Characterization of vacancy-type defects in silicon using deep level ...

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Figure 4. Visualization of the atomicstructure of the O i (a), VO (b) and V 2 (c)defects.Electron and charge states for V 2Figure 5. Illustration of electronstates and charge states for theV 2 centre in silicon.E C2--0.23 eV0.43 eV0E V+0.20 eVand it causes three different electron states in E g corresponding to four charge states of V 2 (+,0, -1, -2), as depicted in Figure 5.I.(b) Emission and capture of electrons/holes by energy states in the band gapLet us consider an electron state at an energy E T below E c and with a concentration of N T .Figure 6(a) shows the total ‘traffic’ of electrons and holes to and from this state. The rate ofemission of an electron to E c and a hole to E v are denoted by e n and e p , respectively. The rateof capture of an electron from E c or a hole from E v are nc n and pc p , respectively, where c n andc p are the so-called capture coefficients, and n and p are the concentrations of electrons in theconduction band and holes in the valence band, respectively.4
Figure 6. The total ‘traffic’ ofcharge carriers to and from a state isshown in (a). The special case ofrecombination is given in (b),trapping and emission in (c), andgeneration in (d).}E TThree typical situations can be identified; first, as shown in Figure 6(b), a state may act as arecombination centre for pairs of electrons and holes. Second, as shown in Figure 6(c), a statecan act as a trap, and trapping and emission of electrons (or holes) are the dominatingprocesses. Third, as shown in Figure 6(d), a state can act as a generation centre for pairs ofelectrons and holes.According to Shockley and Read[5], the capture coefficient for a state can be expressed as:c n(p) = σ n(p) v thwhere σ n(p) is the capture cross section for electrons (holes) and v th is the thermal velocity,v th = (3kT/m* n(p) ) ½with m* n(p) as the effective mass for electrons (holes), T as the absolute temperature, and k asBoltzmann’s constant.For the emission rate, the following relation holds[5]:e n(p) (T) = v th σ n(p) N C(V) exp(-E T /kT) (1)where N C(V) is the effective density of states in the conduction (valence) band.5
Page 1 and 2: Department of Physicshttp://www.uio
Page 3: group III impurities (B, Al, Ga, In
Page 7 and 8: In accordance with section I.(b), l
Page 9 and 10: In reality, the procedure outlined
Page 11 and 12: II.(c) Instrumentation for the meas

Characterization of vacancy-type defects in silicon using deep level ...

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