Mn-In-Cu co-doping to optimize thermoelectric properties of SnTe-based materials

Huang Qing-Song; Duan Bo; Chen Gang; Ye Ze-Chang; Li Jiang; Li Guo-Dong; Zhai Peng-Cheng

doi:10.7498/aps.70.20202020

Abstract

Lead-free chalcogenide SnTe has a similar crystal structure and energy band structure to high performance thermoelectric material PbTe, which has been widely concerned in recent years. However, due to its low Seebeck coefficient, high intrinsic Sn vacancy concentration and high thermal conductivity, its intrinsic thermoelectric performance is poor. In this study, Mn-In-Cu co-doping SnTe-based thermoelectric materials are prepared by hot pressing sintering at high-temperature and high-pressure. Indium (In) doping brings the resonant level in SnTe and increases the density of states which greatly improves Seebeck coefficient at room temperature; the Seebeck coefficient of Sn_1.04In_0.01Te(Cu₂Te)_0.05 reaches 70 μV·K^–1 at room temperature. With adding manganese (Mn), the Seebeck coefficient at room temperature is well preserved, indicating that Mn doping has little effect on the resonant level brought by In doping. In addition, due to the band convergence brought by Mn doping, the high temperature Seebeck coefficient of the material is improved, the maximum Seebeck coefficient reaches 215 μV·K^–1 for the sample with 17% Mn doping amount at 873 K. Owing to the combination of band convergence and resonant level, the Seebeck coefficient of the whole temperature range of the material increases, the power factor of the material is also greatly optimized, and all samples have a power factor of more than 1.0 mW·m^–1·K^–2 at room temperature. On the other hand, the point defects brought by Mn alloying and the interstitial defects introduced by copper (Cu) enhance the phonon scattering and effectively reduce the lattice thermal conductivity of the material, the lattice thermal conductivity decreases to 0.68 W·m^–1·K^–1 at 873 K. The electrical and thermal properties of the materials are optimized simultaneously under the combination of various strategies, the peak zT ≈ 1.45 is obtained at 873 K in the p-type Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05 sample and the average zT of 300–873 K reaches 0.76. In the process of multi-strategy coordinated regulation of SnTe-based thermoelectric materials, the excellent properties of single strategy can be well maintained, which provides a possibility for further improving the performance of SnTe-based thermoelectric materials.

Keywords:

PACS:

74.25.fg	(Thermoelectric effects)
71.20.Nr	(Semiconductor compounds)
72.15.Jf	(Thermoelectric and thermomagnetic effects)

Authors and contacts

1.
Hubei Key Laboratory of Theory and Application of Advanced Materials Mechanics, Wuhan University of Technology, Wuhan 430070, China
2.
State Key Laboratory of Advanced Technology for Materials Synthesis and Processing, Wuhan University of Technology, Wuhan 430070, China

Corresponding author: Duan Bo, duanboabc@whut.edu.cn

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51772231, 51972253) and the Fundamental Research Fund for the Central Universities, China (Grant Nos. 2020IB001, 2020IB013)

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1. 引　言

热电器件能实现热能和电能的相互转化, 在废热回收利用、深海和深空电源及绿色制冷等领域有着巨大应用潜力^[1]. 热电器件的转换效率主要由热电材料的无量纲热电优值zT决定:

$zT = \sigma {S^2}T/\kappa,$

(1)

其中σ为电导率, S为Seebeck系数, T是绝对温度, 热导率κ通常由载流子热导率κ_c和晶格热导率κ_L组成. 由于S, σ和κ_c均与载流子浓度有关, 相互耦合, 很难在其他参数不变的情况下对某一参数单独调控. 因此, 如何通过部分参数的解耦来优化材料的热电性能一直是热电材料研究面临的挑战之一.

PbTe基热电材料作为最早被开发的传统热电材料之一, 具有较高的热电性能, 得到了广泛的研究^[2,3], 但PbTe在高温下不稳定, 且Pb易挥发污染环境, 这些问题限制了其应用. SnTe和PbTe是具有相似晶体结构和能带结构的IV-VI族半导体材料, SnTe对环境的污染较小, 被认为是一种潜在的优良热电材料. 然而, 由于Sn空位的存在, 纯SnTe的载流子浓度在10²⁰—10²¹ cm^–3之间^[4], 过高的载流子浓度使得材料的Seebeck系数较低, 且载流子热导率较高. 同时, 与PbTe相比, SnTe具有更小的带隙(0.18 eV)和更大的轻重价带之间的能量差(0.35 eV)^[5], 导致严重的双极扩散和更低的Seebeck系数. 此外, 纯SnTe还具有较高的晶格热导率, 使得SnTe材料的本征热电性能较低.

