GST 박막 내 열전달 예측 해석모델에 대한 연구

진재식(Jae Sik Jin),원종보(Jongbo Won),권오명(Ohmyoung Kown),이준식(Joon Sik Lee) 대한기계학회 2009 대한기계학회 춘추학술대회 Vol.2009 No.5

The original M-S model is extended to describe the thermal conductivity of Ge₂Sb₂Te? (GST) materials. The structural parameter of original M-S model, which accounts for all types of energy carrier scatterings such as background, grain boundary, and external surface scatterings within polycrystalline films. is modified to consider the structural feature of GST crystalline states. In a modified M-S model. a thickness-independent disorder parameter (β) is introduced to describe the atomic disorder effects of ternary alloy, and we can find its value to be β = 2.4 from theoretical calculations. The results are compared with available experimental data and show a good agreement between them. In addition, the thermal conductivity of amorphous GST is represented, and the structural basis for the fast change between phases of GST is discussed.

포논 평균자유행로 분포를 이용한 실리콘 포노닉 나노 구조에서의 포논 전달 예측 모델

진재식(Jae Sik Jin) 대한기계학회 2018 大韓機械學會論文集B Vol.42 No.3

본 연구는 포논(phonon) 평균자유행로(mean free path, MFP) 스펙트럼(spectrum) 분포 별 열전도 기여도를 이용하여, 실리콘(Si)-포노닉 결정체(phononic crystals, PnC) 내 포논 전달 해석 모델을 제시했다. Si-PnC 내 포논 MFP에 대한 현상학적 접근(phenomenological approach)을 이용하여, Si-PnC 내 복잡한 홀(hole)-포논 산란(scattering) 정도를 표현할 수 있는 간단한 인자를 도입하고, 기존 연구에서 제시한 다양한 실험 조건 및 결과를 활용하여 모델을 완성했다. 이렇게 개발된 모델을 기존의 다른 조건의 Si-PnC 열전도율 측정 결과들에 적용하여, 본 연구에서 제시된 모델의 타당함을 보였고, 모델 개발 과정에서 사용된 홀(hole)-홀 간격의 범위를 벗어나는 경우에 대한 맞춤 매개 변수(fitting parameter) 값을 추가로 구하여, 본 모델의 결과가 기존의 Monte Carlo 기법의 수치적 결과 보다 예측 정확도가 높음을 확인했다. 본 연구결과는 향후 열전모듈 효율 향상 및 반도체 시스템의 열 관리 및 열 제어 연구에 활용될 수 있다. Using data from phonon mean-free path (MFP) spectrum distributions of silicon (Si), a model for estimating the thermal conductivity (K) of Si-phononic crystals (PnC) was developed. Based on the phenomenological approach regarding phonon MFP in a Si-PnC, simple fitting parameters were introduced to express the complex hole-phonon scattering mechanisms. By using previous experimental conditions and measured results, the fitting parameters were determined. The present model was applied to other existing measurement conditions for measuring K in Si-PnC, from which the justification for the method developed here was identified. Additional parametric values for conditions beyond those used in the developed hole-hole intervals were obtained, and we can confirm that the accuracy is higher than the accuracy of the numerical result obtained by the existing Monte Carlo technique. This study can be used in future for thermal management and the thermal control of semiconductor systems.

전자-포논의 열적 상호작용에 대한 해석 모델 개발과 SOI 트랜지스터 내에서의 열에너지 전달 예측

진재식(Jae Sik Jin),이준식(Joon Sik Lee) 대한기계학회 2006 대한기계학회 춘추학술대회 Vol.2006 No.11

The electron-phonon interaction model is proposed and applied to thermal transport in semiconductors at micro/nanoscale. The high electric field in a transistor produces energetic electrons, and their high energies are transferred to the phonon system by electron-phonon scattering in the high field region of transistor. Due to this fact the local hotspot, which is much smaller than the phonon mean free path, occurs in the Si-layer. The full phonon dispersion model based on the Boltzmann transport equation (BTE) with the relaxation time approximation is applied for the phonon-phonon scattering, and the electron-phonon scattering of intervalley and intravalley processes are considered in our proposed model. The simulation results are compared to full phonon dispersion model which treats the electron-phonon scattering as a volumetric heat source term. The comparison shows that the peak temperature in the hotspot region is slightly higher by 4% and more localized than the previous results.

