band gap experiment graph

ENERGY BAND GAP SIMULATION

Among the following graphs which graph is plotted for semiconductors in energy band gap experiment.

TABLE : OBSERVATIONS

NOTE : Enter value of X coordinate and Y coordinate seperated with comma( , )

NOTE : Enter value of Slope calculated above in the below box

©Abhay Gupta

Laboratory Manual for Energy Band Gap Experiment

LABORATORY MANUAL FOR ENERGY BAND GAP EXPERIMENT

Background Semiconductors , PN junction diode, Forward and reverse biasing, Band gap, Fermi level .

Aim: To determine the Energy Band Gap of a Semiconductor by using PN Junction Diode.

Apparatus: Energy band gap kit containing a PN junction diode placed inside the temperature controlled electric oven, microammeter, voltmeter and connections brought out at the socket, a mercury thermometer to mount on the front panel to measure the temperature of oven.

Formula Used: The reverse saturation current, Is is the function of temperature (T) of the junction diode. For a small range of temperatures, the relation is expressed as,

5.036 푋 103퐸 푙표푔 퐼 = 퐶표푛푠푡푎푛푡 − 푔 10 푠 푇

Where, T is temperature in Kelvin (K) and Eg is the band gap in electron volts (eV).

3 Graph between 10 /T as abscissa and log10 Is as ordinate will be a straight line having slope =

5.036 Eg Hence band gap, 푆푙표푝푒 표푓 푙𝑖푛푒 퐸 = 푔 5.036 Theory: A semi-conductor (either doped or intrinsic) always possesses an energy gap between its valence and conduction bands (fig.1). For the conduction of electricity, a certain amount of energy is to be given to the electron so that it can jump from the valence band to the conduction band. The energy so needed is the measure of the energy gap (Eg) between the top and bottom of valence and conduction bands respectively. In case of insulators, the value of Eg varies from 3 to 7 eV. However, for semiconductors, it is quite small. For example, in case of germanium , Eg = 0.72 eV and in case of silicon , Eg = 1.1 eV.

Fig.1. Energy Gap in Metals , Semi-conductors and Insulators

In semi-conductors at low temperatures, there are few charge carriers to move, so conductivity is quite low. However, with increase in temperature, more number of charge carriers get sufficient energy to be excited to the conduction band. This lead to increase in the number of free charge carriers and hence increase in conductivity. In addition to the dependence of the electrical conductivity on the number of free charges, it also depends on their mobility. The mobility of the charge carriers, however decreases with increasing temperature. But on the average, the conductivity of the semiconductors rises with rise in temperature.

To determine the energy band gap of a semi-conducting material, we study the variation of its conductance with temperature. In reverse bias, the current flowing through the PN junction is quite small and internal heating of the junction does not take place.

When PN junction is placed in reverse bias as shown in fig.2(a), the current flows through the junction due to minority charge carriers only. The concentration of these charge carriers depend on band gap Eg.

The saturation value, Is of reverse current depends on the temperature of junction diode and it is given by the following equation,

−퐸푔 퐼푠 = A (Nn e vn + Np e vp ) 푒 푘푇

Where, Nn (Np) is the concentration of electrons (holes) in N(P)-type region, vn and vp are the drift velocities of electrons and holes respectively,

A is the area of junction, k = 1.38 x 10-23 J/K, is Boltzman’s constant and T is absolute temperature of junction.

Taking log of both sides of above equation, we have

퐸푔 푙표푔 퐼 = 푙표푔 A (Nn e vn + Np e vp ) - 푒 푠 푒 푘푇

퐸푔 Or 2.303 푙표푔 퐼 = 2.303 푙표푔 A (Nn e vn + Np e vp ) - 10 푠 10 푘푇

퐸 Or 푙표푔 퐼 = 퐶 − 푔 10 푠 2.303 푘푇

Where C is a constant, which is equal to the first term of RHS of above equation. On substituting the value of k and converting the units of Eg from eV to Joule, we get

1.6 푥 10−19 퐸 푙표푔 퐼 = 퐶 − 푔 10 푠 2.303 푥 1.38 푥 10−23 푇

5.036 푋 103퐸 Or 푙표푔 퐼 = 퐶 − 푔 10 푠 푇

Which can be expressed as,

103 푙표푔 퐼 = 퐶 + (−5.036 퐸 ) 10 푠 푔 푇

This represents the equation of straight line having negative slope (5.036 Eg) for graph drawn 3 between log10 Is and 10 /T. Therefore, by knowing the slope of the line, Eg can be determined through following formula,

Slope = 5.036 Eg

103 푆푙표푝푒 표푓 푔푟푎푝ℎ 푑푟푎푤푛 푏푒푡푤푒푒푛 푙표푔10 퐼푠 and 퐸 = 푇 푔 5.036

Procedure: The experimental setup is shown in fig.2(b).

1. Insert the thermometer in the hole of the oven. 2. Switch ON the instrument using ON/OFF toggle switch provided on the front panel. 3. Keep the temperature control switch to the high side. 4. Adjust the voltage at 1V DC. 5. Switch ON the oven using ON/OFF toggle switch provided on the front panel. Temperature starts increasing and the reading of microammeter also starts increasing. 6. When temperature reaches to 90℃ or 100℃, switch OFF the oven and note down the reading of microammeter (µA). 7. As the temperature starts falling, note down the readings of microammeter after every 5℃ or 10℃ drop in temperature. 8. Repeat the whole procedure for 2V and 3V DC. 3 9. Plot graph between log10 Is and 10 / T for different voltages.

