<< Chapter < Page Chapter >> Page >

We can estimate the mathematical relationship between the current and voltage for a diode using the electric potential concept. Consider N negatively charged majority carriers (electrons donated by impurity atoms) in the n -type material and a potential barrier V across the p-n junction. According to the Maxwell-Boltzmann distribution, the fraction of electrons that have enough energy to diffuse across the potential barrier is N e e V / k B T . However, if a battery of voltage V b is applied in the forward-bias configuration, this fraction improves to N e e ( V V b ) / k B T . The electric current due to the majority carriers from the n -side to the p -side is therefore

I = N e e V / k B T e e V b / k B T = I 0 e e V b / k B T ,

where I 0 is the current with no applied voltage and T is the temperature. Current due to the minority carriers (thermal excitation of electrons from the valence band to the conduction band on the p- side and subsequent attraction to the n -side) is I 0 , independent of the bias voltage. The net current is therefore

I net = I 0 ( e e V b / k B T 1 ) .

A sample graph of the current versus bias voltage is given in [link] . In the forward bias configuration, small changes in the bias voltage lead to large changes in the current. In the reverse bias configuration, the current is I net I 0 . For extreme values of reverse bias, the atoms in the material are ionized which triggers an avalanche of current. This case occurs at the breakdown voltage    .

Graph of I subscript net versus V. An arrow pointing right from the y axis is labeled forward bias. An arrow pointing left from the y axis is labeled reverse bias. The curve goes up and right in the first quadrant and then becomes almost vertical at higher values of x and y. It crosses the positive x axis into the fourth quadrant  and then the negative y axis at minus I subscript 0. It travels left in a horizontal line till a point where it turns sharply down into what becomes an almost vertical line. The x value of the turning point is labeled breakdown voltage.
Current versus voltage across a p-n junction (diode). In the forward bias configuration, electric current flows easily. However, in the reverse bias configuration, electric current flow very little.

Diode current

Attaching the positive end of a battery to the p -side and the negative end to the n -side of a semiconductor diode produces a current of 4.5 × 10 −1 A . The reverse saturation current is 2.2 × 10 −8 A . (The reverse saturation current is the current of a diode in a reverse bias configuration such as this.) The battery voltage is 0.12 V. What is the diode temperature?

Strategy

The first arrangement is a forward bias configuration, and the second is the reverse bias configuration. In either case, [link] gives the current.

Solution

The current in the forward and reverse bias configurations is given by

I net = I 0 ( e e V b / k B T 1 ) .

The current with no bias is related to the reverse saturation current by

I 0 I sat = 2.2 × 10 −8 .

Therefore

I net I 0 = 4.5 × 10 −1 A 2.2 × 10 −8 A = 2.0 × 10 8 .

[link] can be written as

I net I 0 + 1 = e e V b / k B T .

This ratio is much greater than one, so the second term on the left-hand side of the equation vanishes. Taking the natural log of both sides gives

e V b k B T = 19 .

The temperature is therefore

T = e V b k B ( 1 19 ) = e ( 0.12 V ) 8.617 × 10 −5 eV / K ( 1 19 ) = 73 K .

Significance

The current moving through a diode in the forward and reverse bias configuration is sensitive to the temperature of the diode. If the potential energy supplied by the battery is large compared to the thermal energy of the diode’s surroundings, k B T , then the forward bias current is very large compared to the reverse saturation current.

Got questions? Get instant answers now!

Check Your Understanding How does the magnitude of the forward bias current compare with the reverse bias current?

The forward bias current is much larger. To a good approximation, diodes permit current flow in only one direction.

Got questions? Get instant answers now!

Questions & Answers

what is cathodic protection
Ebe Reply
its just a technique used for the protection of a metal from corrosion by making it cathode of an electrochemical cell.
akif
what is interferometer
Sonu Reply
Show that n1Sino1=n2Sino2
javan Reply
what's propagation
Vikas Reply
is it in context of waves?
Edgar
It is the manner of motion of the energy whether mechanical(requiring elastic medium)or electromagnetic(non interference with medium)
Edgar
determine displacement cat any time t for a body of mass 2kg under a time varrying force ft=bt³+csinkt
Felix Reply
A round diaphragm S with diameter of d = 0.05 is used as light source in Michelson interferometer shown on the picture. The diaphragm is illuminated by parallel beam of monochromatic light with wavelength of λ = 0.6 μm. The distances are A B = 30, A C = 10 . The interference picture is in the form of concentric circles and is observed on the screen placed in the focal plane of the lens. Estimate the number of interference rings m observed near the main diffractive maximum.
Jyoti Reply
A Pb wire wound in a tight solenoid of diameter of 4.0 mm is cooled to a temperature of 5.0 K. The wire is connected in series with a 50-Ωresistor and a variable source of emf. As the emf is increased, what value does it have when the superconductivity of the wire is destroyed?
Rupal Reply
how does colour appear in thin films
Nwjwr Reply
hii
Sonu
hao
Naorem
hello
Naorem
hiiiiii
ram
🎓📖
Deepika
yaaa ☺
Deepika
ok
Naorem
hii
PALAK
in the wave equation y=Asin(kx-wt+¢) what does k and w stand for.
Kimani Reply
derivation of lateral shieft
James Reply
hi
Imran
total binding energy of ionic crystal at equilibrium is
All Reply
How does, ray of light coming form focus, behaves in concave mirror after refraction?
Bishesh Reply
Refraction does not occur in concave mirror. If refraction occurs then I don't know about this.
Sushant
What is motion
Izevbogie Reply
Anything which changes itself with respect to time or surrounding
Sushant
good
Chemist
and what's time? is time everywhere same
Chemist
No
Sushant
how can u say that
Chemist
do u know about black hole
Chemist
Not so more
Sushant
Radioactive substance
DHEERAJ
These substance create harmful radiation like alpha particle radiation, beta particle radiation, gamma particle radiation
Sushant
But ask anything changes itself with respect to time or surrounding A Not any harmful radiation
DHEERAJ
explain cavendish experiment to determine the value of gravitational concept.
Celine Reply
 Cavendish Experiment to Measure Gravitational Constant. ... This experiment used a torsion balance device to attract lead balls together, measuring the torque on a wire and equating it to the gravitational force between the balls. Then by a complex derivation, the value of G was determined.
Triio
For the question about the scuba instructor's head above the pool, how did you arrive at this answer? What is the process?
Evan Reply
Practice Key Terms 9

Get the best University physics vol... course in your pocket!





Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
Google Play and the Google Play logo are trademarks of Google Inc.

Notification Switch

Would you like to follow the 'University physics volume 3' conversation and receive update notifications?

Ask