近年来, 人们在优化多晶SnTe热电性能方面做了大量的工作. 一种重要的策略是通过Mn, Mg, Hg, Cd等阳离子掺杂改善SnTe的能带结构, 来优化SnTe的Seebeck系数和功率因子^[6-10]. Zhang等^[11]发现在SnTe中掺杂少量的In能在费米能级附近产生共振能级, 可以有效提高材料室温下的Seebeck系数, 且在其他元素共掺杂的情况下仍明显保持这种效果, 如Pd-In^[12], Mg-In^[13]共掺杂. 此外, 通过缺陷工程如构造纳米结构或引入点缺陷等, 可以有效降低SnTe材料的晶格热导率^[14-16]. Pei等^[17]研究发现, 在(SnTe)_1–_x(Cu₂Te)_x固溶体中, 由于间隙Cu原子引起的强声子散射, 晶格热导率在850 K时下降至0.5 W·m^–1·K^–1, 接近SnTe的非晶态极限. Hu等^[18]利用高熵合金效应, 大幅提高了Mn在SnTe基体中的溶解度, 并诱发了多尺度的微结构, 得到了低于非晶极限的晶格热导率(约0.32 W·m^–1·K^–1@900 K). 相比于单策略的研究, 现阶段研究人员更多地倾向于多策略结合的方式来改善SnTe基材料的热电性能. 如通过掺杂Ge元素来提升Mn元素在SnTe中的溶解度, 提升能带收敛程度, 在此基础上, 引入了Cu间隙缺陷, 进一步降低晶格热导率, 最终材料的zT在900 K时达到1.8^[19]. Tang等^[20]研究发现Sn_1/3Ge_1/3Pb_1/3Te合金中存在大量无序阳离子, 由此产生的强声子散射导致整个温度范围内晶格热导率明显下降, 此外还引入了MnTe合金来优化材料的能带结构, 电性能与热性能的提升使得材料的性能增强. Xu等^[21]通过在Sb₂Te₃(SnTe)_n中引入各向异性的范德瓦耳斯间隙结构, 在降低了晶格热导率的同时优化了能带结构, 并进一步通过Re掺杂调节了载流子浓度和范德瓦耳斯间隙微观结构, 最终在323—773 K的平均zT达到了0.83.

本研究通过高温高压(high-temperature and high-pressure, HTHP)快速合成结合热压的方法制备了Mn, In, Cu共掺杂的SnTe基热电材料, 期望通过能带收敛和引入共振态来优化材料的Seebeck系数与功率因子, 并通过引入Cu间隙缺陷来增强声子散射, 降低材料的晶格热导率. 最终Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品在873 K时的zT值达到了1.45, 300—873 K的平均zT达到了0.76.

2. 实验部分

通过HTHP合成了Sn_1.04–_xMn_xIn_0.01Te (Cu₂Te)_0.05 (x = 0—0.17)材料. 按照化学计量比称量高纯Sn粉(99.9%)、Te粉(99.999%)、Mn粉(99.9%)、In粉(99.95%)、Cu粉(99.9%), 原料混合均匀后在200 MPa的压力下冷压5 min, 将冷压后的块装入钼杯中. 最后将包裹样品的钼杯组装好后放入六面顶压机中, 在973 K, 2.5 GPa的条件下烧结15 min. 将HTHP工艺合成的锭砸碎研磨后装入直径12.7 mm的石墨模具中, 在973 K, 40 MPa的条件下热压烧结2 h, 最后得到直径12.7 mm、厚度4.5 mm的样品.