Fig. 2 (a) Reverse biased PN junction Diode (b) Experimental Setup

Observations:

3 S.No. Temp. Current Is (µA) Temp. 10 / T log10 Is (℃) (K)

V = 1V V = 2V V = 3V

1. 30 2. 40 3. 50 4. 60

5. 70 6. 80 7. 90 8. 100

Calculations:

3 3 Taking 10 / T along X-axis and log10 Is along Y-axis, plot a graph between log10 Is and 10 / T for three different voltages. The graph will be a straight line as shown in fig.3. Determine the slope of straight line from this graph and then calculate band gap using formula,

푆푙표푝푒 Band gap (Eg) = = ______eV. 5.036

Take average of three values of band gap. log Is log

3 Fig.3. Variation of log10 Is v/s 10 /T

The band gap (Eg) of the given semiconductor is found to be ______eV.

Precautions:

The following precautions should be taken while performing the experiment:

1. The diode must be reverse biased. 2. Do not exceed the temperature of the oven above 100℃ to avoid over heating of the diode. 3. The voltmeter and ammeter reading should initially be at zero mark. 4. Bulb of the thermometer should be inserted well in the oven. 5. Readings of microammeter should be taken when the temperature is decreasing. 6. Readings of current and temperature must be taken simultaneously.

Sample viva voce questions:

1. What is PN junction diode? 2. What do you understand by band gap of a semi-conductor? 3. What do you mean by valence band, conduction band and forbidden band? 4. How many types of semi-conductors are there? 5. What are P-type and N-type semi-conductors? 6. Define doping and dopant. 7. Why P-type (N-type) semi-conductor is called Acceptor (Donor)? 8. What do you mean by Fermi energy level ? 9. What is the position of Fermi level in an intrinsic semi-conductor and in a p-type or n- type semi-conductor with respect to the positions of valence and conduction bands? 10. What do you mean by forward biasing and reverse biasing? 11. Why diode is reverse biased in determining the band gap of semi-conductor? 3 12. What is the shape of graph between log10 Is and 10 / T? How do you find band gap energy from this graph? 13. Why conductivity of metals decreases with increase in temperature? 14. Why conductivity of a semi-conductor increases with increase in temperature?

References:

 Solid State Electronic Devices by Streetman and Banerjee  B.sc Practical Physics by Geeta Sanon

Note: Soft copy of this manual will be available on http://www.nitj.ac.in/physics/

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Ssanet-bs: spectral–spatial cross-dimensional attention network for hyperspectral band selection.

1. Introduction

• This paper proposes a deep neural network based on spectral–spatial cross-dimensional attention for hyperspectral BS, named SSANet-BS. This network employs complementary multi-dimensional attention mechanisms to automatically discover salient bands, and improves the performance of BS by exploring the complex spectral–spatial interactions in HSI.
• SSANet-BS, with its three-stage structural design, addresses the issue of existing BS methods that introduce spatial modules, which compromise the independence of the band attention weights. The experimental results demonstrate that SSANet-BS is effective and stable. This offers a novel solution for the field of hyperspectral BS.

2. The Proposed Method

2.1. overview of ssanet-bs, 2.2. the band attention module, 2.3. the spectral–spatial attention module, 2.4. the multi-scale reconstruction network, 3. experiments, 3.1. experimental setup.

• Indian Pines (IP220): IP220 is captured by the AVIRIS sensor in 1992 in an Indian pine forest landscape which located at the northwest of Indiana. It contains 220 bands, with a resolution of 145 × 145 pixels and 16 classes of ground objects labeled.
• Washington DC Mall (DC191): It is an airborne HSI acquired by the HYDICE sensor, which contains 191 bands, with a resolution of 280 × 307 and 6 classes.
• Pavia University (PU103): PU103 is taken in 2002 by the ROSIS sensor in the campus of Pavia University in Italy. It size is 610 × 340 × 103, and has 9 classes.
• QUH-Qingyun (QY176) [ 44 ]: The image was captured on 18 May 2021 in Qingdao, China, utilising a Gaiasky mini2-VN imaging spectrometer mounted on a UAV platform. It comprises 176 spectral bands. After cropping, it is 600 × 200 in size and contains 5 classes of ground labels.

3.2. Parameter Setting

3.3. result analysis, 4. discussion, 4.1. band quanlity, 4.2. computation time, 4.3. ablation study for ssams, 4.4. effectiveness of the three-stage structure, 4.5. comments on existing bs methods and ssanet-bs, 5. conclusions, author contributions, data availability statement, conflicts of interest.

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Share and Cite

Cui, C.; Sun, X.; Fu, B.; Shang, X. SSANet-BS: Spectral–Spatial Cross-Dimensional Attention Network for Hyperspectral Band Selection. Remote Sens. 2024 , 16 , 2848. https://doi.org/10.3390/rs16152848

Cui C, Sun X, Fu B, Shang X. SSANet-BS: Spectral–Spatial Cross-Dimensional Attention Network for Hyperspectral Band Selection. Remote Sensing . 2024; 16(15):2848. https://doi.org/10.3390/rs16152848

Cui, Chuanyu, Xudong Sun, Baijia Fu, and Xiaodi Shang. 2024. "SSANet-BS: Spectral–Spatial Cross-Dimensional Attention Network for Hyperspectral Band Selection" Remote Sensing 16, no. 15: 2848. https://doi.org/10.3390/rs16152848

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