Transcript energy band gap in intrinsic semiconductors_09-09-11

Document that explains the chosen concept to the animator
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Energy Band Gap of intrinsic
semiconductors
Calculation of the energy band gap is explored in this simulation.
Prior Viewing LOs: Energy Band Gap, Intrinsic semiconductors,
Conductivity in intrinsic semiconductors.
Course Name: Semiconducting properties of materials.
Authors
Anura.B.Kenkre
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Learning Objectives
After interacting with this Learning Object, the learner will be able to:
• Determine the band gap of a semiconductor given the equation for
its conductivity.
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Definitions of the components/Keywords:
•Any chemically pure semiconductor has properties which are
characteristic of the material alone. Such a material is called
an intrinsic semiconductor.
•An Extrinsic semiconductor is one in which impurities contribute a
significant fraction of the conduction band electrons and/or valence
band holes.
•The conductivity of a substance is a measure of its ability to conduct
electricity.
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IMPORTANT NOTE TO THE ANIMATOR:
•All the instructions/labels or anything WRITTEN in blue
are CONTENT NOT TO BE DISPLAYED!
•All the instructions WRITTEN in black are CONTENT TO
BE DISPLAYED!
•This is not applicable for images as there can be
overlapping of these colours there. This should be
followed for all the instructions,labels,etc…
Kindly keep a note of this while displaying text in the
animation.
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INSTRUCTIONS SLIDE
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Master layout or diagram
• Make a schematic diagram of the concept
• Explain to the animator about the beginning and ending
of the process.
• Draw image big enough for explaining.
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• In above image, identify and label different components
of the process/phenomenon. (These are like characters
in a film)
• Illustrate the basic flow of action by using arrows. Use
BOLD lines in the diagram, (minimum 2pts.)
• In the slide after that, provide the definitions of ALL the
labels used in the diagram
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INSTRUCTIONS SLIDE
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Master layout or diagram
• You may have multiple master
layouts.
– In this case, number the master
layout. ( e.g. Master layout 1)
– Each Master layout should be
followed by the stepwise description
of the animation stages related to it.
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Master Layout
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2
battery
thermometer
12V
bulb
wires
holder
beaker
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stand
Ge
burner
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sample
water
The black lines along with
the battery, sample and the
bulb is called the circuit. the
image of the thermometer,
beaker, burner,etc is called
the experimental set up..
The sample should look like
it is placed in the water..It is
not looking like that here
since the circuit is drawn
and the experimental set up
is an image.
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Animation design
• Please see the design template
provided in the next slide.
• This is a sample template, and you
are free to change as per your design
requirements.
• Try and recreate the
sections/subsections as shown in the
template.
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Use STAM template
Slide
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Lets Learn!
Slide
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Definitions
Slide
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Slide
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Lets Sum up (summary)
Want to know more…
(Further Reading)
CALCULATION OF BAND GAP:
The temperature dependence of conductivity for an intrinsic semiconductor is given by:
∴σ = (constant) (T 3/2 )(e
-Eg / 2 KT
)
We know that for intrinsic semiconductors, the conductivity varies with the temperature..For
the above equation, one way of calculating the energy band gap is to rearrange the equation
so that a straight line can be plotted. Which of the following options is the equation of a
straight line??
3/ 2
σ
T
1)
= -E g / 2 KT
(Constant)
e
σ
- E g / 2 KT
=
e
2)
[(constant )(T 3 / 2 )]
σ
Eg 1
-E g / 2 KT
σ
) 4) ln{ 3 / 2 }  ln[ (constant) ] - ( )( )
3) 3/2 = (constant) (e
(T )
(T )
2K T
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Credits
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Explain the process
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In this step, use an example to explain the concept. It
can be an analogy, a scenario, or an action which
explains this concept/process/topic
Try to use examples from day-to-day life to make it
more clear
You have to describe what steps the animator should
take to make your concept come alive as a series of
moving images.
Keep the examples simple to understand, and also to
illustrate/animate.
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Stepwise description of process
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The goal of the document is to provide instructions to an animator
who is not a expert.
You have to describe what steps the animator should take to make
your concept come alive as a moving visualization.
