Semiconductores en equilibrio

Charge Neutrality

Charge neutrality occurs when all the charge in a volume adds to zero; it is neutral, neither positive or negative.  The equation for charge density (Coulombs/cm³) is: r = q(whatever has charge) where q = electronic charge.
In a semiconductor, the most common and most prominent sources of charge are electrons holes, and ionized acceptors and ionized donors.
The zero net charge does not mean that the electrons, holes, ionized donors, and ionized acceptors are not present in the semiconductor.  It simply states that in a uniformly doped semiconductor the negative charge associated with an electron or ionized acceptor would be canceled by the positive charge associated with a hole or ionized donor.  This does not mean that the actual electrons, holes, and ionized impurities have ceased to exist in the semiconductor, it means that  r = 0.
If r = q(p_o - n_o + N_D - N_A) = 0, then the sum of the charges associated with the carriers must equal zero:

po - no + ND - NA = 0

This equation is useful in many areas, including computing p_o and n_o in equilibrium.  We usually consider N_A and N_D to be known, so it gives us one equation to relate two unknowns, p_o and n_o.  We also know that p_on_o=n_i² and n_i is considered known, so we can use the two equations to solve for p_o and n_o in terms of N_D, N_A, and n_i

Temperature Dependence

Temperature is one of the most, if not the most, important parameter in semiconductors.  A dictionary will tell you that temperature is the degree of hotness or coldness relative to a standardized scale.  You should be accustomed to the Celsius scale by now; it was established with reference values set to the freezing and boiling of water.  We will typically talk about the absolute scale, in degrees Kelvin, which is written as 300 K or 0 K, etc., without a degree symbol because it is absolute temperature.  (need to review?  check this out!)
Why is temperature important?  The average energy of a solid -- and its components (atoms, electrons, etc.) -- is measured by its temperature.  The higher the temperature, the more (thermal) energy is available to be used by the atoms and electrons.  Since we are talking about "electronic" devices, and temperature has a significant impact on the behavior of electron, temperature must have a significant impact on the behavior of electronic devices.
Temperature directly impacts:

• Carrier concentrations -- by impacting:
• Fermi distribution
• Band gap
• Donor and acceptor ionization
• Intrinsic carrier concentration
• Carrier Energy
, or, in words, the average kinetic energy of an electron in a solid is linearly proportional to the temperature of the solid.  For room temperature, we find that the average velocity of a free electron is approximately 10⁷cm/sec.

The Energy Band Model

The Band Gap Energy

Material Classification

Doping

Related Topics

Description:

Throughout the book, the energy band model, or band diagram, is used to describe the behavior of electrons and holes to externally applied forces like light, heat, and/or voltage; therefore, learning how to interpret them and sketch them is basic for this course. Here we are interested in the microscopic things, like individual or groups of electrons and their actions, so we have to use our imagination quite a bit here.
The band diagram models the allowed states in the semiconductor known as energy bands. The two bands of allowed states are called the conduction band and the valence band. The two are separated by an intervening forbidden gap, which we call the band gap. To review what the allowed states are take a look at the Bohr Model of the Atom.

Band Bending and Potential & Kinetic Energies

Band bending occurs when an electric field is applied to a semiconductor. When there isn't an electric field being applied, the energy bands are not a function of position. Therefore, when an electric field is applied, energy is being supplied to the carriers in the material. Where band bending has occurred, we can measure the energy being given to the electrons or holes by taking a reference energy and measuring the distance between it and the energy the carrier is at.
In essence, the potential energy of an electron is the distance the electron is from the reference energy to E_c, the lowest conduction band energy. The kinetic energy of an electron is the distance between E_c and the energy it is at. For holes, it's similar. A hole's potential energy is measured as being the distance between the reference energy and E_v, the highest valence band energy. The kinetic energy of a hole is measured by taking the difference between E_v and the energy the hole is at.




Pablo Jose Mago
C.I. 18146112
EES

Fuente:http://www.ece.utep.edu/courses/ee3329/ee3329/Studyguide/ToC/Fundamentals/CAction/energies.html