采用X射线衍射仪(Empyrean)对热压后的样品进行物相分析. 用场发射扫描电子显微镜(Zeiss Ultra Plus)对其微观结构进行表征. 材料在300—873 K的电阻率与Seebeck系数由热电材料测试系统(CTA-3)在氦气氛围下测得. 用霍尔效应测试系统(HL5500PC)测得室温下的载流子浓度n_H和载流子迁移率μ_H. 利用激光热导仪(LFA-457)测量氩气保护环境下300—873 K的热扩散系数D. 通过阿基米德排水法测量样品的密度d. 材料的热容c_p来自Blachnik和Igel^[22]的实验值, 可由下式估算:

${c_{\rm{p}}}\left( {{k_{\rm{B}}}/{\rm{atom}}} \right) = 3.07 + 0.00047 \times \left( {T/{\rm{K}} - 300} \right).$

(2)

样品的总热导率由下式计算:

$\kappa = dD{c_{\rm{p}}}.$

(3)

3. 结果与讨论

图1(a)为Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 (x = 0—0.17)样品室温下的X射线衍射(X-ray diffraction, XRD)图谱. 所有样品的主相与SnTe标准PDF卡片(#65-0319)相符合, 均为面心立方晶体结构. 如图1(a)所示, 随着Mn掺杂量的增加, 出现了Cu₂Te的杂峰和其他未知杂峰, *标记的杂峰可能为MnTe, Cu₂SnTe₃或Cu₄₁Sn₁₁杂相, 这可能是由于Mn掺杂降低了Cu₂Te在SnTe中的溶解度以及Mn过量掺杂造成的^[23]. 由图1(b)局部峰位放大图可见, 随着Mn掺杂量的增加, 峰位向高角度偏移, 表明样品的晶格常数减小, 这是由Mn²⁺的半径(约0.66 Å)比Sn²⁺的半径(约0.93 Å)小造成的. 如图1(c)所示, 当0.06 ≤ x ≤ 0.15时计算的晶格常数的变化与Vegard定律基本一致, 随着掺杂量的增加逐渐减小. 当掺杂量超过0.15后, 晶格常数基本不变, 说明Mn在SnTe中的固溶极限约为15% (摩尔分数), 这与文献报道的Mn在SnTe中的固溶极限一致^[24]. 此外, 随着Mn掺杂量的增加, XRD衍射峰出现了宽化和弱化的现象(图1(b)), 表明材料的结晶度有所降低, 这可能是Mn掺杂后点缺陷和晶格应变增加导致的^[25-27].

$图 1 Sn1.04–xMnxIn0.01Te (Cu2Te)0.05 (x = 0—0.17)的(a) XRD图谱, (b) 57.5°—60° XRD图谱局部放大图, (c) 晶格常数随Mn掺杂量x的变化\r\nFig. 1. Sn1.04–xMnxIn0.01Te(Cu2Te)0.05 samples (x = 0–0.17): (a) XRD patterns; (b) enlarged view between 57.5°–60°; (c) lattice parameter as a function of x$

图 1 Sn_1.04–_xMn_xIn_0.01Te (Cu₂Te)_0.05(x = 0—0.17)的(a) XRD图谱, (b) 57.5°—60° XRD图谱局部放大图, (c) 晶格常数随Mn掺杂量x的变化

Fig. 1. Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 samples (x = 0–0.17): (a) XRD patterns; (b) enlarged view between 57.5°–60°; (c) lattice parameter as a function of x

下载: 全尺寸图片幻灯片

为了进一步表征样品的相组成, 对Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品进行了扫描电子显微镜分析. 如图2所示, Sn, Te和In元素在基体内分布均匀, 在二次电子成像图中存在微米级别的浅灰色区域, 元素分布情况显示为Cu元素富集, Sn元素缺少, 表明存在Cu₂Te的杂相, 与XRD结果一致. 此外, 二次电子成像图中还能观察到黑斑的存在, 对应着少量Mn的富集, 这可能是由于Mn元素掺杂过多后开始出现MnTe杂相.

$图 2 Sn0.89Mn0.15In0.01Te(Cu2Te)0.05样品的扫描电子显微镜图像\r\nFig. 2. Scanning electron microscope images of the Sn0.89Mn0.15In0.01Te(Cu2Te)0.05 sample.$

图 2 Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品的扫描电子显微镜图像

Fig. 2. Scanning electron microscope images of the Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05 sample.

