Displacement Damage Effect on Minority Carrier Lifetime

As discussed in Sections 7.4–7.4.1 of [Leroy and Rancoita (2016)] (see also [Leroy and Rancoita (2007)]), among the most important semiconductor material-parameters for practical applications in electronic devices, we have the (excess-) carrier lifetime (e.g. see [Schroder (1997)]), the equilibrium majority-carrier concentration and the majority-carrier mobility. To a first approximation¹, the rate at which the electrical properties of semiconductors degrade by irradiation is often expressed in terms of a damage coefficient. For instance, the minority carrier (recombination) lifetime (τ) is given by

(1)

where τ_irr and τ are the lifetimes after and before the irradiation with a fluence Φ_i of particles, respectively; K_τ,i is the (recombination) lifetime damage coefficient², which may depend on i) the type of substrate, ii) the dopant concentration, iii) the level of compensation and iv) the type (“i”) and energy of irradiating particles (e.g., see Section 5 in Chapter I of Part II of [Vavilov and Ukhin (1977)], [Srour and McGarrity (1988)], Section 3.4 of [Srour, Long, Millward, Fitzwilson and Chadsey (1984)] and references therein). Values of K_τ,i are available in literature. For instance, for low-resistivity silicon experimental results on the lifetime damage constants are presented in [Srour, Othmer and Chiu (1975)] for 0.5, 1.0 and 2.5 MeV electrons with fluences up to ≃ 3 × 10¹⁵ e/cm² and 10 MeV protons with fluences up to ≃ 1.2 × 10¹² p/cm² (see also Section 3.4 of [Srour, Long, Millward, Fitzwilson and Chadsey (1984)]).

To a first approximation (e.g., see discussion in Sections 7.4.1, 11.1.2, 11.1.4., 11.4.1.1 of [Leroy and Rancoita (2016)]), in absence of saturation effects³, (mostly) for low-resistivity silicon we can assume that the concentration of recombination centers is proportional – although the proportionality constant may be slightly varied, in particular, when the cascades of primary defects induced by recoil nuclei are largely different – to the energy deposited by non-ionizing energy-loss (NIEL) processes per unit volume E_dis and, consequently, to the concentration of Frenkel-pairs (FP) introduced as primary point-defects. Furthermore, as treated in Section 7.4.1 of [Leroy and Rancoita (2016)], one can derive that Eq. (1) can be re-written as:

is almost – under the above mentioned assumptions – independent of the type and energy of the incoming particle, but depends on i) the type of substrate, ii) (slightly) the dopant concentration and iii) the level of compensation and, where, v_e is the average speed of minority carriers, σ_m is the cross section for the absorption of minority carriers by recombination centers and γ_dis expresses the proportionality constant between the deep defect concentration and that of Frenkel-pairs FP. Equations (2) indicates that an approximate NIEL scaling is expected for the variation of the reciprocal of the minority-carrier lifetime in low-resistivity silicon.

References