Majority carrier concentration

The equilibrium lever relation, np= n , can be regarded from a chemical kinetics perspective as the result of a balance between the generation and recombination of electrons and holes (21). In extrinsic semiconductors recombination is assisted by chemical defects, such as transition metals, which introduce new eneigy levels in the energy gap. The recombination rate in extrinsic semiconductors is limited by the lifetime of minority carriers which, according to the equilibrium lever relation, have much lower concentrations than majority carriers. Thus, for a >-type semiconductor where electrons are the minority carrier, the recombination rate is A /t. An = n — n0 is the increase of the electron concentration over its value in thermal equilibrium, nQy and Xn is the minority carrier lifetime. This assumes low level injection where An is much smaller than pQy the equilibrium majority carrier concentration. 

Recombination in the depletion layer can become important when the concentration of minority carriers at the interface exceeds the majority carrier concentration. Under illumination minority carrier buildup at the semiconductor-electrolyte interface can occur due to slow charge transfer. Thus surface inversion may occur and recombination in the depletion region can become the dominant mechanism accounting for loss in photocurrent. 

The semiconductor nature of diamond manifests itself in a photoelectrochemical response caused by the photogeneration of free charge carriers. With the dielectric diamond, photoconductance (that is, an increase in the conductance due to an increase in majority carrier concentration) can be observed. With the conducting... 

The majority carrier concentration at the point xRZ, where v = vnz, is then given by... 

In the absence of any trapping phenomenon, the data of Table XII must be compared to the carrier concentrations in the various types of solids in the absence of radiation. In intrinsic semiconductors, this concentration hardly exceeds 10 g. in very pure germanium, for instance, this value is equal to 2.5 X 10 . In extrinsic semiconductors the majority carrier concentration is generally between 10 and 10 g. the corresponding value for minority carriers is generally much lower and may be as small as 10 . Unless very high radiation intensities are used, it is thus seen that in the absence of trapping phenomenon, the influence of radiation upon the number of carriers can become appreciable only in the case of extrinsic semiconductors in other cases only the concentration of minority carriers is affected. 

For a doped silicon, depending on the dopant, one type of carrier is the majority carrier as its concentration far exceeds the other, even at low doping levels. For example, for donor concentration = lO Vcm that is, n = 10 p = 2.1 x 10 which is nearly 10 orders of magnitnde below the majority carrier concentration. 

Surface recombination of electrons and holes is also relatively slow. Usually, the recombination lifetime depends inversely on the majority carrier concentration at the surface. For a n-type semiconductor, the lifetime of a hole trapped at a surface state is given by r, = l/j w/, where is the rate constant for electron capture For example if n /A = 10 cm and the band-bending = ksT, nmrf =... 

The recombination lifetime is the average time an excess electron-hole pair (ehp) exists. It is frequently referred to as the minority carrier lifetime when minority carriers dominate the recombination process. This is generally true under low-level injection conditions when the minority carrier concoitration is small compared to the equilibrium majority carrier concentration. For high level injection, it is no longer the minority carrier lifetime, but the combined minority-majority carrier lifetime that dominates. We will use the general term recombination lifetime to cover all of these possibilities. 

The thermal equilibrium majority-carrier concentration in an n-type semiconductor is given by [4.9]... 

Regardless of the theoretical complications, however, it is clear physically that when a detector is to be used in a certain background radiation flux density, it is not helpful to its performance to lower the majority carrier concentration... 

A heavily doped wafer (p , ean be readily anodized in a variety of HF-based electrolytes to form mesoporous silicon. A lightly doped wafer (p , n , and majority carrier concentration <10 cm ) generally requires an ohmic contact to be made on the backside, either by ion implantation or by depositing a thin metal layer such as A1 (for p-type wafers) and Au-Sb (for n-type wafers) mechanical abrasion of the backside of the wafer, before metal deposition, can often improve the ohmic contact. 

According to the continuity equation of minority carriers from (3.79), again neglecting the diflhision term, and using the conditions that electron and hole concentration gradients are equal and that p = n - (No - Na) we obtain for the majority carrier concentration gradient... 

It can be seen in Figs. 3.9 and 3.10 that no full exclusion occurs under the applied conditions, but only partial instead. Even for the largest values of bias the carrier concentrations are not constant, majority carrier concentrations are not brought near the impurity level and minority concentrations are not below it. Further simulations show that at room temperature exclusion does improve photoconductor characteristics, but cannot lead to qualitative changes and a level of Auger suppression sufficient to furnish a BLIP device. 

Remember that throughout this process, the law of mass action holds which says that the product of hole and electron carrier concentration is a function only of the ratio of the effective masses of the electrons, the Eg, and the absolute temperature. The dopant concentration does not enter into the np product. Increasing the number of donor impurities raises n, but at the expense of p. Conversely, increasing the number of acceptor states increases p, but at the expense of n. In other words, for a given material at a given temperature, increasing the majority carrier concentration is done at the expense of the minority carrier concentration such that their product remains the same. 

For extrinsic semiconductors, on a plot of majority carrier concentration versus temperature, carrier concentration is independent of temperature in the extrinsic region... 

When the direction of electron flow is into n-type material or out of p-type material, it increases the majority carrier concentration of the semiconductor. This increases the conductivity of the semiconductor near the junction and is described as ohmic because the junction acts only as a resistor. Such junctions are desired for contacts to microelectronic devices. Unfortunately, it is often impossible to find a metal of sufficiently high or low work function to arrange the electron flow in the correct direction to obtain an ohmic contact, especially to wide-gap semiconductors and organic electronic materials. 

When the trapped charge carriers are released they may become free or may recombine, for example, with recombination centers or with carriers of the opposite sign. When the release rate is higher than the recombination rate, the localized state is a trap, while for the dominant recombination rate the localized state forms a recombination center. It means that the same state may act as the recombination center or as the trap, depending on certain parameters, such as temperature or a ratio of minority to majority carrier concentrations. The traps can not only reduce the carrier drift mobility but also change the internal field distribution. 

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