Mass action and concentration dependence of the chemical. During doping, impurity atoms are introduced to an intrinsic semiconductor. Donors and acceptors principles for analyzing compensated semiconductors session 3. Donor impurity concentration for ptype semiconductors, n h. The law of mass action forms the basis of the compartmental model of disease spread in mathematical epidemiology, in which a population of humans, animals or other individuals is divided into categories of susceptible, infected, and recovered immune. Feb 28, 20 law of mass action which says that product of electron and hole concentrations is constant for a semiconductor in equilibrium. Law of mass action, law stating that the rate of any chemical reaction is proportional to the product of the masses of the reacting substances, with each mass raised to a power equal to the coefficient that occurs in the chemical equation. Generalized mass action law and thermodynamics of nonlinear. Introduction to semiconductor physics and radioelectronics. Here, the law of mass action provides a relationship between the concentrations of electron holes and free electrons when the semiconductor system is in a state of thermal equilibrium. E 1, e ev above fermi level and e 2, e ev below the fermi level. Semiconductor law of mass action the dispersion relation of electrons in the c.
For systems that are not at equilibrium yet, the ratio calculated from the mass action law is called a reaction quotient q. The material which has electrical conductivity between that of a conductor and that of an insulator. Mass action and concentration dependence of the chemical potential topic. The law of mass action describes how the velocity of a chemical reaction is related to the molecular concentrations of the reactants. P 1 and p 2 are respectively the probabilities of e 1 being. Impurity atoms are atoms of a different element than the atoms of the intrinsic semiconductor. This law states the relation between concentrations of minority and majority carriers at a constant temperature.
What is the theory behind mass action law in doped. Thermal equilibrium is described by a relationship between the concentrations of charge carriers at a. 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. Mass action law the np product is a constant n i 2 that. It states that, under thermal equilibrium, the product of the free electron concentration and the free hole concentration is equal to a constant square of intrinsic carrier concentration. For an intrinsic semiconductor, we have e e i, the intrinsic. Feb 09, 2015 during doping, impurity atoms are introduced to an intrinsic semiconductor. Lawofmass action relates concentration of reactants. The reason why your mental image of a semiconductor doesnt really help here, is because its actually impossible to distinguish whether a free. An intrinsic semiconductor is a pure semiconductor, i. For n type semiconductor p holes represents the minority carrier concentration. It will derive the equations between equilibrium constants at constant partial pressure kp, concentrations kc and discuss some reallife. Impurity atoms act as either donors or acceptors to the intrinsic semiconduc.
Niknejad 6 conductivity of a gas l electrical conduction is due to the motion of positive and negative charges l for water with ph7, the concentration of. There is relationship between intrinsic concentration and density of. This property is referred to as the mass action law. The law of mass action is applied for both intrinsic and extrinsic semiconductors. Cut out a similar pattern on a resistor paper with a known. We introduced the concepts of effective density of states, mass action law, and intrinsic and extrinsic semiconductor. Law of mass action according to law of mass action the product of majority and minority charge carrier concentration at a particular temperature is equal to the square of intrinsic carrier concentration at that particular temperature. This relation is only valid for nondegenerate semiconductors in thermal equilibrium.
In any semiconductor at equilibrium, the law of mass action should be satisfied i. In a semiconductor the law of mass action states that the product of the electron concentration and the hole concentration is always equal to the square of the intrinsic carrier concentration at a given temperature, i. The impurity atoms are called dopants and are usually either third group or fifth group elements. An extrinsic semiconductor is a semiconductor doped by a specific impurity which is able to deeply modify its electrical properties, making it suitable for electronic applications diodes, transistors, etc. The material which has electrical conductivity between that. Hot network questions since the cmb is the oldest thing we can see, how do we know for sure what happened before the cmb. In electronics and semiconductor physics, the law of mass action is a relation about the concentrations of free electrons and electron holes under thermal equilibrium.
Mass action law in semiconductors law of mass action hd. Before we introduce the mass action law, it is important for us to identify a system or a closed system in our discussion. Now dope it with a donor of concentration 1016 cm3. Belarusian state university department of energy physics tempus program of the. In electronics and semiconductor physics, the law of mass action is a relation about the concentrations of free electrons and electron holes under thermal. Fundamentals of semiconductor physics doped extrinsic.
The law of mass action states that the product of number of electrons in the conduction band and the number of holes in the valence band is constant at a fixed temperature and is independent of amount of donor and acceptor impurity added. Imagine a regular crystal lattice composed of identical atoms. Ee143 semiconductor tutorial university of california, berkeley. In a recent research note rose 1957 the massaction laws for the reactions bety,xy3l free carriers and impurities in semiconductors have been derived. For extrinsic semiconductor the law of mass action states that the product of. Ee143 semiconductor tutorial university of california. Generalized mass action law and thermodynamics of nonlinear markov processes a. This is a typical example of the law of mass action. A is complex to calculate in semiconductor diodes consists of both bottom of the well and sidewall areas cj is a strong function of biasing must be recalculated if.
