Assistant Professor, Department of Physics, Narajole Raj College, Narajole.
Paper: C10T (Analog Systems and Applications) Topic: Semiconductor Diodes
In the previous E-material of C10T, we have discussed the basic properties of semiconductors. In that we have also introduced intrinsic semiconductors and extrinsic (n-type and p-type) semiconductors briefly. Today, we will learn more about the n-type and p-type semiconductors, their energy level diagrams and the current flow mechanisms in them.
At the beginning we are going to define some important parameters like
“effective mass”, “drift velocity”, “recombination” etc. so that we understand the latter part of the discussion without any difficulty.
Effective Mass:
The charge carriers i.e. the electrons and holes in a crystal experience forces due to the internal periodic field (majorly the effective Coulomb field) produced by the crystal. When an external field weaker than the internal one is applied to the crystal, the internal field modifies the mass of the carriers in such a way that the carriers follow the classical force-acceleration relation with the modified mass under the external field. This modified mass is called the effective mass of the carrier. In many cases, the effective mass (meff) of a carrier differs very significantly from the electronic mass in vacuum i.e. the rest mass (m 0). The effective mass approximation makes our life easy in the study of the carrier transport and other electronic properties of a crystal by solving these quantum mechanical problems semi-classically.
Drift of Charge Carriers in an External Field:
Normally in a semiconductor, electrons in the conduction band and holes in the valence band move around randomly due to their thermal energy. When the semi - Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Effective Mass, Drift of Charge Carriers
conductor is under an external electric field, free electrons and holes try to align themselves along the field lines as opposed to their random thermal agitations.
The free electrons move in the direction of the applied field and the holes move opposite to the field direction, both producing electric currents in the same direction as they are of opposite charges. This aligned movement of the carriers in an external electric field is called drift of the carriers and the velocity with which the carriers move is called drift velocity. The drift velocities of electrons and holes are represented by vde and vdh respectively and are shown in the figure above.
Recombination of Electrons and Holes:
Recombination is the process of an electron-hole pair getting destroyed in a semiconductor. When a free electron in the conduction band jumps down to the valence band and combines with a hole, the pair which was earlier contributing to the conduction is destroyed and an energy equal to the bandgap of the semiconductor is released in the form of electromagnetic (EM) radiation. If 𝛎(or 𝛌) be the frequency (or wavelength) of the EM radiation and E gbe the bandgap of the semiconductor then
Eg = h𝛎 = hc/𝛌
where h is Planck’s constant = 6.626 x 10-34 J s and c is the speed of light.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Drift Velocity, Recombination
Dept. of Physics, Narajole Raj College, Narajole.
The recombination and generation of e-h pairs are shown in the cartoon diagram below.
The rate of recombination is proportional to the product of the electron concentration and hole concentration. Though some electron-hole pairs are destroyed in the process of recombination, some pairs are generated through the thermal excitations. For an intrinsic semiconductor at a fixed temperature, the rate of recombination is the same as that of thermal excitations so that the electron and hole concentrations remain constant at their thermal equilibrium values. But the electron and hole concentrations increase as the temperature of the semiconductor increases.
Energy Level Diagrams for Extrinsic Semiconductors
We have already introduced extrinsic semiconductors and their types namely n-type and p-type semiconductors in the previous E-material. Here we will mainly talk about the energy level diagrams of n-type and p-type semiconductors which are very important to understand the physics of the p-n junction diodes.
n-type Semiconductor:
When a small amount of pentavalent (group V) element like P, As or Sb is added to a tetravalent pure semiconductor like Ge or Si, there is excess of electrons in the crystal. Such impurity is called the donor as it donates one electron to the conduction band and the doped semiconductor is called n-type semiconductor.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Energy Level Diagrams
When donor impurities are added to a pure semiconductor an allowed energy level which corresponds to the loosely bound valence electron of the donor atom is introduced in the forbidden gap. As the amount of impurity in a semiconductor is usually very low, the impurity atoms are far apart from each other making the interactions among themselves negligible small. So this level remains a discrete one situated just below the conduction band and we call it a donor level. The energy level diagram of an n-type semiconductor is shown below.
Typically, a donor level is about 0.01 eV to 0.1 eV below the conduction band edge. The exact value depends on the type of the impurity and also the host.
