Temperature dependence of the refractive-index dispersion in amorphous germanium at elevated temperatures
Temperature dependence of the refractive-index dispersion in amorphous germanium at elevated temperatures
复制标题
DOI：
10.1103/physrevb.28.7175
复制
发表时间：
1983-12
影响因子：
3.7
通讯作者：
D. Goldschmidt
中科院分区：
文献类型：
--
作者：
D. Goldschmidt
在光学带隙附近（0.2-1.2 eV）测量了非晶锗的折射率色散，并首次在高温下（25 ℃-400 ℃）测量。在每个温度下的结果遵循单个振子的色散，其共振能量和强度随温度线性下降。然而，这些变化的幅度明显不同（例如，分别为2倍或更多）。很明显，在小间隙材料，如非晶锗，来自色散的温度依赖性不反映特定的带间跃迁的温度依赖性（在单振荡器模型的框架内）。一个新的模型，该帐户的温度依赖性的色散取代单个振荡器与其他两个带间电子振荡器。这两个较强的，代表了大多数的带间跃迁，位于最大的光学跃迁强度。假设它的振子强度接近于1，并且它的共振能的温度导数与Penn能隙的温度导数相同，通过拟合数据得到第二振子的参数。这是一个弱振子，位于光学带隙上方，代表了${\ensuremath{\displaystyle}_{2}$光谱的低能部分。此外，其谐振能量的温度导数获得与光学间隙的值相似的值。在该模型中，色散对弱振子的位置敏感，这是由于其谐振能量的低值及其与感兴趣的光谱区域的接近。色散对${\ensuremath{\displaystyle}_{2}$的低能部分的位置同样敏感，这是通过考虑它的矩得到的。因此，在结晶锗中，弱振子和强带间吸收的开始位于比非晶锗更高的能量处，预期单振子能量的较小温度导数。这一预测得到了实验的证实。它的结论是，使用带隙导数，双振子模型可以用来计算色散的温度依赖性，反之亦然。
Refractive-index dispersion in amorphous germanium was measured in the vicinity of the optical gap (0.2-1.2 eV) and for the first time at elevated temperatures (25\ifmmode^\circ\else\textdegree\fi{}C-400\ifmmode^\circ\else\textdegree\fi{}C). The results at each temperature follow the dispersion of a single oscillator, whose resonance energy and strength decrease linearly with temperature. However, the magnitude of these variations differs markedly (e.g., by a factor of 2 or more, respectively) from temperature derivatives of band gaps or of electron density. It is apparent that in small gap materials, such as amorphous germanium, temperature dependences derived from dispersion do not reflect the temperature dependence of specific interband transitions (within the framework of the single-oscillator model). A new model is developed which accounts for the temperature dependence of the dispersion by replacing the single oscillator with two other interband electronic oscillators. The stronger of these two, which represents the majority of interband transitions, is located at the maximum of the optical transition strength. Assuming that its oscillator strength is close to unity, and that the temperature derivative of its resonance energy is identical with that of the Penn gap, the parameters of the second oscillator are obtained by fitting to the data. This is a weak oscillator located closely above the optical gap thus representing the low-energy portion of the ${\ensuremath{\epsilon}}_{2}$ spectrum. Moreover, the temperature derivative of its resonance energy acquires a value similar to that of the optical gap. In this model the dispersion is sensitive to the location of the weak oscillator due to the low value of its resonance energy and its proximity to the spectral region of interest. The dispersion is similarly sensitive to the location of the low-energy portion of ${\ensuremath{\epsilon}}_{2}$, as obtained by considering its moments. Thus in crystalline germanium, where the weak oscillator and the onset of strong interband absorption lie at higher energies than in amorphous germanium, a smaller temperature derivative of the single-oscillator energy is expected. This prediction is confirmed by experiment. It is concluded that using band-gap derivatives, the two-oscillator model may be utilized to calculate the temperature dependence of the dispersion or vice versa.