Accurate prediction of junction temperature is crucial for the efficient thermal design of silicon nano-devices. In nano-scale semiconductor devices, significant ballistic effects occur due to the mean free path of ph...Accurate prediction of junction temperature is crucial for the efficient thermal design of silicon nano-devices. In nano-scale semiconductor devices, significant ballistic effects occur due to the mean free path of phonons comparable to the heat source size and device scale. We employ a three-dimensional non-gray Monte Carlo simulation to investigate the transient heat conduction of silicon nanofilms with both single and multiple heat sources. The accuracy of the present method is first verified in the ballistic and diffusion limits. When a single local heat source is present, the width of the heat source has a significant impact on heat conduction in the domain. Notably, there is a substantial temperature jump at the boundary when the heat source width is 10 nm.With increasing heat source width, the boundary temperature jump weakens. Furthermore, we observe that the temperature excitation rate is independent of the heat source width, while the temperature influence range expands simultaneously with the increase in heat source width. Around 500 ps, the temperature and heat flux distribution in the domain stabilize. In the case of dual heat sources, the hot zone is broader than that of a single heat source, and the temperature of the hot spot decreases as the heat source spacing increases. However, the mean heat flux remains unaffected. Upon reaching a spacing of 200 nm between the heat sources, the peak temperature in the domain remains unchanged once a steady state is reached. These findings hold significant implications for the thermal design of silicon nano-devices with local heat sources.展开更多
In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic system ut = △u ＋ v^P（x0, t） - au^τ, x ∈ Ω, t 〉 0, △u ＋ v^P（x0, t...In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic system ut = △u ＋ v^P（x0, t） - au^τ, x ∈ Ω, t 〉 0, △u ＋ v^P（x0, t） - bu^τ, x ∈ Ω, t 〉 0 subject to homogeneous Dirichlet conditions and nonnegative initial data, where x0 ∈ Ω is a fixed point, p, q, r, s ≥ 1 and a, b 〉 0 are constants. In the situation when nonnegative solution （u, v） of the above problem blows up in finite time, it is showed that the blow-up is global and this differs from the local sources case. Moreover, for the special case r = s = 1, lim t→T＊（T＊-t）^p＋1/pq-1u（x,t）=（p＋1）^1/pq-1（q＋1）^p/pq-1（pq-1）^-p＋1/pq-1, lim t→T＊（T＊-t）^q＋1/pq-1u（x,t）=（p＋1）^1/pq-1（q＋1）^p/pq-1（pq-1）^-p＋1/pq-1 are obtained uniformly on compact subsets of/2, where T＊ is the blow-up time.展开更多
基金supported by the National Natural Science Foundation of China (Grant No. 52076088)the Core Technology Research Project of Shunde District, Foshan, China (Grant No. 2130218002932)。
文摘Accurate prediction of junction temperature is crucial for the efficient thermal design of silicon nano-devices. In nano-scale semiconductor devices, significant ballistic effects occur due to the mean free path of phonons comparable to the heat source size and device scale. We employ a three-dimensional non-gray Monte Carlo simulation to investigate the transient heat conduction of silicon nanofilms with both single and multiple heat sources. The accuracy of the present method is first verified in the ballistic and diffusion limits. When a single local heat source is present, the width of the heat source has a significant impact on heat conduction in the domain. Notably, there is a substantial temperature jump at the boundary when the heat source width is 10 nm.With increasing heat source width, the boundary temperature jump weakens. Furthermore, we observe that the temperature excitation rate is independent of the heat source width, while the temperature influence range expands simultaneously with the increase in heat source width. Around 500 ps, the temperature and heat flux distribution in the domain stabilize. In the case of dual heat sources, the hot zone is broader than that of a single heat source, and the temperature of the hot spot decreases as the heat source spacing increases. However, the mean heat flux remains unaffected. Upon reaching a spacing of 200 nm between the heat sources, the peak temperature in the domain remains unchanged once a steady state is reached. These findings hold significant implications for the thermal design of silicon nano-devices with local heat sources.
基金This study is supported partially by the research program of natural science of universities in Jiangsu province(05KJB110144 and 05KJB110063)the natural science foundation of Yancheng normal institute.
文摘In this paper there are established the global existence and finite time blow-up results of nonnegative solution for the following parabolic system ut = △u ＋ v^P（x0, t） - au^τ, x ∈ Ω, t 〉 0, △u ＋ v^P（x0, t） - bu^τ, x ∈ Ω, t 〉 0 subject to homogeneous Dirichlet conditions and nonnegative initial data, where x0 ∈ Ω is a fixed point, p, q, r, s ≥ 1 and a, b 〉 0 are constants. In the situation when nonnegative solution （u, v） of the above problem blows up in finite time, it is showed that the blow-up is global and this differs from the local sources case. Moreover, for the special case r = s = 1, lim t→T＊（T＊-t）^p＋1/pq-1u（x,t）=（p＋1）^1/pq-1（q＋1）^p/pq-1（pq-1）^-p＋1/pq-1, lim t→T＊（T＊-t）^q＋1/pq-1u（x,t）=（p＋1）^1/pq-1（q＋1）^p/pq-1（pq-1）^-p＋1/pq-1 are obtained uniformly on compact subsets of/2, where T＊ is the blow-up time.