下载: 全尺寸图片幻灯片

图3为Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品电性能随温度的变化曲线. 从图3(a)可以看出, 所有样品的电导率均随温度的增加而降低, 表现为典型的简并半导体行为. 当x < 0.06时, 样品的电导率随掺杂量有所增加, 这与文献报道结果类似^[23], 可能是Mn掺杂导致SnTe中可溶性Cu₂Te的量减少造成的. 当x ≥ 0.06时, 样品的电导率随着Mn含量的增加而逐渐降低, 这主要是由样品的载流子迁移率大幅降低造成的^[28,29], 如图3(b)所示. 迁移率的降低可能是由于Mn掺杂后点缺陷增加, 导致散射增强以及价带收敛带来的载流子有效质量的增加(详细讨论见下文). 随着Mn掺杂量的增加, 载流子浓度先降低后升高. 载流子浓度先降低可能是因为Mn掺杂后降低了Cu₂Te在基体中的溶解度, 使得部分作为电子受体的Cu¹⁺减少^[17,23]. 而随着Mn掺杂量的继续增加, 载流子浓度上升可能是因为Mn取代Sn后引入了更多的Sn空位^[28-30].

$图 3 Sn1.04–xMnxIn0.01Te(Cu2Te)0.05(x = 0—0.17)样品的(a) 电导率随温度的变化, (b) 室温下载流子浓度和迁移率随x的变化, (c) Seebeck系数随温度的变化, (d) 室温下Seebeck系数与载流子浓度关系以及和相关研究的对比图[11,17,30-32], (e) 室温下有效质量对比图, (f) 功率因子随温度的变化\r\nFig. 3. Sn1.04–xMnxIn0.01Te(Cu2Te)0.05 (x = 0–0.17) samples: (a) Electrical conductivities as a function of temperature; (b) carrier concentration and mobility as a function of x at room temperature; (c) Seebeck coefficients as a function of temperature; (d) the relationship between Seebeck coefficient and carrier concentration at room temperature and comparison with the correlation studies[11,17,30-32]; (e) effective mass comparison at room temperature; (f) power factor as a function of temperature.$

图 3 Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品的(a) 电导率随温度的变化, (b) 室温下载流子浓度和迁移率随x的变化, (c) Seebeck系数随温度的变化, (d) 室温下Seebeck系数与载流子浓度关系以及和相关研究的对比图^{[11,17,30-32]}, (e) 室温下有效质量对比图, (f) 功率因子随温度的变化

Fig. 3. Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 (x = 0–0.17) samples: (a) Electrical conductivities as a function of temperature; (b) carrier concentration and mobility as a function of x at room temperature; (c) Seebeck coefficients as a function of temperature; (d) the relationship between Seebeck coefficient and carrier concentration at room temperature and comparison with the correlation studies^{[11,17,30-32]}; (e) effective mass comparison at room temperature; (f) power factor as a function of temperature.

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图3(c)为样品的Seebeck系数随温度的变化曲线. 所有样品的Seebeck系数均为正值, 说明样品为空穴导电的p型半导体. 根据玻尔兹曼方程, 简并半导体材料的Seebeck系数可以简化为下式计算:

$S = \frac{{8{{\rm{\pi }}^2}k_{\rm{B}}^2}}{{3e{h^2}}}{m^ * }T{\left( {\frac{{\rm{\pi }}}{{3n}}} \right)^{2/3}},$

(4)

${m^ * } = N_{\rm{v}}^{2/3}m_{\rm{b}}^ *,$

(5)

式中k_B为玻尔兹曼常数, e为电子电荷量, h为普朗克常数, m^*为载流子有效质量, T为绝对温度, n为载流子浓度, N_v为简并能谷数, $m_{\rm{b}}^ *$ 为能带有效质量^[31]. 室温下Cu掺杂^[17]与纯SnTe^[23]的Seebeck系数相差不大, 为10 μV·K^–1左右, 而Sn_1.04In_0.01Te(Cu₂Te)_0.05样品室温下Seebeck系数达到了72 μV·K^–1, 这可能是In掺杂在费米能级附近引入了局域电子共振态, 增大了能带有效质量 $m_{\rm{b}}^ *$ , 从而大幅度提高了室温下的Seebeck系数^[11]. 此外, 掺入Mn元素后仍能保持较高的室温Seebeck系数, 且随着Mn掺杂含量的增加室温Seebeck系数没有明显变化, 说明室温下Seebeck系数的提升主要由In掺杂贡献, Mn掺杂对Seebeck系数的影响被削弱了, 这与傅铁铮等^[32]报道的In-Sb共掺杂的现象类似. 而在高温下Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品的Seebeck系数整体上随着Mn掺杂含量的增加而逐渐增加, x = 0.17样品在873 K时的Seebeck系数达到215 μV·K^–1. 高温下的Seebeck系数随着Mn掺杂量的增加而明显提升, 这是由于In带来的共振能级对高温Seebeck系数影响较弱^[11], Mn掺杂带来的影响得以体现. Mn掺杂减小了轻重价带的能量差, 导致简并能谷数N_v增加, 提高了能带简并度^[10,28,29], 从而提高了高温下的Seebeck系数.

