Topic: Semiconductor Diodes (Part-2) In t hi s not e , w e

Arif Iqbal Mallick,Assistant Professor,

Department of Physics,Narajole Raj College, Narajole.

Paper: DSE2BT (Digital & Analog Circuits & Instrumentation)Topic: Semiconductor Diodes (Part-2)

In the previous E-material of DSE2BT, we have discussed the basic properties ofsemiconductors. In that we have also introduced intrinsic semiconductors andextrinsic (n-type and p-type) semiconductors briefly. In this note, we are going todiscuss more about the n-type and p-type semiconductors, their energy leveldiagrams and the current flow mechanisms in them. Also, we will show how p-njunctions diodes are fabricated and their characteristics in unbiased and biasedconditions.

At the beginning we are going to define some important parameters like“effective mass”, “drift velocity”, “recombination” etc. so that we understand thelatter part of the discussion without any difficulty.

Effective Mass:

The charge carriers i.e. the electrons and holes in a crystal experience forces due tothe internal periodic field (majorly the effective Coulomb field) produced by thecrystal. When an external field weaker than the internal one is applied to thecrystal, the internal field modifies the mass of the carriers in such a way that thecarriers follow the classical force-acceleration relation with the modified massunder the external field. This modified mass is called the effective mass of thecarrier. In many cases, the effective mass (meff) of a carrier differs verysignificantly from the electronic mass in vacuum i.e. the rest mass (m0). Theeffective mass approximation makes our life easy in the study of the carriertransport and other electronic properties of a crystal by solving these quantummechanical problems semi-classically.

Drift of Charge Carriers in an External Field:

Normally in a semiconductor, electrons in the conduction band and holes in thevalence band move around randomly due to their thermal energy. When the semi -

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Effective Mass, Drift of Charge Carriers

Arif Iqbal Mallick, Asst. Prof.,Dept. of Physics, Narajole Raj College, Narajole.

conductor is under an external electric field, free electrons and holes try to alignthemselves along the field lines as opposed to their random thermal agitations.

The free electrons move in the direction of the applied field and the holesmove opposite to the field direction, both producing electric currents in the samedirection as they are of opposite charges. This aligned movement of the carriers inan external electric field is called drift of the carriers and the velocity with whichthe carriers move is called drift velocity. The drift velocities of electrons and holesare represented by vd

e 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 asemiconductor. When a free electron in the conduction band jumps down to thevalence band and combines with a hole, the pair which was earlier contributing tothe conduction is destroyed and an energy equal to the bandgap of thesemiconductor is released in the form of electromagnetic (EM) radiation. If 𝛎 (or 𝛌)be the frequency (or wavelength) of the EM radiation and Eg be the bandgap of thesemiconductor 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- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Drift Velocity, Recombination


The recombination and generation of e-h pairs are shown in the cartoondiagram below.

The rate of recombination is proportional to the product of the electronconcentration and hole concentration. Though some electron-hole pairs aredestroyed in the process of recombination, some pairs are generated through thethermal excitations. For an intrinsic semiconductor at a fixed temperature, the rateof recombination is the same as that of thermal excitations so that the electron andhole concentrations remain constant at their thermal equilibrium values. But theelectron and hole concentrations increase as the temperature of the semiconductorincreases.

Energy Level Diagrams for Extrinsic Semiconductors

We have already introduced extrinsic semiconductors and their types namelyn-type and p-type semiconductors in the previous E-material. Here we will mainlytalk about the energy level diagrams of n-type and p-type semiconductors whichare 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 toa tetravalent pure semiconductor like Ge or Si, there is excess of electrons in thecrystal. Such impurity is called the donor as it donates one electron to theconduction band and the doped semiconductor is called n-type semiconductor.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Energy Level Diagrams


When donor impurities are added to a pure semiconductor an allowed energylevel which corresponds to the loosely bound valence electron of the donor atom isintroduced in the forbidden gap. As the amount of impurity in a semiconductor isusually very low, the impurity atoms are far apart from each other making theinteractions among themselves negligible small. So this level remains a discreteone situated just below the conduction band and we call it a donor level. Theenergy 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 conductionband 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 donorelectrons 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 atetravalent pure semiconductor like Ge or Si, there is excess of holes in thematerial. Such impurities are called the acceptors as they accept electrons from theneighbouring Ge or Si atoms, creating holes there. This kind of dopedsemiconductor is called a p-type semiconductor.

The discrete energy level due to the acceptor impurities in a semiconductoris introduced just above the valence band. This allowed energy level is known asacceptor level.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Energy Level Diagrams


The energy level diagram of a p-type semiconductor is shown in the figurebelow.

The exact position of the acceptor level depends on the impurity type and thehost 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 fromthe valence band get excited to the acceptor level due to the thermal energy. So, theholes are generated in the valence band in large numbers. Thus in a p-typesemiconductor, the holes become the majority carriers and the free electronsbecome the minority carriers.

Fabrication of p-n Junction Diode

A p-n junction diode is fabricated by doping one side of a single crystal withacceptors and the other side with donors. There are two types of p-n junctiondiodes - (i) step-graded or abrupt p-n junction and (ii) linearly graded p-njunction.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Fabrication of p-n Junction Diode


In a step-graded p-n junction diode, the acceptor and the donorconcentrations are constants up to the junction. A step-graded junction diode canbe made by placing a small pellet of a trivalent impurity like aluminium on oneside of a wafer of n-type silicon and heating the system up to a high temperaturefor a short period of time. In this process, aluminium gets dissolved in the siliconand one side of the wafer transforms from n-type to p-type. That’s how astep-graded p-n junction diode is fabricated.

