrinsic region of a semiconductor, both electrons and holes participate the electric current, the suitable equation for the hall coefficient can be found on page 87 of. At equilibrium, a voltage appears at the semiconductor edges. The hall coefficient for the germanium sample was found to be. This is in agreement with and very close to the literary value of 0. Two solenoids, constant current supply, four probe, digital gauss meter, hall effect apparatus which consist of constant current generator ccg, digital milli voltmeter and hall probe. At the point of zero hall coefficient, it is possible to determine the ratio of mobilities.
An instrument called a hall probe may now be used to measure the flux density b of a magnetic field. Measurement of the hall coefficient 1 measurement of. As discussed below, these quantities are strongly temperature dependent. Hall effect is an effect that is generally used to identify the type of semiconductor. A steady state will be reached when the force of hall voltage and the lorentz force compensate each other, so there is a proportional relation between hall voltage v h, magnetic field h, current i, the so called hall coefficient r h. It could not be compared to a standard value as the exact composition of the semiconductor is unknown. If the concentration of any one kind of carriers is very high as compared to other. In this calculator, you can calculate the hall coefficient of a free electrons in solid semiconductor with known values. The hall coefficient, and the density of free carriers for germanium has been previously found to be 8102 m 3 c, 4 and 1. Kuck physics department, the college of wooster, wooster, ohio 44691 april 30, 1998 this experiment measured the hall coefficient of a sample of germanium to be 1. Hall effect measurements for determining the band gap. Ph 3455mse 3255 the hall effect in a metal and a ptype. Hall effect in ptype semiconductor 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.
Hall effect coefficient an overview sciencedirect topics. An intrinsic semiconductor, with equal numbers of mobile electrons and holes, is predicted to have a zero hall coefficient. You will find the hall voltage and coefficient in the second section. Significance of the hall effect on semiconductors gulpmatrix. In a semiconductor, the hall coefficient can be positive or negative, depending on whether it is p or n type. For example, with hall effect, we can demonstrate that in some semiconductors the current is carried by positively charged holes, and not by electrons. The sign of the charge carriers responsible for conduction. The hall coefficient is defined as the ratio of the induced electric field to the. For example, in nickel, the anomalous hall coefficient is about 100 times larger than the ordinary hall coefficient near the curie temperature, but the two are similar at very low temperatures. The hall coefficient is defined as the ratio of the induced electric field to the product of the current density and the applied magnetic field. Theoretical basics statistics of electrons and holes in semiconductors. What is the method to differentiate between a ptype and an n. Numerical on hall effect, hall coefficient, numerical on hall coefficient, applications of hall effect.
To calculate the hall coefficient and the carrier concentration of the sample material. Now, let us consider a bar of semiconductor, having dimension, x, y and z. B 70 124 view the article online for updates and enhancements. Acknowledgment and disclaimer this material is based upon work supported by the national science. The hall field appears when the sample is placed under an external electric field e r and an external magnetic field b r. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of. The hall coefficient can be defined as the halls field per unit current density per unit magnetic field. Temperature dependences of conductivity and hall effect in semiconductors the goal of this work is to study the method of determination of semiconductor parameters based on the measurement of the conductivity and hall effect.
The hall voltage is much more measurable in semiconductor than in metal i. Consider a semiconductor sample with a rectangular cross section as shown in the figures, a current is flowing in the x direction and a magnetic field is applied in the z direction. If the magnetic field is applied along negative zaxis, the lorentz force moves the charge carriers say electrons toward the ydirection. These charges can be both positive holes and negative electrons in semiconductors. It is a characteristic of the material from which the conductor is made, since its value depends on the type, number, and properties of the charge carriers that constitute the current.
Room temperature hall coefficient and resistivity for. Measurement of semiconductor mobility hall mobility. The hall effect includes the transverse to the flow of current electric field set up by the charges which accumulate on the edges, to counter the magnetic component of the lorentz force acting on them to move towards the edges. The hall effect studies also assumed importance because of an anomaly observed. This experiment measured the hall coefficient of a sample of germanium to be 1. Calculation of hall coefficient for semiconductors answers. Hall coefficient in semiconductors for moderate magnetic. Temperature dependences of hole mobility for different doping levels. These measurements will be used to find the semiconductor type n or p, the doping density, and the majority carrier mobility hall mobility of the silicon sample. Hall observed that when an electrical current passes through a sample placed in a magnetic.
R hall coefficient, uh hall voltage, d semiconductor thickness, i current, b magnitute of flux density. Hall coefficient is the ratio of mobility to conductivity tensor and relaxation time for isotropic tauk on fermi sphere so its simply inverse of carrier density so assuming we have perfect fermi. A steady state will be reached when the force of hall voltage and the lorentz force compensate each other, so there is a proportional relation between hall voltage v h, magnetic field h, current i, the so called hall coefficient r h the hall coefficient also depends on the thickness of the device d. The temperature can have a large effect on the hall coefficient. In these metals, the charge carriers are holes, which act like positive charges. The hall effect is the production of a voltage difference the hall voltage across an electrical. The temperature dependence of the electrical conductivity, and the hall effect in germanium, will be demonstrated. The motivation for compiling this table is the existence of conflicting values in the popular literature in which tables of hall coefficients are given.