为了更直观地展示掺杂对Seebeck系数的影响, 绘制了载流子浓度与Seebeck系数的关系图. 如图3(d)所示, 将几种SnTe基材料的实验值与Pisarenko曲线进行了比较, 其中实线是由Zhang等^[11]在假定轻重带能量差ΔE_v = 0.35 eV条件下基于双价带模型计算得来. Brkbrick和Strauss ^[33]报道的未掺杂SnTe样品的实验值符合Pisarenko曲线的预期, 而Mn掺杂^[30]的样品由于能带收敛作用高于Pisarenko曲线的预期. In掺杂^[11]和In-Cu共掺杂^[34]样品较Pisarenko曲线高出更多, 这主要是In带来的共振能级造成的^[11]. Mn-In-Cu共掺杂样品提升的幅度与In-Cu共掺杂类似, 说明掺入Mn后共振现象仍然存在且室温下Seebeck系数的提升主要由In掺杂贡献^[32]. 图3(e)计算了x = 0和x = 0.15样品的载流子有效质量m^*. 与纯SnTe^[35]相比, x = 0的In-Cu共掺杂的样品由于共振态的引入载流子有效质量从0.70m_e提高到了1.63m_e. 而x = 0.15的Mn-In-Cu共掺杂样品的载流子有效质量相比In-Cu共掺杂样品进一步提升, 从1.63m_e提高到了2.23m_e, 说明Mn掺杂后提高了能带简并度, 与前文的推测一致. Seebeck系数的提升最终也导致了功率因子的提升, 如图3(f)所示, 室温下Mn-In-Cu共掺杂样品的功率因子均在1.0 mW·m^–1·K^–2以上, 相比Mn-Cu^[23]共掺杂样品提高了2倍以上.

Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)的热性能随温度的变化如图4所示. 晶格热导率为总热导率减去载流子热导率所得, 载流子热导率可由下式计算:

$图 4 Sn1.04–xMnxIn0.01Te(Cu2Te)0.05 (x = 0—0.17)样品的(a) 总热导率、(b) 洛伦兹数、(c) 载流子热导率、(d) 晶格热导率随温度的变化\r\nFig. 4. Thermoelectric properties of Sn1.04–xMnxIn0.01Te(Cu2Te)0.05 (x = 0–0.17) as a function of temperature: (a) Total thermal conductivity; (b) Lorenz number; (c) carrier thermal conductivity; (d) lattice thermal conductivity.$

图 4 Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品的(a) 总热导率、(b) 洛伦兹数、(c) 载流子热导率、(d) 晶格热导率随温度的变化

Fig. 4. Thermoelectric properties of Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 (x = 0–0.17) as a function of temperature: (a) Total thermal conductivity; (b) Lorenz number; (c) carrier thermal conductivity; (d) lattice thermal conductivity.

下载: 全尺寸图片幻灯片

${\kappa _{{\rm{c}}}} = L\sigma T.$

(6)

这里L为洛伦兹数, 可由考虑声子散射的单抛物带模型公式估算^[36]:

$L = 1.5 + \exp \left( {\frac{{ - \left| S \right|}}{{116}}} \right).$

(7)

如图4(a)所示, 随着Mn元素掺杂量的提高, 样品的总热导率先升高后降低, 这是载流子热导率和晶格热导率共同作用的结果. 此外, Sn_1.04In_0.01Te(Cu₂Te)_0.05样品由于Cu间隙缺陷的强散射作用^[17], 高温下的总热导率和晶格热导率均为最低, 晶格热导率在873 K降至0.46 W·m^–1·K^–1, 接近非晶态极限κ_min = 0.4 W·m^–1·K^–1, 与Guo等^[34]报道一致. 而随着Mn元素的掺入, 样品高温下的晶格热导率先增加后降低, 在Mn掺杂摩尔分数为15%时降低到0.68 W·m^–1·K^–1, 与非晶态极限仍有一定差距. 这与Li等^[23]报道的高温下Cu₂Te能较好地溶解在Mn掺杂SnTe样品中有所不同, 这可能是Mn, In共掺杂后Cu₂Te在整个温度范围内溶解性降低, Cu间隙缺陷的散射效果下降造成的, 因此高温下的晶格热导率相比Sn_1.04In_0.01Te(Cu₂Te)_0.05样品有所上升. 另一方面, 随着Mn掺杂量的增加, Mn合金化产生的点缺陷散射增强, 样品的晶格热导率降低, 而Mn掺杂摩尔分数为17%时晶格热导率出现了反常的增高, 这可能是Mn掺杂过量导致的.