Use one slide per step. This will ensure clarity of the explanation.
Add a image of the step in the box, and the details in the table
below the box.
You can use any images for reference, but mention about it's
copyright status
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The animator will have to re-draw / re-create the drawings
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Add more slides as per the requirement of the animation
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CALCULATION OF BAND GAP:
From the LO on Conductivity in Intrinsic Semiconductors, we know that for intrinsic
semiconductors, the conductivity varies with the temperature. The mathematical
relationship describing the temperature dependence of conductivity for an intrinsic
semiconductor is given by the equation below (Ref. 3 in Further References):
∴σ = (constant) (T
3/2
)(e
-Eg / 2 KT
)
For the above equation, one way of calculating the energy band gap is to
rearrange the equation so that a straight line can be plotted. Which of the
following options is the equation of a straight line??
OPTIONS ARE DISPLAYED ON THE NEXT PAGE DUE TO
SPACE CONSTRAINTS…PLEASE DISPLAY THEM BELOW
THIS QUESTION…
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1)
σ
T3 / 2
= -E g / 2 KT
(Constant)
e
σ
- E g / 2 KT
=e
2)
3/ 2
[(constant )(T )]
3)
σ
-E g / 2 KT
)
3/2 = (constant) (e
(T )
σ
Eg
1
)( )
4) ln{ 3 / 2 } = ln[ (constant) ] - (
2K T
(T )
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Step 1:
Refer to the figures on the previous slide.
Description of the action/ interactivity
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Audio
Narration
Give the following feedback depending upon the answer selected by the
user:
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If the user selects option 1:
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The equation of a straight line is y = mx + c.
For this ‘y’ and ‘x’ , what is the slope and what is the intercept??Recall that
slope(m) and intercept(c) must be constant and should not vary if ‘x’and ‘y’
are varied.
Rethink your options keeping the above hints in mind and choose once
again…
• If the user selects option 2:
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The equation of a straight line is y = mx + c.
For this ‘y’ and ‘x’ , what is the slope and what is the intercept??Recall that
slope(m) and intercept(c) must be constant and should not vary if ‘x’and ‘y’
are varied.
Besides, you have only an exponential on the right hand side which will not
give a straight line graph. Rearrange the equation such that the equation
has the form y= mx + c , where ‘m’ and ‘c’ are constants and either ‘m’ or ‘c’
must contain Eg .
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Rethink your options keeping the above hints in mind and choose once
again…
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Step 1 continued:
Refer to the figures on slide 13,14
Description of the action/ interactivity
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Audio
Narration
Give the following feedback depending upon the answer selected
by the user:
• If the user selects option 3:
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Your arrangement is on the right track but you need to do one
more step. Due to the exponential term ob the right hand side,
you will not get a straight line.
Think of a way to eliminate the exponential term to convert it into a
straight line.
Rethink your options keeping the above hints in mind and choose
once again…
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If the user selects option 4:
That’s absolutely right!!!
This is the equation of a straight line with
Y = ln [σ/ (T^3/2)]
X = 1/T
m = - Eg /2k
Now go ahead and see how the graph is plotted…
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Step 1 continued:
Refer to the figures on slide 13,14.
Description of the action/ interactivity
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Audio
Narration
•Only if the user selects option 4,let a button pop up
saying ‘Plot Graph’
•If the user clicks on it, go to step 2.
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CALCULATION OF BAND GAP:
Eg 1
σ
ln{ 3/2 } = ln[ (constant) ] + ()( )
2K T
(T )
c
y
m
x
1/T
0
0
1
2
3
-1
Temperature(K)
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1000
0
-2
100K
-3
12V
-4
-5
-6
Ge
-7
-8
-9
-10
σ
ln{
(T
3/2
}
)
Find slope
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Step 2:
Refer to slides 18. 20, 21
Description of the action/ interactivity
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Audio
Narration
1. let the temperature slider bar be clickable.
2. Put the markings on the temperature slider bar
according to the values on slide 20.In the image on the
previous slide,only the end points are givenon the
temperature slider bar due to space constraints.
