Law of Mass Action: Intrinsic & Extrinsic Semiconductors

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In summary, the law of mass action states that the product of the electron concentration and the hole concentration in a semiconductor is equal to the square of the intrinsic carrier concentration at a given temperature. This law applies to both intrinsic and extrinsic semiconductors, as long as the density of states is constant and the temperature is constant. However, in an extrinsic semiconductor, charge neutrality may not hold and the concentration of one carrier may increase while the other remains constant. This can be explained by the rate of recombination and the effect of doping on carrier concentration. For example, in a pn junction, the carrier concentrations on each side of the junction depend on the doping levels and the temperature.
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Repetit
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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.e.:

[tex]
n p = n_i^2
[/tex]

My book states that this law is valid for extrinsic semiconductors (with impurities) as well as for intrinsic semiconductors. I don't understand how it can be valid for extrinsic semiconductors. In an intrinsic semiconductor charge neutrality requires n=p. I understand that the law is valid for intrinsic semiconductors. But if I start out with an intrinsic semiconductor and put in some electron donors, only [tex]n[/tex] will increase, [tex]p[/tex] and [tex]n_i[/tex] will not change. So how can it be valid in the extrinsic case?
 
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  • #2
That's because of how n and p are given in the mathematical expression.

Using the effective density of states approximation for n and p in the conduction and valence band respectively:

[tex]n = N_C exp(-\frac{E_C - E_F}{kT}) \ \mbox{and} \ p = N_V exp(-\frac{E_F - E_V}{kT})[/tex]

Multiplying them together gives [tex]np=N_C N_V exp(-\frac{E_g}{kT})[/tex] since [tex]E_C - E_V[/tex] is equivalent to Eg, the bandgap.

Note that the expression on the right is independent of Ef, the fermi level and hence independent of doping. This is of course valid only under the assumption that Nc and Nv is given at some constant temperature.
 
  • #3
Repetit said:
But if I start out with an intrinsic semiconductor and put in some electron donors, only [tex]n[/tex] will increase, [tex]p[/tex] and [tex]n_i[/tex] will not change

That's not true at equilibrium. [tex]n[/tex] will increase initially, but after a few moments some electrons added will fall in valence band, reducing holes concentration. mass action law rules matter flow between two (classical) systems at equilibrium
 
  • #4
Thank you for the answers! It makes more sense to me now.
 
  • #5
I still don't understand this. Can anyone please elaborate?
What I understand is, Intrinsic carriers are the are electron hole pairs formed without doping, after doping the number of majority carriers is increased by a large number. Now how can the law holds true??
 
  • #6
I was asked why the law of mass action in not valid at very low temperatures. I thought that it was, since for very low temperature it holds the condition [tex] E_g >> k_B T [/tex] (I think so...). But maybe for some other reason it breaks. Does someone know why?
 
  • #7
Boltzmann statistics as a high temperature approximation of Fermi-Dirac statistics?
 
  • #8
Repetit said:
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.e.:

[tex]
n p = n_i^2
[/tex]

My book states that this law is valid for extrinsic semiconductors (with impurities) as well as for intrinsic semiconductors. I don't understand how it can be valid for extrinsic semiconductors. In an intrinsic semiconductor charge neutrality requires n=p. I understand that the law is valid for intrinsic semiconductors. But if I start out with an intrinsic semiconductor and put in some electron donors, only [tex]n[/tex] will increase, [tex]p[/tex] and [tex]n_i[/tex] will not change. So how can it be valid in the extrinsic case?
The rate of recombination is R=Bnp and increasing the n would increase recombination rate so that both n and p decrease and their product remains constant.
 
  • #9
Realise this is an old thread, but I am similarly confused. If I have a ##pn## junction, then on the ##n## side of the junction, it's doped by ##N_{D}##, the p by ##N_{A}##. ##N_{D}## and ##N_{A}## (within operating temperature) should not depend on the temperature ##T##.

So how come my solution sheet says that:

$$ n_{n} = N_{C} exp\bigg( -\big[\frac{ E_{C} - E_{Fn}}{k_{B}T} \big] \bigg) =N_{D} $$

##E_{Fn}## is the intrinsic fermi level on the ##n## side of the junction, and ##E_{C}## the conduction band energy.

I think that perhaps this equation from my notes might help - but it's been derived from nowhere, and I don't understand it... Would really appreciate some help on this! Thanks
Screen Shot 2016-05-25 at 15.10.51.png
 
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1. What is the Law of Mass Action?

The Law of Mass Action is a fundamental principle in chemistry and physics that describes the relationship between the concentrations of reactants and the rate of a chemical reaction. It states that the rate of a reaction is directly proportional to the product of the concentrations of the reactants.

2. What is the difference between intrinsic and extrinsic semiconductors?

Intrinsic semiconductors are pure semiconducting materials, such as silicon or germanium, that have an equal number of electrons and holes (deficient electrons). Extrinsic semiconductors, also known as doped semiconductors, have impurities intentionally added to them to increase their conductivity. These impurities can either introduce extra electrons (n-type) or holes (p-type) into the material.

3. How does the Law of Mass Action apply to semiconductors?

In semiconductors, the Law of Mass Action describes the relationship between the concentration of electrons and holes and the conductivity of the material. As the concentration of free electrons and holes increases, the conductivity of the material also increases.

4. How does temperature affect the Law of Mass Action in semiconductors?

According to the Law of Mass Action, the rate of a reaction increases with an increase in temperature. This also applies to semiconductors, as an increase in temperature leads to a higher concentration of free electrons and holes, thus increasing the conductivity of the material.

5. What practical applications rely on the Law of Mass Action in semiconductors?

The Law of Mass Action is essential in understanding and designing electronic devices such as transistors, diodes, and solar cells. It also plays a crucial role in the development of semiconducting materials for use in various industries, including electronics, optoelectronics, and energy production.

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