19. Diodes and Jupyter Notebook example

19.1. Objective

The purpose of this activity is to investigate the current vs. voltage characteristics of various solid state PN junction diodes such as the conventional Si diode, the Schottky barrier diode, the Zener diode and Light emitting diode (LED).

19.2. Notes

In this tutorials we use the terminology taken from the user manual when referring to the connections to the Red Pitaya STEMlab board hardware.

Extension connector pins used for -3.3V and +3.3V voltage supply are show in the documentation here.

Oscilloscope & Signal generator application is used for generating and observing signals on the circuit.

19.3. Background

The PN junction diode is a device which is commonly used in circuit applications such as rectification where current is allowed to flow in only one direction. When the diode is fabricated in silicon, the forward voltage drop is typically 0.7 V and the \({V_D}\) vs. \({I_D}\) characteristic relating diode voltage and current can be described by an exponential relationship:

\[I_D = I_S \bigg( e^{\frac{V_Dq}{nkT}} - 1 \bigg) \quad (1)\]

where \(I_{S}\) and n are scale factors, and \(kT/q\) (25.4 mV at room temperature) is the so called thermal voltage \({V_T}\).

19.4. Diode schematic symbols

Each type of diode has a specific schematic symbol which are variations of the conventional diode symbol shown on the left in figure 1. A sort of “Z” shaped cathode denotes a zener diode as in the second symbol in figure 1. An “S” shaped cathode denotes a Schottky diode as in the next symbol. The arrows pointing away from the diode denotes an LED as in the symbol on the right. Arrows pointing toward the diode would represent a photo diode light detector.

_images/Activity_19_Fig_01.png

Figure 1: Diode schematic symbols

19.5. Zener Diode Fundamentals

A Zener diode is similar in construction and operation to an ordinary diode. Unlike a conventional diode where the intended use is to prevent current in the reverse direction, a zener diode is mostly used in the reverse region above the breakdown voltage. Its \(I\) vs, \(V\) characteristic curve is similar to ordinary diode. By adjusting the doping of the P and N sides of the junction, it is possible to design a Zener diode that breaks down at anywhere from a few volts to a few hundred volts. See Figure 2. In this breakdown or zener region the diode voltage will remain approximately constant over a wide range of currents. The maximum reverse-bias potential that can be applied before entering the Zener region is called the Peak Inverse Voltage (PIV) or the Peak Reverse Voltage (PRV).

_images/Activity_19_Fig_02.png

Figure 2: Forward and reverse zener diode \(I/V\) characteristic

At voltages above the onset of breakdown, an increase in applied voltage will cause more current to flow in the diode, but the voltage across the diode will stay very nearly at \(V_Z\). A Zener diode operated in reverse breakdown can provide a reference voltage for systems like voltage regulators or voltage comparators.

19.6. Schottky Diode Fundamentals

A Schottky barrier diode uses a rectifying metal-semiconductor junction formed by plating, evaporating or sputtering one of a variety of metals onto n-type or p-type semiconductor material. Generally, n-type silicon and n-type GaAs are used in commercially available Schottky diodes. The properties of a forward biased Schottky barrier diode are determined by majority carrier phenomena. A conventional PN junction diode’s properties are determined by minority carriers. Schottky diodes are majority carrier devices that can be switched rapidly from forward to reverse bias without minority carrier storage effects.

The normal current vs. voltage \(I/V\) curve of a Schottky barrier diode resembles that of a PN junction diode with the following exceptions:

  1. The reverse breakdown voltage of a Schottky barrier diode is lower and the reverse leakage current higher than those of a PN junction diode made using the same resistivity semiconductor material.
  2. The forward voltage at a specific forward current is also lower for a Schottky barrier diode than for a PN junction diode. For example, at 2 mA forward bias current a low barrier silicon Schottky diode will have a forward voltage of ~0.3 volts while a silicon PN junction diode will have a voltage of ~0.7 volts. This lower forward voltage drop can cut the power dissipated in the diode by more than one half. This power savings can be very significant when the diodes need to carry large forward currents. The current vs. voltage (\(I/V\)) relationship for a Schottky barrier diode is given by the following equation known as the Richardson equation. The primary difference from the conventional diode equation is in \(I_S\) with the addition of the modified Richardson constant \(A^*\).
\[I_D = I_S \bigg( e^{\frac{V_Dq}{nkT}} - 1 \bigg) \quad (2)\]
\[I_S = A A^* T^2 e^{-\frac{q \Phi B}{kT}} \quad (3)\]

Where:

  • \(A\) = junction area
  • \(A^*\) = modified Richardson constant (value varies by material and dopant) = \(110 A/(°K^2-cm^2)\) for n-type Si
  • \(T\) = absolute temperature in \(K\) (Kelvins)
  • \(q\) = electronic charge = \(1.6E-19 \quad C\)
  • \(\Phi B\) = barrier height in volts k = Boltzman’s constant = 1.37 * 10-23 J/K = \(1.37E-23 \quad J/K\)
  • \(n\) = ideality factor (forward slope factor, determined by metal-semiconductor interface)

19.7. LED Fundamentals

The LED is a junction diode that emits light when forward biased. Actually all PN junction diodes emit photons when forward biased, it is just that the photons are in the infrared band and the physical shape of the diode does not allow the photons to escape the package. To achieve the visible light emitting property, it is necessary to fabricate the LED from materials with larger band-gaps other than silicon. As a result, the forward voltage drop of the LED is greater than 0.7V; usually on the order of 1.5 to 2 volts depending on the wavelength of the emitted light. The LED is also built in a special transparent package as shown in figure 3.