Hall effect apparatus holmarc optomechatronics pvt. Determine the hall coefficients for an ntype and ptype ge semiconductor having same thickness. Here a wafer of semiconductor has two contacts on opposite sides which are connected to a high impedance voltmeter, v. Hoedem06 is designed with state of the art modules and components.
Hall coefficient is not generally a constant, but a function of the applied magnetic. In the metal, the charge carriers are conduction electrons, so we expect a negative value of the hall coefficient. When a magnetic field is applied to a conductor in a direction perpendicular to that of the flow of current, a potential difference is. As an example, the hall coefficient in aluminum changes sign as the field increases, indicating that at high fields conduction is dominated by holes see r. Hall effect and its applications in semiconductorsphysics. Information essential to your understanding of this lab. In general n h so that inversion may happen only if p n. Hall effect hall effect in conductor, ntype semiconductor and p. Electron hall mobility versus temperature for different electron concentration. The hall coefficient for the germanium sample was found to be1. The hall effect and hall effect sensors university of denver. The carrier mobility can also be extracted from the hall coefficient. Thanks for contributing an answer to physics stack exchange.
The hall coefficient can be calculated from the measured current, i x, and measured voltage, v h. 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. Hall effect is another important transport phenomenon and has been extensively studied in amorphous semiconductors. Semiconductor hall effect basic concepts, numerical on. The hall coefficient also depends on the thickness of the device d. The dependence of the hall coefficient of a mixed semiconductor upon magnetic induction as exemplified by indium antimonide to cite this article. The hall field eh r is orthogonal on both e r and b r. Hall effect applications of hall effect electrical4u. In this graph a clear exponential law is seen and the data coincide very well with the results obtained by ando ando et al. In this experiment we use the hall effect to determine the sign of the charge carriers in samples of semiconductors and measure the electrical resistivity, the hall coefficient, and the hall mobility for each of two samples of germanium, one ntype, the other ptype. 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 hall effect in conductor, ntype semiconductor. Belarusian state university department of energy physics. The hole hall factor versus temperature for high purity pge morin 1954.
Thus, the sign of the hall coefficient can be used to determine whether a given semiconductor is n or. In this calculator, you can calculate the hall coefficient of a free electrons in. For a particular material, the hall coefficient is found. From the hall coefficient it was deduced that the charge carriers are positive. Ccg constant current generator, j x current density e electron, b applied magnetic field t thickness, w width v h hall voltage. So we expect to observe a positive value of the hall coefficient.
When a current carrying semiconductor is placed in a magnetic field, the charge carriers experience force in the direction which is perpendicular to the flow of current and magnetic field, which results in development of voltage. The result of the measurement is called the hall mobility meaning mobility inferred from a hall effect measurement. Measurement of the hall coefficient in a germanium crystal andrew j. Hall effect hall effect derivation electronics tutorials. Suppose that n is about 10 25 per meter 3 in a semiconductor, and b 1 t wb m2. The hall coefficient, and the density of free carriers for germanium has been previously found to be 810 2 m 3 c, 4 and 1. Ph 3455mse 3255 the hall effect in a metal and a p. In both cases, you will be able to determine the charge carrier density. The vectors e r, eh r and b r determine a right orhogonal trihedron figure 1.
The hall coefficient, r h, is in units of 104 cm 3 c 1010 m 3 c 1012 v. This is because hall coefficient is negative for ntype semiconductor while the same is positive in the case of ptype semiconductor. It could not be compared to a standard value as the exact composition of the semiconductor. Show that the hall coefficient of a material is independent of its thickness. In semiconductors, charge carriers transition from the valence band to the. Hence the hall voltage at b 1t and i10a and t 1 mm for copper and silicone are, 0. So the hall voltage produced in the ntype semiconductor is negative.
Recalling equation iii and expressing in terms of current density and hall field we get. Aug, 2018 determine the type of semiconductor by knowing the direction of the hall voltage, one can determine that the given sample is whether ntype semiconductor or ptype semiconductor. The setup was a rectangular germanium semiconductor placed perpendicular to a magnetic field generated by a large coil. This experiment measured the hall coefficient of a sample of germanium to be. Therefore, the value of charge density can be determined if we know the values of b, i, v h and w hall coefficient. What is the hall voltage for intrinsic semiconductor.
Mar 09, 2012 hall effect in electronics is explained with ntype semiconductor and ptype semiconductor in this video along with few applications of hall effect. How is the hall coefficient related to temperature in metals. Aug, 20 semiconductor hall effect basic concepts, numerical on hall effect, hall coefficient. Again a value for the hall coefficient was calculated to. For more information, see the advanced lab syllabus. For the semiconductor, you will be using a doped semiconductor ptype germanium where the majority charge carriers are holes. Semiconductor hall effect basic concepts, numerical on hall. But avoid asking for help, clarification, or responding to other answers. Rode 1975 electron hall mobility versus electron concentration. Related content the electrical conductivity and hall effect of silicon e h putley and w h mitchell. Determine the hall coefficient for a typical ntype germanium semiconductor having thickness 0. Hall coefficient of germanium wooster physics the college of. What is the method to differentiate between a ptype and. When the hall sensor is placed in a zone with a magnetic field and it is crossed by an electric current that.
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