What is bandgap? What is doping?

The band gap

    The band gap usually refers to the energy difference between the valence band (E_V) and conduction band (E_C) energy. In other words, it is the minimum energy that is required for an electron to move from the valence band to the conduction band. In the conduction band, the electron freely moves, resulting in conduction into the semiconductor. Figure 1 shows the basic band diagram of an intrinsic semiconductor. The valence band is lower and the conduction band is higher energy level. The energy gap is Eg. Usually, thermal energy excites the electron from the valence band to the conduction band. If the electron moves from the valence band to the conduction band another electron comes to the empty place from the neighboring atom in the valence band. This continues the electron transfer from the valence band to the conduction band. The sequence represents an electron in the conduction band and a hole in the valence band. The free electron and hole can act as a carrier for conduction. The electron and hole move on opposite sides in crystal material. The fundamental of fermi level E_F has broadly discussed elsewhere.

Figure.1. An schematic of the energy band diagram of semiconductor materials

    

Necessity of doping

    However, the intrinsic carrier density (n_i) depends on temperature and band gap which influence device performance. The thermal energy (300K) can create a free carrier from the valence band to the conduction band. In the intrinsic semiconductor, the number of electrons and holes are the same in the semiconductor crystal. The thermal energy (300K) corresponds to 0.025 eV. It is difficult to have free electrons and holes for a wide band gap (2-5 eV) semiconductor because the larger thermal is insufficient to exceed the band gap. It is necessary to high temperature to over the band gap.  Anyway, the typical value of intrinsic carrier density in Si at 300 K is around 1E10 [cm^-3]. To modulate the carrier concentration, it is necessary to doping into the intrinsic semiconductor.

Doping techniques

    The doping is done by various techniques to increase electrons or holes depending on the purpose. N-type forms when group IV is doped with group-V atoms, and p-type forms when group IV is doped with group III. We can easily choose groups III, IV, or V from the periodic table. The enhancement of the free carrier increases the conductivity of the semiconducting crystal. Figure 2 shows the n-type and p-type semiconductor formation with widely used Si. N-type materials are chosen from group V and added with group IV Si. Group IV Si has four valence electrons and group V has five valence electrons. When the doping process is complete the 2 groups make covalent bonding by sharing their electrons. But group V has one extra electron which is loosely bonded with the group V atom. The thermal energy (300K) is sufficient to free the additional electron into the crystal. This free electron named the materials is n-type. The number of dopants determines the free carrier density for conduction. The n-type doping increases the electron concentration higher in the doped crystal. Now the doped crystal contains the majority of free carrier electrons and minority carrier holes. The opposite is true for the p-type doped cases.

Figure 2: n-type and p-type formation process

Figure 3: After doping the donor and acceptor levels in the band diagram are free to conduct.

 

Figure 3 shows the band diagram of p and n-type semiconductors. When no external bias is applied then the number of carrier concentrations is called equilibrium carrier concentration. According to the mass action law, we can write down the relation of intrinsic carrier concentration with the electron concentration (no) and hole concentration (PO) at equilibrium.

n₀p₀=n_i²  (1)

In n-type, the intrinsic and doped electron makes majority electrons (n₀=N_D), and minority (p₀ as it was before doping). The case is similarly treated for the p-type crystal. In terms of majority and minority carriers, similarly, we can write get for n-type and p-type as follows,

n-type: n₀=N_D,p₀=n_i²/N_D   (2)

p-type: p₀=N_A, n₀=n_i²/N_A  (3)

Here, N_D is a donor, and N_A is an acceptor atoms concentration. The number of minority carriers decreases if the doping is increased. The doping wide modulates carrier concentration which is necessarily interesting for the research community to develop new device technology.

 

P-N junction

    One of the fundamental device structures is a p-n junction. The junction is formed by connecting the p-type semiconductor with the n-type as shown in figure 4. Just after their contact holes from the p-side move to the n-side and electrons from the n-side move to the p-side. This is due to the diffusion process because of the high concentration of their respective side. Static or space charge carriers are generated mainly near the junction which can not move freely. This is due to diffusion. On the p-side negative static and n-side positive static charges are created which are separated by the junction. As a result, an electric field is induced between the positive and negative charges. The static region near the junction is called the depletion region. The electric field (E) sweeps free carrier from the region. That means the region depleted free carriers. The electric field generates a built-in potential at the junction. The detail of the p-n junction under no bias condition is shown in figure 4.

Figure 4: Schematic of p-n junction contact>> neutral region, and dopant, electric field, and potential barrier distribution

The above discussion is a very fundamental explanation to understand the electronics device concept and the associated terms used in device evaluation. Please find a more detailed explanation of the electric field equation, dopant relation with fermi energy, and band diagram of the p-n junction in the subsequent discussion. Also, you can find other valuable technical and scientific discussions here.