Semiconductor PN junction
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Two pieces of uniformly doped P-type silicon and N-type silicon with doping concentrations of NA and ND, respectively. At room temperature, the impurity atoms are all ionized, and holes with a concentration of pp and electrons (minority carriers) with a concentration of np are distributed in P-type silicon; electrons with a concentration of nn and holes (minority carriers) with a concentration of pn are distributed in N-type silicon. When P-type silicon and N-type silicon are in contact with each other, due to the different concentrations of electrons and holes on both sides of the interface, the electrons and holes generate diffusion motions, as shown in Figure 1(a), (b) and (c) ; fixed ionized impurities appear on both sides of the PN interface to form negative and positive charge regions, as shown in Figure 1(d). Because almost all of the electrons or holes in the galvanic double layer are lost or recombined, this layer is called the blocking layer or depletion layer (also known as the space charge region). Correspondingly, a self-built electric field (also called built-in electric field) from the N region to the P region is established, as shown in Fig. 1(e).
Under the action of the self-built electric field, the drift motion of holes and electrons will be generated, and their directions are opposite to their respective diffusion motions. The diffusion motion and drift motion of the carriers reach a dynamic equilibrium, and the net current is zero. At this time, the space charge region is called the junction region of the PN junction at equilibrium. The width of the space charge region narrows as the doping concentration increases; the potential difference between the two sides of the self-built electric field is called the contact barrier of the PN junction. Electrons or holes must overcome this barrier to cross the PN junction, so the space charge region is also called the barrier region. The height of the potential barrier is related to the properties of the material, the doping concentration of the N and P regions, and the temperature.
Figure 1(c) shows the impurity distribution of the N region and P region; (d) shows the charge distribution of the space charge region; (e) shows the electric field intensity distribution in the space charge region, and it can be seen that the maximum value appears at the interface between the N region and the P region; (f) shows the carrier distribution in each region; (g) shows the band diagram of the PN junction.
According to the energy band theory, the electron concentration in the N-type semiconductor is large, and the Fermi level EFn position is high; the P-type semiconductor hole concentration is large, the Fermi level EFP position is low. When the two form a PN junction, electrons flow from high to low Fermi levels, and holes do the opposite. at the same time, under the action of the self-built electric field, the energy band of the N region moves down, and the energy band of the P region moves up until there is a unified Fermi level EF (EFn=EFP=EF) in the semiconductor forming the PN junction, and the equilibrium is reached. In the PN junction in the equilibrium state, the valence band and conduction band bend to form a potential barrier. Eip and Ein in Figure 1(g) represent the intrinsic Fermi levels in the P and N regions, respectively, VFp=(Eip-EFp)/e, VFn=(EFn-Ein)/e are the Fermi potentials of the P and N regions, respectively, and VD=VFn+VFp is the total Fermi potential. In thermal equilibrium, the total Fermi potential V% is the potential difference Un between the two ends of the space charge region, that is, the self-built voltage of the PN junction, also known as the contact potential difference.
in solar cells, PN junction is usually made by diffusion method. The surface impurity concentration of silicon wafer is very high, and the junction depth and depletion region are very small. It can be approximately regarded as a unilateral abrupt PN junction.
Outside the space charge region of the PN junction, the electron concentration nN0 in the N region and the electron concentration nP0 in the nP0 region are
Therefore, the self-built voltage UD is
It can be seen that at a certain temperature, the self-built voltage UD increases with the increase of the doping concentration on both sides of the PN junction and the increase of the forbidden band width. In a balanced PN junction, the two sides of the galvanic double layer carry equal and opposite charges respectively, as shown in Figure 1(b).
where xn and xp are the thicknesses of the space charge layers in the N and P regions, respectively. The maximum electric field intensity E’max, the self-built voltage UD and the potential barrier width W in the PN junction can be obtained by using Poisson’s equation.
where U(x) is the electrostatic potential at x; εr and ε0 are the relative permittivity of the material and the vacuum permittivity, respectively.
When there is an external voltage U, and a unilateral abrupt junction is approximated (NG>>N), the potential barrier width is
If you want to learn more about the basics of crystalline silicon solar cell physics, please read the article Basic physical and chemical properties of crystalline silicon.