为了进一步解释共掺杂前后热导率降低效果差异的原因, 用Debye-Callaway公式^[37]拟合了Sn_1.04In_0.01Te(Cu₂Te)_0.05样品和Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品的晶格热导率:

${\kappa _{\rm{L}}} = \frac{{{k_{\rm{B}}}}}{{2{{\rm{\pi }}^2}{v_s}}}{\left( {\frac{{{k_{\rm{B}}}T}}{\hbar }} \right)^3}\int_0^{{\theta _D}/T} {\frac{{{x^4}{{\rm{e}}^x}}}{{\tau _{\rm{C}}^{ - 1}{{{\rm{(}}{{\rm{e}}^x} - 1{\rm{)}}}^2}}}} {\rm{d}}x,$

(8)

式中x为简约频率(x = ħω/(k_BT)), ħ为简约普朗克常数, ω为声子频率, v_s为声速, θ_D为德拜温度, τ_C^–1为声子弛豫时间, 本文的散射类型选择了PD散射(点缺陷散射)、U散射(声子-声子散射)、NP散射(纳米沉淀物引起的散射)和strain散射(Cu间隙缺陷带来的应变场散射), 与In-Cu共掺杂文献一致^[34].

$\tau _{\rm{C}}^{ - 1} = \tau _{\rm{PD}}^{ - 1} + \tau _{\rm{U}}^{ - 1} + \tau _{\rm{NP}}^{ - 1} + \tau _{\rm{strain}}^{ - 1},$

(9)

$\tau _{{\rm{PD}} + {\rm{U}}}^{ - 1} = A{\omega ^4} + BT{\omega ^2},$

(10)

$\tau _{\rm NP}^{-1} \!=\! v_{\rm s} \bigg\{ \dfrac1{2\pi R^2} \!+\! \bigg[ \frac{4}{9}{\pi}{R^2} \Big(\frac{\Delta D}{D} \Big)^2 \Big( \frac{\omega R}{v_{\rm s}} \!\Big)^4 \bigg]^{-1} \bigg\}^{-1} V_{\rm P},$

(11)

$\tau _{{\rm{strain}}}^{ - 1} = \left\{ {\begin{aligned} &0, &{\left( {\omega < {\omega _0}} \right)}, \\ &{C\frac{{{{(\omega - {\omega _0})}^3}}}{{{\omega _{\rm{D}}}}}}, &{\left( {\omega \geqslant {\omega _0}} \right)} , \end{aligned}} \right.$

(12)

式中A, B, C为拟合参数; R为纳米析出相的平均粒子半径; D为基体的质量密度; ∆D为基体与纳米粒子的质量密度差; V_P为纳米粒子的数目密度; ω₀为应变场中声子散射的临界频率; ω_D为德拜频率. 晶格热导率拟合曲线如图5(a)所示, 整体上来看Sn_1.04In_0.01Te(Cu₂Te)_0.05表现出的拟合效果较好, 对Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品进行拟合时, 在Sn_1.04In_0.01Te(Cu₂Te)_0.05样品的基础上降低了V_P的值, 拟合后发现A的值增大, 而C的值减小, 在一定程度上反映了Mn掺杂后点缺陷的增强和Cu间隙缺陷的减弱. 如图5(a)所示, 对Mn-In-Cu共掺杂样品拟合后的低温晶格热导率与实验值符合较好, 而在高温时拟合值与实验值相差较大, 这可能是因为高温时产生了双极扩散效应. 图5(b)所示为晶格热导率与T^–1函数关系图, 在高温下发现Mn-In-Cu共掺杂样品明显的非线性行为, 说明了双极扩散效应的存在^[38]. 一般来说, Mn掺杂后会增大带隙抑制双极扩散效应, 而本研究Mn掺杂后在高温下出现双极扩散效应, 这可能是高掺杂量下杂相的增加以及高压合成工艺对其带隙的影响造成的^[39], 这一问题还需进一步深入研究.

