Interband tunneling current in a highly-doped nitride heterojunction¶
Header¶
- Related input files and scripts:
InterbandTunneling_Duboz2019_nnp.py
InterbandTunneling_Duboz2019_nnp.in
InterbandTunneling_Duboz2019_formulation.pdf
- Important output files:
bias_xxxxx/integrated_density_electron.dat
bias_xxxxx/integrated_density_hole.dat
bias_xxxxx/mobility_electron.dat
Introduction¶
We compute interband tunneling current through a highly-doped heterojunction by nextnano++ simulation and Python post-processing. We follow the methods in the following publication of Jean-Yves Duboz and Borge Vinter [Duboz2019], using fewer approximations wherever possible:
This tutorial uses the Python script nextnanopy/templates/InterbandTunneling_Duboz2019_nnp.py to automate the simulation of the nextnano++ input file InterbandTunneling_Duboz2019_nnp.in and post-calculation of interband tunneling current.
The script¶
The Python script does the following while sweeping the bias:
Runs the nextnano++ simulations based on the user-defined parameters
From the simulation output folder, load the envelopes \(F_{\mathrm{vj,z1}}(z)\), \(F_{\mathrm{vj,z2}}(z)\), and \(F_{\mathrm{ci}}(z)\) together with the electrostatic potential \(\phi(z)\). The units are 1/nm1/2 and V, respectively.
Differentiates the potential.
Calculates the dipole matrix elements using the position-dependent material parameters.
Plots the matrix elements as a function of position.
Integrates the product over the device.
Calculates tunneling current density for individual transitions in units A/cm2.
Sums up the tunnel current density for all possible transitions.
After all simulations and post-calculations, the Python script exports the tunnel I-V curve in the following formats:
Image file with the format specified by the user
*.dat file
The output folders are indicated in the console log. The *.dat format is useful if you compare I-V curves using the nextnanomat overlay feature.
Options in the script¶
- Effective ffield
If the Boolean variable
CalculateEffectiveField_fromOutput = True
(the default), then the script calculates the position-dependent effective field\[M_{ij}^{\sigma} =\alpha_{Z\sigma}^{j*} \int\frac{P_1}{E_g}F_{vj,z\sigma}^{*}(z)F_{ci\sigma}(z) q\frac{\partial\phi(z)}{\partial z} dz\]based on the computed electrostatic potential. When
CalculateEffectiveField_fromOutput = False
, the assumption in the paper is used.\[\frac{\partial\phi(z)}{\partial z} = 1 \mathrm{\frac{V}{nm}}\]- Kane’s parameter
If the Boolean variable
KaneParameter_fromOutput = True
(the default), then the script reads in the Kane’s parameter \(P\) in from the nextnano++ output to evaluate\[\bra{Z} z \ket{S} = \frac{1}{E_g} \bra{Z} p_z \ket{S} = \frac{P}{E_g}\]In this case, an 8-band \(\mathbf{k} \cdot \mathbf{p}\) simulation with exactly the same device geometry will be performed so that nextnanopy can extract the Kane parameter.
If
KaneParameter_fromOutput = False
, then \(P\) is calculated from the assumption in [Duboz2019] (\(E_P\) = 15 eV).- Reduced mass
If the Boolean variable
CalculateReducedMass_fromOutput = True
, then the script calculates the position-dependent reduced mass \(m_r\) in\[I_{ij} = \frac{2\pi q}{\hbar} \sum_\sigma |M_{ij}^\sigma|^2 \cdot \frac{m_r}{2 \pi \hbar^2} = \frac{q m_r}{\hbar^3} \sum_\sigma |M_{ij}^\sigma|^2\]using the nextnano++ outputs of the effective masses.
When
CalculateReducedMass_fromOutput = False
(the default), then the assumption as in [Duboz2019] is used.
Results¶
The structure is an AlGaN/GaN p-i-n junction with 2 nm GaN interlayer.
The energy overlap between the hole states and electron states increases as the bias, leading to larger tunnel current.
![../../../../_images/bandedge_02.png](../../../../_images/bandedge_02.png)
![../../../../_images/bandedge_07.png](../../../../_images/bandedge_07.png)
The Python script calculates dipole matrix elements from the simulation results:
![../../../../_images/Dipole_matrix_element.png](../../../../_images/Dipole_matrix_element.png)
from which we obtain the tunnel current as a function of bias:
![../../../../_images/TunnelCurrent_vs_bias.png](../../../../_images/TunnelCurrent_vs_bias.png)
Figure 2.4.18.3 Interband tunneling current in a nitride p-i-n junction. Following the paper, backward bias is taken to be positive in this plot.¶
Last update: nn/nn/nnnn