Hi all,

While I am not an expert in solid state physics, i can propose the following.

First the flow of electricity is due to the transport of mobile charges (carriers) through a material. (aside: We usually view these carriers as electrons because in metals the carrier is the electron. However, in Semiconductors, the carrier can either be an electron or a hole (the absence of an electron).) Most materials contain vast quantities of charges (electrons and protons), however, the majority of these charges are fixed (or non-mobile) and can do nothing for conductance. Think of an insulator (eg glass) where there are plenty of charges (electrons and protons in the constituent atoms) but they cant move, hence the conductivity is very low. In order for a material to conduct, there must be mobile charges. That is, the existing charges in the atoms must be able to easily pop out of their sites in the lattice and move around freely. Since the atoms are too tightly bound to move, that leaves the outermost electron from each atom as the most likely candidate (there is more to say about density of states, but I'm trying to keep this simple)

Thus, we can see three difference classes of materials. Insulators, where all the charges are locked down (large binding energy). Conductors (usually metals), where there is a 'sea of electrons' that are freely able to slosh around in material (zero binding energy). And semiconductors, where the electrons are lightly bound (small binding energy) and, if given enough of a nudge can be made to move around and to conduct.

The nudge needed to cause electrons in a semiconductor to wander away from their original state is often small enough that room temperature energy can be used to cause them to activate. In fact, the dopants, which are added to silicon to allow it to conduct, are specifically chosen to ensure that these electrons do in fact activate at room temperature. This is the beauty of semiconductors, since one can actually engineer the local conductivity of the material.

For a metal there are plenty of electrons available to conduct, regardless of the temperature (mostly true). As one applies a voltage, the electrons stream through the lattice of the material and we now have the current that we are all familiar with.

These electrons travel through a lattice of fixed atoms, much like a shopper making their way through a crowd of other pedestrians. If the crowd is not too dense one can make their way through the crowd in a series of straight but short lines, turning left and right as one finds a person in their way.

As the electrons flow, they will bump into obstacles just like the pedestrian example above. The obstacles are the atoms in the lattice. The question you are asking is: why would the electrons be more inclined to bump into atoms (i.e. resistance) when the material is hotter than when it is colder. The answer has to due with thermal energy. Think of Brownian motion. Atoms at absolute zero sit locked into their lattice sites and don't move; they are frozen in place. But at any temperature warmer than absolute zero, they bounce and wiggle around, causing them to move slightly out of their lattice sites. These warmer atoms can begin to choke off the channels through the lattice and to interfere with electrons travelling through the channels. The warmer they are, the more they wiggle and the more interfere. Effectively, they start to block electrons on their path, causing electrons to scatter.

If we return to the example of the crowd, now imagine each standing person as wiggling back and forth by a centimeter or two; this would interfere with your travel through the crowd, but only slightly. Now imagine the people in the crowd and wiggling by tens of centimeters, now travel becomes difficult. The more motion, the more interference.

Thus, as we cool a metal, the atoms stay more closely to their centers and it is easier for the electrons to make their way through the channels between the atoms.

While this is a very simplistic explanation, it hits the high points.

In conclusion:

With metals there are plenty of mobile carriers; and the motion of the lattice atoms due to thermal energy causes them to interfere with the transport of mobile carriers through the lattice.

With semiconductors, there are insufficient mobile carriers at low temperatures and resistance is high; but as one heats the material, more and more of the lightly bound carriers escape and become free to conduct. It should be noted that once all the soon-to-be-mobile carriers in a semiconductor are fully activated, it then behaves like a 'metal' and further increases in temperature will cause it to reduce conductivity.

I hope this helps. This is an intentionally high level overview of a fairly esoteric field (Solid State Physics) and I have glossed over a lot of details to make for easier reading. Let me know if anything is incorrect.

Kevin A. Shaw, Ph.D.

Chief Technology Officer

Sensor Platforms, Inc.

Mathivanan, you have several fundamental misconceptions about conductivity. Please read the following article carefully and then ask us if there's something that you did not understand: http://en.wikipedia.org/wiki/Electrical_resistivity_and_conductivity

The band gap in the metal is small and thus the electrons can easily take a leap to conduction band and conduct electricity but with increase in temperature, the thermal motion makes the electrons to collide and disturb the free flow. Thus, conductivity is decreased. However, with decrease in temperature, the thermal effect is nullified and the electrons can flow smoothly without hindrance and thus conductivity increases.

In semi conductors, the band gap is big but small enough for few electrons to take a leap to the conduction band and conduct electricity to some extent. However with increase in temperature they get charged with thermal energy which is sufficient to overcome the energy barrier and leap to the conduction band and thus, their conductivity increases.

Hi all,

While I am not an expert in solid state physics, i can propose the following.

First the flow of electricity is due to the transport of mobile charges (carriers) through a material. (aside: We usually view these carriers as electrons because in metals the carrier is the electron. However, in Semiconductors, the carrier can either be an electron or a hole (the absence of an electron).) Most materials contain vast quantities of charges (electrons and protons), however, the majority of these charges are fixed (or non-mobile) and can do nothing for conductance. Think of an insulator (eg glass) where there are plenty of charges (electrons and protons in the constituent atoms) but they cant move, hence the conductivity is very low. In order for a material to conduct, there must be mobile charges. That is, the existing charges in the atoms must be able to easily pop out of their sites in the lattice and move around freely. Since the atoms are too tightly bound to move, that leaves the outermost electron from each atom as the most likely candidate (there is more to say about density of states, but I'm trying to keep this simple)

Thus, we can see three difference classes of materials. Insulators, where all the charges are locked down (large binding energy). Conductors (usually metals), where there is a 'sea of electrons' that are freely able to slosh around in material (zero binding energy). And semiconductors, where the electrons are lightly bound (small binding energy) and, if given enough of a nudge can be made to move around and to conduct.