3. The graph to be plotted takes vales of 1/T and ln [σ/
(T^3/2)]. These values are given on slide 21. For each
value of T, refer to the corresponding value of 1/T and
plot the graoh.
4. plot the graph dynamically ..that is,the graph is to be
plotted upto that point to which the slider bar is
dragged.
5. When the user reaches T= 1000K, let the radio
button for ‘Find Slope’ appear.
6. When the user clicks on it,show the animation and the
text as given on slide22.
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The scale to be followed for the temperature slider bar is as follows:
300
400
500
600
700
800
900
1000
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T
1/T
ln [σ/ (T^3/2)]
300
400
500
600
700
800
900
1000
3.33
2.5
2
1.66
1.428
1.25
1.11
1
-8.68
-6.5175
-5.214
-4.345
-3.724
-3.258
-2.896
-2.607
Find the value of 1/T
by comparing with
these values of T.
Plot on X axis
Plot on Y axis
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CALCULATION OF BAND GAP:
ln{
σ
(T
3/ 2
)
} = ln[ (constant) ] +
c
y
0
0
1
2
3
-1
4
Eg
1
()( )
2K T
m
1/T
x
Temperature(K)
1000
0
-2
-3
Slope = - Eg /2k
100K
12V
-4
-5
-6
Ge
-7
-8
-9
-10
ln{
σ
3/2
}
(T
)
The slope of the graph is - Eg /2k and on substituting the values of boltzman
constant we can obtain the energy band gap of the semiconductor.
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Interactivity and Boundary limits
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In this section, you will add the ‘Interactivity’ options to the
animation.
Use the template in the next slide to give the details.
Insert the image of the step/s (explained earlier in the
Section 3) in the box, and provide the details in the table
below.
The details of Interactivity could be:
 Types: Drop down, Slider bar, Data inputs etc.
 Options: Select one, Multiple selections etc
 Boundary Limits: Values of the parameters, which won’t
show results after a particular point
 Results: Explain the effect of the interaction in this column
Add more slides if necessary
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INSTRUCTIONS SLIDE
Self- Assessment Questionnaire for
Learners
• Please provide a set of questions that a user
can answer based on the LO. They can be of
the following types:
– These questions should be 5 in number and can be of
objective type (like MCQ, Match the columns, Yes or
No, Sequencing, Odd One Out).
– The questions can also be open-ended. The user
would be asked to think about the question. The
author is requested to provide hints if possible, but a
full answer is not necessary.
– One can include questions, for which the user will
need to interact with the LO (with certain
parameters) in order to answer it.
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INSTRUCTIONS SLIDE
Questionnaire for users to test their
understanding
• Please make sure that the questions can be
answered by interacting with the LO. It is
better to avoid questions based purely on
recall.
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Links for further reading
Books:
1)Solid state physics-MA Wahab.(chapter 13)
2)Solid state physics-Ashcroft/Mermin. (Chapter 28)
3)Introduction to modern physics-Richtmyer, Kennard,
Cooper.(Chapter 23)
Links:
http://www.virginia.edu/bohr/mse209/chapter19.htm
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INSTRUCTIONS SLIDE
Summary
• Please provide points to remember to
understand the concept/ key terms of the
animation
• The summary will help the user in the quick
review of the concept.
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Summary
•
•
•
•
Temperature causes electrons to be promoted to the conduction band and
from donor levels, or holes to acceptor levels. The dependence of
conductivity on temperature is like other thermally activated processes:
s = A exp(–Eg/2kT)
where A is a constant (the mobility varies much more slowly with
temperature). Plotting ln s vs. 1/T produces a straight line of slope Eg/2k from
which the band gap energy can be determined. Extrinsic semiconductors
have, in addition to this dependence, one due to the thermal promotion of
electrons from donor levels or holes from acceptor levels. The dependence
on temperature is also exponential but it eventually saturates at high
temperatures where all the donors are emptied or all the acceptors are filled.
This means that at low temperatures, extrinsic semiconductors have larger
conductivity than intrinsic semiconductors. At high temperatures, both the
impurity levels and valence electrons are ionized, but since the impurities are
very low in number and they are exhausted, eventually the behavior is
dominated by the intrinsic type of conductivity.
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