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2013/5/8
Physics of Semiconductors (4)
Shingo Katsumoto
Institute for Solid State Physics,
University of Tokyo
Hall effect
2013/5/8 1
Hall coefficient :
Thermal transport and electric transport
2013/5/8 2
Thermal conductivity
Thermal flux
vector format
Thermoelectric effect
Seebeck effect Peltier effect
Thomson effect Kelvin relation
Boltzmann equation and thermoelectric
coefficients
2013/5/8 3
Material specific Seebeck coefficient
Boltzmann equation for steady states Replace f in LHS with f0.
𝑎 = −𝐸 − 𝐸𝐹
𝑘𝐵𝑇
Boltzmann equation and thermoelectric
coefficients
2013/5/8 4
Peltier device
2013/5/8 5
Metal-insulator transition
2013/5/8 6
Insulator Metal
Metal-insulator transition
2013/5/8 7
Spin Seebeck effect
2013/5/8 8
K. Uchida, S. Takahashi, K. Harii, J. Ieda, W. Koshibae, K. Ando, S. Maekawa
and E. Saitoh, Nature 455, 778 (2008).
Spin Seebeck effect
2013/5/8 9
Spin Seebeck effect (?) in a ferromagnetic
semiconductor
2013/5/8 10
Jarowski et al.
Nature Materials
9, 898 (2010)
Spin Seebeck effect (?) in a ferromagnetic
semiconductor
2013/5/8 11
Spin Seebeck effect (?) in a ferromagnetic
semiconductor
2013/5/8 12
Exercise
2013/5/8 13
1. p-Ge has Seebeck coefficient of 300mV/K and n-type Bi2Te3 -230mV/K.
If one makes a thermocouple from these two materials, how high is the
voltage caused by the temperature difference of 50K.
2. Obtain expressions for electron mobility and for diffusion constant in
terms of the conductivity and the Hall coefficient.
3. Obtain the Mott's criterion 𝑛𝑐1/3𝑎B
∗=0.26 along the following guide.
−ℏ2
2𝑚∗𝛻2 −
𝑒2
4𝜋𝜀0𝜀𝑟𝑒
−𝑟𝜆 𝜓 𝒓 = 𝐸𝜓 𝒓 , 𝜆 =
2𝜀𝜀0𝐸F3𝑛𝑒2
𝐸𝐹 =ℏ2
2𝑚∗3𝜋2𝑛 2/3
Obtain the condition for the Schrodinger equation with screened Coulomb potential
to have bound state with variational method.