JP6655918B2 - Thermoelectric material - Google Patents
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- JP6655918B2 JP6655918B2 JP2015178611A JP2015178611A JP6655918B2 JP 6655918 B2 JP6655918 B2 JP 6655918B2 JP 2015178611 A JP2015178611 A JP 2015178611A JP 2015178611 A JP2015178611 A JP 2015178611A JP 6655918 B2 JP6655918 B2 JP 6655918B2
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Description
本発明は、熱電材料に関する。 The present invention relates to thermoelectric materials.
従来より、工場、焼却施設などで生じる廃熱や、太陽熱や地熱などの自然エネルギーなどを有効利用するため、熱電変換を効率的に行うことができる熱電材料の研究が進められている。 2. Description of the Related Art In order to effectively use waste heat generated in factories, incineration facilities, and the like, and natural energy such as solar heat and geothermal heat, thermoelectric materials capable of efficiently performing thermoelectric conversion have been studied.
ここで、熱電材料の熱電特性評価に用いられる無次元性能指数ＺＴは下式で表される。 Here, the dimensionless figure of merit ZT used for the thermoelectric property evaluation of the thermoelectric material is expressed by the following equation.
（数１）
ＺＴ＝Ｓ２σＴ／κ
Ｚ：性能指数、Ｔ：絶対温度、Ｓ：ゼーベック係数、σ：導電率、κ：熱伝導率
(Equation 1)
ZT = S 2 σT / κ
Z: figure of merit, T: absolute temperature, S: Seebeck coefficient, σ: electrical conductivity, κ: thermal conductivity
熱電特性を向上させる（無次元性能指数ＺＴを増大させる）ためには、ゼーベック係数及び導電率が大きく、熱伝導率が小さいことが必要である。 In order to improve thermoelectric characteristics (increase the dimensionless figure of merit ZT), it is necessary that the Seebeck coefficient and the electrical conductivity are large and the thermal conductivity is small.
上述の特性のうち、特に熱伝導率を下げる試みが広く行われている。例えば、特許文献１には、熱電材料の母相にナノ粒子を分散させることにより熱伝導率を下げる方法が開示されている。
Attempts to lower the thermal conductivity, among others, have been widely made. For example,
しかし、上記の技術により熱伝導率を低減した場合、抵抗率が高い材料を母相に分散させるため導電率も低下してしまうので、無次元性能指数ＺＴはトレードオフとなり、大幅な向上は認められないという問題があった。 However, when the thermal conductivity is reduced by the above-described technology, the material having a high resistivity is dispersed in the matrix, so that the conductivity is also reduced. Therefore, the dimensionless figure of merit ZT is a trade-off, and a significant improvement is recognized. There was a problem that can not be.
そこで、本発明は、熱伝導率を低減しつつ、導電率を向上させることにより熱電特性を向上させた熱電材料を提供することを目的とする。 Therefore, an object of the present invention is to provide a thermoelectric material having improved thermoelectric properties by improving the electrical conductivity while reducing the thermal conductivity.
請求項１に記載の発明では、熱電特性を発現する母材にフォノンを散乱する物質からなるナノ粒子が分散された熱電材料であって、前記母材及びナノ粒子は、一方がｐ型半導体、他方がｎ型半導体からなり、前記ｐ型半導体の価電子帯の最上部のエネルギー準位が、前記ｎ型半導体の伝導帯の底部のエネルギー準位よりも高く、前記母材と前記ナノ粒子とのｐｎ接合部においてトンネル効果を発現するように構成されており、前記ナノ粒子は、粒子径、密度及び前記母材に対する添加量に基づいて算出される平均間隔Ｌが、キャリアのコヒーレント長以下になるように前記母材に添加されている、という技術的手段を用いる。
The invention according to
請求項１に記載の発明によれば、ナノ粒子によるフォノン散乱により、熱伝導率を下げることができるとともに、母材とナノ粒子とのｐｎ接合部においてトンネル効果を発現させることができるため、従来の熱電材料に比べて導電率を向上させることができるので、熱電特性を向上させることができる。また、ナノ粒子は、平均間隔Ｌがキャリアのコヒーレント長以下になるように母材に添加されているため、多くのナノ粒子の粒子間隔がコヒーレント長以下になるために、散乱せずに伝搬可能なキャリアが増大するので、移動度を増大させることができる。 According to the first aspect of the present invention, the thermal conductivity can be reduced by phonon scattering by the nanoparticles, and a tunnel effect can be developed at the pn junction between the base material and the nanoparticles. Since the conductivity can be improved as compared with the thermoelectric material, the thermoelectric properties can be improved. Also, since the nanoparticles are added to the base material such that the average interval L is equal to or less than the coherent length of the carrier, the nanoparticles can be propagated without scattering because the particle interval of many nanoparticles is equal to or less than the coherent length. Since the number of carriers increases, the mobility can be increased.