_images/Activity_19_Fig_03.png

Figure 3: Light emitting diodes

An LED is a semiconductor device that emits electromagnetic radiation at optical and infrared frequencies. The device is a PN junction diode made from p-type and n-type semiconductors, usually GaAs, GaP or SiC. They emit light only when an external applied voltage is used to forward bias the diode above a minimum threshold value. The gain in electrical potential energy delivered by this voltage is sufficient to force electrons to flow out of the n-type material, across the junction barrier, and into the p-type region. This threshold voltage for the onset of current flow across the junction and the production of light is \(V_0\). The emission of light occurs after electrons enter into the p-region (and holes into the n-region). These electrons are a small minority surrounded by holes (essentially the anti-particles of the electrons) and they will quickly find a hole to recombine with. Energetically, the electron relaxes from the excited state (conduction band) to the ground state (valence band). The diodes are called light emitting because the energy given up by the electron as it relaxes is emitted as a photon. Above the threshold value, the current and light output increases exponentially with the bias voltage across the diode. The quanta of energy or photon has an energy E = hf. The relation between the photon energy and the turn-on voltage \(V_0\), is:

\[eV_0 = E_g = hf = \frac{hc}{\lambda} \quad (4)\]

where:

  • \(E_g\) is the size of the energy gap
  • \(V_0\) is the threshold voltage
  • \(f\) and \(\lambda\) are the frequency and wavelength of the emitted photons
  • \(c\) is the velocity of light
  • \(e\) is the electronic charge
  • \(h\) is Planck’s constant

19.7.1. Experiments

19.8. PN junction diode VI characteristic

The current vs. voltage characteristics of the PN junction diode can be measured using the STEMlab and the following connections shown in figure 4. Set up the breadboard with the generator OUT1 channel output attached to one end of the resistor. The other end of the resistor is connected to one end of the diode being measured as shown in the diagram. The inputs channels IN1 and IN2 are also connected different ends the resistor, therefore diode current and voltage will be given as:

\[ \begin{align}\begin{aligned}I_d = (IN_1 - IN_2) / R_1\\.\\V_d = IN_2\end{aligned}\end{align} \]
_images/Activity_19_Fig_04.png

Figure 4: Connection diagram for diode I vs. V curves

For measuring current vs. voltage characteristics of the PN junction diode OUT1 generator should be configured as 1kHz triangle wave with 1 V max and 0 V min values. For measuring \(VI\) curve an “XY” plot is required where x-axis will represent diode voltage \(IN_2\) and y-axis a diode current \((IN_1 - IN_2) / R_1\). For this task we will use Jupyter Notebook Web application.

Note

The Jupyter Notebook is a web application that allows you to create and share documents that contain live code, equations, visualizations and explanatory text. They have also ensured support for the Jupyter application with Red Pitaya libraries enabling control of all features of the STEMlab boards such as: signal acquisition, signal generation, digital signal control, communication etc. The Jupyter Notebook is started on the same way as any other applications. After starting Jupyter application a web based notebook is opened. This combination of the notebook, STEMlab and Python features makes the STEMlab an excellent tool for prototyping and quick programing. Since Jupyter Notebook enables text, equation and picture editing this is a perfect tool for tutorials, examples etc.

But before measuring \(VI\) curve you should check voltages signals using Oscilloscope & Signal generator application.

19.9. Materials

  • Solder-less Breadboard
  • Resistor 10 Ω
  • Conventional diode (1N4001 or similar)

19.10. Procedure - time domain measurements

  1. Build the circuit from figure 4 on the breadboard
_images/Activity_19_Fig_05.png

Figure 5: Connections on the breadboard

  1. Start the Oscilloscope & Signal generator application
  2. In the OUT1 settings menu set Amplitude value to 0.5V, DC offset to 0.5V to apply a triangle wave as the input voltage. From the waveform menu select TRIANGLE, deselect SHOW button and select enable.
  3. On the left bottom of the screen be sure that IN1 V/div is set to 200mV/div (You can set V/div by selecting the desired channel and using vertical +/- controls)
  4. On the left bottom of the screen be sure that IN2 V/div is set to 200mV/div (You can set V/div by selecting the desired channel and using vertical +/- controls)
  5. Set t/div value to 200us/div (You can set t/div using horizontal +/- controls)
  6. In the MATH settings menu set IN1-IN2 and select enable. Math trace scaled by factor R1 represent diode current
_images/Activity_19_Fig_06.png

Figure 6: Voltages and current on the diode (Time dependent)

From figure 6 we can see that diode start conducting when the voltage on it exceed diode threshold voltage which is around 0.6V.

