Hello Soumendu,

Good that you are asking after reading proper books. Unfortunately, many do the other way.

The concept of work function is not limited to semiconductors. It is rather more important for metals and was introduced in the context of metals. It is an experimentally obtained parameter and is most simply determined from the photoelectric effect experiment. Since in metals electrons are filled up to the Fermi level, and there is no band gap, the minimum energy required to extract an electron from a metal is assigned as its work function. The question about bulk and surface is tricky. You cannot extract electrons from the bulk of a material without extracting it from its surface. So, strictly speaking, work function is a surface property - it has been reported to vary with the surface conditions of the same material. For all practical purposes, work function can be taken as a bulk property if you know what you are doing.

If you extend the concept of work function to semiconductors, there are complications as they have energy band gaps, and when you are extracting electrons by the same photoelectric experiment, electrons are not coming out of the Fermi level. At any finite temperature, there are some electrons available at the bottom of the conduction band, so the photoelectric effect experiment gives a different quantity assigned as the electron affinity of the semiconductor. Now if you still like to calculate the work function, you have to add the energy difference between the bottom of the conduction band and the Fermi level to the electron affinity. That is why the work functions of p- and n-type of the same semiconductor (say, Si) are different. This is also the reason that the work function is not that much useful as a parameter for semiconductors as the electron affinity.

The dilemma of matching the definition of electron affinity in chemistry and semiconductor physics is genuine. In the context of what I said above, you may notice that physically they mean the same thing with the energy measured in the opposite ways.

Hope this clarifies your doubts.

Hello Soumendu,

Good that you are asking after reading proper books. Unfortunately, many do the other way.

The concept of work function is not limited to semiconductors. It is rather more important for metals and was introduced in the context of metals. It is an experimentally obtained parameter and is most simply determined from the photoelectric effect experiment. Since in metals electrons are filled up to the Fermi level, and there is no band gap, the minimum energy required to extract an electron from a metal is assigned as its work function. The question about bulk and surface is tricky. You cannot extract electrons from the bulk of a material without extracting it from its surface. So, strictly speaking, work function is a surface property - it has been reported to vary with the surface conditions of the same material. For all practical purposes, work function can be taken as a bulk property if you know what you are doing.

If you extend the concept of work function to semiconductors, there are complications as they have energy band gaps, and when you are extracting electrons by the same photoelectric experiment, electrons are not coming out of the Fermi level. At any finite temperature, there are some electrons available at the bottom of the conduction band, so the photoelectric effect experiment gives a different quantity assigned as the electron affinity of the semiconductor. Now if you still like to calculate the work function, you have to add the energy difference between the bottom of the conduction band and the Fermi level to the electron affinity. That is why the work functions of p- and n-type of the same semiconductor (say, Si) are different. This is also the reason that the work function is not that much useful as a parameter for semiconductors as the electron affinity.

The dilemma of matching the definition of electron affinity in chemistry and semiconductor physics is genuine. In the context of what I said above, you may notice that physically they mean the same thing with the energy measured in the opposite ways.

Hope this clarifies your doubts.

Yes Sir,

Thank you for taking out time to answer the question.

It does clarify the concepts. Yet, if you could answer this question using Bohr's model, it will be give more clarity to me. I can note from your answer how photoelectric effect was originally used for metals. But, when it comes to semiconductors, especially Silicon which I am dealing with in my research and its your area of interest too, things become confusing. Surely, your answer has given me lot of clarity. Still, out of curiosity, I would appreciate more if you could explain whether Bohr's model of K,L,M shells could be used to explain the three terminologies i.e. work function, electron affinity and ionization potential in a more fundamental manner. It will be helpful for everyone who go through these conversations.

Dear Soumendu,

You are right to think that work function and electron affinity are related to atomic ionization potentials - not just in Si, but in all materials. There is, however, no straight forward relationship known, at least to my knowledge. Vast amount of research has gone into the development of ab-initio quantum mechanical techniques to calculate electronic structures of semiconductors (and solids, in general), but to my knowledge, there is no single theory that can explain everything quantitatively. You may refer to "Electronic Structure and the Properties of Solids" by Walter Harrison for an insight. This book gives a thorough account of the ideas and techniques in a way suitable for workers in semiconductors.

By the way, what is your specific area of research in silicon?

Best wishes

Thank you Sir. I will try to go through the reference.

