Suppose an intrinsic sc crystal with 10 atoms (not possible, but assumed). 4 out of 10 atoms are thermally excited, resulting in 4 electron-hole pairs ($n=4;p=4$). It is converted into n-semiconductor by doping it with 2 atoms of pentavalent impurities. The 2 impurity atoms replace the 2 host atoms to maintain the total number of atoms, i.e. 10. The equation applies to both intrinsic and extrinsic semiconductors and says 2 important facts about extrinsic semiconductors: Le Chatelier`s principle states that for reactions that are in dynamic equilibria, changes in concentration, pressure, or temperature shift the equilibrium position to counteract the change and establish a new state of equilibrium. The equilibrium constant for this reaction can be calculated using the formula of the law of mass action: For a general reaction denoted aA + bB → products, the reaction rate according to the law of mass action is given as follows: If Qc takes place > Kb, the reaction takes place in reverse. The law of mass action explains the relationship between the rate of a chemical reaction and the molar concentration of the reactants at a given temperature. The law of mass action in chemistry, proposed in 1864 by Norwegian scientists Peter Wage and Cato Gulberg, underlies many types of physiological, biochemical and pharmacological phenomena. Now, to chemically balance a reaction, „When a pure semiconductor is doped with n-type impurities, the number of electrons in the conduction band exceeds one level and the number of holes below one level. Similarly, adding p-type impurities to a pure semiconductor increases the number of holes in the valence band above a level and decreases the number of electrons in the conduction band below a level.
The concentration quotient (QC) of a chemical reaction at a given temperature is defined as the ratio of the product to the concentrations of the products and those of the reactants. However, when the system reacts, the Qc value fluctuates, but the equilibrium concentrations determine the equilibrium constant Kc. Temperature: In endothermic reactions, an increase in temperature shifts the equilibrium to the right. Conversely, in exothermic reactions, an increase in temperature shifts the balance to the left. The law of mass action is applied to both intrinsic and extrinsic semiconductors. For extrinsic semiconductors, the law of mass action states that the product of the majority and minority carriers is constant at a fixed temperature and is independent of the amount of donor and acceptor impurity added. The law of mass action is also useful in the following areas: Pressure: Pressure affects gas reactions. These can be classified into three types of gaseous reactions: In an intrinsic semiconductor in thermal equilibrium, the charge carrier generation and recombination rate are balanced so that the net carrier density is constant. The n and p concentrations, electrons and holes are also the same. When an intrinsic semiconductor is doped with a dopor impurity, such as phosphorus, the electron concentration increases due to the excess electrons provided by each of the doping atoms. The concentration of the hole remains the same.
The net effect is -> $ np> n_i^2 $. But even in doped-up semiconductors, the law on mass actions must be followed. Thus, when doped, the rate of recombination increases compared to its previous rate to reduce the concentration of the hole. It returns the semiconductor to thermal equilibrium. i.e. $ np = n_i^2 $. Using the charge carrier concentration equations given above, the law of mass action can be expressed as one in n-semiconductor, since the number of electrons (majority) in the conduction band increases the number of holes (minority) in the valence band. Reactions without volume change: Reactions in which the volume remains unchanged are independent of pressure changes. Their second hypothesis, however, is a more basic explanation.
With the Mass Action Act, you are essentially assuming that doping has no influence on the number of states, that is, on an undisturbed state density. And with simple calculations of permutation and combination (multinomial theorem in combinatorics), we arrive at the law of mass action. The above discussion shows that doping impurities of both types in an intrinsic semiconductor cause an increase in conductivity and cause free electrons or holes to dominate the situation. You see, in n-semiconductors, holes can only be created by thermal excitation. Reactions with increased volume: In reactions accompanied by an increase in volume, a reduction in pressure increases the reaction rate. The law of mass action for n-semiconductors is mathematically written as follows: Suppose we have an intrinsic semiconductor. It is known that in an intrinsic semiconductor, $n=p=n_i$ It is doped and converted into an n-type semiconductor. As mentioned earlier, the concentration of free electrons and holes in an intrinsic semiconductor is always the same. When N-type impurities are added to an intrinsic semiconductor, the concentration of free electrons is increased (or the concentration of holes is reduced below the intrinsic value). Similarly, the addition of P-type impurities results in a reduction in the concentration of free electrons below the intrinsic value. Theoretical analysis shows that in thermal equilibrium, the product of the concentration of free electrons and the concentration of holes is constant and independent of the amount of doping by donor and acceptor impurities. This is called the law of mass action in semiconductors.
Thus, for n-type semiconductors, $ n>n_i $ so $ pn_i $ so $ n<n_i $ Consider hypothetically the following reversible reaction: In the same way, the inverse reaction rate will be: According to the definition of the law of mass action, the reaction rate "R" is given as follows: In p-semiconductors, The number of electrons in the conduction band (minority) decreases as the number of holes (majority) in the valence band increases. Therefore, the product of holes (majority) and electrons (minority) remains constant at a fixed temperature. The rate of each chemical reaction is proportional to the product of the masses of the reactive substances, each mass being raised to a power equal to the coefficient that occurs in the chemical equation according to the law of mass action.