Minority carrier density

There are many ways of increasing tlie equilibrium carrier population of a semiconductor. Most often tliis is done by generating electron-hole pairs as, for instance, in tlie process of absorjition of a photon witli h E. Under reasonable levels of illumination and doping, tlie generation of electron-hole pairs affects primarily the minority carrier density. However, tlie excess population of minority carriers is not stable it gradually disappears tlirough a variety of recombination processes in which an electron in tlie CB fills a hole in a VB. The excess energy E is released as a photon or phonons. The foniier case corresponds to a radiative recombination process, tlie latter to a non-radiative one. The radiative processes only rarely involve direct recombination across tlie gap. Usually, tliis type of process is assisted by shallow defects (impurities). Non-radiative recombination involves a defect-related deep level at which a carrier is trapped first, and a second transition is needed to complete tlie process. 

The responsivity and g-r noise may be analyzed to obtain background photon flux and temperature dependence of responsivity, noise, and detectivity. Typically, n > p, and both ate determined by shallow impurity levels. The minority carrier density is the sum of thermal and optical contributions. 

The photopotential can also be expressed in terms of the relative change in the minority carrier density, Anmin, introduced by photoexcitation. By using... 

Fig. 10.4 (a) Computed minority carrier generation rate in bulk silicon for different wavelengths of monochromatic illumination of an intensity corresponding to a photocurrent density of 10 mA crrf2. (b) Bulk minority carrier density for carrier collection at the illumi-... 

In the presence of surface recombination, the minority carrier density at the surface is determined by the rate of their arrival from the collection region W + LP and the rate of their removal by the routes illustrated in Fig. 8.5. The concentration of holes accumulating at the surface can be expressed in terms of the equivalent surface concentration, ps (cm-2) = (Px=o since this allows a convenient formulation of the kinetic equations. Further simplification is achieved by considering the concentrations of redox species and majority carriers to be time invariant. This simplified scheme is illustrated for the case of an n-type semiconductor in Fig. 8.5. 

Brattain and Garrett took a thin wafer of germanium and by alloying one side of it with indium formed a p-n junction with the p-side very much more heavily doped than the n-side, so that any current flow across the junction would be due to holes (5). The n-side of the junction was brought into contact with the electrolyte and current was then passed across the electrolyte interface under various potentials. Under these conditions the voltage which develops between the two ohmic contacts to the semiconductor is a measure of the minority-carrier density on the less-heavily-doped side of the junction. 

As already mentioned, we have a forward bias if the n-type semiconductor is made positive with respect to the metal. Under these conditions holes are injected into the semiconductor and we have pn > In this case the quasi-Fermi level of holes, Ep p, occurs below that of electrons, Ep , in Fig. 2.8, i.e. it is closer to the valence band which is equivalent to the fact that the minority carrier density is increased. The externally applied voltage is then determined by... 

In the case of doped semiconductors, the assumption < no or 6n < po is almost impossible to fulfill for minority carriers under experimental conditions. An increase of the light intensity then leads to a decrease of the surface recombination velocity along the branch determined by the minority carrier density (for details see ref. [5]). 

Taking a p-type electrode as an example, the electrode is illuminated through the electrolyte as illustrated in Fig. 4.6. The diffusion of the excess minority carrier density An is given by the continuity equation [10]... 

It is obvious that the device efficiency, rj, must also be very sensitive to the barrier height, since the efficiency is limited by upon the minority carrier density. As suggested by Eqs. (4.3) and (4.4), Fig. 4.13 plots rt(r]) vs >3/2. The excellent agreement between the theory and the data confirms the use of the Fowler-Nordheim tunneling model for describing the carrier injection into the band structure of the semiconducting polymer. 

Most of the recombination occurs in the neutral regions and is dominated by the minority carriers, so that the recombination rate R varies linearly with the minority carrier density. For electrons in p-type material... 

They are valid for exhaustion or inversion layers as long as t/phl< Ulc - 0.1 V. Above this value, t/ph saturates. According to Eq. (50), large photovoltages are already obtained at rather low intensities because the carrier density created by light excitation can easily exceed the minority carrier density po(n) in n-type or o(p) in p-type material. 

Equation (7.2) expresses the net minority-carrier density/unit area as the product of the bulk minority-carrier density/unit volume nj/Ns, with the depth of the minority-carrier distribution diNv multiplied in turn by the customary Boltzmann factor exp(g(0s — Vs)/kT) expressing the enhancement of the interface density over the bulk due to lower energy at the interface. The depth diNv is related to the carrier distribution near the interface using the approximation (valid in weak inversion) that the minority-carrier density decays exponentially with distance from the oxide-silicon surface. In this approximation, diNv is the centroid of the minority-carrier density. For example, for a uniform bulk doping of 10 dopant ions/cm at 290 K, using Eq. (7.2) and the surface potential at threshold from Eq. (7.7) (0th = 0.69 V), there are Qp/q = 3 x 10 charges/cm in the depletion layer at threshold. This Qp corresponds to a diNv = 5.4 nm and a carrier density at threshold of JVinv = 5.4 x 10 charges/cm. ... 

This is known as the jimction law and says that the minority carrier density at the edge of the space charge region is enhanced by exp eV/kT), where V is the applied forward bias. The excess hole density is... 

Reverse current density is important in deterrnining the power that a device consumes when in the off state as it determines the effective resistance of the device in reverse bias. Hence reverse current is also referred to as leakage current. From Equation 3.24, the reverse current is carried by drift of minority carriers from the lightly doped side of the junction (that is the side having the higher minority carrier density) toward the heavily-doped side. If one assumes a p -n diode (the p-type side is very heavily doped) then Equation 3.24 becomes ... 

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