UV- VIS Spectrum

Jeet Bhattacharjee, Int. PhD - 24483

September 2024

1 OBJECTIVE
The objective of this project is to spectrum of UV light getting difracted from materials,
and to consequently study material properties.

1. To find the energy band gap of given samples by measuring the absorption spectrum
using UV-VISIBLE spectrometer and identify the type of material.

2. To find the thickness of the thin film (aluminium) using absorption spectrum.

2 APPARATUS
The apparatus needed for this experiment are given below;

• UV-VIS Photo Spectrometer

• Semiconductor samples

• Glass plate

• Aluminium Coated Glass plate

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3 Setup Diagram

Figure 1: UV Spectroscopy Setup

4 THEORY
4.1 Band Gap
The term “band gap” refers to the energy difference between the top of the valence band to
the bottom of the conduction band (See Figure 2); electrons are able to jump from one band
to another. In order for an electron to jump from a valence band to a conduction band, it
requires a specific minimum amount of energy for the transition, the band gap energy.This
fact is used to calculate the band gap of various materials.

Figure 2: Direct and Indirect band Gap

The band gap energy of insulators is large (> 4eV), but lower for semiconductors (< 3eV).

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A diagram illustrating the band gap is shown in Figure 1. UV-Visible spectrometer measures
the intensity of light passing through the sample (I) and compares it to the calibrated
intensity (I0 ). The ratio I/I0 is called the transmittance for a particular wavelength.
The absorbance A is defined as,

A = −Log(I/I0 ) (1)

The sources of UV Visible light are tungsten and deuterium lamps. If the current in the
circuit is gradually increased from zero, the tungsten lamp filament at first can be felt to
be emitting warmth, then glows dull red and then gradually brightness until it emits an
intense white light (visible light). Later, source of light will be switched to Deuterium lamp,
which emits UV (ultra violet) light. The diffraction setup incorporated in the spectrometer
selectively separates different wavelengths from 200 to 1100 nm with desired step size.

The band gap of the given sample can be measured using multiple methods. Two of
such methods are described below:

4.2 Method 1
From the Absorption vs Wavelength graph we note down the wavelength where a absorption
peak is observed (say λp ), now the band gap energy can be given as:

hc
Eg = (2)
λ

4.3 Method 2
A more precise way to calculate energy band gap (Eg ) is the Tauc method, given as follows:

A(hv − Eg )n
α= (3)
hv

Where, α = ln(1/T
x
)

α = absorption coefficient
T = Transmittance
x = Thickness of the sample
Eg =band gap of the material
n= 2, 1/2, 2/3 and 1/3 for direct allowed, indirect allowed, direct forbidden, and indirect
forbidden transitions respectively.

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 On rearranging the above equation we get:

(αhv)1/n = A1/n hv − A1/n Eg (4)

Plotting graph of (αhv)1/n Vs hv , we will get a straight line around the transition phase.
Thus on comparing (4) with y = mx + c we get slope m = A1/n and y intercept
c = −A1/n Eg . Dividing y intercept by A1/n , we can estimate the band gap.

4.4 Thickness Calculation

For Calculating the thickness of the glass plate (coated with aluminum) we use the formula:

−t
I = I0 e δ (5)

Where,
I0 = intensity of the glass plate
I= intensity of the coated glass sample
t= thickness of the sample
δ= skin depth of the material given by:

s
ρλ
δ= (6)
πcµ

Where,
ρ= resistivity (for Aluminium 2.8 x 10−8 Ω m)
λ= wavelength
c= velocity of light
µ= absolute magnetic permeability. (1.256 x 10−6 H/m)
from equation (1) and (5) we can write:

t = Aδ (7)

where A is the absorption coefficient of almunium film.

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5 Procedure
1. Switch on the device and leave it for 15-20 mins for warm up.

2. Press on Main menu and select “wavelength scan” and press “Enter”.

3. Calibration: To take reference, choose “T%” as 100, “Abs” and press “Enter” to
confirm. Here our reference is air, now press start/stop to start the scan.

4. Now for the band gap/thickness measurement, place the sample plate inside the box
of spectrometer such that the light falls on the sample. Then press start.

5. Now connect a pen drive to the device and save the data in it, by clicking on Save
once the scan is complete. After that press clr (to clear screen for the next scan).

