Re: Photoelectric effect - free electrons or those of atoms?

Dear Simon,

First, I want to confirm your reasoning and your conclusions.  Indeed, if 
you can “pump” an intense beam of specific, low-energy photons into a 
material, you will be able to electronically excite it and induce 
photoemission. This is the basis for such techniques as “Infrared 
Multiphoton Ionization” (IRMPI) and “Resonance-Enhanced Multiphoton 
Ionization” (REMPI).  The specificity of the photon energy depends on the 
energy transitions you are exciting within the material, and thus depends 
on the electronic make-up of the material.  It also depends on the “free 
carrier lifetime” (how long the electrons stay energized before decaying) 
and give up their energy to the crystal lattice in the form of heat, 
etc.  This research into photon-matter interaction has exploded since the 
advent of laser technologies into the physical sciences in the last 
century.

Second, I want to answer your specific question….In the photoelectric 
where DO electrons come within the metal?  They come from the highest 
occupied electronic state within the metal. This electronic state, named 
the “Fermi level”, is near the middle of a series of closely-packed 
electronic states called a “band”.  That part of the band below the Fermi 
level are states full of electrons and that part above are states empty 
of electrons ( defined at absolute zero temperature).  But since this is 
a band of nearly continuous states, electrons - in a spontaneous manner – 
are “free” to roam from the Fermi level upto the empty or “unoccupied” 
states above the Fermi level.  This process is called “conduction”, and 
the band as a whole is called the conduction band. Thus, the 
photoelectrons may also be thought of as “free electrons”, but this is 
not exactly correct.

So what is the nature of the “photoelectric work function”?  The work 
function for a metal in Einstein’s Nobel-winning equation is the 
difference in energy from the top, unoccupied level, of the conduction 
band and the Fermi level – from which photoelectrons arise.  The key to 
all of this is to realize that the discrete atomic levels of all the 
metal atoms are highly interactive in a crystal lattice of that metal.  
This leads to a “continuum” of states – the conduction band.

For an understanding of the photoelectric effect in semiconductors and 
insulators a direct quantum mechanical analysis is necessary.  This 
necessity arises from the fact that in semiconductors and insulators, the 
highest occupied electronic state is energetically separated from the 
unoccupied levels.  This is called a “band gap”.  Two separate bands are 
formed.  The occupied levels are within the lower “valence band” and the 
unoccupied levels -as before - are within the upper “conduction band”.  
But now, electrons cannot spontaneously roam free and conduction cannot 
occur.  But this is leads us into another, interesting subject area.

The key physical concept which Einstein illustrated in his work on the 
photoelectric effect is this: light is made up of discrete particles, 
quanta, we call photons.  In the 19th Century, Newton’s great insight 
that light was made up of photons was discarded in favor of a “wave 
theory about light”.  Einstein’s worked helped correct this fallacy.  You 
may be taught in the educational process you’re enduring that there is a 
thing called the “wave-particle duality” about light…that light sometimes 
acts like a wave; sometimes like a particle.  Understand what your 
teachers explain about the empirical phenomena and the calculations 
related to interference, diffraction, etc. but ignore the physical 
concept that they might say explains it – the so-called “wave theory of 
light”.  Light, as we measure it, ALWAYS acts like particles - like 
photons - but in statistical manner.  Archaic traditions in science 
sometimes die hard.   I’ll end with a quote from Richard Feynman from his 
book “QED” (Chapter 1).  He won the Nobel Prize in 1964 for his 
explanation of quantum electron dynamics:

“I want to emphasize that light comes in this form – particles.  It is 
very important to know that light behaves like particles, especially for 
those of you who have gone to school, where you were probably told 
something about light behaving like waves.  I’m telling you the way it 
DOES behave – like particles.”

---* Dr. Ken Beck