請求項２に記載の発明では、請求項１に記載の熱電材料において、前記母材は合金系熱電材料からなる、という技術的手段を用いる。
In the invention described in
請求項２に記載の発明のように母材に合金系熱電材料を用いると、熱電材料を溶解法により作製することができ、焼結法などで作製した場合に比べ、ナノ粒子をより均質に分散させることができるので好ましい。
When an alloy-based thermoelectric material is used for the base material as in the invention according to
請求項３に記載の発明では、請求項１または請求項２に記載の熱電材料において、前記ナノ粒子は、セラミックス材料からなる、という技術的手段を用いる。 According to a third aspect of the present invention, in the thermoelectric material according to the first or second aspect , a technical means is used in which the nanoparticles are made of a ceramic material.
請求項３に記載の発明のように、ナノ粒子としてセラミックス材料を用いることができる。ナノ粒子は耐熱性に優れているため、例えば、母材の溶湯中でも安定しており、母材中に均一に分散させることができる。 As in the third aspect , a ceramic material can be used as the nanoparticles. Since the nanoparticles are excellent in heat resistance, for example, they are stable even in the molten metal of the base material, and can be uniformly dispersed in the base material.
本発明の熱電材料について、図を参照して説明する。 The thermoelectric material of the present invention will be described with reference to the drawings.
図１に、本発明の熱電材料（以下、「熱電材料Ｈ」という）における導電率向上に寄与するトンネル効果の説明図を示す。 FIG. 1 shows an explanatory diagram of a tunnel effect that contributes to an improvement in conductivity in the thermoelectric material of the present invention (hereinafter, referred to as “thermoelectric material H”).
熱電材料Ｈは、熱電特性を発現する母材にフォノンを散乱する物質からなるナノ粒子が分散されて形成されている。母材及びナノ粒子は、一方がｐ型半導体、他方がｎ型半導体からなる。 The thermoelectric material H is formed by dispersing nanoparticles made of a substance that scatters phonons in a base material that exhibits thermoelectric characteristics. One of the base material and the nanoparticles is a p-type semiconductor, and the other is an n-type semiconductor.
図１では、母材がｐ型熱電材料、ナノ粒子がｎ型半導体である場合について示す。図１（Ａ）に、母材のエネルギー準位（左）とナノ粒子のエネルギー準位（右）とをそれぞれ示す。 FIG. 1 shows a case where the base material is a p-type thermoelectric material and the nanoparticles are n-type semiconductors. FIG. 1A shows the energy level of the base material (left) and the energy level of the nanoparticles (right), respectively.
ＥＣは伝導帯の底部のエネルギー準位、ＥＶは価電子帯の最上部のエネルギー準位、Ｅｇはバンドギャップ、Ｅｆはファルミ準位をそれぞれ示し、添字のｐ、ｎはそれぞれ母材、ナノ粒子のものであることを示している。また、○は正孔を、●は電子を示す。 E C represents the energy level of the bottom of the conduction band, the top of the energy level of E V is the valence band, E g is the band gap, E f is the Farumi levels respectively, subscripts p, n respectively mother Material and nanoparticles. ○ indicates holes, and 正 indicates electrons.
熱電材料Ｈは、母材の価電子帯の最上部のエネルギー準位Ｅｖｐが、ナノ粒子の伝導帯の底部のエネルギー準位Ｅｃｎよりも高くなるように構成されている。 The thermoelectric material H is configured such that the energy level E vp at the top of the valence band of the base material is higher than the energy level E cn at the bottom of the conduction band of the nanoparticles.
