tepkit.formulas.dp

This module contains the formulas related to deformation potential theory.

Functions

carrier_mobility_3d_i(*, c_i, e1_i, m_i, t[, method])	Get carrier mobility component \(\mu_i\) by deformation potential theory for bulk materials.
carrier_mobility_2d_i(*, c_i, e1_i, m_i, c_j, e1_j, m_j, t)	Get carrier mobility component \(\mu_i\) by deformation potential theory for 2D materials.
carrier_mobility_2d_v(*, c_i, e1_i, m_i, c_j, e1_j, m_j, t)	Get carrier mobility 2D vector \((\mu_i, \mu_j)\) by deformation potential theory for 2D materials.
relaxtion_time(mu, m[, unit])	Get carrier relaxtion time \(\tau\) by carrier mobility and effective mass.

Module Contents

carrier_mobility_3d_i(*, c_i, e1_i, m_i, t, method='dp_3d')

Get carrier mobility component \(\mu_i\) by deformation potential theory for bulk materials.

Argument	Unit	Explanation
Input	—	—
c	GPa	Elastic constants
e1	eV	Deformation Potential
m	m_0	Effective Mass
t	K	Absolute Temperature
Output	—	—
mu	cm²·s⁻¹·V⁻¹	Carrier Mobility

Formula

Ref: Link Deformation Potentials and Mobilities in Non-Polar Crystals | Phys. Rev.

Formula A.39:

\[\mu_i = \frac{2 (2\pi)^{1/2} e \hbar^4 C_{ii}}{3 {m_i}^{5/2} (k_\mathrm{B} T)^{3/2} {E_1}_i^2}\]

carrier_mobility_2d_i(*, c_i, e1_i, m_i, c_j, e1_j, m_j, t, method='dp_2d')

Get carrier mobility component \(\mu_i\) by deformation potential theory for 2D materials.

Argument	Unit	Explanation
Input	—	—
c	N/m	2D Elastic constants
e1	eV	Deformation Potential
m	m_0	Effective Mass
t	K	Absolute Temperature
Output	—	—
mu	cm²·s⁻¹·V⁻¹	Carrier Mobility

Formula

Ref: Mobility anisotropy of two-dimensional semiconductors | Phys. Rev. B

You can choose from three different methods by method argument.

• dp_2d (See Ref. Formula 33) (Default)

  The most widely used version of the deformation potential theory for 2D materials.

  \[\begin{split}\mu_i = \frac {e \hbar^3 C^\mathrm{(2D)}_{ii}} { (k_{\mathrm{B}} T) (m_i)^{\frac{3}{2}} (m_j)^{\frac{1}{2}} {(E_1)}_i^2} \\\end{split}\]

• lang (See Ref. Formula 26) (Recommended)

  The modified version from Haifeng Lang that better accounts for anisotropy.

  \[\mu_i = \frac {e \hbar^3} { (k_{\mathrm{B}} T) (m_i)^{\frac{3}{2}} (m_j)^{\frac{1}{2}} } \cdot F_{\mathrm{ani}} (E_1) \cdot F_{\mathrm{ani}} (C^{\mathrm{(2D)}})\]

• lang_simplified (See Ref. Formula 27)

  The low order approximation of the above formula.

  \[\mu_i = \frac {e \hbar^3} { (k_{\mathrm{B}} T) (m_i)^{\frac{3}{2}} (m_j)^{\frac{1}{2}} } \cdot \left( \frac{9 E_{1i}^2 + 7 E_{1i} E_{1j} + 4 E_{1j}^2} {20} \right)^{-1} \cdot \left( \frac{5 C^{\mathrm{(2D)}}_{ii} + 3 C^{\mathrm{(2D)}}_{jj} } {8} \right)\]

carrier_mobility_2d_v(*, c_i, e1_i, m_i, c_j, e1_j, m_j, t, method='dp_2d')

Get carrier mobility 2D vector \((\mu_i, \mu_j)\) by deformation potential theory for 2D materials.

relaxtion_time(mu, m, unit: dict = None)

Get carrier relaxtion time \(\tau\) by carrier mobility and effective mass.

Argument	Unit	Explanation
Input	—	—
mu	cm²·s⁻¹·V⁻¹	Carrier Mobility
m	m_0	Effective Mass
Output	—	—
tau	s or fs	Relaxation Time

Formula

\[\tau = \mu * m / e\]