# 9.7 Semiconductor devices  (Page 2/12)

 Page 2 / 12

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 $N{e}^{\text{−}eV\text{/}{k}_{\text{B}}T}$ . However, if a battery of voltage ${V}_{b}$ is applied in the forward-bias configuration, this fraction improves to $N{e}^{\text{−}e\left(V-{V}_{b}\right)\text{/}{k}_{\text{B}}T}$ . The electric current due to the majority carriers from the n -side to the p -side is therefore

$I=N{e}^{\text{−}eV\text{/}{k}_{\text{B}}T}\phantom{\rule{0.2em}{0ex}}{e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}={I}_{0}{e}^{e{V}_{b}\text{/}{k}_{\text{B}}T},$

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 $\text{−}{I}_{0}$ , independent of the bias voltage. The net current is therefore

${I}_{\text{net}}={I}_{0}\left({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1\right).$

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 ${I}_{\text{net}}\approx \text{−}{I}_{0}$ . 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    .

## 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 $4.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-1}\phantom{\rule{0.2em}{0ex}}\text{A}\text{.}$ The reverse saturation current is $2.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-8}\phantom{\rule{0.2em}{0ex}}\text{A}\text{.}$ (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

${I}_{\text{net}}={I}_{0}\left({e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}-1\right).$

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

${I}_{0}\approx -{I}_{\text{sat}}=2.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-8}.$

Therefore

$\frac{{I}_{\text{net}}}{{I}_{0}}=\frac{4.5\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-1}\phantom{\rule{0.2em}{0ex}}\text{A}}{2.2\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-8}\phantom{\rule{0.2em}{0ex}}\text{A}}=2.0\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{8}.$

[link] can be written as

$\frac{{I}_{\text{net}}}{{I}_{0}}+1={e}^{e{V}_{b}\text{/}{k}_{\text{B}}T}.$

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

$\frac{e{V}_{b}}{{k}_{\text{B}}T}=19.$

The temperature is therefore

$T=\frac{e{V}_{b}}{{k}_{\text{B}}}\left(\frac{1}{19}\right)=\frac{e\left(0.12\phantom{\rule{0.2em}{0ex}}\text{V}\right)}{8.617\phantom{\rule{0.2em}{0ex}}×\phantom{\rule{0.2em}{0ex}}{10}^{-5}\phantom{\rule{0.2em}{0ex}}\text{eV}\text{/}\text{K}}\left(\frac{1}{19}\right)=73\phantom{\rule{0.2em}{0ex}}\text{K}\text{.}$

## 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, ${k}_{\text{B}}T,$ then the forward bias current is very large compared to the reverse saturation current.

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.

#### Questions & Answers

what is the difference between a molecule and atom
Natanim Reply
Atoms are single neutral particles. Molecules are neutral particles made of two or more atoms bonded together.
Manfred
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Elias Reply
A body quadruples its momentum when its speed doubles.What was the initial speed in units of c.i.e..what was u/c ?
Lekshmi Reply
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prabir Reply
a thermodynamic quantity equivalent to the total heat content of a system
RAMLA
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bloch
What is the meaning of Nuclear Fission?
Benita Reply
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عند قذف جسم إلى أعلى بسرعة إبتدائية فإنه سيصل إلى ارتفاع معين (أقصى ارتفاع) ثم يعود هابطاً نحو سطح الأرض .   إذا قُذِفَ جسم إلى أعلى ووجد أن سرعته 18 م / ث عندما قطع 1/4 المسافة التي تمثل أقصى ارتفاع سيصله فالمطلوب إيجاد السرعة التي قُذِف بها بالمتر / ث . إن هذه السرعة هي واحدة من الإجابات التالية
Aml Reply
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Ayebanifesunday Reply
light is a kind of radiation That stimulates sight brightness a source of illumination.
kenneth
Electromagnet radiation creates space 7th, 8th, and 9th dimensions at the rate of c.
John
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John
This creation of new space is "Dark Energy".
John
The first two sets of three dimensions, 1 through 6, are "Dark Matter".
John
As matter decays into luminous matter, a proton, a neutron, and an electron creat deuterium.
John
There are three sets of three protons, 9.
John
There are three sets of three neutrons, 9.
John
A free neutron decays into a proton, an electron, and a neutrino.
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There are three sets of five neutrinoes, 15.
John
Neutrinoes are two dimensional.
John
A positron is composed of the first three dimensions.
John
An electron is composed of the second three dimensions.
John
What is photoelectric
Hsssan Reply
light energy (photons) through semiconduction of N-P junction into electrical via excitation of silicon purified and cristalized into wafers with partially contaminated silicon to allow this N-P function to operate.
Michael
i.e. Solar pannel.
Michael
Photoelectric emission is the emission of electrons on a metal surface due to incident rays reflected on it
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If you lie on a beach looking at the water with your head tipped slightly sideways, your polarized sunglasses do not work very well.Why not?
Rakhi Reply
it has everything to do with the angle the UV sunlight strikes your sunglasses.
Jallal
this is known as optical physics. it describes how visible light, ultraviolet light and infrared light interact when they come into contact with physical matter. usually the photons or light upon interaction result in either reflection refraction diffraction or interference of the light.
Jallal
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Jallal
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hi
Tr
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Hi
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hi
Siddiquee
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Propessor Reply
1.79×10_¹⁹ km per hour
Swagatika
3×10^8
Benita
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কাজের একক কী
Jasim
কাজের একক কী
Jasim
Energy is ability so capacity to do work.
kenneth
friction ka direction Kaise pata karte hai
Rahul Reply
friction is always in the opposite of the direction of moving object
Punia

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Source:  OpenStax, University physics volume 3. OpenStax CNX. Nov 04, 2016 Download for free at http://cnx.org/content/col12067/1.4
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