$图 5 Sn1.04In0.01Te(Cu2Te)0.05样品和Sn0.89Mn0.15In0.01Te(Cu2Te)0.05样品的(a) 晶格热导率的实验值与拟合结果对比, (b) 晶格热导率与1000/T的函数关系图\r\nFig. 5. (a) Experimental and fitting results of lattice thermal conductivity for Sn1.04In0.01Te(Cu2Te)0.05 and Sn0.89Mn0.15In0.01Te(Cu2Te)0.05; (b) lattice thermal conductivity as a function of 1000/T for Sn1.04In0.01Te(Cu2Te)0.05 and Sn0.89Mn0.15In0.01Te(Cu2Te)0.05.$

图 5 Sn_1.04In_0.01Te(Cu₂Te)_0.05样品和Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品的(a) 晶格热导率的实验值与拟合结果对比, (b) 晶格热导率与1000/T的函数关系图

Fig. 5. (a) Experimental and fitting results of lattice thermal conductivity for Sn_1.04In_0.01Te(Cu₂Te)_0.05 and Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05; (b) lattice thermal conductivity as a function of 1000/T for Sn_1.04In_0.01Te(Cu₂Te)_0.05 and Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05.

下载: 全尺寸图片幻灯片

图6(a)为材料Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)的zT值随温度的变化. 随着Mn含量的增加, 样品的zT值整体上呈现先降低后升高的变化趋势, Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品在873 K时获得最大zT ≈ 1.45, 相比纯SnTe提高了260%. 由于整体较高的功率因子和较低的热导率使得样品的平均zT较优, Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品在300—873 K的平均zT达到0.76. 图6(b)为本工作与已报道的SnTe最优掺杂成分^{[11,19,23,30,32,40-43]}在300—873 K的平均zT对比图, 相比其他掺杂方式, 本文研究的Mn-In-Cu共掺杂的样品在保持了较高zT的同时获得了较优的平均zT.

$图 6 (a) Sn1.04–xMnxIn0.01Te(Cu2Te)0.05 (x = 0—0.17)样品的zT值随温度的变化; (b) 不同掺杂样品300—873 K的zTave[11,19,23,30,32,40-43]\r\nFig. 6. (a) Temperature dependent zT for Sn1.04–xMnxIn0.01Te(Cu2Te)0.05 (x = 0–0.17) samples; (b) comparison of zTave with a temperature gradient of 300–873 K[11,19,23,30,32,40-43].$

图 6 (a) Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品的zT值随温度的变化; (b) 不同掺杂样品300—873 K的zT_ave^{[11,19,23,30,32,40-43]}

Fig. 6. (a) Temperature dependent zT for Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 (x = 0–0.17) samples; (b) comparison of zT_ave with a temperature gradient of 300–873 K^{[11,19,23,30,32,40-43]}.

下载: 全尺寸图片幻灯片

4. 结　论

通过HTHP结合热压烧结制备了Mn, In, Cu共掺杂的SnTe样品. 结果表明, Mn和In掺杂带来的能带简并和共振能级的作用提高了材料整个温度范围内的Seebeck系数, 使得样品整体功率因子提高. Mn取代产生的点缺陷和Cu带来的间隙缺陷增强了声子散射, 导致了晶格热导率的降低. 电性能和热性能的优化使得Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品在873 K时取得最大zT约1.45, 在300—873 K的平均zT达到了0.76. 相比单个策略某一性能较优而整体性能不足的情况, 多策略结合的方式较好地保留了单一策略的优异特性, 从而使得材料的整体性能得到了较大提升. 此外, 研究表明, 单一策略的优异特性并没有被发挥到极致, 多策略结合的方式仍有较大的提升空间.

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其他类型引用(5)

图 1 Sn_1.04–_xMn_xIn_0.01Te (Cu₂Te)_0.05(x = 0—0.17)的(a) XRD图谱, (b) 57.5°—60° XRD图谱局部放大图, (c) 晶格常数随Mn掺杂量x的变化

Figure 1. Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 samples (x = 0–0.17): (a) XRD patterns; (b) enlarged view between 57.5°–60°; (c) lattice parameter as a function of x

DownLoad: Full-Size Img PowerPoint

图 2 Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品的扫描电子显微镜图像

Figure 2. Scanning electron microscope images of the Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05 sample.

