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