도핑 된 박막 실리콘 내 포논과 전자의 열전도 기여도에 대한 수치적 예측

진재식(Jae Sik Jin),이준식(Joon Sik Lee) 대한기계학회 2008 대한기계학회 춘추학술대회 Vol.2008 No.5

The modified electron-phonon interaction model is proposed, and the relative contributions of phonons and electrons to the thermal conduction in doped silicon films are investigated. The carrier contributions in sub-micro scale heat conduction are validated by an order of magnitude analysis and comparison with previous data. The simulation results show that the electron contribution in Si-layer is not negligible when the doping concentration is higher than 10¹? ㎝?³, which can be classified as semimetal or metal by the value of its electrical resistivity at 300 K. The electron thermal conductivity increases with increasing doping density, and its fraction is about 57.2% of the total thermal conductivity when the doping concentration is 5.0 × 10²? ㎝?³ and silicon film thickness 100 ㎚.

실리콘 내 온도 변화에 따라 포논 분극이 Akhiezer와 Landau-Rumer 소산 영역 사이의 천이에 미치는 영향에 대한 연구

진재식(Jae Sik Jin) 대한기계학회 2022 大韓機械學會論文集B Vol.46 No.3

실리콘에 대해서 기존 연구에서는 온도 300 K까지만 제시되었던 Akhiezer 소산(damping)에 대한 포논 이완시간(relaxation time)을 온도 500 K까지 확장하여 Akhiezer 소산에 대한 포논 산란율(scattering rate)을 구했다. 이 결과를 포논 기체 운동론(kinetic theory)에 적용하여 검증한 후, 열적 분광학(thermal spectroscopy)기법의 결과를 이용한 Landau-Rumer 소산에 대한 포논 산란율과 비교하여, Akhiezer 소산 영역과 Landau-Rumer 소산 영역 사이의 천이가 일어나는 포논 평균자유행로(mean-free-path)는 300 K~500 K 온도범위에서 열전도율 기여도가 큰 LA(longitudinal acoustic) 포논 모드에 의해 결정됨을 보였다. The phonon scattering rate for Akhiezer damping was obtained by extending the phonon relaxation time, which was suggested only up to a temperature of 300 K, to a temperature of 500 K in silicon. It was used for the direct calculation of thermal conductivity (K) considering the kinetic theory. After verifying this result by comparing it to the thermal spectroscopy results at 300 and 500 K, it is compared to the phonon scattering rate for the Landau-Rumer damping derived using the thermal spectroscopy method. Then, the phonon critical mean-free-path (Λc) corresponding to a transition between Akhiezer and Landau-Rumer damping regions was obtained, and it was observed that Λc is determined by the longitudinal acoustic phonons, which has a large contribution to K within temperature ranges of 300~500 K.