DownLoad: Full-Size Img PowerPoint

图 3 Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品的(a) 电导率随温度的变化, (b) 室温下载流子浓度和迁移率随x的变化, (c) Seebeck系数随温度的变化, (d) 室温下Seebeck系数与载流子浓度关系以及和相关研究的对比图^{[11,17,30-32]}, (e) 室温下有效质量对比图, (f) 功率因子随温度的变化

Figure 3. Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 (x = 0–0.17) samples: (a) Electrical conductivities as a function of temperature; (b) carrier concentration and mobility as a function of x at room temperature; (c) Seebeck coefficients as a function of temperature; (d) the relationship between Seebeck coefficient and carrier concentration at room temperature and comparison with the correlation studies^{[11,17,30-32]}; (e) effective mass comparison at room temperature; (f) power factor as a function of temperature.

DownLoad: Full-Size Img PowerPoint

图 4 Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品的(a) 总热导率、(b) 洛伦兹数、(c) 载流子热导率、(d) 晶格热导率随温度的变化

Figure 4. Thermoelectric properties of Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 (x = 0–0.17) as a function of temperature: (a) Total thermal conductivity; (b) Lorenz number; (c) carrier thermal conductivity; (d) lattice thermal conductivity.

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图 5 Sn_1.04In_0.01Te(Cu₂Te)_0.05样品和Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05样品的(a) 晶格热导率的实验值与拟合结果对比, (b) 晶格热导率与1000/T的函数关系图

Figure 5. (a) Experimental and fitting results of lattice thermal conductivity for Sn_1.04In_0.01Te(Cu₂Te)_0.05 and Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05; (b) lattice thermal conductivity as a function of 1000/T for Sn_1.04In_0.01Te(Cu₂Te)_0.05 and Sn_0.89Mn_0.15In_0.01Te(Cu₂Te)_0.05.

DownLoad: Full-Size Img PowerPoint

图 6 (a) Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05(x = 0—0.17)样品的zT值随温度的变化; (b) 不同掺杂样品300—873 K的zT_ave^{[11,19,23,30,32,40-43]}

Figure 6. (a) Temperature dependent zT for Sn_1.04–_xMn_xIn_0.01Te(Cu₂Te)_0.05 (x = 0–0.17) samples; (b) comparison of zT_ave with a temperature gradient of 300–873 K^{[11,19,23,30,32,40-43]}.

DownLoad: Full-Size Img PowerPoint

[1]	Wood C 1988 Rep. Prog. Phys. 51 459 Google Scholar
[2]	Biswas K, He J, Blum I D, Wu C I, Hogan T P, Seidman D N, Dravid V P, Kanatzidis M G 2012 Nature 489 414 Google Scholar
[3]	Pei Y, Shi X, LaLonde A, Wang H, Chen L, Snyder G J 2011 Nature 473 66 Google Scholar
[4]	Brebrick R F 1963 J. Phys. Chem. Solids 24 27 Google Scholar
[5]	Rogers L M 1968 J. Phys. D: Appl. Phys. 1 845 Google Scholar
[6]	Wu H, Chang C, Feng D, Xiao Y, Zhang X, Pei Y, Zheng L, Wu D, Gong S, Chen Y, He J, Kanatzidis M G, Zhao L D 2015 Energy Environ. Sci. 8 3298 Google Scholar
[7]	Banik A, Shenoy U S, Anand S, Waghmare U V, Biswas K 2015 Chem. Mater. 27 581 Google Scholar
[8]	Tan G, Shi F, Doak J W, Sun H, Zhao L D, Wang P, Uher C, Wolverton C, Dravid V P, Kanatzidis M G 2015 Energy Environ. Sci. 8 267 Google Scholar
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[10]	Tan X J, Shao H Z, He J, Liu G Q, Xu J T, Jiang J, Jiang H C 2016 Phys. Chem. Chem. Phys. 18 7141 Google Scholar
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[12]	Ma Z, Lei J, Zhang D, Wang C, Wang J, Cheng Z, Wang Y 2019 ACS Appl. Mater. Interfaces 11 33792 Google Scholar
[13]	Bhat D K, Shenoy U S 2017 J. Phys. Chem. C 121 7123 Google Scholar
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