Comprehensive Study of p-n Junction
Majharul Hoque
Department of EEE, Ahsanullah University of Science and technology, Dhaka, Bangladesh.
Email:Aoni5500@yahoo.com
Abstract: To deal with electrical devices a study of p-n junction is very much important. It essential for designing electrical devices. Study of p-n junction demands some basic knowledge about electrons and its nature in an atom corresponding to the other components of the atom. This is much related to the knowledge of conductor, insulator and semiconductor. P-n junction is made of semiconductors. So the concept of semiconductor, majority and minority carrier of p-type and n-type semiconductor, depletion region of p-n junction, fermi energy level, mobility and conductivity, drift and diffusion current is actually the comprehensive study of p-n junction.
1. Introduction
Semiconductor materials are the main element from which In the market today the vast majority of all solid state devices are fabricated. Semiconductor family of materials includes the elemental semiconductors Si and Ge, compound semiconductors such as GaAs and some alloys also includes in this list. Some of the major attributes of the present-day age (i.e., the age of electronics) are such common tools as computers and fibre-optic telecommunication systems, in which semiconductor materials provide vital components for various micro-electronic and optoelectronic devices in applications such as computing, memory storage, and communication. The reason why the semiconductor materials are so vastly used is that we can easily vary its characteristics by adding impurity content to it. The process is called doping. Semiconductor conductivity can be controlled by introduction of an electric field, by exposure to light, and even pressure and heat; And the semiconductor devices are the combination of p-type and n-type semiconductor material. P-n junction has an intimate collaboration with the operation and characteristics of semiconductor device. Thus understanding the basic of p-n junction is an important step towards the study of semiconductor device which is our main concern in this report.
2. Matter
All physical objects are composed of matter. Matter is any substance which has mass and occupies space. Matter can exist in three phases: * Solid * Liquid * Gas
As liquids and gases can not be used to make electronic devices our prime concern is solid matters. Solid matters can be classified according to: * Conductivity * Orientation
Here we will discuss solid matters according to conductivity.
3. Conductivity:
Conductivity is defined as the current carrying capability of matter. Current is the amount of charge carrier that flows in a unit time. Charge is immobile. Electron and hole are the charge carrier, where holes are positive charge carrier and electrons are negative charge carrier. Conductivity is denoted by and defined by, σ=1R (1) where R is the resistance
We can classify solids in three groups on the basis of conductivity. They are: * Conductor: The resistance level of conductor is very low ( From µΩ-mΩ range ) and so they can work as a short circuit. * Insulator: The resistance level of insulator is very high ( in MΩ level ) .So they can work as an open circuit. * Semi-conductor: Their resistance level is in between conductor and insulator.
So in brief we can write, RC<RSC<RI
Where RC ,RSC and RIis the resistance of conductor,semiconductor and insulator respectively. the main function of a device is not only to conduct current through it, but also to control it. A conductor can be used to make device. But current through it cannot be controlled easily. So it is not suitable to design a device. On the contrary the conductivity of a semiconductor can be varied over a range of magnitude by changing: * Temperature: 1. A conductor has a positive temperature co-efficient of resistance that is resistance of a conductor increases with increasing temperature 2. A semiconductor has a negative temperature co-efficient i.e. resistance of a conductor decreases with increasing temperature * Optical excitation * Adding impurity contents. So it is suitable for device design. That’s why semiconductor is the base for any kind of electrical device.
4. Semiconductor:
Semiconductor are a group of materials with electrical conductivity , intermediate in magnitude between that of a conductor and an insulator. Specific resistance is in the order of 10^-4Ωm. Some common characteristics of semiconductor are given below. * It’s conductivity increases with the use of impurity. * At absolute (0k) temperature they acts like an insulator. * It’s conductivity increases with the increase of temperature.
Classification of semiconductor 1. Based on purities: a. Intrinsic semiconductor
b. Extrinsic semiconductor * P-type * N-type 2. Based on band gap energy a. Direct band gap semiconductor b. Indirect band gap semiconductor 3. Based on metal composition a. Elementary semiconductor: * Si * Ge b. Compound semiconductors: * III – IV * IV – IV * IV -V 4. Alloys * Binary:GaAs * Teranary: GaInp * Quaternary: GaAsIn
5. Intrinsic material:
The term intrinsic is applied to any semiconductor material that has been carefully defined to reduce the number of impurities to a very low level –essentially as pure as can be made available through modern technology.