실리콘 지지와 뜬 그래핀 나노메쉬 내 포논 산란 특성의 정량적 연구

진재식(Jae Sik Jin) 대한기계학회 2019 大韓機械學會論文集B Vol.43 No.3

본 연구는 포논(phonon) 평균자유행로(mean free path, MFP) 스펙트럼(spectrum) 분포 별 열전도 기여도를 이용하여, 실리콘(Si) 기질로 지지된 그래핀 나노메쉬(Si-GNM) 내 포논 산란 특성을 살폈다. 그래핀 나노메쉬(GNM) 내 포논 MFP에 대한 현상학적 접근(phenomenological approach)을 이용하여, Si-GNM와 뜬(suspended) GNM(Sus-GNM) 내 복잡한 포논 산란(scattering) 정도(n)를 표현할 수 있는 간단한 함수를 도입하고, 기존 연구에서 제시하지 못한 다공도(porosity, Ø) 증가에 따라 Si-GNM이 Sus-GNM 경우 보다 열전도율 억제 효과가 작아짐을 정량적으로 설명했다. 즉, 1.52%≤ Ø ≤ 9% 범위에서 Ø 가 커지면서 nsup/nsus=2.81에서 2.37로 감소함을 보였다. 본 연구 방법은 향후 GNM 기반 시스템에 대한 열 관리 및 열 제어 연구에 활용될 수 있다. In this study, the phonon scattering of a graphene nanomesh (Si-GNM) supported by a silicon substrate was investigated using the spectral thermal conductivity contribution of the phonon mean free path (MFP) at room temperature. Using the phenomenological approach to phonon MFPs in a GNM, we can express the complex scattering degree (n) in Si-GNM and suspended GNM (Sus-GNM) by proposing a simple form as a function of the hole spacing, phonon MFP, and porosity, showing a lower thermal conduction suppression effect than that of Sus-GNM as the porosity (Ø) increases, which has not been presented in previous studies. It was shown that the relative value of nsup/nsus is changed from 2.81 to 2.37 within the range of 1.52%≤Ø≤ 9%. This method can be applied to future thermal management and thermal control studies for GNM-based systems.

실험적 포논 평균자유행로 스펙트럼 분포를 이용한 포논 스펙트럼 포논-표면 산란율 모델

진재식(Jae Sik Jin) 대한기계학회 2016 大韓機械學會論文集B Vol.40 No.9

본 연구에서는 실험적 데이터를 근간으로 박막재료의 스펙트럼(spectrum) 분포 별 포논-표면 산란율을 직접 계산할 수 있는 모델을 제시했다. 실험 측정결과인 포논 평균자유행로(mean free path, MFP) 스펙트럼 분포 별 열전달 기여도로부터 스펙트럼 의존적 포논-표면 산란율을 직접 도출하는 모델을 개발했고, 이 모델을 아직 실험적 방법으로 포논-표면 산란율을 측정하지 못한 Si0.9-Ge0.1 나노선(Nanowire, NW)에 적용하여, Si0.9-Ge0.1 NW 내 포논 MFP 스펙트럼 분포를 구하고, 주파수에 따른 포논 전달특성을 살폈다. 이를 바탕으로 Si0.9-Ge0.1 NW 단위길이당 포논-표면 산란율을 제시하여, 가로갈래 포논 주파수 의존성을 살폈다. 본 연구에서 제시한 모델은 향후 나노재료의 공학적 응용을 위한 나노구조물 열전달 해석모델 개발 및 나노재료 열전달 특성 조정(tailoring)을 위한 나노재료 최적설계에 활용될 수 있다. In this study, we present a model that can be used to calculate the phonon-surface scattering rate directly from the experimental data on phonon mean free path (MFP) spectra of nanostructures. Using this model and the recently reported length-dependent thermal conductivity measurements on Si0.9Ge0.1 nanowires (NWs), we investigate the spectral reduced MFP distribution and the spectral phonon-surface scattering rate in the Si0.9Ge0.1 NWs. From the results, it is found that the phonon transport properties with the material and the phonon frequency dependency of the spectral phonon-surface scattering rate per unit length of the NW. The model presented in this study can be used for developing heat transfer analysis models of nanomaterials, and for determining the optimum design for tailoring the heat transfer characteristics of nanomaterials for future applications of phonon nanoengineering.