The thermal energy at room temperature is sufficient enough to excite the donor electrons to the conduction band and ionizes practically all the donor atoms. Thus, in an n-type semiconductor, electrons are the majority carriers.
p-type Semiconductor:
When a small amount of trivalent (group III) element like Al, Ga or In is added to a tetravalent pure semiconductor like Ge or Si, there is excess of holes in the material. Such impurities are called theacceptors as they accept electrons from the neighbouring Ge or Si atoms, creating holes there. This kind of doped semiconductor is called a p-type semiconductor.
The discrete energy level due to the acceptor impurities in a semiconductor is introduced just above the valence band. This allowed energy level is known as acceptor level.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Energy Level Diagrams
Dept. of Physics, Narajole Raj College, Narajole.
The energy level diagram of a p-type semiconductor is shown in the figure below.
The exact position of the acceptor level depends on the impurity type and the host semiconductor. Typically, it lies around 0.01 - 0.1 eV above the valence band.
At room temperature, most of the acceptor atoms are ionized as the electrons from the valence band get excited to the acceptor level due to the thermal energy. So, the holes are generated in the valence band in large numbers. Thus in a p-type semiconductor, the holes become the majority carriers and the free electrons become the minority carriers.
Fabrication of p-n Junction Diode
A p-n junction diode is fabricated by doping one side of a single crystal with acceptors and the other side with donors. There are two types of p-n junction diodes - (i) step-graded or abrupt p-n junction and (ii) linearly graded p-n junction.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Fabrication of p-n Junction Diode
In a step-graded p-n junction diode, the acceptor and the donor concentrations are constants up to the junction. A step-graded junction diode can be made by placing a small pellet of a trivalent impurity like aluminium on one side of a wafer of n-type silicon and heating the system up to a high temperature for a short period of time. In this process, aluminium gets dissolved in the silicon and one side of the wafer transforms from n-type to p-type. That’s how a step-graded p-n junction diode is fabricated.
However, in a linearly-graded p-n junction diode, the acceptor/ donor concentration varies linearly with the distance from the junction. This kind of junction is fabricated by drawing a single crystal from a melt of silicon containing one type of impurity initially. And once the crystal is drawn the other type of impurity is added at a controlled rate to change the type of the semiconductor in a continuous manner. The precise control of the impurity concentrations can be obtained by solid state diffusion method. In this method, p-type impurities are diffused into an n-type single crystal in the form of a substrate. That is how a linearly-graded p-n junction diode is fabricated in a lab/industry.
Unbiased p-n Junction Diode
An unbiased p-n junction diode is schematically presented in the figure below. We have shown here only majority carriers of both sides and the positive and negative ions. As there is a concentration gradient across the junction, the electrons will initially diffuse through the junction from n-type to p-type and the holes diffuse other way around. So, near the junction the electrons and the holes recombine with each other and as a result the acceptor ions in the p-side and the donor ions in the n-side become unneutralized. These unneutralized ions near the junction are called uncovered charges. These positive and the negative uncovered charges produce an electric field across the junction which is directed from n-side to p-side. This field is known as the barrier field and is shown in the figure below. This barrier field opposes the diffusion of the majority carriers (i.e electrons and holes) through the junction.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Unbiased p-n Junction Diode
Dept. of Physics, Narajole Raj College, Narajole.
When the barrier field is just sufficient to prevent the further diffusion of the majority carriers, an equilibrium will be established and there will be no further movement of the majority carriers across
the junction. As the vicinity of the junction is depleted of the mobile charges, it is called the depletion region or the space-charge region.
The variations of acceptor and donor concentrations are shown in figure (b). The acceptor and donor concentrations reduce from a constant value at two sides to zero at the junction.
The hole concentration and the electron concentration are shown in (c). The mobile charge (holes or electrons) concentration is zero in the depletion region.
The variation of uncovered charge density is presented in (d). It is negative in the p-side, zero at the junction and positive in the n-side.
The variation of the barrier fieldand barrier potentialare depicted in (e) and (f) respectively. The magnitude of the barrier field is maximum at the junction. The potential due to the barrier field rises towards the n-side to give a potential barrier of height VB.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Unbiased p-n Junction Diode
Energy-Band Diagram:
As we know from our previous discussion that the Fermi level (EF) lies near the conduction band edge for an n-type semiconductor, while it lies near the valence band edge for a p-type semiconductor. But, when a p-n junction is formed, the Fermi level attains a constant value throughout the system as shown in the figure below.
