Silicon electron concentration

Fio. 3. Dependence on hydrogenation temperature of the free-electron concentration (a) and the electron Hall mobility (b) in phosphorus-implanted n-type silicon (Johnson et al., 1987c). 

The diffusion of hydrogen in highly or lightly silicon doped GaAs induces a modification of the electrical properties of the material a reduction of the free electron concentration (Fig. 2) and a significant increase of the electron mobility up to values close to the mobility in nonhydrogenated materials with the same net carrier concentration (Jalil et al., 1986 Pan... 

It is shown that the rate-limiting step in the photoelectrochemical evolution of hydrogen in an HF electrolyte is linearly dependent on the excess electron concentration at the surface of the p-type silicon electrode. The rate of this step does not depend on the electrode potential and the H+ concentration in the solution, but is sensitive to the surface pretreatment [Sell]. The plateau in the I-V curve, slightly... 

Impurity Semiconductors, n-Type andp-Type. The discussion has been restricted so far to pure intrinsic semiconductors exemplified by germanium and silicon. In these substances, there is a low concentration of charge carriers (compared with metals). Further, the hole and electron concentrations are equal, and their product is a constant given by the law of mass action... 

The temperature dependence of the linear rate constants for various electron concentrations in phosphorus-doped silicon indicate that the doping has only a slight effect on the associated activation energy. Thus, because B/A is proportional to the rate of the interface reaction, the doping effect is buried in the chemical, electrical, or, possibly, mechanical dependence of surface rate on doping. 

In practice, nothing is absolutely pure, so the word substance is an idealization. Among the purest materials ever prepared are silicon (Fig. 1.5) and germa-ninm. These elements are used in electronic devices and solar cells, and their electronic properties require either high purity or else precisely controlled concentrations of deliberately added impurities. Meticulous chemical and physical methods have enabled scientists to prepare germanium and silicon with concentrations less than one part per billion of impurities. Anything more would alter their electrical properties. 

The potential range where gold deposition and hydrogen evolution take place is negative with respect to the flat band potential, hence, the silicon is expected to be in accumulation and the electron density at the surface is higher than in the bulk. Note that the surface electron concentration in this case is still several orders of magnitude lower than at metal surfaces, which may have a significant effect on the deposition characteristics. 

Effects of reducing Electron Concentration. The1 restricted solid solubility of a solute of lower valency is not te>o difficult to explain if, first, we1 deal with an extreme case, e.g. the mutual solid solubilities e>f silicon and copper. The size-factors are be>th favourable (Cu, atomic diameter, 2-5oA Si, atomic diameter, 2-doA), and from our previous work we1 should oxpe ed copper to be1 able1 to take into solid solution about as mam atoms per rent, of quadri alrnt silicon as it docs of quadri alont tin, i.e. about 10 atomic per cent. Tim actual figure for the maximum solid solubility of silicon in copper is... 

Electron-phonon coupling has been investigated in heavily doped silicon at subkelvin temperatures. The heat flow between electron and phonon systems is found to be proportional to F. The coupling constant significantly increases with the increase of the electron concentration. 

Inside the silicon semiconductor, electrons diffuse from the n-type side (with a high electron concentration) in the direction of thep-type side. Holes diffuse from the p-side in the opposite direction. This results in a region where all charge carriers are depleted (space charge region). At thep-n junction both electrons and holes accumulate electrons on one side of the junction, and holes at the other side. Thus, a double layer of electric charges is formed, which leads to a potential difference of about 0.6-0.7 V. This is the solar cell s open-circuit voltage (OCV). When both sides of the... 

Only a few ternary silicon nitrides have been prepared in a pure form and characterized. The isotypic compounds MSiN2 (M = Be, Mg, Mn, Ca, Zn), with the same valence electron concentration of 4, can be considered as ternary substitution variants of AlN [247]. These compounds contain three-dimensional (3-D) infinite network structures, with SiN4 tetrahedra linked through all four vertices by comer-sharing, which forms condensed [SieNe] twelve-membered rings in MgSiN2 [248]. 

In the extrinsic or doped semiconductor, impurities are purposely added to modify the electronic characteristics. In the case of silicon, every silicon atom shares its four valence electrons with each of its four nearest neighbors in covalent bonds. If an impurity or dopant atom with a valency of five, such as phosphorus, is substituted for silicon, four of the five valence electrons of the dopant atom will be held in covalent bonds. The extra, or fifth electron will not be in a covalent bond, and is loosely held. At room temperature, almost aU of these extra electrons will have broken loose from their parent atoms, and become free electrons. These pentavalent dopants thus donate free electrons to the semiconductor and are called donors. These donated electrons upset the balance between the electron and hole populations, so there are now more electrons than holes. This is now called an N-type semiconductor, in which the electrons are the majority carriers, and holes are the minority carriers. In an N-type semiconductor the free electron concentration is generally many orders of magnitude larger than the hole concentration. 

FigMre 18.17 Electron concentration versus teii rera-tnre for silicon (n-type) that has been doped with of a donor impurity and for intrinsic silicon (dashed Une). Freeze-out, extrinsic, and intrinsic temperature regimes are noted on this plot. 

Concept Check 18.7 On the basis of the electron-concentration-versus-temperature curve for n-type silicon shown in Rgure 18.17 and the dependence of the logarithm of electron mobility on temperature (Figure 18.19a), make a schematic plot of logarithm electrical conductivity versus temperature for silicon that has been doped with 10 m of a donor impurity. Now, briefly explain the shape of this curve. Recall that Equation 18.16 expresses the dependence of conductivity on electron concentration and electron mobility. 

The hole concentration is known to be 2.0 X 10 m". Using the electron and hole mobilities for silicon in Table 18.3, compute the electron concentration. 

Figure 2.10 A plot of the electron concentration in a piece of silicon doped with 10 cm donor atoms having an ionization energy of 0.04 eV. The steep slope at high temperature (low inverse temperature) corresponds to the intrinsic behavior for carriers crossing the energy gap. The lower temperature behavior occurs in the presence of the 10 cm electron donors. The slopes of the two curves correspond to the 1.1 eV energy gap and the 0.04 eV donor ionization energies, respectively.

Figure 7.8 Phosphorous concentration resulting fiom diffusion into silicon. Formation of dopant clusters at high coneentrations limits the diifusivity. Autocompensation limits the electron concentration to a value (the doping limit) below the solubility limit. Redrawn with permission from Fair, Richard B, Concentration profiles of diffused dopants in Silieon, in Wang, F.F.Y., ed., Impurity Doping Processes in Silicon (North Holland, Amsterdam, 1981), chapter 7. Copyright Elsevier, 1981.

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