diode-characteristic-curve.py

#r# This example shows how to simulate and plot the characteristic curve of a diode.
#r#
#r# Theory
#r# ------

#r# A diode is a semiconductor device made of a PN junction which is a sandwich of two doped silicon
#r# layers.

#f# tikz('diode.tex', width=500)

#r# Before two explains the purpose of the silicon doping.  We will give a quick and simplified look
#r# on the atomic world.  An atom is made of the same number of protons and electrons, this number
#r# is so called Z and characterise the atom.  Each electron is coupled to the proton's kernel by
#r# the electromagnetic interaction, but with different levels of energy.  The reason is due to the
#r# fact each electron screens each other.  There is thus some electrons which are strongly coupled
#r# and other ones which are weakly coupled, so called valence's electrons.  An atom is a neutral
#r# object when we observe it at a large distance, but when the pressure and temperature of the
#r# environment match some conditions, the weakly coupled electrons can be shared with atoms in the
#r# neighbourhood and create the electromagnetic interaction between atoms which make the cohesion
#r# of the matter.

#r#
#r# Depending on the weakness of the electrons, an atom can be an insulated material or a conductor.
#r# Semiconductors are between them.

#r#
#r# The doping consists to diffuse a small quantities of atoms with a larger or smaller number of
#r# valence electron in a silicon layer.  Since a silicon atom has four valence electrons, we use
#r# atoms having 3 or 5 valence electrons for the doping.  A doping using a larger number of valence
#r# electrons is called N for negative, and P respectively.  In a silicon lattice doped with atoms
#r# having a larger number of valence electrons, the additional electrons do not participate to the
#r# lattice cohesion and are weakly coupled to the atoms.  The conductivity is thus improved.  In
#r# other hands, a silicon lattice doped with atoms having a smaller number of valence electrons,
#r# some electrons are missing for the lattice cohesion.  These missing electrons are called holes
#r# since the P doping atoms will catch free electrons so as to normalise the lattice cohesion.

#r#
#r# When we make a sandwich of P and N doped silicon layers, the weak electrons of the N layer
#r# diffuse to the P layer until an equilibrium state is achieved.  Indeed this diffusion creates a
#r# depletion region which acts as a barrier to the electrons, since a P doping atom becomes negative
#r# (anion) when it catches an electron and reciprocally a N doping atom becomes positive (cation)
#r# when it lost an electron.  The depletion region is thus a kind of capacitor.

#r#
#r# The volume of the depletion region can be changed by applying a tension across the PN junction.
#r# If the tension between the PN junction is negative then the depletion region is enlarged, and
#r# only a very small current can flow through the junction due to the thermal agitation.  But if we
#r# apply a positive tension, the depletion region is pressurised, and if it reaches a threshold, an
#r# electron flow will be able to pass through the junction.

#r#
#r# A PN junction can thus only conduct a current from the anode to the cathode and only if a
#r# minimal bias tension is applied across it.

#r#
#r# However if a large enough inverse tension is applied to the junction then the electrostatic
#r# force will become sufficiently large enough to pull off electrons across the junction and the
#r# current will flow from the cathode to the anode. This effect is called breakdown.

#r#
#r# Simulation
#r# ----------

####################################################################################################

import numpy as np
import matplotlib.pyplot as plt
import matplotlib.ticker as ticker

####################################################################################################

import PySpice.Logging.Logging as Logging
logger = Logging.setup_logging()

####################################################################################################

from PySpice.Doc.ExampleTools import find_libraries
from PySpice.Spice.Netlist import Circuit
from PySpice.Spice.Library import SpiceLibrary
from PySpice.Unit import *
from PySpice.Physics.SemiConductor import ShockleyDiode

####################################################################################################

libraries_path = find_libraries()
spice_library = SpiceLibrary(libraries_path)

####################################################################################################

#r# For this purpose, we use the common high-speed diode 1N4148.  The diode is driven by a variable
#r# voltage source through a limiting current resistance.

#f# circuit_macros('diode-characteristic-curve-circuit.m4')

circuit = Circuit('Diode Characteristic Curve')

circuit.include(spice_library['1N4148'])

circuit.V('input', 'in', circuit.gnd, 10@u_V)
circuit.R(1, 'in', 'out', 1@u_Ω) # not required for simulation
circuit.X('D1', '1N4148', 'out', circuit.gnd)

#r# We simulate the circuit at these temperatures: 0, 25 and 100 °C.

