Point Defects and Diffusion in Semiconductors
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equilibrium concentrations in compound semiconductors dépend on the vapor pressure of the more volatile component.47 Thèse features will ail be mentioned in the rest of the article. We will discuss various types of point defects and diffusion mechanisms in semiconductors, including the long standing controversy on vacancies versus self-interstitials in silicon.2,4,49 Point Defects In a two-dimensional représentation, Figure 1 schematically shows various kinds of basic point defects in an elemental semiconductor. Extrinsic point defects include interstitially dissolved éléments
foreign interstitial atoms e.g.,Cu,Ni,Fe,Li,H
selfinterstitial I
vacancy V interstitial impurity, A,
substitutional dopants B, AI, Go p-type
;
substilutional Impurity.A, e.g., Au.Pt
P, As, Sb n-type
(such as copper or hydrogen in silicon), substitutionally dissolved foreign atoms such as the common group-III and groupV dopants, and electrically inactive groupIV éléments such as carbon or germanium in silicon. The two basic types of intrinsic point defects are vacancies (V) and selfinterstitials (I). Under thermal equilibrium conditions any crystal will contain a certain concentration of the intrinsic point defect species X (V or I), C| q , which leads to a lower Gibbs free energy of the crystal as compared to a defect-free crystal. This thermal equilibrium concentration, in atomic fraction (number of defects/number of lattice atoms), is given by C?(T) = Z e x p ( - G ^ T )
(1)
where k is Boltzmann's constant, T the absolute température and G'x the Gibbs free energy of formation of the intrinsic point defect X. The dimensionless prefactor Z accounts for the number of possible defect sites per lattice atom and is unity for single vacancies. In spitè of impressive progress, ab initio quantum mechanical calculations of Gx are not yet accurate enough to reliably predict the vacancy and self-interstitial concentrations at a given température. Intrinsic point defects may occur in one or more charge States with accompanying changes in G x . The thermal equilibrium concentration of a charged point defect X ' (where r stands for a positive or négative integer, representing the charge type and number) dépends on the doping type and level of the semiconductor, or its Fermi level, which is directly related to the électron concentration n and the hole concentration p. The thermal equilibrium concentration of the charged point defect also dépends on its energy level position in the energy bandgap. The ratio of this point defect concentration in a doped semiconductor (with électron concentration n) to that in an undoped or intrinsic semiconductor (with intrinsic électron concentration n-,) is independent of the point defect energy level and may be expressed as a function of the carrier concentrations:1"4,8
Q>0 C?'(n,) '
(2) "i
or impurities: e.g.,C,Ge,Sn
Figure 1. Schematic two-dimensional représentation of various types of intrinsic and extrinsic point defects in an elemental semiconductor crystal such as silicon.
where n and p are related via
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