Table of Contents
Introduction
The PN junction diode is one of the most fundamental components in electronics. Understanding how it is created—starting from doping, depletion region formation, and biasing—provides essential insight into how it controls current flow. This blog explores the step-by-step process of diode formation and concludes with the mathematical explanation of current flow using the Shockley diode equation.
Doping and Formation of Extrinsic Semiconductors
Formation of Donor and Acceptor energy level
In n-type materials, each pentavalent atom forms four covalent bonds with the surrounding silicon atoms. The fifth valence electron remains unbonded and is loosely bound to the atom. At room temperature, this electron gains sufficient thermal energy and moves into the conduction band, becoming a free carrier. As a result, the pentavalent atoms are known as donor atoms because they donate free electrons to the conduction band. as we have seen in this blog Doping introduces discrete energy levels within the band gap of the semiconductor. In n-type semiconductors, a donor energy level is formed by this discrete energy levels just below the conduction band. At the donor level, atoms can easily donate an extra electron to the conduction band with minimal thermal energy, increasing the number of free electrons, thereby making the material n-type.
In p-type materials, each trivalent atom forms three covalent bonds with the silicon atom, leaving one bond incomplete, which results in the formation of a hole. An electron from a nearby silicon atom fills this hole, and in doing so, the trivalent atom accepts an electron and becomes an acceptor atom. In p-type semiconductors, an acceptor energy level is formed just above the valence band. In p-type materials, electrons from the valence band fill the incomplete bond of the acceptor atoms, resulting in the formation of holes, which act as the majority charge carriers. Thereby making the material p-type.
Formation of Donor and Acceptor Ions
Two important phenomena occur during the doping process:
A donor ion is a positively charged ion formed when a donor atom loses its fifth electron to the conduction band. This ion remains fixed in the crystal lattice and contributes to the internal electric field of the semiconductor.
An acceptor ion is a negatively charged ion formed when an acceptor atom accepts an electron from the valence band of a nearby silicon atom. It also remains immobile in the lattice.
Although these ions do not move, they play a critical role in shaping the electric field and charge distribution within the semiconductor device.
Majority and Minority Carriers in Intrinsic and Extrinsic Semiconductors
In an intrinsic semiconductor (pure material), a small number of free electrons are present due to thermal energy and residual impurities introduced during the manufacturing process. These free electrons leave behind holes in the covalent bonds. As a result, the number of free electrons and holes are equal and very small.
When the material is doped:
In an n-type semiconductor, the number of free electrons increases significantly due to donor atoms, while the number of holes remains nearly the same as in the intrinsic material. so electrons are the majority carriers, and holes are the minority carriers.
In a p-type semiconductor, the number of holes increases due to acceptor atoms, while the number of free electrons remains nearly unchanged. Holes are the majority carriers, and electrons are the minority carriers.
PN Junction Diode – Bias Conditions Explained
When n-type and p-type materials are joined to form a PN junction, electrons (majority carriers in n-type) diffuse into the p-type region, and holes diffuse into the n-type region. This diffusion (movement from high to low concentration without external force) leaves behind immobile donor and acceptor ions, creating a depletion region at the junction. The resulting internal electric field opposes further diffusion, and the system reaches equilibrium, this is the no-bias condition.
Forward Bias
When a positive voltage is applied to the p-side and negative to the n-side, majority carriers are pushed toward the junction. They enter the depletion region and neutralize fixed ions, causing the depletion region to narrow. This allows a large current to flow, and the diode conducts, known as forward bias.
Reverse Bias
When the positive terminal is connected to the n-side and the negative to the p-side, majority carriers are pulled away from the junction, exposing more fixed ions and widening the depletion region. Very few carriers remain to neutralize the fixed charge, and only a tiny leakage current (from minority carriers) flows. This is the reverse bias condition, where the diode does not conduct.
Shockley's Equation For General Characteristics of Semiconductor Diode
Before going to Shockley’s equation we need to understand smaller units of ampere and vlot.
milliampere = \(10^{-3} A\) = 0.001 A = denoted as mA
microampere = \(10^{-6} A\) = 0.000001 A = denoted as \(\mu A\)
Nanoampere = \(10^{-9} A\) = 0.000000001 A = denoted as nA
Picoampere = \(10^{−12}A\) = 0.000000000001 A = denoted as pA
millivolt = \(10^{-3} V\) = 0.001 V = denoted as mV
microvolt = \(10^{-6} V\) = 0.000001 V = denoted as \(\mu V\)
nanovolt = \(10^{-9} V\) = 0.000000001 V = denoted as nV
Characteristics of semiconductor diod is defined by shockley’s equation
\[I_d = I_s(e^{V_d/n.V_T}-1)\]
\(I_d\) = diode current = unit in ampere A
\(V_d \)= voltage across the diode
n = Ideality factor = range from 1 to 2.
\(I_s\) = reverse saturation current ( the current due to minority carrier in reverse bias) typically in Nanoampere range.
\(V_T \)= thermal voltage with Unit Volt V.
\[V_T = \frac {k\cdot T}{q}\]
q = charge of an electron \(1.6 \times 10^{-19} C\)
k = Boltzmann constant ( it is used because semiconductors are temperature-sensitive and electrons get energy from heat to jump from the valence band to the conduction band.)
= \(1.38 \times 10 ^{-23} J/K \)(Joules per Kelvin)
= \(8.617 \times 10^{-5} eV/K\)
T = temperature in Kelvin = 273 + temp in \(^{\circ}C\)
Question
At \(33^{\circ}C\), what will be the Thermal voltage \(V_T\)?
Answer
T in kelvin = \(273 + 33^{\circ}C\) = 306 kelvin
k= \(1.38 \times 10 ^{-23}\) J/K
q= \(1.6 \times 10^{-19} C\)
\(V_T= \frac{(1.38 \times 10 ^{-23} J/K \times 306 kelvin)}{ 1.6 \times 10^{-19} C}\)
= \(\frac{1.38 \times 306 \times 10^{-23}) J }{(1.6 \times10^{-19}) C}\)
= \(\frac{422.28 \times 10^{-4} J}{ 1.6 C}\)
=\(263.925 \times 10^{-4} V\)
= \(26.3925 \times 10^{-3 }V\) =\(26.3925 mV\)
Conclusion
From the atomic level doping of semiconductors to the creation of depletion regions and carrier movement under different biasing conditions, the behavior of a diode is both fascinating and critical in electronics. The Shockley equation captures this behavior mathematically, offering a precise way to predict diode current based on applied voltage. A solid understanding of these concepts builds the foundation for exploring more advanced electronic devices and circuits. If yoy find this blog helpful, please write to us.
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