図１（Ｂ）に、母材とナノ粒子との接合後におけるエネルギー準位を示す。図１（Ｂ）に示すように、連続した準位が形成される。このとき、ナノ粒子における量子閉じ込め効果が作用し、キャリアの移動度が増大するので、導電率を向上させることができる。 FIG. 1B shows an energy level after bonding the base material and the nanoparticles. As shown in FIG. 1B, continuous levels are formed. At this time, the quantum confinement effect of the nanoparticles acts to increase the mobility of carriers, so that the conductivity can be improved.
母材としては、上述したナノ粒子とのエネルギー準位の関係を充足する組み合わせで各種材料、例えば、合金系熱電材料を用いることができる。合金系熱電材料は溶解法で製造可能な合金系の熱電材料であって、Ｓｂ、Ｂｉ等のＶ族元素とＳｅ、Ｔｅ等のＶＩ族元素と、からなるＶ族元素−ＶＩ族元素系熱電材料などを用いることができる。例えば、Ｂｉ２Ｔｅ３、Ｂｉ２Ｓｅ３、Ｓｂ２Ｔｅ３、Ｓｂ２Ｓｅ３、ＦｅＳｉ２、Ｍｇ２Ｓｉ、Ｍｇ２Ｇｅ、ＣｏＳｂ３、Ｚｎ４Ｓｂ３、ＰｂＴｅ、ＡｇＳｂＴｅ２、ＳｎＳｅ、ＳｎＳなど、Ｂｉ−Ｔｅ系、Ｐｂ−Ｔｅ系、Ａｇ−Ｓｂ−Ｔｅ系、Ｚｎ−Ｓｂ系熱電材料、Ｓｎ−Ｓｅ系またはＳｎ−Ｓ系熱電材料を用いることができる。母材に合金系熱電材料を用いると、熱電材料Ｈを溶解法により作製することができ、焼結法などで作製した場合に比べ、ナノ粒子をより均質に分散させることができるので好ましい。
As the base material, various materials, for example, alloy-based thermoelectric materials can be used in a combination that satisfies the above-described energy level relationship with the nanoparticles. The alloy-based thermoelectric material is an alloy-based thermoelectric material that can be produced by a melting method, and is a V-group element-VI element-based thermoelectric material composed of a V-group element such as Sb and Bi and a VI-group element such as Se and Te. Materials and the like can be used. For example, Bi 2 Te 3, Bi 2 Se 3,
添加するナノ粒子は、フォノンの散乱効果を有するものを用い、母材の融点で溶融しないものが好ましい。例えば、ＺｎＯ、ＴｉＯ２などの酸化物、ＳｉＣなどの炭化物、ＢＮなどの窒化物を用いることができる。ここで、ナノ粒子をセラミックス系熱電材料とすると、母材の溶湯中でも安定しており、熱電材料でないナノ粒子を用いる場合に比べて熱電特性を更に向上させることができるので好ましく、ＺｎＯ、ＴｉＯ２、Ｆｅ２Ｏ３、ＬａＴｉＯ３、ＳｒＴｉＯ３、Ｃａ３Ｃｏ４Ｏ９、Ｃａ３Ｃｏ２Ｏ６、ＬａＮｉＯ３、Ｃｕ１＋ｘＭｎ１−ｘＯ２などを好適に用いることができる。 As the nanoparticles to be added, those having a phonon scattering effect are used, and those which do not melt at the melting point of the base material are preferable. For example, oxides such as ZnO and TiO 2 , carbides such as SiC, and nitrides such as BN can be used. Here, when the nanoparticles are made of a ceramic-based thermoelectric material, they are stable even in the molten metal of the base material, and the thermoelectric properties can be further improved as compared with the case of using nanoparticles that are not thermoelectric materials. Therefore, ZnO, TiO 2 , Fe 2 O 3 , LaTiO 3 , SrTiO 3 , Ca 3 Co 4 O 9 , Ca 3 Co 2 O 6 , LaNiO 3 , and Cu 1 + x Mn 1-x O 2 can be preferably used.
