Percolation on a Continuum and the Localization-Delocalization Transition in Amorphous Semiconductors
Percolation on a Continuum and the Localization-Delocalization Transition in Amorphous Semiconductors
复制标题
连续体渗流和非晶半导体中的局域-离域转变
DOI：
10.1103/physrevb.4.4471
复制
发表时间：
1971
影响因子：
3.7
通讯作者：
H. Scher
中科院分区：
文献类型：
--
作者：
R. Zallen;H. Scher
The concept of percolation has been set in a form which is more directly germane than the existing theory of percolation on lattices to the question of the localization-delocalization transition (mobility edge) in amorphous semiconductors. The problem of percolation on a continuum has been formulated in the context of motion in a random potential $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$. An energy-dependent dimensionless density $\ensuremath{\varphi}(E)$ is introduced which specifies the fraction of space satisfying $VlE$. Extended states appear above a critical density ${\ensuremath{\varphi}}_{c}$; this provides our working criterion $\ensuremath{\varphi}({E}_{c})={\ensuremath{\varphi}}_{c}$ for the location of the percolation threshold ${E}_{c}$. In one dimension ${\ensuremath{\varphi}}_{c}=1$, and in two dimensions we find that ${\ensuremath{\varphi}}_{c}=\frac{1}{2}$ for an important class of random potentials. In three dimensions we obtain an estimate of ${\ensuremath{\varphi}}_{c}=0.15$ from an empirical rule. The percolation criterion for the location of the mobility edge ${E}_{c}$ has been applied to several types of disordered potentials. The oft-invoked Gaussian potential distribution has been treated and the results compared with those of several recent calculations. Random-walk techniques can be used to attack more general random potentials; we have used this approach to explicity calculate ${E}_{c}$ for the potential of an array of random dipoles, which is an initial model for an amorphous molecular solid. A way of including short-range order is briefly discussed.
The concept of percolation has been set in a form which is more directly germane than the existing theory of percolation on lattices to the question of the localization-delocalization transition (mobility edge) in amorphous semiconductors. The problem of percolation on a continuum has been formulated in the context of motion in a random potential $V(\stackrel{\ensuremath{\rightarrow}}{\mathrm{r}})$. An energy-dependent dimensionless density $\ensuremath{\varphi}(E)$ is introduced which specifies the fraction of space satisfying $VlE$. Extended states appear above a critical density ${\ensuremath{\varphi}}_{c}$; this provides our working criterion $\ensuremath{\varphi}({E}_{c})={\ensuremath{\varphi}}_{c}$ for the location of the percolation threshold ${E}_{c}$. In one dimension ${\ensuremath{\varphi}}_{c}=1$, and in two dimensions we find that ${\ensuremath{\varphi}}_{c}=\frac{1}{2}$ for an important class of random potentials. In three dimensions we obtain an estimate of ${\ensuremath{\varphi}}_{c}=0.15$ from an empirical rule. The percolation criterion for the location of the mobility edge ${E}_{c}$ has been applied to several types of disordered potentials. The oft-invoked Gaussian potential distribution has been treated and the results compared with those of several recent calculations. Random-walk techniques can be used to attack more general random potentials; we have used this approach to explicity calculate ${E}_{c}$ for the potential of an array of random dipoles, which is an initial model for an amorphous molecular solid. A way of including short-range order is briefly discussed.