The conduction band edge (Ecp) of the p-side is at a higher level compared to the conduction band edge (Ecn) of the n-side. Similarly Evp is at a higher level than Evn.
The barrier energy is given by EB = Ecp - Ecn = Evp - Evn.
Biased p-n Junction Diode
A p-n junction is said to be biased when it is connected to a power supply. There can be two types of biases of a p-n junction diode - (i) forward-biased diodeand (ii) reverse-biased diode.
(i) Forward-biased p-n Junction Diode:
When the positive pole of a battery is connected to the p-side and negative pole to the n-side of the junction, the diode is said to be forward-biased.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Biased p-n Junction Diode
Dept. of Physics, Narajole Raj College, Narajole.
In this condition, the barrier energy is reduced and hence a large current due to the majority carriers flows across the junction. The schematic of a forward-biased p-n junction diode and its circuit representation are shown in the diagram below.
The biasing voltage V supplied by the battery exerts force on the holes in the p-side and on the electrons in the n-side and drives them towards the junction.
Thus, the width of the depletion region and the barrier energy are decreased. If the bias voltage is V then the barrier energy is reduced by the amount eV. This decrease in the barrier energy/potential increases the rate of current flow by the majority carriers. As holes and electrons are oppositely charged, their flows in opposite directions give currents in the same direction i.e. from p-side to the n-side through the junction. The flow of minority carriers is not affected by the bias and it is solely controlled by the temperature of the diode.
(ii) Reverse-biased p-n Junction Diode:
When the negative pole of a battery is connected to the p-side and positive pole to the n-side of the junction, then the diode is said to be reverse-biased. The schematics of a reverse-biased junction diode and its circuit representation are depicted in the figure below.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Biased p-n Junction Diode
In this situation, the bias voltage V pulls the holes of the p-side and electrons of the n-side away from the junction and as a result the width of the depletion layer and barrier height are increased. The increase in the barrier energy is given by eV.
This increase in the barrier height decreases the current flow across the junction by the majority carriers to a negligibly small value. But, the flow of minority carriers again remains unaffected as it depends only on the temperature. As a result, a small current called reverse saturation current (Is) flows through the diode. It is practically independent of the bias voltage but it increases with the increase in the temperature.
The energy level diagrams for a forward-biased and a reverse-biased p-n junction diodes are presented below in (a) and (b) respectively.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Biased p-n Junction Diode
Dept. of Physics, Narajole Raj College, Narajole.
Current-Voltage Characteristics of a p-n Junction Diode
Here we will discuss the current-voltage relationship for a p-n junction diode in biased condition. When a bias voltage V is applied across a junction diode, the net current I which flows through the junction is given by
where Is is the reverse saturation current, 𝜂 is a dimensionless parameter called emission coefficient. The other terms hold their usual (standard) meaning. This equation is known as the diode equation. The value of 𝜂 lies between 1 and 2 depending on the material of the diode. For example, in the case of germanium and gallium arsenide diodes the value of 𝜂 is close to 1 while for silicon it is nearly 2.
For a forward-biased diode, V is positive and for a reverse-biased diode V is negative. The current I vs the voltage V as described by the diode equation is plotted in the figure below.
This plot is known as current-voltage characteristics of a p-n junction diode.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Current-Voltage Characteristics
Static and Dynamic resistance:
The static or dc resistance of a p-n junction diode is defined as the ratio of the applied voltage V across the junction to the current I flowing through the junction.
Mathematically,
rdc = V / I.
For a p-n junction diode, Ohm’s law is not valid and r dc is not constant rather it varies with the applied voltage V.
Now, the dynamic or ac resistance of a diode is defined as the inverse of the slope of the current-voltage (I-V) characteristic of the diode. Mathematically,
r
ac=
dVdIAgain, the dynamic resistance rac of a junction diode is also not constant and it is dependent on the applied voltage.
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Reference: Some of the figures are taken from the book called “Electronics Fundamentals and Applications” by D. Chattopadhyay and P.C. Rakshit and used for the teaching purposes only.
Paper- C10T (Analog Systems and Applications) Topic- Semiconductor Diodes; Sub-topic(s)- Zener Diode as Reference Diode
