阿伦尼乌斯方程带来的误导:芯片运行寿命随温度的变化

当芯片过热时,其可靠性会下降。但这只是一个定性的规律。为了能预测芯片的运行寿命或者故障率,必须获得可靠性和温度之间的具体关系。

一个被广泛使用的简单方式是温度每上升10℃,元器件运行寿命减半。这一结论的依据是阿伦尼乌斯方程(或公式):

阿伦尼乌斯方程带来的误导:芯片运行寿命随温度的变化

式中A是化学反应常数,EA是活化能,k是玻尔兹曼常数,T是绝对温度。阿伦尼乌斯方程描述的是化学反应的速率常数与温度之间的关系式,适用于基元反应和非基元反应。

对于同一个芯片,在比较不同问工作温度下其可靠性差别时,可以作如下变化:

阿伦尼乌斯方程带来的误导:芯片运行寿命随温度的变化

可以看到,衰减因子与温度之间的关系实际上和活化能有关。不同失效机制下的活化能是不同的。只有在活化能为~0.8 ev时,衰减因子在常规芯片温度范围内(~80C)才接近2.下表列示了不同失效机制下化学反应的活化能范围,可以看到,活化能为0.8 ev仅能代表电子迁移过程,氧化、腐蚀、硅形变等均低于此值。而污染、电荷注入过程的活化能则高于此值。

Failure
Mechanism
Activation
Energy
Screening and Testing
Methodology
Control Methodology
Corrosion 0.45ev Highly Accelerated Stress Test
ing (HAST).
Passivation dopant control, hermetic seal
control, improved mold compounds, and
product handling.
Oxide Defects 0.3 – 0.5eV High Temperature operating life (HTOL) and voltage stress. Statistical Process Control of oxide
parameters, defect density control, and
voltage stress testing.
Silicon Defects
(Bulk)
0.3 – 0.5eV HTOL and voltage stress screens. Vendor statistical Quality Control pro
grams, and Statistical Process Control on
thermal processes.
Assembly Defects 0.5 – 0.7eV Temperature cycling, tempera
ture and mechanical shock, and
environmental stressing.
Vendor statistical Quality Control pro
grams, Statistical Process Control of
assembly processes, and proper handling.
Electromigration
– Al line
– Contact/Via
0.6eV
0.9eV
Test vehicle characterizations at
highly elevated temperatures.
Design process groundrules to match
measured data, statistical control of met
als, photoresist and passivation.
Mask Defects/
Photoresist
Defects
0.7eV Mask Fab comparisons, print
checks, defect density monitor in
Fab, voltage stress test and
HTOL.
Clean room control, clean mask, pellicles,
Statistical Process Control of photoresist/
etch processes.
Contamination 1.0eV C-V stress of oxides, wafer fab
device stress test and HTOL.
Statistical Process Control of C-V data,
oxide/interconnect cleans, high integrity
glassivation and clean assembly process.
Charge Injection 1.3eV HTOL and oxide characteriza
tion.
Design groundrules based on test results,
wafer level Statistical Process Control of
gate length and control of gate oxide
thickness.

Acceleration Factor for a 10°C Temperature Increase

阿伦尼乌斯方程带来的误导:芯片运行寿命随温度的变化

芯片的失效机制非常复杂,这一方程实际上只是针对特定失效机制才有意义的。大量数据证实“10C=1/2”的公式是不合适的。当活化能变高,衰减程度会加剧;活化能降低,衰减程度又会缓解。

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