Figure1: Intrinsic semiconductor with no impurity.

The free electrons in a material due to external causes are referred to as intrinsic carriers. Ge has the highest number of intrinsic carriers and GaAs has the lowest. In fact Ge has more than twice the number as GaAs. For determining its use in the field other characteristics of the material are more significant, Such as relative mobility of the free carriers in the material. Intrinsic material Semiconductor | Intrinsic carriers (per cubic c.m.) | GaAs | 1.7×106 | Si | 1.5×1010 | Ge | 2.5×1013 |

6. Extrinsic material:
The characteristics of a semiconductor material can be altered significantly by the addition of specific impurity atoms to the relatively pure semiconductor material. These impurities, although only added at 1 part in 10 million, can alter the band structure sufficiently to totally change the electrical property of the material.

“A semiconductor material that has been subjected to the doping process is called an extrinsic material.”

There are two extrinsic materials of immeasurable importance to semiconductor device fabrication: n-type and p-type materials.

7. n-type material:
An n-type material is created by introducing impurity elements that have five valence electrons (pentavalent) , such as antimony ,arsenic and phosphorus. The effect of such impurity elements is indicated in the fig. below

Figure2: n-type Si with donor
The four covalent bonds are still present. There is, however, an additional fifth electron due to the impurity atom, which is unassociated with any particular covalent bond. This remaining electron, loosely bound to its parent (antimony) atom, is relatively free to move within the newly formed n-type material. Since the inserted impurity atom has donated a relatively free electron to the structure.
“Diffused impurities with five valence electrons are called donor atoms.”

It is important to realize that even though a large number of free carriers have been established in the n-type material, it is still electrically neutral since ideally the number of positively charged protons in the nuclei is still equal to the number of free and orbiting negatively charged electrons in the structure.
8. p-type material:
The p-type material is formed by doping a pure germanium or silicon crystal with impurity atoms having three valence electrons. The elements most frequently used for this purpose are boron, gallium and indium. The effect of one of these elements, boron, on a base of silicon is indicated in fig. shown below-

Figure3: p-type Si with acceptor
There is now an insufficient number of electrons to complete the covalent bonds of the newly formed lattice. The resulting vacancy is called a hole and is represented by a small circle or a plus sign, indicating the absence of a negative charge. Since the resulting vacancy will readily accept a free electron.

“ The diffused impurities with three valence electrons are called acceptor atoms.”

The resulting p-type material is also electrically neutral as n-type material.
9. Majority and Minority charge carrier:
In the intrinsic state of a semiconductor there are a few number of electrons and holes are present. These have broken the covalent band and move to covalent band. So, for each movement a pair of electron and hole is created. These are responsible for carrying charge.

The more abundant charge carriers are called majority carriers. Majority charge carriers in the N-type side of a semiconductor material are electrons, because N-type semiconductor is doped with a material with 5 valence electrons. Semiconductor materials have 4 valence electrons and hold tightly to 8, so there is a "loose" electron for every atom of dopant. Therefore most of the charge carriers available are electrons. IE, electrons are the majority charge carriers in n-type semiconductor and in p-type they are holes.

The less abundant charge carriers are called minority carriers. Minority charge carriers in N-type semiconductor are holes. Only a few holes (lack of an electron) are created by thermal effects, hence holes are the minority carriers in N-type material. Again some electrons are loosened by thermal effects, they are the minority charge carriers in P-type semiconductor.
10. Donor and Acceptor:
For a semiconductor, donor is an atom which donates electrons to other compound. Donating an electron it creates n-type semiconductor.
Example: arsenic ( As), antimony (Sb).