Also, diode current represented with MATH trace is observable. We can clearly see that when the diode voltage is below 0.6 the diode current is 0A. At point when the diode voltage exceed 0.6V diode starts conducting and the path current is only limited by resistor R1.

19.11. Procedure - VI characteristics measurements

For this task we will use Jupyter Notebook Web application. How to start Jupyter Notebook and create new project is shown on figure 7 flow chart.

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Figure 7: Creating new Jupyter notebook

If you have successfully created new Jupyter notebook then copy-paste code bellow and run it. Code bellow will generate same signal as from figure 6 but it will plot them in XY graph. For measuring \(VI\) curve an “XY” plot is required where x-axis will represent diode voltage \(IN_2\) and y-axis a diode current \((IN_1 - IN_2) / R_1\).

Note

Copy code from below into cell 1

# Import libraries
from redpitaya.overlay.mercury import mercury as overlay

from bokeh.io import push_notebook, show, output_notebook
from bokeh.models import HoverTool, Range1d, LinearAxis, LabelSet, Label
from bokeh.plotting import figure, output_file, show
from bokeh.resources import INLINE
output_notebook(resources=INLINE)

import numpy as np

# Initialize fpga modules
fpga = overlay()
gen0 = fpga.gen(0)
osc = [fpga.osc(ch, 1.0) for ch in range(fpga._MNO)]

# Configure OUT1 generator channel
gen0.amplitude = 0.5
gen0.offset = 0.5
gen0.waveform = gen0.sawtooth(0.5)
gen0.frequency = 2000
gen0.start()
gen0.enable = True
gen0.trigger()

# R1 resistor value
R1 = 10

# Configure IN1 and IN2 oscilloscope input channels
for ch in osc:
ch.filter_bypass = True
# data rate decimation
ch.decimation = 10
# trigger timing [sample periods]
N = ch.buffer_size
ch.trigger_pre  = 0
ch.trigger_post = N
# osc0 is controlling both channels
ch.sync_src = fpga.sync_src["osc0"]
ch.trig_src = fpga.trig_src["osc0"]
# trigger level [V], edge ['neg', 'pos'] and holdoff time [sample periods]
ch.level = 0.5
ch.edg = 'pos'
ch.holdoff = 0

# Initialize diode current and voltage
V = I = np.zeros(N)

# Plotting
hover = HoverTool(mode = 'vline', tooltips=[("V", "@x"), ("I", "@y")])
tools = "wheel_zoom,box_zoom,reset,pan"
p = figure(plot_height=500, plot_width=900,
           title="XY plot of diodes VI characteristic",
           toolbar_location="right",
           tools=(tools, hover))
p.xaxis.axis_label = 'Voltage [V]'
p.yaxis.axis_label = 'Current [mA]'
r = p.line(V,I, line_width=1, line_alpha=0.7, color="blue")

# get and explicit handle to update the next show cell
target = show(p,notebook_handle=True)

Create new cell (Insert -> Cell Below) and copy code from below into it.

# Measuring I, V and re-plotting
while True:
# reset and start
osc[0].reset()
osc[0].start()
# wait for data
while (osc[0].status_run()): pass
V0 = osc[0].data(N-100)  # IN1 signal
V1 = osc[1].data(N-100)  # IN2 signal
I=((V0-V1)/R1)*1E3     # 1E3 convert to mA
r.data_source.data['x'] = V0
r.data_source.data['y'] = I
push_notebook(handle=target)

Run Cell 1 and Cell 2. Notice cell 2 is a main loop for the acquisition and re-plotting. If you stop the acquisition just run only cell 2 for starting measurements again.

After running the code above you should get diode VI characteristic as is shown on figure 8.

_images/Activity_19_Fig_08.png

Figure 8: Didoes VI characteristic measured using Jupyter Notebook

From the figure 8 the typical diode VI characteristic is shown. From the figure 8 we can see that, as the voltage on the diode is increasing (from 0-0.5V) the diode current stays near zero until voltage reaches values near threshold voltage (~0.6V). At this point diode is “turned on” and the path current (diode current) is only limited by resistor R1. In case when the diode voltage is decreasing the VI curve is not the same, resulting in the diode hysteresis. Upper curve from figure 8 shows that once the diode was “turned on” the lower diode voltage will cause higher current than in the case when the diode was previously “turned off”. An ideal diode would not have hysteresis i.e the diode current would be independent of previous diode states but only on the diode voltage.

Note

Try to answer on what is causing diode hysteresis?