Let a bar of silicon have an intrinsic concentration of 1010 cm3. Silicon, germanium and graphite are some examples of semiconductors. 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. Sociophysics social physics mathematical epidemiology. The definition of mass action law, along with its mathematical. For extrinsic semiconductor the law of mass action states that the product of majority carriers and minority carriers is constant at fixed temperature and is independent of amount of donor and acceptor impurity added. The equations below come from applying the law of mass action to two reactions. It drives the semiconductor back to the thermal equilibrium. Arkfeld on electronic discovery and evidence, by michael r. The law of conservation of mass states that a mass of an object or the amount of matter composed inside an object or thing will not change unless it is added or removed of the matter that is contained in the object itself. While the importance of this and their later publication of 1867 is generally appreciated by writers on the history of chemistry, the usual presen.
Pdf the law of mass action does not force a series of chemical reactions to have. A quaternary example, which is taken from gallant et al. 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. This law can be used to explain the behavior exhibited by solutions in dynamic equilibria. While the importance of this and their later publication of 1867 is generally appreciated by writers on the history of chemistry, the usual presen tation of guldberg and waages work, commonly found.
Electronics engineering lectures and circuit simulations. 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. The principle of detailed balance for the mal kinetics means that k. 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. Kinetic proof of law of mass action physics stack exchange. Mass action law in semiconductors law of mass action hd. The classical mass action law mal systems are dense among the differential equations which preserve positivity different versions of this theorem are proven in 34, 17, see also discussion in 35. The law of mass action also suggests that the ratio of the reactant concentration and the product concentration is constant at a state of chemical equilibrium. Mass action, law of article about mass action, law of by. The second application is concerned with linear gradient elution with steric mass action law. Mclean department of physiology, university of chicago, chicago, illinois the concept of balanced chemical reactions, introduced by wenzel in 1777l and made more exact by berthollet in 1801, was put into the. Guldberg and waages intuition and mathematical formulation may have been all but forgotten by many, but the impact of the mass action law on the fields of chemistry, biochemistry, biology, pathway analysis, and systems biology can hardly be overstated. Information and translations of law of mass action in the most comprehensive dictionary definitions resource on the web.
Massaction law of semiconductors electrical engineering. Generalized mass action law and thermodynamics of nonlinear. Introduction to semiconductor the material which has electrical conductivity between that of a conductor and that of an insulator is called as semiconductor. Depending upon the type of substance, the actual curves can run above or below the logarithmic ones. The reason why your mental image of a semiconductor doesnt really help here, is because its actually impossible to distinguish whether a free. Learn more about the law of mass action in this article. Jan 19, 2018 this video is about mass action law in semiconductors. Semiconductors are the foundation of modern electronics, including transistors, lightemitting diodes, solar cells etc. The law of mass action also has applications in the following fields. But mass action law has to be obeyed in the doped semiconductor too.
Introduction to semiconductor physics and radioelectronics. This, together with the fact that the mass action laws can be written independent of the constant activity species as well, makes the transport equations of these last three. The law of mass action also has implications in semiconductor physics. This constant depends on the thermal energy of the system i. Terms used in this law the following terms are used in this law. The law of mass action mass action in science is the idea that a large number of small units, especially atoms or molecules, acting randomly by themselves can in fact have a larger pattern. May 09, 2015 typically, the dopant concentration is at least 47 orders of magnitude 107 larger than the intrinsic concentration. These developments precede the introduction to ecology but not necessarily because one influenced the other. Law of mass action an overview sciencedirect topics. Now dope it with a donor of concentration 1016 cm3. If you are not sure from the above general theory, here are some examples.
Carrier concentration a intrinsic semiconductors pure single. The definition of mass action law, along with its mathematical representation has. In this chapter i concentrate mainly on epidemiological mass action. But a fundamental law of normal or pathological physiology is that a living organism is organized in.
