semiconductores en equilibrio

How does temperature affect the Fermi distribution?

When we are trying to determine the position of the Fermi level we assume the semiconductor is in equilibrium.  E_F on the band diagram is a function of temperature and carrier concentration.  This can be seen from the equations used to determine the position of the Fermi level.

Intrinsic semiconductor  no = po
n-type semiconductor  ND >> NA, ND >> ni
p-type semiconductor  NA >> ND, NA >> ni

If the temperature is varied, the Fermi level will also vary.

How does temperature affect the band gap?

As temperature increases, the band gap energy decreases because the crystal lattice expands and the interatomic bonds are weakened.  Weaker bonds means less energy is needed to break a bond and get an electron in the conduction band.  The relationship between temperature and the band gap energy can be seen by the following equation:

E_G(0) is the limiting value of the band gap at 0 K.  a and b are constants chosen to obtain the best fit to experimental data.

How does temperature affect donor and acceptor ionization?

A donor is an element with typically one more valence electron than the element that forms the semiconductor..  An acceptor is an element with typically one fewer valence electron than the element that forms the semiconductor.  An ion is an electrically charged atom or group of atoms.  Ionization occurs when an electron is removed from or added to an atom, in this case it would be the dopant atoms.
The donor's extra electron is weakly bound and needs very little energy, thermal or otherwise, to break the bond and become a free electron.  As temperature is increased, more and more of these bonds are broken, until all the donors are ionized, producing an increase in electron concentration.  At room temperature, we assume all the donors are ionized.
Figure 2.22(a) on page 66 illustrates the temperature dependence of the carrier concentration in a doped semiconductor.  At 0 K the electrons at the donor sites do not receive enough energy to make it to the conduction band, so the ratio between the majority carrier concentration and the doping concentration n/N_D = 0.  As the temperature is increased , more donor electrons make it to the conduction band, but at temperatures below 150 K all the donor sites have not been ionized so the ratio n/N_D < 1 and the majority carrier concentration is made up of the donor electrons that have made it to the conduction band.  At room temperature, we assume all the donors are ionized, meaning all donor electrons are in the conduction band, so the ratio n/N_D = 1 and the majority carrier concentration is made up of the donor electrons.  At very high temperatures, above 500 K, electrons from the valence band receive enough energy to make it to the conduction band and out number the electrons from the donor sites, so the ratio n/N_D > 1 and the majority carrier concentration is now made up of electrons from the valence band in the conduction band, as in an intrinsic semiconductor.
Acceptors have one fewer valence electron than the neighboring semiconductor atoms and will readily accept an electron in order to completely bond. Very little energy is needed for an electron to travel to one of the acceptor sites and be trapped. As the temperature is increased, more electrons become trapped in acceptor sites, until all the acceptors are ionized, causing the hole concentration to increase.  At room temperature, we assume all the acceptors are ionized.
Figure 2.22(a) can be applied toward acceptors by substituting p/N_A in place of n/N_D.  At 0 K the electrons in the valence band do not receive enough energy to jump to an acceptor site and create a hole, so the ratio p/N_A = 0.  At temperatures below 150 K the ratio p/N_A < 1 because all the acceptor sites have not been ionized, so the majority carrier concentration is made up of the holes left behind by trapped electrons in the acceptor sites.  At room temperature we assume all the acceptors have been ionized.  The ratio p/N_A = 1 because the majority carrier is made up of the holes created by the ionized acceptors.  At very high temperatures, above 500 K, the ratio p/N_A > 1 because the holes created by electrons from the valence band jumping to the conduction band out number the holes that had been created by acceptors, so the majority carrier concentration is made up of holes created by valence electrons in the conduction band, as in an intrinsic semiconductor.

How does temperature affect intrinsic carrier concentration?

When we speak of an intrinsic semiconductor several factors come to mind:

1. It is extremely pure, containing an insignificant amount of impurities.
   
2. The properties of the material depend only on the element(s) the semiconductor is made of.
   
3. For every electron created, a hole is created also, n_o = p_o = n_i.

For an electron-hole pair to be created in an intrinsic semiconductor, a bond must be broken in the lattice, and this requires energy.  An electron in the valence band must gain enough energy to jump to the conduction band and leave a hole behind.  n_i represents the intrinsic carrier concentration, or we can see it as the number of bonds broken in an intrinsic semiconductor.
As the temperature is increased, the number of broken bonds (carriers) increases because there is more thermal energy available so more and more electrons gain enough energy to break free.  Each electron that makes it to the conduction band leaves behind a hole in the valence band and there is an increase in both the electron and hole concentration.  As the temperature is decreased, electrons do not receive enough energy to break a bond and remain in the valence band.  If electrons are in the conduction band they will quickly lose energy and fall back to the valence band, annihilating a hole.  Therefore, lowering the temperature causes a decrease in the intrinsic carrier concentration, while raising the temperature causes an increase in intrinsic carrier concentration.

Pablo Jose Mago
C.I. 18146112
EES

fuente:http://www.ece.utep.edu/courses/ee3329/ee3329/Studyguide/ToC/Fundamentals/Carriers/explain.html