Dear Ahmad,

The following text covers the answer to your question:

The Seebeck effect is the conversion of heat directly into electricity at the junction of different types of wire. It is named for the Baltic German physicist Thomas Johann Seebeck. Seebeck, in 1821, discovered that a compass needle would be deflected by a closed loop formed by two different metals joined in two places, with a temperature difference between the joints. This was because the electron energy levels in each metal shifted differently and a voltage difference between the junctions created an electrical current and therefore amagnetic field around the wires. Seebeck did not recognize there was an electric current involved, so he called the phenomenon the thermomagnetic effect. Danish physicist Hans Christian Ørsted rectified the oversight and coined the term "thermoelectricity".

The Seebeck effect is a classic example of an electromotive force (emf) and leads to measurable currents or voltages in the same way as any other emf. Electromotive forces modify Ohm's law by generating currents even in the absence of voltage differences (or vice versa); the local current density is given by

J = sigma (-deltaV + Eemf)

where V is the local voltage[2] and sigma is the local conductivity. In general, the Seebeck effect is described locally by the creation of an electromotive field

Eemf = -SdeltaT

where S is the Seebeck coefficient (also known as thermopower), a property of the local material, and deltaT is the gradient in temperature T.

The Seebeck coefficients generally vary as function of temperature, and depend strongly on the composition of the conductor. For ordinary materials at room temperature, the Seebeck coefficient may range in value from −100 μV/K to +1,000 μV/K (see Seebeck coefficient article for more information).

If the system reaches a steady state where , then the voltage gradient is given simply by the emf: . This simple relationship, which does not depend on conductivity, is used in the thermocouple to measure a temperature difference; an absolute temperature may be found by performing the voltage measurement at a known reference temperature. A metal of unknown composition can be classified by its thermoelectric effect if a metallic probe of known composition is kept at a constant temperature and held in contact with the unknown sample that is locally heated to the probe temperature. It is used commercially to identify metal alloys. Thermocouples in series form athermopile. Thermoelectric generators are used for creating power from heat differentials.

References:

1- Disalvo, F. J. (1999). "Thermoelectric Cooling and Power Generation". Science 285 (5428): 703–6. doi:10.1126/science.285.5428.703. PMID 10426986. Any device that works at the Carnot efficiency is thermodynamically reversible, a consequence of classical thermodynamics.

2- The voltage in this case does not refer to electric potential but rather the 'voltmeter' voltage \scriptstyle V\;=\;-\mu /e, where \scriptstyle \mu is the Fermi level.

3-a b c "A.11 Thermoelectric effects". Eng.fsu.edu. 2002-02-01. Retrieved 2013-04-22.

Other Important links:

https://books.google.ps/books?id=8PgCCAAAQBAJ&pg=PA65&lpg=PA65&dq=explanation+for+increased+thermopower+(Seebeck+coefficient)+with+rising+temperature&source=bl&ots=080GZszgLL&sig=7kJe2QmRjeF4w9qMb-u7sgIcYvQ&hl=en&sa=X&ved=0ahUKEwjuzZy49u3JAhXG1RQKHc_qAjMQ6AEIMjAF#v=onepage&q=explanation%20for%20increased%20thermopower%20(Seebeck%20coefficient)%20with%20rising%20temperature&f=false

https://books.google.ps/books?id=1qnL0qO9KNcC&pg=PA150&lpg=PA150&dq=explanation+for+increased+thermopower+(Seebeck+coefficient)+with+rising+temperature&source=bl&ots=XbYlmV-yeX&sig=iIm_en4zcr-lJGYWdWONxvyhutA&hl=en&sa=X&ved=0ahUKEwjuzZy49u3JAhXG1RQKHc_qAjMQ6AEINDAG#v=onepage&q&f=false

Details on the identification of the inclusion of Seebeck Coefficient  in the semiconductor current equations can be found in the following link:

http://www.iue.tuwien.ac.at/phd/mwagner/node47.html

Hoping this will be helpful,

Rafik

   Dear Ahmad,

   There is a thermal region where the electron-phonon is maximum and it is around one fifth of the Debye temperature (strongly dependent of the kind of material, e.g. carbon is 2230K while caesium 38K). Below this region there are few phonons available for the interaction while at higher temperatures the phonon-phonon interaction is higher than the one of electron-phonon. Thus if you increase the temperature in such a form that you enters in this thermal region (around fifth Debye temperature) then your thermopower increase. In the same form if you follow increasing the temperature leaving such region then will be decreasing.

  Notice that this is not the figure of merit which is the most important parameter and which always want to have a small thermal conductivity besides the electronic one.

   I hope that this could be helpful. 

Dear Prof. Baldomir, Prof. Rafik Karaman, and Peng Gao,

Thanks for your responds.

The temperature region you are referring to probably is the same as the region for phonon-drag mechanism to dominate thermopower (Seebeck coefficient).

In fact, I hope further understanding of the temperature correlation of thermopower far above that regime such as around or above Debye temperature for commonly investigated thermoelectric materials.

As I have recently attention to, experts commonly explain the thermally increased thermopower using the expression such as " metallic behavior" or equivalent phrases.

I am searching for more familiar explanations that is already provided for this behavior (mechanisms and / or concepts).

assuming the semiconductor is n type, the temperature rise lower the Fermi Level. As consequence the seebeck increases. Nevertheless if you increase the temperature further, the Fermi Level will be in the middle of the band gap and in this case you will get electrons and holes contributing to the Transport properties. As a consequence the Sebeck will begin to decrease.

Dear Dr.  Alexandre Jacquot ,

Thanks for your response. In fact your response brings about another question for me to ask why the Fermi level shifts down respect to the bottom of the C. B. edge for e.g. n-type semiconductors in elevated temperature?

Dear Peng Gao,

I have read your answer and thank you for it.

But, as you also mentioned, in case of intrinsic activation, the effective thermopower should decrease in elevated temperature.

My focus is temperature regimes before the intrinsic features dominant the properties.

Dear Peng,

Thanks.