Etienne fournier, marielouise efthymiou, in what risk. Mass action and concentration dependence of the chemical. For an intrinsic semiconductor, the concentration of electrons in the conduction band is equal to the. In electronics and semiconductor physics, the law of mass action is a relation about the concentrations of free electrons and. It demonstrates the applicability of the numerical approach to feed conditions that are not piecewise constant. It is 150 years this year that the seminal work of two norwegians, cato maximilian guldberg and peter waage, was first published. Lecture 2 mit massachusetts institute of technology. What is the theory behind mass action law in doped. Law of mass action definition of law of mass action by the. Typically, the dopant concentration is at least 47 orders of magnitude 107 larger than the intrinsic concentration. In chemistry textbooks we often see reactions going.
It states that, under thermal equilibrium, the product of the free electron concentration. I would keep it short and to the topic this will give you in depth knowledge of what law of ma. At this stage, you should be able to write the equilibrium expression for any reaction equation. The material which has electrical conductivity between that of a conductor and that of an insulator. Law 1 of mass action definition of law 1 of mass action. 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. Regardless of doping, the product of electron and hole densities is a constant at equilibrium. For extrinsic semiconductor the law of mass action states that the product of. Pdf mass action and conservation of current researchgate. Formation of homogenous and hetrojunction diodes and their energy band diagrams, calculation of contact potential and depletion width, vi characteristics, small signal models of diode, diode as a circuit element, diode. Molecular interactions and how to take them into account when deriving the law of mass action is discussed in some detail sketching a way. You will learn here the basics of law of mass action in semiconductors. Kolokoltsov generalized mass action law the reaction kinetics mal equations are dc dt x.
So when it is doped, recombination rate will increase from its earlier rate to reduce the hole concentration. Guldberg and waages intuition and mathematical formulation may have been all but forgotten by many, but the impact of the mass action law on the fields of chemistry, biochemistry, biology, pathway analysis, and. The law of mass action and the kinetic equations to derive the dynamics of the reaction network, we invoke the law of mass action 1, which states that, for an elementary reaction, that is, a reaction in which all of the stoichiometric coefficients of the reactants are one, the rate of reaction is proportional to the product of the. A few years earlier, fate had brought them together. Mass action law definition of mass action law by medical. Ever thought how a molecule converts to another and how a simple seeming reaction even carries out. Mass action, law of one of the fundamental laws of physical chemistry. A statistical mechanical derivation of the law of mass action for gases and solids is presented, and the problems arising in the application of the law of mass action to the liquid state are addressed. The law of mass action is applied for both intrinsic and extrinsic semiconductors. This law was formulated over the period 186479 by the norwegian scientists cato m. Mass action and concentration dependence of the chemical potential 4 for small concentrations, the measured curve approximates the dotted logarithmic function very well while, at higher concentrations, the two diverge noticeably. Law of mass action definition and meaning collins english. This law states the relation between concentrations of minority and majority carriers at a constant temperature.
In deriving the mass action law, we have to allow for this by allowing arbitrary starting concentrations c i 0 of the particles involved including, if we wish, some concentration of the reaction products even before a reaction took place nobody keeps us from filling some water into the container with h 2 and o 2 before we start the reaction. Definition of law of mass action in the dictionary. Im having trouble understanding this step of the proof the quoted paragraph in the question, and since im trying to understand the proof, i cant assume the law of mass action. Thus maxwell boltzmann and gibbs statistical thermodynamics, and quantum statistics are made considerable use of. I am working through some questions in a book and have got stuck on one. Mass action and concentration dependence of the chemical potential 3. The mass action law gives us a general method to write the expression for the equilibrium constant of any reaction. The law of mass action is the foundation of chemical kinetics and states that the rate of an elementary reaction i. Law of mass action definition of law of mass action by. The law of mass action is the essential principle of chemical reactions and applies to the first stage of genotoxicity direct reaction of the pure chemical on pure cna. Due to the structure of the component matrix the lefthand part is the identity matrix, the last three components labelled. 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. It explains and predicts behaviors of solutions in dynamic equilibrium.
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