Positron trapping in semiconductors

Abstract

Positron trapping into vacancies in semiconductors is studied on the basis of Fermi's golden-rule calculations. The emphasis is put on the comparison of the trapping properties into defects in different charge states. In particular, the temperature dependences are investigated. Important features for vacancy-type defects in semiconductors are the localized electron states within the forbidden energy gap and (in the case of negatively charged defects) the weakly bound Rydberg states for positrons. Compared to vacancy-type defects in metals, these features make possible new kinds of trapping mechanisms with electron-hole and phonon excitations. For charged defects the Coulomb wave character of the delocalized positron states before trapping determines the amplitude of the wave function at the defect and thereby strongly affects the magnitude of the trapping rate. As a result, trapping into positively charged defects is effectively forbidden while negatively charged defects show remarkable properties which differ from the picture established for positron trapping in metals. The trapping rate into negative defects increases strongly with decreasing temperature and at very low temperatures "gigantic" values may result.

Introduction and recovery of point defects in electron-irradiated ZnO

“…Assuming a trapping coefficient of V,Zn =3ϫ 10 15 s −1 at 300 K for the Zn vacancy as for the Ga vacancy in GaN, 29 we obtain ͓V Zn ͔ Ӎ 2 ϫ 10 16 cm −3 . At 30 K, st Ӎ V,Zn , and assuming that the trapping coefficient of the negative-ion-type defect is similar to that of a negative vacancy, 23,26 the concentrations are also similar, c st Ӎ 2 ϫ 10 16 cm −3 . These results are the same as reported previously.…”

“…[23][24][25][26] In this model, the trapping coefficient V to a neutral vacancy is independent of temperature and to a negatively charged vacancy it varies as T −0.5 . The trapping rate of positrons into the vacancies ͑concentration c V ͒ is V = V c V .…”

“…The positron trapping rate at the Rydberg state R varies also as T −0.5 , which is the result predicted by theory for the transition from a free state to a bound state in a Coulomb potential. 26 The thermal escape rate from the Rydberg state can be written as The temperature dependence of the positron data can also arise from a change in the charge state of the positron trapping defect ͑vacancy or negative ion͒ due to the dependence of the Fermi level E F on temperature. Then a vacancy that is neutral ͑as is expected for, e.g., the O vacancy͒ at low temperatures can be ionized and become positive and thus repulsive to positrons when the temperature is raised.…”

Introduction and recovery of Ga and N sublattice defects in electron-irradiated GaN

“…[13][14][15][16] In this model, the trapping coefficient V to a neutral vacancy is independent of temperature and to a negatively charged vacancy it varies as T −0.5 . The trapping rate of positrons into the vacancies ͑concentration c V ͒ is V = V c V .…”

Positron annihilation lifetime spectroscopy of ZnO bulk samples

“…12 The detrapping process from the ionic traps is thermally activated and the activation energy is equal to the binding energy E b . 13 The escape rate ͑␦ ion ͒ can be written as…”