Lecture
Enrichment mode and depletion mode. A near-surface layer with an increased concentration of free charge carriers is called enriched, and one with a decreased concentration is called depleted.
A p-n junction cannot be obtained by mechanically contacting two semiconductors with different types of conductivity, because:
Two methods of obtaining a p-n junction are most widespread.
a) The fusion (alloying) method.
b) The diffusion method.
Let us consider method (b). The planar design of p-n junctions is the most common, in which the p-n junction is created by diffusion into one of the sides of a semiconductor wafer.
a) b)
The p-n junction is characterized by two main parameters:
1. The contact potential difference φk, also called the height of the potential barrier. This is the energy that a free charge must have in order to overcome the potential barrier:
where Na, ND are the concentrations of the acceptor and donor impurities; k is the Boltzmann constant; e is the electron charge; T is the temperature; are the concentrations of acceptors and donors in the hole and electron regions, respectively; pp and pn are the concentrations of holes in the p- and n-regions, respectively; ni is the intrinsic concentration of charge carriers in an undoped semiconductor,
jT = kT/e is the thermal potential. At a temperature of T=27°C, jT=0.025V, while jk=0.3-0.3V for Ge, and jk=0.6-0.8V for a silicon (Si) junction.
2. The width of the p-n junction lp-n = lp + ln: - this is the boundary region depleted of charge carriers, located in the p- and n-regions:
where ε is the relative permittivity of the semiconductor material; ε0 is the permittivity of free space.
The thickness of electron-hole junctions is on the order of lp-n = (0.1-10) μm; it is proportional to the voltage across the p-n junction and inversely proportional to the impurity concentration in the p- and n-regions.
If the impurity concentrations are equal, the p-n junction is called symmetric; if they are not, the p-n junction is called asymmetric, and in this case it is located mainly in the region of the semiconductor with the lower impurity concentration.
Ip-n = Idiff + Idr = 0
Extraction - the process of converting minority charge carriers into majority carriers as reverse current flows. The width of the p-n junction increases:
lp-n ~(φk+U)1/2
The current-voltage (I-V) characteristic of a p-n junction is the dependence of the current through the junction on the voltage applied to it, i=f(u).
Analytically, for forward and reverse bias, the I-V characteristic is written as:
For clarity, the I-V characteristic is represented in the form of graphs (fig. 1.3).
If the forward and reverse branches are plotted on the same scale, the I-V characteristic of the p-n junction has the form shown in fig. a. The figure clearly shows that the p-n junction has one-way conductivity, i.e., Ifwd >> Irev, or Rfwd <
To study the features of the forward and reverse branches of the I-V characteristic, they are plotted on different scales; for example, the current scales may differ by a factor of a thousand.
The graph shows that the forward branch of the I-V characteristic of a silicon-based diode is shifted to the right, while its reverse branch has a current much smaller than that of a germanium diode.
The differential resistance of the p-n junction under forward bias is determined from the relation rdiff= φT/I.
For example, at I=1mA and φT=25mV, rdiff=25Ohm.
The fact that near the p-n junction there are uncompensated electric charges indicates that it has capacitance. The capacitance of the p-n junction consists of two components - the barrier capacitance Cbar and the diffusion capacitance Cdiff are distinguished.
a) Under reverse bias, the barrier capacitance predominates, Cbar > Cdiff.
It is associated with immobile impurity ions, whose concentration is small. The magnitude of this capacitance depends on the magnitude of the voltage U across the p-n junction, on the junction area S, and also on the impurity concentration.
where C0 is the capacitance at zero voltage, - is the reverse voltage,
the exponent depends on the type of p-n junction (n=1/2 for an abrupt junction, n=1/3 for a graded junction),
ε is the permittivity of the semiconductor material;
S is the area of the p-n junction.
A model analog of the barrier capacitance can be the capacitance of a parallel-plate capacitor whose plates are the p- and n-regions, and whose dielectric is the p-n junction, which has practically no mobile charges. The value of the barrier capacitance ranges from tens to hundreds of picofarads, and the change in this capacitance with changing voltage can reach a factor of ten.
b) Diffusion capacitance predominates (Cdiff >> Cbar) under forward bias of the p-n junction.
It is characterized by the accumulation of minority charge carriers near the p-n junction as the forward diffusion current (injection current) flows
where is the lifetime of minority charge carriers,
is the time during which the forward current Ifwd flows.
The values of the diffusion capacitance can be on the order of hundreds to thousands of picofarads.
Overall, comparing the diffusion and barrier capacitances, Cdiff >> Cbar.
This is because the diffusion capacitance is associated with the forward, diffusion current (the current of majority charge carriers), which can reach large values.
In practice, the barrier capacitance is used, since the diffusion capacitance has a low quality factor, because a forward-biased p-n junction with low forward resistance is connected in parallel with this capacitance.
A sharp increase in current under reverse bias of the p-n junction is called breakdown of the p-n junction, and the voltage at which this occurs is called the
It can be tunnel breakdown - curve 2, or avalanche breakdown - curve 1. Avalanche breakdown arises due to avalanche multiplication of minority charge carriers by impact ionization. Tunnel breakdown arises due to the transition of electrons from a bound state to a free state without imparting additional energy to them.
2. Thermal breakdown - irreversible, leads to the destruction of the p-n junction - curve 3.
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