However, in a linearly-graded p-n junction diode, the acceptor/ donorconcentration varies linearly with the distance from the junction. This kind ofjunction is fabricated by drawing a single crystal from a melt of silicon containingone type of impurity initially. And once the crystal is drawn the other type ofimpurity is added at a controlled rate to change the type of the semiconductor in acontinuous manner. The precise control of the impurity concentrations can beobtained by solid state diffusion method. In this method, p-type impurities arediffused into an n-type single crystal in the form of a substrate. That is how alinearly-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. Wehave shown here only majority carriers of both sides and the positive and negativeions. As there is a concentration gradient across the junction, the electrons willinitially diffuse through the junction from n-type to p-type and the holes diffuseother way around. So, near the junction the electrons and the holes recombine witheach other and as a result the acceptor ions in the p-side and the donor ions in then-side become unneutralized. These unneutralized ions near the junction are calleduncovered charges. These positive and the negative uncovered charges produce anelectric field across the junction which is directed from n-side to p-side. This fieldis known as the barrier field and is shown in the figure below. This barrier fieldopposes the diffusion of the majority carriers (i.e electrons and holes) through thejunction.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Unbiased p-n Junction Diode


When the barrier field is just sufficient to prevent the further diffusion of themajority carriers, an equilibrium will be established and there will be no furthermovement of the majority carriers acrossthe junction. As the vicinity of the junctionis depleted of the mobile charges, it is calledthe depletion region or the space-chargeregion.

The variations of acceptor and donorconcentrations are shown in figure (b). Theacceptor and donor concentrations reducefrom a constant value at two sides to zero atthe junction.

The hole concentration and theelectron concentration are shown in (c). Themobile charge (holes or electrons)concentration is zero in the depletionregion.

The variation of uncovered chargedensity is presented in (d). It is negative inthe p-side, zero at the junction and positivein the n-side.

The variation of the barrier field andbarrier potential are depicted in (e) and (f)respectively. The magnitude of the barrierfield is maximum at the junction. Thepotential due to the barrier field risestowards the n-side to give a potential barrierof height VB.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Unbiased p-n Junction Diode


Energy-Band Diagram:

As we know from our previous discussion, the Fermi level (EF) lies near theconduction band edge for an n-type semiconductor, while it lies near the valenceband edge for a p-type semiconductor. But, when a p-n junction is formed, theFermi level attains a constant value throughout the system as shown in the figurebelow.

The conduction band edge (Ecp) ofthe p-side is at a higher level comparedto the conduction band edge (Ecn) of then-side. Similarly Evp is at a higher levelthan Evn.

The barrier energy is given byEB = 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. Therecan be two types of biases of a p-n junction diode - (i) forward-biased diode and(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 tothe n-side of the junction, the diode is said to be forward-biased.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Biased p-n Junction Diode


In this condition, the barrier energy is reduced and hence a large current dueto the majority carriers flows across the junction. The schematic of aforward-biased p-n junction diode and its circuit representation are shown in thediagram below.

The biasing voltage V supplied by the battery exerts force on the holes in thep-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 thebias voltage is V then the barrier energy is reduced by the amount eV. Thisdecrease in the barrier energy/potential increases the rate of current flow by themajority carriers. As holes and electrons are oppositely charged, their flows inopposite directions give currents in the same direction i.e. from p-side to the n-sidethrough the junction. The flow of minority carriers is not affected by the bias and itis 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 tothe n-side of the junction, then the diode is said to be reverse-biased. Theschematics of a reverse-biased junction diode and its circuit representation aredepicted in the figure below.



In this situation, the bias voltage V pulls the holes of the p-side and electronsof the n-side away from the junction and as a result the width of the depletion layerand 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 bythe majority carriers to a negligibly small value. But, the flow of minority carriersagain remains unaffected as it depends only on the temperature. As a result, a smallcurrent called reverse saturation current (Is) flows through the diode. It ispractically independent of the bias voltage but it increases with the increase in thetemperature.

The energy level diagrams for a forward-biased and a reverse-biased p-n junctiondiodes are presented below in (a) and (b) respectively.



Current-Voltage Characteristics of a p-n Junction Diode

Here we will discuss the current-voltage relationship for a p-n junction diode inbiased condition. When a bias voltage V is applied across a junction diode, the netcurrent I which flows through the junction is given by

where Is is the reverse saturation current, 𝜂 is a dimensionless parameter calledemission coefficient. The other terms hold their usual (standard) meaning. Thisequation is known as the diode equation. The value of 𝜂 lies between 1 and 2depending on the material of the diode. For example, in the case of germanium andgallium 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 isnegative. The current I vs the voltage V as described by the diode equation isplotted in the figure below.

This plot is known as current-voltage characteristics of a p-n junction diode.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)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 theapplied 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 rdc is not constant rather itvaries with the applied voltage V.

Now, the dynamic or ac resistance of a diode is defined as the inverse of the slopeof the current-voltage (I-V) characteristic of the diode. Mathematically,

rac= 𝑑𝑉𝑑𝐼

Again, the dynamic resistance rac of a junction diode is also not constant and it isdependent on the applied voltage.

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Reference: Some of the figures are taken from the book called “ElectronicsFundamentals and Applications” by D. Chattopadhyay and P.C. Rakshit and usedfor teaching purposes only.

Paper- DSE2BT (Digital & Analog Circuits & Instrumentation); Sem-VI (G)Topic- Semiconductor Diodes; Sub-topic(s)- Zener Diode as Reference Diode

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Topic: Semiconductor Diodes (Part-2) In t hi s not e , w e