ここで、例えば、母材としてｐ型熱電材料であるＺｎ４Ｓｂ３を用いた場合、ナノ粒子はとしてｎ型半導体材料であるＺｎＯ、またはＴｉＯ２などを用いることができる。図２にナノ粒子としてＺｎＯ、図３にナノ粒子としてＴｉＯ２、を用いたときの各エネルギー準位の状態を示す。図２（Ａ）、図３（Ａ）では、左図が母材のエネルギー準位、右図がナノ粒子のエネルギー準位をそれぞれ示す。両者ともに図１に示すエネルギー準位の関係を充足している。 Here, for example, when Zn 4 Sb 3 that is a p-type thermoelectric material is used as the base material, ZnO or TiO 2 that is an n-type semiconductor material can be used as the nanoparticles. FIG. 2 shows the state of each energy level when ZnO is used as nanoparticles and TiO 2 is used as nanoparticles. 2A and 3A, the left diagram shows the energy level of the base material, and the right diagram shows the energy level of the nanoparticles. Both satisfy the energy level relationship shown in FIG.
ナノ粒子の大きさは、格子振動を抑制し熱伝導率を下げるためにフォノンの散乱効果が十分に発現する大きさ（数１００ｎｍ以下）とする必要がある。また、トンネル効果を有効に発現させるためには、１０〜３００ｎｍであることが好ましい。 The size of the nanoparticles needs to be a size (several hundreds nm or less) at which the scattering effect of phonons is sufficiently exhibited in order to suppress lattice vibration and reduce thermal conductivity. In order to effectively exhibit the tunnel effect, the thickness is preferably 10 to 300 nm.
また、ナノ粒子の添加量は、熱伝導率を勘案するとともに、下記条件を満足するように適宜設定することが好ましい。 In addition, it is preferable that the addition amount of the nanoparticles be appropriately set so as to satisfy the following conditions while considering the thermal conductivity.
図４に、ナノ粒子の平均間隔Ｌを有するナノ粒子における粒子間隔の分布とキャリアのコヒーレント長との関係を示す。ここで、キャリアのコヒーレント長とは、キャリアが散乱することなく伝搬可能な距離である。 FIG. 4 shows the relationship between the distribution of the particle spacing and the coherent length of the carrier in the nanoparticles having the average spacing L between the nanoparticles. Here, the coherent length of the carrier is a distance over which the carrier can propagate without being scattered.
ナノ粒子の平均間隔Ｌは、図５に示すように、ナノ粒子が母材中において面心立方格子の格子点に配置されているモデルを仮定して算出した。ナノ粒子の平均間隔Ｌは、粒径分布の最大粒子径で代表させたナノ粒子の直径２ｒ、母材に対する添加量及び密度に基づいて、ナノ粒子の表面間距離ｄの平均値として算出した。当該式より、ナノ粒子の最大粒子径で代表される２ｒ及び添加量ＷＮが増大すると、平均間隔Ｌ（＝ｄ）が小さくなることがわかる。
The average spacing L of the nanoparticles was calculated assuming a model in which the nanoparticles were arranged at lattice points of a face-centered cubic lattice in the base material as shown in FIG. The average distance L between the nanoparticles was calculated as the average value of the distance d between the surfaces of the nanoparticles based on the
図４に示すように、平均間隔Ｌがコヒーレント長より長い分布（Ａ）では、ほとんどのナノ粒子の粒子間隔がコヒーレント長より大きくなるために、キャリアが散乱しやすくなり、散乱による熱損失により移動度が低下してしまう。 As shown in FIG. 4, in the distribution (A) in which the average interval L is longer than the coherent length, since the particle interval of most nanoparticles is larger than the coherent length, carriers are easily scattered, and the carriers move due to heat loss due to scattering. The degree will decrease.
一方、平均間隔Ｌがコヒーレント長より短い分布（Ｂ）では、多くのナノ粒子の粒子間隔がコヒーレント長より小さくなるために、散乱せずに伝搬可能なキャリアが増大するので、移動度が増大する。 On the other hand, in the distribution (B) in which the average interval L is shorter than the coherent length, since the particle interval of many nanoparticles is smaller than the coherent length, the number of carriers that can propagate without being scattered increases, so that the mobility increases. .