I am currently working in MEMS area. The devices are built using silicon as the substrate. I am trying to understand silicon as a semiconductor. I am specifically not into material analysis of silicon, its more of technology oriented work.

Yet, I do have plans to work in the materials domain. Its very important to understand them when we are going for fabrication of MEMS or any other semiconductor devices.

Regards,

Soumendu

Dear collegues

Dear Sinah,

You asked a complex question concerning specific energy levels in a solid state material. To answer this question we can say:

-When electrons move in vacuum it can assume continuous values of momentum and energy. They move like a classical particle.

- When the electrons move in a limited space like their movement in atoms , molecules,and solid materials they move as waves and their motion is no longer described by the classical newton laws. Their motion will be governed by the schroedinger wave equation. The solution of the schroedinger wave equation results in the quantization of momentum and energy of the electrons inside the atoms and the solid state material. This means that every electron inside an atom or a solid material has its own quantum values.

In case of atoms the electrons has discrete energy levels as the Bohr model for the hydrogen atom.

In case of crystalline solid material energy bands will be formed instead of discrete level for single isolated atom. This is because of the energy level splitting upon densifying the material by reducing the inter atomic distance and increasing the interaction between the atoms.

In metals the upermost energy band , the valence band,is partially filled with electrons or it overlaps with the adjacent higher empty band called the conduction band.

In semiconductors the valence band occupied by the valance electrons is nearly filled.

The higher band, the coduction band is separated by an energy gap from the valence band and is nearly empty at room temperature.

The occupation of an energy level is determined by Fermi- Dirac function. The fermi level is that level with an occupation probability of one half. As said before it lies inside the conduction band in metals and in the energy gap in semiconductors.

In order to transfer any electron from a lower filled level to a higher empty one must supply the electron by the energy difference between the two level and vice verse.

This energy may be thermal by heating, may be optical photons or any other radiation.

Contact difference of potential between two materials is governed by the work function. Thermionic and opto electronic emission is controlled by the work function also.

I hope i covered some aspects of the energy levels electrons in materials.

You can see this comprehensive report by Prof. R. T. Tung, "Materials Science and Engineering R 35 (2011) 1-138". I am sure you will get your all answers.

Thank you Dr. Abhay. I will go through the review paper.

Thank you Dr. Zerky for the detailed explanation.

Thanks for your discussion. This clear my some doubts.

Do my answer deserve no up vote?. YOU thanked Abhay before me and i answered the question before him. My answer is in the focus of your question.

Dear Sir,

I did vote up your answer. Your answer is as important as others. You took pain to explain the fundamentals, which forms the foundation of all that we are discussing here. Please excuse me if you felt bad. Your contribution IS valuable.

Thank you.

You can think of the terms work function, electron affinity and ionisation potential as in a photo emission experiment on a semiconductor: The work function is the position of the Fermi level at the surface (photo emission is surface sensitive and you may observe band bending), you measure the secondary cut off and subtract it from the photon energy used. The ionisation potential is the position where you observe the valence band edge. Both values are obtained by an UPS measurement. The electron affinity will show up as an unoccupied level in inverse photo emission. In normal cases you can add the value of Egap to the as above measured ionisation potential to obtain the electron affinity. You have to take care, that all measurements are taken from the same sample under the same conditions (temperature, photon flux, clean sample)

Thank you all for your contributions. very usefull.

A really helpful discussion, thank you all for sound clarifications.

nice clarification ....

Really, a nice conversation but I have a doubt that whether work-function of a semiconductor is invariant or it varies with change in fermi-level either due to change in temperature or doping.

Yes, it varies with change in Fermi level.

electron work function is chemical potential of electron in materials, it is equivalent to electronegativity. you can evaluate electron work function by electron work function=(ionization energy + affinity energy) / 2

What is the difference between ionisation potential and work function for insulators?

Thank you all for your valuable discussions.  I am more benefited.

To put in simple words: these are positions of Fermi level, the valance band (Γ-point) maximum and conduction band (Γ-point) minimum respectively from a reference (Vacuum). Work-function will be energy required (or work done) to remove (or add) electron from Fermi level from (or to) infinite distance (Vacuum level). So the energy required for removing electron from valance band to Infinite distance (Vacuum) can be called Ionization potential and energy required for adding an electron to conduction band from vacuum can be called electron affinity.

Thanks to every one for such valuable discussions.

To Vimal: of course changes the workfunction with the position of the Fermi level in a semiconductor e.g. by doping. In the case of band bending you have a work Funktion which also depends on the position!