6. Repeat the above two steps for different samples and glass plate.

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 Following are the observed graphs and data used for the band gap (Eg ) and thickness
(t) calculation

5.1 Determining Band gap

(a) Eg for the B-Bi 45:55 thickness = 1.17mm

Figure 3: Method 1 (Direct)

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Figure 4: Method 2 (Tauc)

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(b) Eg for the B-Bi 60:40, thickness = 1.34mm

Figure 5: Method 1 (Direct)

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Figure 6: Method 2 (Tauc)

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(c) Eg for the B-Bi 55:45, thickness = 0.73 mm

Figure 7: Method 1 (Direct)

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Figure 8: Method 2 (Tauc)

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6 Calculations (for band gap energy)
6.0.1 Method 1:
hc
Wavelength at absorption Band gap, Eg = λ
Sample
edge, λ (nm) (eV)
B-Bi 45:55 474.44 2.62
B-Bi 60:40 467 2.66
B-Bi 55:45 416.66 2.98

Method 2:
c 1
Sample Slope, m y-intercept, c Eg = − m ∗ 1.6x10−19
(eV)
25:75 7.8528 × 10−11 −3.3965 × 10−29 2.699
45:55 7.7691 × 10−11 −3.544 × 10−29 2.847
60:40 5.9317 × 10−11 −2.937 × 10−29 3.088

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6.1 Determining thickness of thin film:

Figure 9: Absorption vs wavelength graph for plain glass

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Figure 10: Absorption vs wavelength graph for Al coated glass

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Calculations (for thickness)

Absorbance Absorbance Absorbance

Wavelength, Skin depth, Thickness,
of coated of plain of Al-film,
λ (nm) δ (nm) t (nm)
glass, A glass, Ag AAl = A−Ag
500 3.439 1.2547 0.0494 1.2053 4.145
600 3.768 1.2899 0.0515 1.2384 4.666
700 4.0696 1.3357 0.0623 1.2734 5.182
Average 4.664

7 Error analysis:
7.1 % error in band gap energy:
Method 1: Equation (2) gives:

hc ∆Eg ∆λ
Eg = ⇒ = .
λ Eg λ

Here, ∆λ = 1 nm = least count of the spectrometer.

∆λ
Sample Eg (in eV) λ (in nm) % error = λ × 100
25 : 75 2.62 474.44 0.210%
45 : 55 2.66 467 0.214%
60 : 40 2.98 416.66 0.240%

Method 2: Since the Tauc plot fits to the linear function y = mx + c, it implies
c
Eg = −
m
∆Eg ∆c ∆m
⇒ = + .
Eg c m

∆c and ∆m are obtained from the curve fitting details in ’Origin’

Sample m ∆m c ∆c % error
25 : 75 7.8528 × 10−11 4.744 × 10−12 −3.3965 × 10−29 2.147 × 10−30 12.3
45 : 55 7.7691 × 10−11 5.697 × 10−12 −3.544 × 10−29 2.718 × 10−30 15
60 : 40 5.9317 × 10−11 3.045 × 10−12 −2.937 × 10−29 2.224 × 10−30 13

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7.2 % error in thickness of thin film:
From Equations (6) and (7),
√ ∆t 1 ∆λ
t∝ λ⇒ = .
t 2 λ

Wavelength (nm) ∆t/t

500 0.1%
600 0.0833%
700 0.0714%

8 Results and Discussions

1. Band gap for different samples of B-Bi measured using Method-1 and Method-2 are
given in the tables above.

2. As can be observed, the value of band gap is increasing with a increase in Boron and
decrease in Bismuth composition.

3. The average thickness of aluminium is measured to be 4.664 nm with a average %

error of 0.0849.

4. We need to place the samples carefully and ensure radiation is passing through them
into the detector.

5. As can be seen from equation (4) we will get a negative value of Eg for a positive
value of y-intercept. Thus we cannot take n=2 (case for direct band gap). This is also
justified by the graphs, i.e. we donot get a line parallel to y-axis for the absorption
vs wavelength curve. Thus here we are having indirect band gap so we take n=1/2.

6. Here the % error calculated for method-1 are less than as calculated for method-2 this
can be due to the fact that we have considered the least count method which does not
take into account the other types of error possible.

References

https://www.researchgate.net/figure/UV-Vis

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