# Fixme: Xyce ???
temperatures = [0, 25, 100]@u_Degree
analyses = {}
for temperature in temperatures:
    simulator = circuit.simulator(temperature=temperature, nominal_temperature=temperature)
    analysis = simulator.dc(Vinput=slice(-2, 5, .01))
    analyses[float(temperature)] = analysis

####################################################################################################

#r# We plot the characteristic curve and compare it to the Shockley diode model:
#r#
#r# .. math::
#r#
#r#     I_d = I_s \left( e^{\frac{V_d}{n V_T}} - 1 \right)
#r#
#r# where :math:`V_T = \frac{k T}{q}`
#r#
#r# In order to scale the reverse biased region, we have to do some hack with Matplotlib.
#r#

silicon_forward_voltage_threshold = .7

shockley_diode = ShockleyDiode(Is=4e-9, degree=25)

def two_scales_tick_formatter(value, position):
    if value >= 0:
        return '{} mA'.format(value)
    else:
        return '{} nA'.format(value/100)
formatter = ticker.FuncFormatter(two_scales_tick_formatter)

figure, (ax1, ax2) = plt.subplots(2, figsize=(20, 10))

ax1.set_title('1N4148 Characteristic Curve ')
ax1.set_xlabel('Voltage [V]')
ax1.set_ylabel('Current')
ax1.grid()
ax1.set_xlim(-2, 2)
ax1.axvspan(-2, 0, facecolor='green', alpha=.2)
ax1.axvspan(0, silicon_forward_voltage_threshold, facecolor='blue', alpha=.1)
ax1.axvspan(silicon_forward_voltage_threshold, 2, facecolor='blue', alpha=.2)
ax1.set_ylim(-500, 750) # Fixme: round
ax1.yaxis.set_major_formatter(formatter)
Vd = analyses[25].out
# compute scale for reverse and forward region
forward_region = Vd >= 0@u_V
reverse_region = np.invert(forward_region)
scale =  reverse_region*1e11 + forward_region*1e3
#?# check temperature
for temperature in temperatures:
    analysis = analyses[float(temperature)]
    ax1.plot(Vd, - analysis.Vinput * scale)
ax1.plot(Vd, shockley_diode.I(Vd) * scale, 'black')
ax1.legend(['@ {} °C'.format(temperature)
            for temperature in temperatures] + ['Shockley Diode Model Is = 4 nA'],
           loc=(.02,.8))
ax1.axvline(x=0, color='black')
ax1.axhline(y=0, color='black')
ax1.axvline(x=silicon_forward_voltage_threshold, color='red')
ax1.text(-1, -100, 'Reverse Biased Region', ha='center', va='center')
ax1.text( 1, -100, 'Forward Biased Region', ha='center', va='center')

#r# Now we compute and plot the static and dynamic resistance.
#r#
#r# .. math::
#r#
#r#   \frac{d I_d}{d V_d} = \frac{1}{n V_T}(I_d + I_s)
#r#
#r# .. math::
#r#
#r#   r_d = \frac{d V_d}{d I_d} \approx \frac{n V_T}{I_d}

ax2.set_title('Resistance @ 25 °C')
ax2.grid()
ax2.set_xlim(-2, 3)
ax2.axvspan(-2, 0, facecolor='green', alpha=.2)
ax2.axvspan(0, silicon_forward_voltage_threshold, facecolor='blue', alpha=.1)
ax2.axvspan(silicon_forward_voltage_threshold, 3, facecolor='blue', alpha=.2)
analysis = analyses[25]
static_resistance = -analysis.out / analysis.Vinput
dynamic_resistance = np.diff(-analysis.out) / np.diff(analysis.Vinput)
ax2.semilogy(analysis.out, static_resistance, base=10)
ax2.semilogy(analysis.out[10:-1], dynamic_resistance[10:], base=10)
ax2.axvline(x=0, color='black')
ax2.axvline(x=silicon_forward_voltage_threshold, color='red')
ax2.axhline(y=1, color='red')
ax2.text(-1.5, 1.1, 'R limitation = 1 Ω', color='red')
ax2.legend(['{} Resistance'.format(x) for x in ('Static', 'Dynamic')], loc=(.05,.2))
ax2.set_xlabel('Voltage [V]')
ax2.set_ylabel('Resistance [Ω]')

plt.tight_layout()
plt.show()

#f# save_figure('figure', 'diode-characteristic-curve.png')

#r# We observe the forward voltage threshold increase with the temperature.
#?# #r# Indeed the thermal agitation overcome the electron flow.