Determination of the Si Young's modulus between room and melt temperature using the impulse excitation technique
Determination of the Si Young's modulus between room and melt temperature using the impulse excitation technique
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使用脉冲激励技术测定室温和熔体温度之间的 Si 杨氏模量
DOI：
10.1002/pssc.201300101
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
J. Vanhellemont
中科院分区：
文献类型：
--
作者：
A. Swarnakar;O. Biest;J. Vanhellemont
熔体-固界面附近的热梯度引起的应力影响熔体生长的单晶Si的本征点缺陷性质和质量。同样在器件处理期间，Si衬底中的应力影响热处理期间的点缺陷行为。为了能够模拟和控制应力分布，需要知道高温下单晶Si的弹性常数。本文采用脉冲激发技术研究了室温和熔体温度之间单晶硅样品的振动特性。
根据测量结果，提取了中等掺杂直拉硅样品在、和晶向上的杨氏模量随温度的变化。接近熔融温度时，根据晶体学方向，可以获得110至160 GPa之间的非常高的杨氏模量值。导出了E_（100）、E_（110）、E_（111）、E_（111）与温度关系的经验表达式，以及弹性柔量s_（11）、s_（12）+s_（44/2）的经验表达式，可用于过程模拟。（© 2014 WILEY-VCH Verlag GmbH & Co. KGaA，魏因海姆）
Stress induced by the thermal gradients near the meltsolid interface affects the intrinsic point defect properties and the quality of single crystal Si grown from a melt. Also during device processing, stress in the Si substrate influences point defect behavior during thermal treatments. To be able to simulate and control the stress distribution one needs to know the elastic constants of single crystal Si at high temperatures. In the present study, the vibrational properties of single crystal Si samples are studied between room and melt temperature using the impulse excitation technique.
From the measurements, the temperature dependent Young's moduli E〈ijk〉 of moderately doped Czochralski-grown Si samples are extracted in the 〈100〉, 〈110〉 and 〈111〉 crystallographic directions. Close to the melt temperature, very high Young's moduli values between 110 and 160 GPa are obtained, depending on the crystallographic direction. Empiric expressions are derived for the temperature dependence of E〈100〉, E〈110〉 and E〈111〉 and of the elastic compliances s11 and s12 + s44/2, useful for application in process simulation. (© 2014 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)