ナノ粒子の添加量が増大し、平均間隔Ｌがコヒーレント長より更に短くなった分布（Ｃ）では、ナノ粒子の凝集が数多く発生する。トンネル効果を有効に活用するためには、ナノ粒子が適切に分散され、凝集する領域が少ないことが必要となる。ナノ粒子が凝集した領域は高抵抗な領域となるとともに、ナノ粒子における量子閉じ込め効果が低下するため、導電率の向上に有効に作用しなくなる。 In the distribution (C) in which the amount of added nanoparticles is increased and the average interval L is shorter than the coherent length, a large number of nanoparticles are aggregated. In order to effectively utilize the tunnel effect, it is necessary that the nanoparticles are appropriately dispersed and the area where the nanoparticles are aggregated is small. The region where the nanoparticles are aggregated becomes a high-resistance region, and the quantum confinement effect of the nanoparticles decreases, so that the region does not effectively work to improve the conductivity.
ナノ粒子の添加量は、
・平均間隔Ｌがコヒーレント長以下である。
・ナノ粒子の凝集が少ない。
ように設定することが好ましい。
The amount of nanoparticles added
-The average interval L is equal to or less than the coherent length.
-Less aggregation of nanoparticles.
It is preferable to set as follows.
上述の実施形態では、母材にｐ型半導体、ナノ粒子にｎ型半導体を用いたが、エネルギー準位の関係を充足する組み合わせであれば、母材にｎ型半導体、ナノ粒子にｐ型半導体を用いることもできる。 In the above-described embodiment, a p-type semiconductor is used for the base material and an n-type semiconductor is used for the nanoparticles. However, if the combination satisfies the energy level relationship, the base material is an n-type semiconductor and the nanoparticles are a p-type semiconductor. Can also be used.
（実施形態の効果）
本発明の熱電材料によれば、ナノ粒子によるフォノン散乱により、熱伝導率を下げることができるとともに、母材とナノ粒子とのｐｎ接合部においてトンネル効果を発現させることができるため、従来の熱電材料に比べて導電率を向上させることができるので、熱電特性を向上させることができる。
また、ナノ粒子の添加量を、ナノ粒子の平均間隔Ｌがコヒーレント長以下になるようにすると、多くのナノ粒子の粒子間隔がコヒーレント長以下になるために、散乱せずに伝搬可能なキャリアが増大するので、移動度を増大させることができる。
(Effects of the embodiment)
According to the thermoelectric material of the present invention, the thermal conductivity can be reduced by phonon scattering by the nanoparticles, and a tunnel effect can be developed at the pn junction between the base material and the nanoparticles. Since the conductivity can be improved as compared with the material, the thermoelectric characteristics can be improved.
Also, if the amount of nanoparticles added is such that the average spacing L between the nanoparticles is less than the coherent length, the spacing between many nanoparticles will be less than the coherent length. Since the mobility increases, the mobility can be increased.
Ｚｎ−Ｓｂ系の熱電材料であるＺｎ４Ｓｂ３を母材とし、ナノ粒子としてＺｎＯまたはＴｉＯ２を添加した熱電材料を作製し、特性を評価した。Ｚｎ４Ｓｂ３の原料としては、ＺｎとＳｂの数１０μｍの粉末をモル比で６０：４０となるように混合し、これにナノ粒子を所定量添加した。 A thermoelectric material was prepared using Zn 4 Sb 3 , which is a Zn-Sb-based thermoelectric material, as a base material and ZnO or TiO 2 added as nanoparticles, and the characteristics were evaluated. As a raw material of Zn 4 Sb 3 , powder of Zn and Sb of several tens μm was mixed at a molar ratio of 60:40, and a predetermined amount of nanoparticles were added thereto.
