— NEW/EDU — p-n junction in the dark
Attention
This tutorial is under construction
Header
- Files for the tutorial located in nextnano++\examples\education
pn-junction-dark_GaAs_Nelson_2003_1D_nnp.in
- Scope of the tutorial:
- Main adjustable parameters in the input file:
parameter
$min_density
parameter
$max_density
- Relevant output files:
bias_XXXXX\bandedges.dat
bias_XXXXX\density_electon.dat
bias_XXXXX\density_hole.dat
bias_XXXXX\electric_field.dat
bias_XXXXX\potential.dat
IV_characteristics.dat
Introduction
In this tutorial, you can learn fundamentals of p-n junction.
We refer to
At equilibrium
Figure 2.4.63 shows the schematic illustration of the p-n junction.

Figure 2.4.63 The schematic illustration of the p-n junction.
At equilibrium, the built-in-potential
Figure 2.4.64 shows the basic characteristics of the diode at equilibrium.
Figure 2.4.64 Some characteristics are shown across a p-n junction. (a) shows the dopant profile. (b) and (c) are the electric field and the potential across the space charge region, respectively.
Note that we assume the all dopants are ionized in the result to be consistent with Fig. 6.3. in [NelsonPSC2003].
You can see that the electric field is formed within the space change region and the voltage is equivalent to
Figure 2.4.65 shows (a) the band profiles and (b) the carrier densities at equilibrium. bandedges.dat, density_electon.dat, and density_hole.dat are used to produce this figure.
Figure 2.4.65 The band profiles are plotted in (a). The carrier densities are plotted in (b). The hole density is shown in violet, whereas the electron density is in green.
In (a),
Since
and
Thus,
Each parameter corresponds to a value in the table below.
Parameter |
Value |
---|---|
Thus,
From the equation (2.4.4), you can see that the higher the dopant concentration is, the thinner
The derivation of the equations is explained in
Under applied bias
We look into the case of the diode under forward bias. Figure 2.4.66 shows animation of (a) the band profiles, (b) the electric field, and (c) the space charge, respect to the applied bias.

Figure 2.4.66 Some characters, (a) the band profiles, (b) the electric field, and (c) the space charge, respect to the applied bias.
As you see in Figure 2.4.66, the width
As the width
Whereas the current density across the diode is 0 at equilirium, applied bias enables majority carriers to diffuse across the junction. This means that a net current of electrons flow from n to p, and a net current of holes from p to n.
To see the effects of applied bias more clearly, let us look at the band profiles and carrier densities at
Figure 2.4.67 The band profiles are plotted in (a). The carrier densities are plotted in (b). The hole density is shown in violet, whereas the electron density is in green.
The results are consistent with Fig. 6.6. in [NelsonPSC2003] with high accuracy.
The built-in-potential is reduced to
Thus,
This relation can be seen from Figure 2.4.67 (a).
J-V curve
In this section, we sweep forward bias to acquire J-V curve. You can refer to — DEV — I–V characteristic of GaAs p–n junction | 1D/2D/3D to understand how to apply bias in nextnano++.
Figure 2.4.68 shows the J-V curve of the diode. IV_characteristics.dat is used to produce this figure.
Figure 2.4.68 J-V curve of the diode. (i) space charge recombination current region, (ii) diffusion current region, (iii) high-injection region, (iv) series-resistence effect region.
The light-blue curve shows the numerical result in nextnano++.
The violet and orange dashed-dotted curves are acquired analytically. They correspond to
where
where
The parameters used in the expressions above are in the table.
Parameters |
Description (unit) |
Value used for the analytical J-V curve |
---|---|---|
Boltzmann constant (J/K) |
1.3806E-23 |
|
The temperature (K) |
300 |
|
The intrinsic carrier density (cm-3) |
2.318E+6 |
|
The lifetimes of electrons/holes (s) |
3.333 |
|
The diffusion coefficients of electrons/holes (cm2/Vs) |
219.73 / 20.681 |
|
The diffusion lengths of electrons/holes (cm) |
1.4823 |
Attention
- (*) There seems to be some errors related to the units in Fig. 6.7. in [NelsonPSC2003]
Therefore we used the lifetimes as fittig parameters.
The derivation of those equations above are described in
Our result shows the four distinct regions as marked Figure 2.4.68 (region (i), (ii), (iii), (iv)). In the next section, we identify the origins of the appearance of the regions.
Recombination current region
The region (i) is attributed to the recombination current region, where the contribution of
Diffusion current region
The region (ii) is the diffusion current region. The contribution of
High-injection region
With increasing the forward bias towards
Figure 2.4.69 The band profiles are plotted in (a). The carrier densities are plotted in (b). The hole density is shown in violet, whereas the electron density is in green.
Then, the electron density must increase to maintain the neutrality.
As a result,
Because of the law of the junction,
we acquire the equation as follows.
Therefore, the current density becomes roughly proportional to
Series-resistance effect
At large currents, the voltage drop outside the space charge region becomes too large to ignore.
This is equivalent to considering a single resistance (
where
Numerical control
Since we solve the current equation and the poisson equation (explanation: Optoelectronic characterization) self-consistently, we need some techniques to make the calculations more stable.
In this section, we introduce the effects of minimum_density_electrons, minimum_density_holes, maximum_density_electrons, and maximum_density_holes.
You should also check Convergence.
In Figure 2.4.68, we divide the simulation scheme into 3, depending on the magnitudes of minimum and maximum carrier densities (scheme (A), (B), and (C)).
Scheme (A):
First, the code below defines the magnitudes of the minimum and maximum carrier densities.
Note that we use the variables $min_density
and $max_density
for convenience.
178currents{
179 minimum_density_electrons = $min_density
180 minimum_density_holes = $min_density
181 maximum_density_electrons = $max_density
182 maximum_density_holes = $max_density
183
184}
Usually, you can set the values of $min_density_*
and $max_density_*
by referring to bias_XXXXX\density_electon.dat and bias_XXXXX\density_hole.dat.
In the scheme (C), the maximum electron and hole densities are about 1.0E+20
.
Similarly, you can set $minimum_density_*
.
Since the minimum electron and hole densities are about $minimum_density_electrons = 1.0E-2
and $minimum_density_holes = 1.0E-2
are enough low to evaluate the current density accurately.
Note that
In the scheme (B), $minimum_density_electrons = 1.0E-2
and $minimum_density_holes = 1.0E-2
is enough low as well.
However, you have to take care of the magnitude of $minimum_density_*
.
Figure 2.4.70 (a) shows the effect of the magnitude of $minimum_density_*
on the current density under
Figure 2.4.70 The effect of the magnitude of $minimum_density_*
on the current density. (a) is under
Although the current density has to be constant through the diode, it becomes unstable at minimum_density_*
set to 1.0E+16
and minimum_density*_
set to 1.0E+20
.
Thus, you should set $minimum_density_*
to 1.0E+15
, which shows the constant current density.
In the scheme (A), the same techniques should be applied.
Figure 2.4.70 (b) shows the effect of the magnitude of $maximum_density_*
on the current density under maximum_density_*
should be set to 1.0E+12
to keep the current density constant through the diode.
Exercises
under construction
Last update: 16/07/2024