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准确预测GaN半导体材料的热导率对GaN基功率电子器件的热设计具有重要意义. 本文基于第一性原理计算和经典Debye-Callaway模型,通过分析和完善Debye-Callaway模型中关于声子散射率的子模型, 建立了用于预测温度、同位素、点缺陷、位错、薄膜厚度、应力等因素影响的GaN薄膜热导率的理论模型. 具体来说, 对声子间散射项和同位素散射项基于第一性原理计算数据进行了系数拟合, 讨论了两种典型的处理点缺陷和位错散射的散射率模型, 引入了应用抑制函数描述的各向异性边界散射模型,并对应力的影响进行了建模. 热导率模型预测值和文献中典型实验数据的对比表明, 基于第一性原理计算数据拟合的热导率模型和实验测量值总体符合较好, 300 K温度附近热导率数值及其随温度变化的趋势存在20%左右的偏差. 结合实验数据和热导率模型进一步确认了第一性原理计算会高估同位素散射的影响, 给出了薄膜热导率随薄膜厚度、位错面密度、点缺陷浓度的具体变化关系, 同位素和缺陷散射会减弱薄膜热导率的尺寸效应, 主要体现在100 nm附近及更小的厚度范围.
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关键词:
- GaN薄膜/
- 热导率/
- Debye-Callaway模型/
- 第一性原理计算
The accurate predicting of thermal conductivity of GaN semiconductors, especially GaN films, is of great importance for the thermal management in electronic devices. In this paper, a theoretical model based on the first-principles calculations and Debye-Callaway model is proposed to predict the thermal conductivity of GaN films, which is a function of temperature, isotope, point defects, dislocations, film thickness, and strain fields. Specifically, the coefficients in our theoretical model that used to capture umklapp scattering and phonon-isotope scattering are fitted with the data from first-principles calculations, and two sub-models for point defects scattering and dislocation scattering are discussed, respectively. The sub-model of boundary scattering with suppression function is introduced to describe the anisotropy of size effect, and the effect of in-plane strain (perpendicular to polar axis) is also discussed. The comparison between theoretical predictions and experimental data shows that the model performs well roughly in a large temperature range from 300 to 500 K, with an around 20% difference at room temperature. Our predicted temperature dependent thermal conductivity deviates slightly from the measurements, which may result from the lack of high-order phonon scattering in our model, e.g., four-phonon scattering. Our results also show that the first-principles calculations for GaN overestimates the influence of isotope scattering. We further study the thermal transport properties of GaN film which are influenced by the thickness, dislocation density, and point defect density through using the new theoretical model. Significant reduction of thermal conductivity is found to occur at a film thickness of 10 μm, which is consistent with the findings from the first-principles calculations. The isotope and defects including point defects and dislocations are found to have a weak influence on the thermal conductivity when the thickness of GaN film is larger than 100 nm, while the influence becomes significant for the film with and below 100 nm in thickness. In addition, dislocations and point defects start to reduce thermal conductivity significantly when the surface density of dislocations increases to 10 10cm –2and point defect density reaches10 18cm –3.[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51] -
文献/样品 室温热导率/
(W·m–1·K–1)厚度/μm 点缺陷浓度(缺陷元素)/cm–3 位错面密
度/cm–2同位素 Zheng et al.[13] KMiF 234 7—12 1.5 × 1018(Al),
5 × 1017cm–3(O)< 107 无 KMF 195 6—8 1.5 × 1018(Al),
5 × 1017cm–3(O)< 107 有 AM/KM 197 300—600 0.1 × 1018—20 × 1018cm–3(H)
0.1 × 1018—5 × 1018cm–3(O)< 107 有 Shibata et al.[4] 1 252 1000 2.1 × 10–17cm–3(Si) 5 × 106 有 Slack et al.[5] 1 — 200 2.1 × 1016cm–3(O),
0.37 × 1016cm–3(Si)— 有 Jezowski et al.[6] 1 218 100 1 × 1020cm–3(O),
1 × 1019cm–3(C),
1 × 1018cm–3(Mg),
7 × 1017cm–3(H),
1017cm–3(Si),
1 × 1018cm–3(Ga原子空位)— 有 2 188 3 157 Jeżowski et al.[7] 1 78 300 4 × 1016cm–3(O) — 有 2 162 2.6 × 1018cm–3(O) 3 275 1.1 × 1020cm–3(O) Simon et al.[8] 1 226 300 2.3 × 1018cm–3(O),
2.3 × 1018cm–3(Mg)— 有 2 211 9.7 × 1017cm–3(O) 3 163 2 × 1019cm–3(O) Rounds et al.[9] 1 203 300—600 4 × 1016cm–3(O) — 有 2 223 2.2 × 1017cm–3(Si) 3 182 8.4 × 1018cm–3(H),
8.9 × 1018cm–3(O)4 200 1.5 × 1019cm–3(H),
1.4 × 1018cm–3(O),
9.8 × 1018cm–3(Mn)5 163 3.5 × 1018cm–3(H),
1.4 × 1018cm–3(O),
9.3 × 1017cm–3(Mg)Li et al.[10] S1 190 3.19 — 1.8 × 108 有 S2 195 3.52 2.36 × 109 S3 220 400 2 × 107 Mion et al.[11] A 184 200 4 × 1017(H),
1017(C),
3 × 1016(O),
1017(Si)4.06 × 107 有 B 200 370 1.47 × 107 C 214 1400 8.96 × 106 D 229 2000 5.1 × 104 
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参数 数值 参数 数值 a/Å 3.219 $ \bar v $ (垂直轴向)/m·s–1 3621 c/Å 5.245 $ \bar v $ (沿轴向) /m·s–1 3915 V0/m3 1.176 × 10–29 $ \nu $(泊松比) 0.255 下载:
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[1] [2] [3] [4] [5] [6] [7] [8] [9] [10] [11] [12] [13] [14] [15] [16] [17] [18] [19] [20] [21] [22] [23] [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34] [35] [36] [37] [38] [39] [40] [41] [42] [43] [44] [45] [46] [47] [48] [49] [50] [51]
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