An acceptor is the atom which collects electron from a donor. These atoms have three valence electrons.
Example: boron (B), aluminum (Al).
11. Band theory:
A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands. figure4: band diagram
This band diagram is showing energy levels where electrons may exist in a particle. Those electrons moving around the nucleus in orbit occupy the valance band. Those drifting free in the spaces have an energy level in conduction band. Electron normally cannot exist in a certain energy level represented by the forbidden gap.
Valance band is the energy level where electrons are normally present at absolute zero temperature. It is located in the lower part of the band diagram separated from insulator and semiconductor by band gap.
The energy level of conduction band is higher than valance band. These electrons are free from bindings with its atom. So it can move freely in the lattice. For this they are able to flow electric current through metal.
12. Drift current:
An electric field applied to a semiconductor will produce a force on electrons and holes so that they will experience a net acceleration and net movement, provided there are available energy states in the conduction and valence bands. Electron cannot travel in a straight line between the positive and negative terminals. Instead of moving along, they move bouncing from one atom to another. The flow of electric current due to this motion of charge carriers under the influence of the external electric field is called drift current
13. Drift Current Density:
The drift current density due to holes,
Jpdrift=pqμpE (2)
The drift current due to holes is in the same direction as the applied electric field.
Similarly, the drift current due to electrons, Jndrift=nqμnE (3)
Here, μn is the electron mobility and is a positive quantity. The drift current is also in the same direction as the applied electric field though electron movement is in the opposite direction.
Since, electrons and holes contribute to the drift current, the total drift current density is the sum of the individual electron and hole drift current densities, so we can write
Jdrift=Jpdrift+Jndrift
⟹Jdrift=eμnn+μpp ⟹Jdrift=σE (4)
Where σ is the conductivity.
14. Diffusion current:
Diffusion current is a type of current which is occurred when charge carriers diffuse from a point of concentration, to spread uniformly throughout the volume of a piece of material.

15. Diffusion Current Density:
Consider the diffusion of electrons from a region of high concentration to a region of low concentration produces a flux of electrons flowing in the negative x direction. Since electrons have a negative charge, the conventional current direction is in the positive x direction. So, the electron diffusion current density for one-dimensional case,
Jndiff=qDndndx (5)

Where, Dn is called the electron diffusion coefficient, has units of cm2/s and is positive quantity.
Figure5: Diffusion of electrons due to a density gradient

Figure6: Diffusion of holes due to a density gradient.
The diffusion of holes from a region of high concentration to a region of low concentration, produces a flux of holes in the negative x direction. Since holes are positively charged particles, the conventional diffusion current density is also negative x direction. So,
Jpdiff=-qDpdpdx (6)

Where, Dp is called the hole diffusion coefficient, has units of cm2/s and is a positive quantity.

Figure: Diffusion of holes due to a density gradient
16. Total Current Density:
We have four possible independent current mechanisms in a semiconductor. These components are electron drift and diffusion currents and hole drift and diffusion currents. The total current density is the sum of these four components, or for one dimensional case,
J=Jndrift+Jpdrift+Jndiff+Jpdiff
or J=nqμnE+pqμpE+qDndndx-qDpdpdx … … … (7)
17. Equilibrium distribution of electrons and holes:
The distribution of electrons in the conduction band is given by the density of allowed quantum states times the probability that a state is occupied by an electron. n(E)=gc(E)fF(E) … … … (8)
Similarly, the distribution of holes in the valence band is the density of allowed quantum states in the valence band multiplied by the probability that a state is not occupied by an electron. We may express this as n(E)=gv(E)[1- fF(E)] … … … (9)
The total hole concentration per unit volume is found by integrating this function over the entire valence-band energy.
To find the thermal-equilibrium electron and hole concentrations, we need to determine the position of the Fermi energy EF with respect to the bottom of the conduction-band energy Ec and the top of the valence-band energy Ev.
18. Fermi level:

The probability of finding an electron in a conduction band for semiconductor is given by Fermi equation, fE=11+eE-EF/KT …. …. …. ….(10)
Here,
EF=Fermi energy level
K=Boltzmann constant
T=Temperature in Kelvin
If E>Ef then (10) becomes, fE=e-E-EF/KT …. …. …. ….(11)
Now,
No. of electrons, n=Nc×f(E)
Putting the value from (10) & (11) we get, n=Nce-E-EF/KT…. …. …. ….(12)
Here,
Nc= No. of energy states in conduction band
Similarly total number of hole in the valence band is given by, p=NV{1-fEV}
⟹p=NV e-EF-EV/KT …. …. …. ….(13)
Now,
n.p=NC e-EC-EFKT.NV ⟹n.p=NCNV e-EC-EV/KT ⟹n.p=NCNV e-Eg/KT .…. …. ….(14)
Equation (14) can be written as, n.p=ni2 …. …. …. ….(15)
19. Position of Fermi Level
Taking ln on both sides of equation (12) we have, lnn=lnNC-EC-EFKT ⟹EC-EFKT=lnNC-lnn ⟹EC-EF=KT lnNC n ⟹EF=EC-KT lnNCn …. …. (16)
Similarly from equation (13) lnp=lnNV-EF-VKT ⟹EF-EVKT=lnNV-lnp ⟹EF-EV=KT lnNVp ⟹EF=EV+KT lnNVp …. …. … (17)
Adding equation (16) and (17) we have
2EF=EC-KT lnNCn+EV+KT lnNVp
⟹EF=EC+EV2+KT2 lnNV.nNC.p . …. …. (18)
For intrinsic material, from equation (18) we have,
EF=EC+EV2
For intrinsic material the Fermi energy level is in the middle of valence band and conduction band.