The nudge needed to cause electrons in a semiconductor to wander away from their original state is often small enough that room temperature energy can be used to cause them to activate. In fact, the dopants, which are added to silicon to allow it to conduct, are specifically chosen to ensure that these electrons do in fact activate at room temperature. This is the beauty of semiconductors, since one can actually engineer the local conductivity of the material.

For a metal there are plenty of electrons available to conduct, regardless of the temperature (mostly true). As one applies a voltage, the electrons stream through the lattice of the material and we now have the current that we are all familiar with.

These electrons travel through a lattice of fixed atoms, much like a shopper making their way through a crowd of other pedestrians. If the crowd is not too dense one can make their way through the crowd in a series of straight but short lines, turning left and right as one finds a person in their way.

As the electrons flow, they will bump into obstacles just like the pedestrian example above. The obstacles are the atoms in the lattice. The question you are asking is: why would the electrons be more inclined to bump into atoms (i.e. resistance) when the material is hotter than when it is colder. The answer has to due with thermal energy. Think of Brownian motion. Atoms at absolute zero sit locked into their lattice sites and don't move; they are frozen in place. But at any temperature warmer than absolute zero, they bounce and wiggle around, causing them to move slightly out of their lattice sites. These warmer atoms can begin to choke off the channels through the lattice and to interfere with electrons travelling through the channels. The warmer they are, the more they wiggle and the more interfere. Effectively, they start to block electrons on their path, causing electrons to scatter.

If we return to the example of the crowd, now imagine each standing person as wiggling back and forth by a centimeter or two; this would interfere with your travel through the crowd, but only slightly. Now imagine the people in the crowd and wiggling by tens of centimeters, now travel becomes difficult. The more motion, the more interference.

Thus, as we cool a metal, the atoms stay more closely to their centers and it is easier for the electrons to make their way through the channels between the atoms.

While this is a very simplistic explanation, it hits the high points.

In conclusion:

With metals there are plenty of mobile carriers; and the motion of the lattice atoms due to thermal energy causes them to interfere with the transport of mobile carriers through the lattice.

With semiconductors, there are insufficient mobile carriers at low temperatures and resistance is high; but as one heats the material, more and more of the lightly bound carriers escape and become free to conduct. It should be noted that once all the soon-to-be-mobile carriers in a semiconductor are fully activated, it then behaves like a 'metal' and further increases in temperature will cause it to reduce conductivity.

I hope this helps. This is an intentionally high level overview of a fairly esoteric field (Solid State Physics) and I have glossed over a lot of details to make for easier reading. Let me know if anything is incorrect.

Kevin A. Shaw, Ph.D.

Chief Technology Officer

Sensor Platforms, Inc.

Kevin, it's basically correct and a good popular level explanation :).

Yes, Mathivanan follow Tapio Ala-Nissila's advice. You pose a question and seem satisfied with an answer below your question which hardly addresses the issue. Electrical current is based upon number density (n) or number of carriers or electrons in case of metals and their drift velocity (v) attained under applied electrical field (E). If the electrons were free, the velocity will continue to increase with time under an accelerating field (acceleration E/m), but that does not happen as collisions (various sources) decide a collision time and the upper limit to velocity in an average collision time t as t E/m where t becomes smaller if the collisions increase. The velocity is limited by collisions. Since there are already very large number of electrons in metals, temperature increase only results in more collisions and thus reduction in velocity at constant E resulting in decrease of conductivity with increase in temperature. Conductivity is a ratio of current density and E gets reduced with increase in temperature as n is practically unaltered.

For semiconductors, the number of carriers is not very large and temperature increase brings in increased number density and thus increase in conductivity. For alloys I think it becomes more complicated to get to a thumb rule.

What in your case means the alloys? There are metallic or semiconducting alloys such as АuFe or CdMnTe alloys. Their temperature dependence of conductivity is similar to metals and semiconductors, respectively.

I would request to please complete your homework.

Dear Kevin A Shaw.. your answer is correct except this information:

"We usually view these carriers as electrons because in metals the carrier is the electron."

According to Hall effect Experiment,  the carrier in metal could be positive charge or negative. So, any positive value of RH it means the carrier is positive"hols not electron" and it listed in Tables.

thanks for the explanation Kevin

I would like to answer in a more quantum mechanical way. So, Lowering temperature means lowering the kinetic energy or momentum of the particles (Atoms) inside material. In return, it increases the uncertainty of the position of the particles (According to Heisenberg's uncertainty principle,now its difficult to locate them). This causes the particles of material to expand their probability space making it easier for electrons to hop between the particles (because their wave functions are expanded as well) which means they need less energy  and more ease to jump from one particle to another. Ease in movement of a charge in a space is named as conductivity. 

Many Thanks Kevin. That was very helpful.