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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.
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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 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 C11 C33 C12 C13 C44 C66 322.7 356.6 110.4 77.7 106.2 90.0 拟合参数 A B C 垂直轴向 (a/m) 1.94 × 10–19 139 2.91 × 10–44 轴向 (c) 1.85 × 10–19 139 2.30 × 10–44 -
[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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