1.2 Doped semiconductors  (Page 3/3)

If an electron deficient material such as boron is present, then the material is called p-type silicon, and the hole concentration is just $p\approx N_a$ the concentration of acceptors , since these atoms "accept" electrons from the valence band.

If both donors and acceptors are in the material, then whichever one has the higher concentration wins out. (This is called compensation .) If there are more donors than acceptors then the material is n-type and $n\approx N_d-N_a$ . If there are more acceptors than donors then the material is p-type and $p\approx N_a-N_d$ . It should be noted that in most compensated material, one type of impurity usually has a much greater(several order of magnitude) concentration than the other, and so the subtraction process described above usually does notchange things very much. ( $10^{18}-10^{16}\approx 10^{18}$ ).

One other fact which you might find useful is that, again,because of quantum mechanics, it turns out that the product of the electron and hole concentration in a material must remain a constant. In siliconat room temperature:

The picture of "cups" of different allowed energy levels is useful for gaining a pictorial understanding of whatis going on in a semiconductor, but becomes somewhat awkward when you want to start looking at devices which are made up ofboth n and p type silicon. Thus, we will introduce one more way of describing what is going on in our material. The pictureshown in is called a band diagram. A band diagram is just a representation of the energy as a function of position with a semiconductor device. In aband diagram, positive energy for electrons is upward, while for holes, positive energy is downwards. That is, if an electron moves upward , its potential energy increases just as a with a normal mass in a gravitational field. Also, just as a mass will "fall down" if given a chance, an electron will move down a slope shown in a band diagram. On the other hand, holes gain energy by moving downward and so they have a tendancy to "float" upward if given the chance - much like a bubble in a liquid. The line labeled $E_e$ in shows the edge of the conduction band, or the bottom of the lowestunoccupied allowed band, while $E_v$ is the top edge of the valence, or highest occupied band. The band gap, $E_g$ for the material is obviously $E_c-E_v$ . The dotted line labeled $E_f$ is called the Fermi level and it tells us something about the chemical equilibrium energy of the material, and also something about thetype and number of carriers in the material. More on this later. Note that there is no zero energy level on a diagram such as this. We often useeither the Fermi level or one or other of the band edges as a reference level on lieu of knowing exactly where "zero energy" is located.