줄 가열 변화에 따른 박막 트랜지스터 내 포논 열 흐름에 대한 수치적 연구

진재식(Jae Sik Jin),이준식(Joon Sik Lee) 대한기계학회 2009 大韓機械學會論文集B Vol.33 No.10

The anisotropic phonon conductions with varying Joule heating rate of the silicon film in Silicon-on-Insulator devices are examined using the electron-phonon interaction model. It is found that the phonon heat transfer rate at each boundary of Si-layer has a strong dependence on the heating power rate. And the phonon flow decreases when the temperature gradient has a sharp change within extremely short length scales such as phonon mean free path. Thus the heat generated in the hot spot region is removed primarily by heat conduction through Si-layer at the higher Joule heating level and the phonon nonlocality is mainly attributed to lower group velocity phonons as remarkably dissimilar to the case of electrons in laser heated plasmas. To validate these observations the modified phonon nonlocal model considering complete phonon dispersion relations is introduced as a correct form of the conventional theory. We also reveal that the relation between the phonon heat deposition time from the hot spot region and the relaxation time in Si-layer can be used to estimate the intrinsic thermal resistance in the parallel heat flow direction as Joule heating level varies.

포논 기체 운동론을 이용한 실리콘 내 포논 평균자유행로 스펙트럼 열전도율 기여도 예측

진재식(Jae Sik Jin) 대한기계학회 2017 大韓機械學會論文集B Vol.41 No.5

본 연구는 해석적 접근이 용이한 실리콘 내 포논 평균자유행로(mean free path, MFP) 스펙트럼(spectrum) 열전도 특성 예측 모델을 제시했다. 해석이 용이한 포논 기체 운동론(kinetic theory)을 적용하기 위해, 나노구조물의 현상학적 접근으로 열전도에 관여하는 포논 모드(mode)들만 추출하고, 300 K의 실리콘에 대한 포논의 분산관계(dispersion relations) 및 분극(polarization) 효과가 고려된 포논의 주파수 변화에 따른 비열(specific heat)과 군속도(group velocity) 및 MFP 정보를 사용했다. 300 K의 실리콘 내 포논의 MFP 스펙트럼 열전도율 기여를 계산하고, 기존 실험결과 및 제1원리 기법 결과와 비교하여, 본 방법의 타당함을 보였다. 본 연구를 통해, 나노구조물 열전달 해석모델 개발 및 나노재료 열전달 특성 조정(tailoring) 전략 설계에 필요한 포논 MFP 스펙트럼 열전도 특성 정보를 해석이 용이한 방법으로 구할 수 있는 방법을 제공했다. Knowing the mean free paths (MFPs) of thermal phonons is an essential step in performing heat transfer analysis for nanomaterials, and in determining the optimum design for tailoring the heat transfer characteristics of nanomaterials. In this study, we present a method that can be used to calculate accurately the phonon MFP spectra of nanostructures based on simple phonon kinetic theory. Here, the kinetic theory may be employed by extracting only the diffusive-transport part of the phonon spectrum (i.e., the MFPs are less than a thermal length). By considering phonon dispersion and polarization effects, the phonon MFP distributions of silicon at room temperature are calculated from phonon transport properties and the spectral MFP. Our results are validated by comparison with those of the first principle and MFP spectroscopy data.

박막 실리콘 내 도핑 농도 변화에 따른 포논과 전자의 열전도율 기여도에 대한 수치해석

진재식(Jae Sik Jin),이준식(Joon Sik Lee) 대한기계학회 2007 대한기계학회 춘추학술대회 Vol.2007 No.5

The relative contributions of phonon and electron to the thermal conductivity of silicon film with varying doping density are evaluated from the modified electron-phonon interaction model, which is applicable to the micro/nanoscale simulation of energy transport between energy carriers. The thermal conductivities of intrinsic silicon layer thicknesses from 20 ㎚ to 500 ㎚ are calculated and extended to the variation in n-type doping densities from 1.0 × 10¹? to 5.0 × 10²? ㎝?³, which agree well with the experimental data and theoretical model. From simulation results, the phonon and electron contributions to thermal conductivity are extracted. The electron contribution in the silicon is found to be not negligible above 10¹? ㎝?³, which can be classified as semimetal or metal by the value of its electrical resistivity at room temperature. The thermal conductivity due to electron is about 57.2% of the total thermal conductivity at doping concentration 5.0 × 10²? ㎝?³ and silicon film thickness 100 ㎚.