（実施例１）
上記Ｚｎ４Ｓｂ３の原料に最大粒径５０ｎｍのＺｎＯナノ粒子（シグマアルドリッチ社製）を０、０．３、０．５、１、３重量％添加してアルミナるつぼに充填し、Ａｒ雰囲気中で１０℃／ｍｉｎで７００℃まで昇温し、３０分間保持した後に炉冷した。作製した試料について、導電率、移動度及びキャリア濃度を評価した。ここで、導電率はｖａｎ ｄｅｒ Ｐａｕｗ法、移動度及びキャリア濃度はホール効果の測定により、それぞれ評価した。
(Example 1)
ZnO nanoparticles having a maximum particle size of 50 nm (manufactured by Sigma-Aldrich) are added to the above-mentioned Zn 4 Sb 3 raw material in an amount of 0, 0.3, 0.5, 1, 3% by weight and filled in an alumina crucible. Then, the temperature was raised to 700 ° C. at a rate of 10 ° C./min. The conductivity, mobility, and carrier concentration of the manufactured sample were evaluated. Here, the conductivity was evaluated by a van der Pauw method, and the mobility and carrier concentration were evaluated by measuring the Hall effect.
評価結果を図６に示す。図６（Ａ）に示すように、導電率は０．５重量％添加で９２５Ｓ／ｃｍという極大値を示した。従来、熱伝導率を低下させるためにナノ粒子の添加量を増大させると、それに伴い導電率も低下すると考えられており、このような低濃度の添加により、Ｚｎ４Ｓｂ３単体（添加量０重量％）の導電率の約１．６倍という大きな導電率を示すことを明らかにしたことの技術的意義は大きい。 FIG. 6 shows the evaluation results. As shown in FIG. 6A, the conductivity showed a maximum value of 925 S / cm when 0.5% by weight was added. Conventionally, it has been considered that when the added amount of nanoparticles is increased in order to lower the thermal conductivity, the electrical conductivity is also reduced. Thus, by adding such a low concentration, Zn 4 Sb 3 alone (added amount 0 (% By weight) has a significant technical significance.
図６（Ｂ）及び（Ｃ）に示すように、キャリア濃度は添加量に寄らず１０１９ｃｍ−３オーダーであるが、移動度は導電率同様に０．５重量％添加で極大値を示した。これにより、導電率の増大は、移動度の増大によるものであり、母材とナノ粒子接合部のトンネル効果によるものであると言える。 As shown in FIGS. 6B and 6C, the carrier concentration is on the order of 10 19 cm −3 regardless of the amount of addition, but the mobility shows a maximum value when 0.5% by weight is added similarly to the conductivity. Was. Thus, it can be said that the increase in conductivity is due to an increase in mobility, and is due to a tunnel effect between the base material and the nanoparticle junction.
（実施例２）
Ｚｎ４Ｓｂ３の原料に最大粒径１００ｎｍのＺｎＯナノ粒子（シグマアルドリッチ社製）を０、０．３、０．５、１、３、５重量％添加した熱電材料を作製した。作製条件は実施例１と同様である。
(Example 2)
A thermoelectric material in which ZnO nanoparticles having a maximum particle diameter of 100 nm (manufactured by Sigma-Aldrich) were added to a raw material of Zn 4 Sb 3 at 0, 0.3, 0.5, 1, 3, 5 wt% was prepared. The manufacturing conditions are the same as in Example 1.
導電率の評価結果を図７に示す。導電率は実施例１と同様に、０．５重量％添加した場合に９４５Ｓ／ｃｍという極大値を示した。 FIG. 7 shows the evaluation results of the conductivity. As in Example 1, the conductivity showed a maximum value of 945 S / cm when 0.5% by weight was added.
（実施例３）
上記Ｚｎ４Ｓｂ３の原料に最大粒径１００ｎｍのＴｉＯ２ナノ粒子（シグマアルドリッチ社製）を０、０．０５、０．０７、０．１０、０．１２、０．１５、０．５０、１．０、１．５重量％添加した熱電材料を作製した。作製条件は実施例１と同様である。
(Example 3)
TiO 2 nanoparticles having a maximum particle size of 100 nm (manufactured by Sigma-Aldrich) were added to the raw material of Zn 4 Sb 3 at 0, 0.05, 0.07, 0.10, 0.12, 0.15, 0.50, Thermoelectric materials with 1.0 and 1.5% by weight added were prepared. The manufacturing conditions are the same as in Example 1.