For p-type material (p>n) the Fermi energy level is below the middle of valence band and conduction band and for n-type material it is above.

20. Mobility and Conductivity:
The mobility is an important parameter of the semiconductor as we can know from this that how well a particle will move due to an electric field. The unit of mobility is usually expressed in terms of cm2/v-s. µn is called the electron mobility and µp is called the hole mobility. It is related with average drift velocity of a carrier in the electric field. When an electric field E is applied across a piece of material, the electrons respond by moving with an average velocity called the drift velocity ,. Then the electron mobility μ is defined as μn=ϑdE ,where E= Electric field. . Under the action of electric field electrons move in the lattice. But it cannot move straight to the electric field. It collides with atoms.
There are two collisions or scattering mechanism that dominate in a semiconductor and affect the carrier mobility. Those are: * Lattice scattering (μL): Atoms in a semiconductor crystal vibrate about the position within the crystal due to the energy obtained by temperature. It causes a disruption in the perfect periodic potential function. Since lattice scattering is related to the thermal motion of atoms, the rate at which the scattering occurs is function of temperature. μL∝T-32. Mobility, due to lattice scattering increases as the temperature decreases. * Ionized impurity scattering (μ1): We have seen that impurity atoms are added to the semiconductor to control its characteristics. These impurities are ionized at room temperature so that a coulomb interaction exists between the electrons or holes and ionized impurities. This coulomb interaction produces scattering and also alerts the velocity characteristics of the charge carrier. μ1∝T32N1 So, the total mobility (μ) of a semiconductor can be written as follows,
1μ= 1μL + 1μ1…. …. … (19)

Table 2|Typical mobility values at T=300k and low doping concentrations: Semiconductor | µn(cm2/v-s) | µp(cm2/v-s) | Silicon | 1350 | 480 | Gallium Arsenide | 8500 | 400 | Germanium | 3900 | 1900 |
We know the drift current equation: jdrf=e(μnn+μpp)E=σE …. …. … (20)

where σ is the conductivity of the semiconductor material and it’s units is(Ω-cm)-1 .it is a function of the electron and hole concentrations and mobilitiy. We have just seen that the mobilities are functions of impurity concentration, Then conductivity may be a complicated function of impurity concentration.
Conductivity is just opposite to the resistivity, ρ= 1σ= 1q [nμp+ pμp] …. …. … (21) where ρ is the resistivity. Conductivity varies with the variation of temperature. conductivtity rises with the rise of temperature and decrases with temperature decrease .
21. Depletion Region:
Because no free electrons or holes can exist is the region about the junction, there are no mobile charges to neutralize the ions in this region. This is illustrated in Fig
. Figure10 : Diagram of a p-n junction with the width of the depletion region greatly exaggerated.

The ions on the n-type side have a positive charge on them and those on the p-type side have a negative charge.
These charges are called uncovered charges. The region about the junction in which the uncovered charges exist is called the depletion region. Other names for this are the space-charge region and the transition region. Figure 11: Plot of the charge density as a function of distance from the junction. illustrates the plot of the net uncovered charge density in the p-n junction as a function of distance from the junction. The charge distribution is called a dipole distribution because the charge on one side of the junction is the negative of the charge on the other side.
Because of charge neutrality, the total uncovered charge on the n-type side of the depletion region must be equal to the negative of the total uncovered charge on the p-type side. If the n and p concentrations are equal, it follows that the widths of the uncovered charge regions on the two sides of the junction must be equal. Now, suppose the p concentration is increased while holding the n concentration constant. Charge neutrality requires the width of the p-type side of the depletion region to decrease if the total uncovered charge is to remain constant. Similarly, if the n concentration is increased while holding the p concentration constant, the width of the n-type side must decrease. We conclude, in general, that increasing either p or n or both decreases the total width w of the depletion region this has an important effect on the reverse-bias breakdown characteristics of a junction.
22. Built-In Potential:
Because there is an electric field in the depletion region of a p-n junction that is directed from the n-type side to the p-type side, it follows that there is a difference in potential or voltage across the junction. This voltage difference is called the built-in potential or the contact potential. It can be calculated from either
V2 – V1=V T ln(p1p2) (22)
V2 – V1=-V T ln(n1n2) (23)

