Solution of the kinetic equations governing trap filling. Consequences concerning dose dependence and dose-rate effects
Solution of the kinetic equations governing trap filling. Consequences concerning dose dependence and dose-rate effects
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DOI：
10.1103/physrevb.24.4931
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发表时间：
1981-11
影响因子：
3.7
通讯作者：
Reuven Chen;S. McKeever;S. Durrani
中科院分区：
文献类型：
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作者：
Reuven Chen;S. McKeever;S. Durrani
数值求解了绝缘体中陷阱和发光中心在电离辐射填充过程中载流子输运的方程。数值解是一组四个联立的微分方程组，它们控制着电子和空穴在导带和价带以及陷阱和中心中的浓度随时间变化的函数。结果比以前报道的结果更普遍和准确，因为不需要做出关于接近平衡的假设。此外，所有以前的计算都考虑了辐射结束时的累积浓度，而我们考虑了激发后的额外时间段，这允许带中载流子的驰豫。这更准确地模拟了实验条件，因为在这段时间里，任何可能积累在导带和价带中的载流子都会松弛到陷阱和中心，在这样做的过程中，将有助于陷阱电荷的最终集中。在我们的计算中，我们已经考虑到这一点，在辐射停止(发生在时间$T$)之后，让带内的电荷衰减一段时间$T$。因此，陷阱电荷的能级在时间$t+T$被计算，这被认为是陷阱电荷密度的更好表示。获得了非常高和非常低的辐射剂量率(强度)的结果。热释光(TL)的剂量依赖关系的实验结果很容易用我们开发的方法进行分析。通过增加竞争陷阱水平和适当改变方程组，我们得到了一组五个联立的微分方程组。通过这种方式，我们可以测试之前的近似结果，从而产生对其中一个陷阱的超线性填充。结果表明，在适当的参数选择下，虽然结果与以往的近似结果不完全相同，但出现了超线性现象。此外，从分析中得出的一个重要结果是，对于恒定的总剂量，热释光输出可能依赖于剂量率。最近的实验结果表明，这种对石英中热释光的依赖关系与数值结果基本一致。
The equations governing the traffic of charge carriers during the filling, by ionizing radiation, of traps and luminescence centers in an insulator are numerically solved. The numerical solution is that of a set of four simultaneous differential equations governing the time-dependent functions of concentrations of electrons and holes in the conduction and valence bands and in traps and centers. The results are more general and accurate than those reported previously since no assumptions concerning the proximity to equilibrium have to be made. Moreover, all previous calculations took into account the accumulated concentrations at the end of the irradiation, whereas we have considered an additional period of time after the excitation which allows for the relaxation of carriers in the bands. This simulates the experimental conditions more accurately because during this time any charge carriers which may have accumulated in the conduction and valence bands will relax into the traps and centers and, in doing so, will contribute to the final concentration of trapped charge. In our calculations we have allowed for this by letting the charge in the bands decay for a period of time $T$ following the cessation of the irradiation (which occurs at time $t$). Thus, the level of trapped charge $n$ is calculated at time $t+T$ and this is taken to be a better representation of the trapped charge density. Results were obtained for very high and very low dose rates (intensities) of the radiation. Experimental findings of the dose dependence of thermoluminescence (TL) are susceptible to analysis by the approach developed by us. By adding a competing trapping level and changing the set of equations appropriately, we get a set of five simultaneous differential equations. In this way we can test the previous approximative results yielding a superlinear filling of one of the traps. It is found that, under an appropriate choice of parameters, superlinearity emerges, although the results are not identical to those of the previous approximations. In addition, an important result to emerge from the analysis is the possible dependence of TL output on the dose rate for a constant total dose. Recent experimental results of such a dependence on TL in quartz are shown to be in general accord with the numerical results.