評価結果を図８に示す。図８（Ａ）に示すように、導電率は０．０５−０．１２重量％添加の範囲で高い値を示し、０．０７重量％添加で８２２Ｓ／ｃｍという極大値を示した。図８（Ｂ）及び（Ｃ）に示すように、実施例１同様に、キャリア濃度は添加量に寄らず１０１９ｃｍ−３オーダーであるが、移動度は導電率同様に０．０５−０．１２重量％添加の範囲で高い値を示した。 FIG. 8 shows the evaluation results. As shown in FIG. 8A, the conductivity showed a high value in the range of 0.05 to 0.12% by weight addition, and showed a maximum value of 822 S / cm when 0.07% by weight was added. As shown in FIGS. 8B and 8C, as in Example 1, the carrier concentration is on the order of 10 19 cm −3 regardless of the amount of addition, but the mobility is 0.05-0 as in the case of the conductivity. A high value was shown in the range of .12% by weight .
導電率の上昇度合いは、母材の価電子帯の最上部のエネルギー準位とナノ粒子の伝導帯の底部のエネルギー準位との差に起因する。このエネルギー準位の差が大きいと、より小さなナノ粒子にまでトンネル効果が発現するので、導電率の上昇度合いは大きくなる。このエネルギー準位の差はＴｉＯ２よりもＺｎＯの方が大きいので、ＺｎＯナノ粒子を添加した方が導電率の上昇度合いは大きくなる。
このように、導電率を向上させるためには、上述のエネルギー準位の差が大きくなる組み合わせが好適である。
The degree of increase in conductivity is caused by the difference between the energy level at the top of the valence band of the base material and the energy level at the bottom of the conduction band of the nanoparticles. If the difference between the energy levels is large, the tunnel effect is exerted even on smaller nanoparticles, so that the degree of increase in the conductivity is large. The difference in the energy level towards the ZnO is greater than TiO 2, who was added ZnO nanoparticles increases the degree of conductivity increases.
As described above, in order to improve the conductivity, a combination in which the difference in the energy levels described above is large is preferable.
図９に、図５のモデルに基づいて算出したＺｎＯの添加量と平均間隔Ｌとの関係を示す。最大粒径５０ｎｍのＺｎＯを添加したときの添加量に対する平均間隔Ｌは、導電率が極大値を示した０．５重量％添加において２００ｎｍ程度、最大粒径１００ｎｍのＺｎＯを添加したときの添加量に対する平均間隔Ｌは、導電率が極大値を示した０．５重量％添加において４００ｎｍ程度であった。これは、一般的なキャリアのコヒーレント長が数１００ｎｍであることに対応している。 FIG. 9 shows the relationship between the amount of ZnO added and the average interval L calculated based on the model of FIG. The average distance L with respect to the addition amount when ZnO having a maximum particle size of 50 nm is added is about 200 nm when 0.5% by weight is added at which the conductivity shows a maximum value, and the addition amount when ZnO with a maximum particle size of 100 nm is added. Was about 400 nm at the addition of 0.5% by weight at which the conductivity showed a maximum value. This corresponds to a general carrier having a coherent length of several 100 nm.
（実施例４）
実施例１同様に、Ｚｎ４Ｓｂ３の原料に最大粒径５０ｎｍのＺｎＯナノ粒子を０、０．３、０．５、１、３、５、７重量％添加して作製した試料について、導電率の温度依存性を評価した。図１０に示すように、同じ添加量の場合、温度が高い程、導電率は低下する傾向が認められた。また、導電率が極大となる添加量は温度によらず、０．５重量％添加した場合であり、室温と同様の傾向を示した。これは、トンネル効果には温度依存性がほとんどないことによる。
(Example 4)
As in Example 1, a sample prepared by adding ZnO nanoparticles having a maximum particle size of 50 nm to a raw material of Zn 4 Sb 3 by 0, 0.3, 0.5, 1, 3 , 5, and 7% by weight was used. The temperature dependence of the rate was evaluated. As shown in FIG. 10, in the case of the same addition amount, the conductivity tends to decrease as the temperature increases. Further, the amount of addition at which the conductivity becomes maximum is the case where 0.5% by weight is added regardless of the temperature, and showed the same tendency as at room temperature. This is because the tunnel effect has almost no temperature dependence.
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