Bandgap Energy of Semiconductors - SIGH

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1 Νοε 2013 (πριν από 3 χρόνια και 7 μήνες)

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Presentation

By

Michael Olinski

Quantum Model



Band Structure


Valence Band
-

electrons
are bound to individual
atoms


Conduction Band
-

electrons are free to move
within the material


Bandgap


Energy difference between
these layers


Dependant upon material


Semiconductor Terminology

P
-
Type and N
-
Type Doping

1.
Forms the basis for all
semiconductor technology

2.
Created by introducing impurities
into a crystalline structure



Diode

1.
Contains a P
-
N junction

2.
Allows current to flow in only one
direction




Experimental Theory


Ideal Diode Equation





Bandgap energy can be
found through the
measurement of I
0




q


fundamental charge of
e

V


applied voltage

k


Boltzmann constant

T


Temperature

Experimental Theory

1.
Measure
I

across a
range of voltages

2.
Plot
Ln
(
I
) to obtain the
intercept I
0

3.
Alter temperature

4.
Plot intercepts versus
1
/T

5.
T
3/2

will be ignored
(non
-
linear)





Ideal Diode Equation





Current & Bandgap
Energy


Experimental Setup


Semiconductor selected
is silicon


Temperature baths


Alcohol & dry ice mix


Ice & water mix


Room temperature


Boiling water


Computer increases
voltage and records
current change


Experimental Results

Dry Ice Bath

Hot Water Bath

Experimental Results

Dry Ice Bath

Hot Water Bath

Experimental Results

Experimental Results

Average Slope

Middle Slope

Analysis


Slope of I
0

intercepts is equal to
E
g
/k


Bandgap energy is found by
multipying by Boltzmann’s
constant

Slope

+/
-

Boltzman
(ev/K)

Eg

+/
-

Accepted

Relative Error

1.390E+4

381

8.61734E
-
05

1.198E+00

3.29E
-
02

1.13

6.00%

1.373E+4

387

8.61734E
-
05

1.183E+00

3.33E
-
02

1.13

4.70%

Error Analysis


Systematic Types
Dominate


Resistive Heating


Affects higher end of linear
region


Will artificially inflate
internal temperature


Meter Readings


Affects lower end of linear
region


Results from poor contacts
or meter offsets


Thermal Equilibrium

Error Analysis


Systematic Types
Dominate


Resistive Heating &
Meter Readings



Thermal Equilibrium


Wait sufficient time


Thermometer Readings