Crystal Medium on Electron Tunneling

Let us examine the structure of expression (16). The influence of the dielectric medium constant e0 affects the factor aroused from the long-range Coulomb s field of the donor and acceptor charges, (i ri,A)iZ +ZA,/ci,K. But the influence of medium on the second, exponential factor in g(rDA) is not yet examined. Note, the expression — (l/r )exp —differs from the Green s function of a free electron Go( D,r E) by the numeric factor l/2n only (see formula (6)). Therefore it will be considered that the influence of the medium on Green s function of a free electron does not interact with the donor and the acceptor. 

Naturally, it is suggested that the concentrations of the free carriers, i.e. electrons in the conductivity band and holes in the valence band, are epsilon squared. In another case, electrons from the conductivity band will be captured by the acceptor, or holes from the valence band will get annihilated by the electron on the donor. Then, the tunneling transition becomes impossible because either the acceptor level becomes populated or the donor level is emptied. 

The Green s function of electron in a crystal has the following spectral representation [9,10]  

The physical sense of the electron and hole parts of Green s function in expression (21) is quite obvious. Green s function G(f,f E) is the propagator of the electron motion from point f near the donor to point r near the 

The electron wave functions i/zj(r) are Bloch s functions normalized on the volume Q of the crystal  

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