Electronics devices and circuits semiconductor introduction to semiconductor. This video is about mass action law in semiconductors. In this chapter, we have first described the equilibrium properties of charge carriers in a semiconductor. Intrinsic semiconductors definition an intrinsic semiconductor is a semiconductor in which no other material is intentionally doped similar to mixing. Given effective density of states nc, nv, bandgap eg values at t300k, write a program that calculates p, n and all band energies ec, ev, ef, ei for a given donor concentration nd and acceptor concentration na, solve for hole and electron concentrations p and n first using the solution given below. This doped semiconductor is called an extrinsic material. Law of mass action the np product is constant in te n o p o n i 2 t second equation where does this last equation come from. Eele 414 introduction to vlsi design mosfet operation. May 09, 2015 typically, the dopant concentration is at least 47 orders of magnitude 107 larger than the intrinsic concentration. Physics 301 30nov2005 261 semiconductor basics in solids, the electron energy levels are organized into bands. L l in intrinsic semiconductor, expressions for the electron and hole concentrations are. Quick python programming with semiconductor device. R s resistor r s paper ic resistor pattern resistor paper pattern microns centimeters magnified resistance of arbitrary layout patterns before you do the layout and fabricate the structure which is expensive and time consuming.
Mar 04, 2020 law of mass action, law stating that the rate of any chemical reaction is proportional to the product of the masses of the reacting substances, with each mass raised to a power equal to the coefficient that occurs in the chemical equation. Diodes and diode circuits tlt8016 basic analog circuits 20052006 18 p type semiconductor material the mass action law acceptor. Intrinsic semiconductor definition, examples, diagrams. The doping process can greatly alter the electrical characteristics of the semiconductor. Is the principle of mass action law applicable in a pn. It is a powerful relation, which enables to quickly find the hole density if the electron density is known or vice versa. Mass action law the np product is a constant n i 2 that depends on the material from ee at university of california, santa cruz. The nonlinear markov processes are the measurevalued dynamical systems which.
Equilibrium carrier concentration engineering libretexts. Sep 16, 2015 semiconductor law of mass action electron density hole density. Semiconductor industry clients have relied on pillsbury for legal counsel since 1968. Why n and p are not additive in law of mass action. Learn more about the law of mass action in this article.
The acceptor atoms always accept an extra electron, creating negative ionized cores and shortage of free electrons. Law of mass action which says that product of electron and hole concentrations is constant for a semiconductor in equilibrium. Semiconductor law of mass action electron density hole density. Massaction law of semiconductors electrical engineering. You will learn here the basics of law of mass action in semiconductors. Extrinsic semiconductor definition, examples, diagrams.
Typically, the dopant concentration is at least 47 orders of magnitude 107 larger than the intrinsic concentration. Now, if acceptor impurities are concentration of n a. Ee143 s06 semiconductor tutorial r ic resistor r paper. The semiconductor is in internal turmoil, with bonds being broken and reformed continuously. Mass action and concentration dependence of the chemical potential 1 5. On the massaction laws in degenerate semiconductors iopscience. Kolokoltsovb adepartment of mathematics, university of leicester, leicester, le1 7rh, uk bdepartment of statistics, university of warwick, coventry, cv4 7al, uk abstract. The equilibrium of the carriers in a semiconductor always follows the mass action law this means there is an equal number of p and n charge carriers in intrinsic silicon electrons vs. When an intrinsic semiconductor is doped with a dopor impurity like phosphorus, electron concentration will increase, due to the surplus electron provided by each of the doper atom. Law of mass action extrinsic semiconductors law according to law of mass action, n e n h n i 2 for ntype semiconductors, n e. So, inversely proportional to doping concentration option b 16. Today, our semiconductor industry practice is the largest in the country, drawing from a multidisciplinary group of attorneys covering all areas of law including corporate, intellectual property, regulatory and licensing and litigation. Equilibrium charge carrier statistics in semiconductors. Let a bar of silicon have an intrinsic concentration of 1010 cm3.
Belarusian state university department of energy physics. Lecture 2 mit massachusetts institute of technology. Another important equation for finding the carrier concentrations in the material is provided by the law of mass action, which before discussing we must first become acquainted with a description of thermal equilibrium. Addition of an impurity to a semiconductor greatly increases the conductivity of the semiconductor and the process is called doping of a semiconductor.
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