Mechanism of Electronically Enhanced Defect Reactions in Semiconductors
Yuzo Shinozuka
Faculty of Systems Engineering, Wakayama University, Sakaedani 930 Wakayama 640-8510, JAPANe-mail: yuzo@sys.wakayama-u.ac.jp
Keywords: defect reaction, lattice relaxation, multiphonon process, phonon kick, coherent capture
Electronic transitions sometimes induce or enhance
defect reactions in semiconductors, such as impurity
diffusion, structural change of a defect (creation,annihilation and multiplication), and climb and glide
motions of dislocation [1]. It has been suggested that thetransient vibration induced by a carrier capture enhances
the probability of a following capture of the opposite
carrier [2,3]. Recently Shinozuka and Karatsu havesimulated the transient lattice vibration induced bysuccessive captures and it effect on the next capture
process [4]. If N pairs of electrons and holes aresequentially captured by a defect, each occurred at te1< th1<te2< th2< … < teN < thN, the time evolution of Q1(t) for thN<tis given by
NbeforeQ1( t)  Q1( t)  Q1 {  exp[ (t  tej ) / 4] cos 0 (t  tej )2N2enhanced defect reaction in connection with the transientinduced lattice vibration. The condition for the coherent
captures turns out to be peph >1. Then if
N pairs of electron and hole are captured within a shortperiod ~2π/, the amplitude of the interaction mode Q1(t)increases remarkably. If the central frequency the reaction coordinate QR is not so much different fromQ1, more than the band gap
energy Eg= Eeth+Ehth can be transformed by a series ofcoherent carrier captures into the lattice vibration energy.
The defect reaction rate is given by ( /2π)exp(- Eiact/kBT)
because only the first capture (i=e, h) is to be activated.
On the other hand, if Rthe rate is ( /2π)exp(-U0*/kBT) with U0-(Eiact+Eith)
because the N phonon-kick’s are out of phase.

j exp[  ( t  t ) / 4] cos (t  t )} , (1)

22hj

0hj

for a system j whose phonon frequency  k distribution isgiven by a Gaussian with the central frequency 0 and thewidth . Here Q1before(t) is the time dependence if all
the captures of N electron-hole pairs would not haveoccurred at all. Thus, Q1(t) is shown to be a linear
combination of damping oscillations, each starts at time tej
or thj and lasts in the same duration ~2/. It should
be reminded that the capture time tej and thj do not take anarbitrary value but should be obeyed by probability.
We will discuss the effect of the transient vibration(eq. 1) to defect reactions using following assumptions:a) The first electron capture takes place by a thermalactivation Q1 to Qe with the activation energy Eeact.
b) If Q1(t) crosses at Qe (Qh), there is a probability pe (ph)per time to capture an electron (hole) nonradiatively. pe(ph) ~  /2π in the adiabatic limit.
c) The defect reaction coordinate is given by QR (t )  f k qk (t) , whose frequency distribution is a Gaussiank

with the central frequency R and the width .
d) If QR(t) crosses the critical point Qc, the defect reaction
takes place.
We have found that every capture process enhances thevibration of Q1(t). On the other hand, it is not so forQR(t) in 0  R case, because the timing of push and pullfor QR(t) is out of phase (Fig.1).
Let us discuss the possibility of recombination-Fig. 1 The time evolution of QR(t). Large (small) circle
indicates the capture time tei (thi) for an electron (hole).
1. O. Ueda, “Reliability and degradation of III-V opticaldevices” (Artech House Publishers) 1996.
2. Y. Shinozuka, Defects in Optoelectronic Materials, ed.
K. Wada and S. W. Pang (Gordon and Bleach SciencePublisher, 2001) Chapter 8.
3. Y. Shinozuka: J. Phys. Soc. Jpn. 51 (1982) 2852 ; Jpn. J.
Appl. Phys. 32 (1993) 4560.
4. Y. Shinozuka and T. Karatsu: Physica B273-274 (1999)
999.