P Type Semiconductor Examples

N-type Semiconductors

An n-type semiconductor is one that has donor dopants deposited into its crystal lattice. Here, electrons are called the majority carriers and holes are the minority carriers. One of the most common examples of this is Silicon or Germanium, from group IV in the periodic table, being doped with Phosphorus or Arsenic atoms (from group V), both of which has one extra valence electron per atom. The dopant atom is able to enter the lattice, substitute in for one Si atom while bound to four others (a covalent bond), and release its extra, loosely bounded valence electron into the Si lattice.

As stated before, the primary reason to inject the semiconducting wafer with impurities is to increase its conductivity, found to be

[sigma = qmu_n n(T) + qmu_p p(T) tag{1}]

where q is the charge of an electron (~ 1.6 *10^-19 Coulombs), (mu_n) and (mu_p) are the electron and hole mobilities respectively, and n(T) and p(T) are the concentrations of electrons in the conduction band or holes in the valence band. Both the mobilities and the two concentration variables are temperature dependent, however for right now consider the temperature as constant at around room temperature. For all practical purposes in an n-type semiconductor at room temperature, the conductivity term from the hole concentration is negligible because usually, (N_D) > (n_i) where (N_D) is the concentration of donor dopants, all of whose electrons are in the conduction band at 300 K, and (n_i) is the intrinsic carrier concentration of the semiconductor. If the donor electron concentration is much greater than the intrinsic carrier concentration, then the hole concentration contributing to the conductivity is even smaller at (dfrac{n_i ^2}{N_D}), allowing it to be neglected.

Once inserted into the semiconductor, the donor dopants are able to form a donor level in the band gap near the conduction band, previously where there were no existing states, because it is now energetically favorable to do so. This means that the donated electrons will require a much smaller increase in energy to be excited into the conduction band, where the free flowing electrons can increase conductivity. Therefore, as doping increases, the conductivity of an n-type semiconductor increases as well (more donor states means more donated free electrons that can be promoted into the conduction band).

Figure 1: Detailed diagram of an n-type semiconductor at 300 K.

Figure 1 displays the behavior of the donor doped semiconductor at room temperature. Ec represents the conduction band, Ev is the valence band, (E_D) shows the donor level (containing the immobile donor ions), and (E_F) is the Fermi level. The black circles are electrons, while the white squares represent the empty, immobile donor states (because all the donor electrons are able to be promoted into the conduction band at room temperature) that do not affect the conductivity. The electrons below Ev are shown, only to point out that there are still many intrinsic carriers in the valence band that are still yet to be promoted to the conduction band (a minimal amount of intrinsic have been promoted from the valence band so far, though). There is a minimal hole concentration in the valence band but this has not been shown in figure 1, mainly to illustrate the greater importance of electrons in n-type semiconductors. Considering that the Fermi level is defined as the states below which all allowable energy states are filled and all states above are empty at the temperature approaches 0 Kelvin, it makes sense that (E_F) would increase from from its middle of the band gap intrinsic position because of the donor level near the conduction band (filled states are those that are occupied by electrons). Another way to think about this is that the majority of the density of energy states should be contained underneath the Fermi level (at 0 Kelvin, the Fermi level is at the middle of the band gap but the donor dopants are not considered as energy states yet, since all motion ceases). Looking at the equation for Fermi level (ignoring temperature dependence for now since it is constant) confirms this, as [E_F = kTln(dfrac{N_D}{n_i}) - E_i]. where (E_i) is the is the energy level in the middle of the band gap. With everything else constant, increasing the donor concentration increases the Fermi level, meaning that electrons can more easily reach the conduction band.

From this point, the most important calculation (other than conductivity) that can lead to building efficient devices with multiple applications is to find the concentration of electrons in the conduction band. At room temperature, this concentration is simply (N_D) but in general, it is [N_C e^dfrac{E_F - E_C}{kT}] where (N_C) is the density of energy states in the conduction band and k is the Boltzmann constant (1.38 * 10^ -23 Joules/(degree Kelvin)). (N_C) can be further simplified as

[2[dfrac{2pi m_e ^* kT}{h^2}]^dfrac{3}{2} tag{2}]

where (m_e ^*) is the effective mass of an electron and h is Planck's constant (6.626 * 10^-34 J*seconds).

P-type Semiconductors

A p-type semiconductor is one that has acceptor dopants deposited into its crystal lattice. Here, holes are called the majority carriers and electrons are the minority carriers. One of the most common examples of this is Silicon or Germanium, from group IV in the periodic table, being doped with Boron or Gallium atoms (from group III), both of which has one fewer valence electron per atom. The dopant atom is able to enter the lattice, substitute in for one Si atom while bound to four others, and accept an electron from an adjacent atom into its covalent bond. This is how the lack of an electron, or hole, moves through the valence band of the material, making it conductive (the same process of replacing a hole with an electron, moving the hole to another location in the lattice keeps repeating).

As mentioned earlier, the primary reason to inject the semiconducting wafer with impurities is to increase its conductivity, which is

[sigma = qmu_n n(T) + qmu_p p(T) tag{3}]

where q is the charge of an electron, (mu_n) and (mu_p) are the electron and hole mobilities respectively, and n(T) and p(T) are the concentrations of electrons in the conduction band or holes in the valence band. Both the mobilities and the two concentration variables are temperature dependent, however for right now consider the temperature as constant at around room temperature. For all practical purposes in a p-type semiconductor at room temperature, the conductivity term from the electron concentration is negligible because usually, (N_A) > (n_i) where (N_A) is the concentration of acceptor dopants, all of whose holes are in the valence band by 300 K, and (n_i) is the intrinsic carrier concentration of the semiconductor. If the hole concentration is much greater than the intrinsic carrier concentration, then the electron concentration contributing to the conductivity is even smaller at (dfrac{n_i ^2}{N_A}), allowing it to be neglected.

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