We use Eq. (22). In this equation, p1 is the hole concentration in the p-type side and p2 is the hole concentration in the n-type side. By Eq. in a p-type semiconductor, we can write p = n + NA ≈NA .…. …. … (24)

The hole concentration in the p-type side is p1≈NA, where NA is the acceptor concentration per m3. the hole concentration in the n-type side is p2≈ni2/ND, where ni is the intrinsic concentration per m3 and ND is the donor concentration per m3.

23. Reverse biased junction:
When an external bias voltage is applied to a pn-junction, positive to the n-side and negative to the p-side, electrons from the n-side are attracted to the positive terminal, and holes from the p-side are attracted to the negative terminal. As shown in the Figure, holes on the p-side of the away from the junction and electrons are attracted away from the junction on the n-side. This causes the depletion region to be widened and the barrier voltage to be increased, as illustrated. With the barrier voltage increase, there is no possibility of a majority charge carrier current flow across the junction, and the junction is said to be reverse biased. Because there is only a very small reverse current, a reverse-biased p-n-junction can be said to have a high resistance.Although there is no possibility that a majority charge carrier current can flow across a reverse biased junction, minority carriers generated on each side can still cross the junction. Electrons in the p-side are attracted across the junction to the positive side voltage on the n-side. Holes on the n-side may flow across to the negative voltage on the p-side. Since only a very small reverse bias voltage is necessary to direct all available minority carriers across the junction, further increases in bias voltage do not increase the current level. This current is referred to as a reverse current. The reverse saturation current is normally a very small quantity, ranging from nano-amps to micro-amps, depending on the junction area, temperature, and semiconductor material.

24. Forward Biased Junction:
The effect of an external bias voltage applied with the polarity is shown in Figure. Positive is on p-side and negative is on n-side. The holes on the p-side, being positively charged particles, are rippled from the negative terminal towards the junction. Here the width of the depletion region and the barrier potential are both reduced. When the applied bias voltage is progressively increased from zero, the barrier voltage gets smaller until it effectively disappears and charge carriers easily flow across the junction. Electrons from the n-side are now attracted across to the positive bias terminal on the p-side, and holes from the p-side flow across to the negative terminal on the n-side (thinking of holes as positively charged particles). A majority carrier current flows, and the junction is said to be forward biased.

There is very little forward current until VF exceeds the junction barrier voltage (0.3 V for germanium, 0.7 for silicon).When VF is increased from zero towards the knee of characteristic, IF increases almost linearly with increase in VF. The level of current that can be made to forward across a forward biased pn-junction largely depends on the area of the junction.
25. P- N junction:
When a p-type semiconductor is joined to a n-type semiconductor such that the crystal structure remains continuous at the boundary, the junction is called the p-n junction. The p-n junction diode itself provides characteristics that are used in rectifiers and switching circuits. In addition, the analysis of the p-n junction device establishes some basic terminology and concepts that are used in the discussion of other semiconductor devices.
A p-n junction is formed by mixing one half of a pure semiconductor in a controlled way at high temperature with a p-type impurity and the half region with n-type impurity. The interface separating the n and p regions is referred to as the metallurgical junction. Initially, at the metallurgical junction, there is a very large density gradient in both the electron and hole concentrations. If we assume there are no external connections to the semiconductor, then this diffusion process cannot continue indefinitely.
26. Conclusion:
We have focused on the basic properties of the semiconducting material and the factors that control these properties thoroughly in this report.
In order to understand the proper functionality of semiconductor devices and to properly apply them we need to understand its properties under variable condition In this report we have mainly focused on the conducting properties of semiconducting materials and we used various
Approved models to explain it. For device designing and cicuit designing we need to understand the physical properties of semiconducting materials and this report tries to draw summary to overall semiconducting properties.