3.)tunnel and photoelectric effects

[GAGS]

hello,
'QUERY3
I think we all know about tunnel effect of quantum, Also when I was studying photoelectric effect, I studied that emission of electrons for a electro-magnteic radiation of frequency less than threshold frequency is quite impossible.
But then how can we say that particle having less energy than that of barrier,is probable to pass through or in short having finite TRANSMISSION PROBABILITY

 

[cmos]

Tunneling has three components: 1) energy of the particle, 2) energy of the barrier, and 3) width of the barrier. Obviously, we would decrease tunneling with an increased barrier width.

Well, the case of the photoelectric effect, the energy barrier is the difference in the vacuum level and the Fermi level; this is called the workfunction of the metal. How about the width of the barrier? Well if we're just talking about metal to vacuum, then the barrier width is infinite. Therefore tunneling will not occur.

 

[ZapperZ]

hello,
'QUERY3
I think we all know about tunnel effect of quantum, Also when I was studying photoelectric effect, I studied that emission of electrons for a electro-magnteic radiation of frequency less than threshold frequency is quite impossible.
But then how can we say that particle having less energy than that of barrier,is probable to pass through or in short having finite TRANSMISSION PROBABILITY

In addition to what has been said, there is also another aspect that you need to consider - the length of time that the electron is in a particular state.

When an electron is in the ground state of the conduction band (i.e. the top of the Fermi level), the "barrier", which is the work function, is rather large. This means that the probability of transmission is very, very small to insignificant. Now, if you excite it with a photon of energy less than the work function, the electron will be in an excited state that sees a potential barrier that is less than the work function. So technically one expects some transmission probability. However, the particle isn't in that excited state for very long. For a metal, the lifetime of the electron to be in that state is of the order of femtoseconds. It doesn't get to see that kind of potential barrier that long before it decays back to the ground state. So even though it did see a smaller potential barrier that might allow it to have a significant transmission probability, the shortness of the lifetime will be a major factor on the lack of any detected transmission.

Note that there are ways to change the nature of the potential barrier and still allow for a longer "lifetime" to enable a transmission. Field emission phenomenon does exactly just that. By applying a strong electric field on the surface of the metal, one can actually reduce the width of the potential barrier for the electrons at the Fermi level. At a sufficiently high enough electric field, you can start to observe significant tunneling effect from electrons at the Fermi level going through the barrier and leaving the metal. This is what is described in the Fowler-Nordheim model for field emission.

Zz.