• Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Semiconductor bandgap Report. In this work, transmission spectroscopy was used under continuous light excitation to determine the optical band gap of semiconductors. The experiment was performed using indirect and direct semiconductors, Gallium Phosphate

Free essay example:

image01.jpg

Division of Electronic Engineering and Physics

Spectroscopy Determination of Semiconductor Bandgaps

Jonathan Hynd

November 2011                                                        3rd Year Physics MSci.


  1. Abstract

The measurement of the band gap of materials is important in the semiconductor, nanomaterial and solar industries. In this work, transmission spectroscopy was used under continuous light excitation to determine the optical band gap of semiconductors. The experiment was performed using indirect and direct semiconductors, Gallium Phosphate (GaP) and Gallium Arsenide (GaAs) within a grating monochromator. The non-radiative relaxation processes are discussed in terms of the generated signal. A mechanism to describe the signal increase/decrease under the continuous excitation is presented. The results obtained were 1.41eV and 2.33eV for GaAs and Gap respectively which are consistent with the accepted values of 1.43eV and 2.26eV showing that this method was useful to locate the band gap directly from the optical absorption spectra.

  1. Introduction

Energy bands consisting of a large number of closely spaced energy levels exist in crystalline materials. The bands can be thought of as the collection of the individual energy levels of electrons surrounding each atom. The wavefunctions of the individual electrons, however, overlap with those of electrons confined to neighboring atoms. The Pauli Exclusion Principle does not allow the electron energy levels to be the same so that one obtains a set of closely spaced energy levels, forming an energy band. The energy band model is crucial to any detailed treatment of semiconductor devices. It provides the framework needed to understand the concept of an energy bandgap and that of conduction in an almost filled band as described by the empty states. The bandgap is related to the electric conductivity of the materials. There is generally no band gap in metals, but the band gap value in insulators is known to be large.         

Most Optical and electrical properties of semiconductors can be well explained by the band gap model. As metals, semiconductors are arranged in periodic structures called crystals. Let us explore shortly the origin of the band gap starting from the free electron model. The free electron model of metals has been used to explain the photo-electric effect. This model assumes that electrons are free to move within the metal but are confined to the metal by potential barriers as illustrated by Figure 2.1. The minimum energy needed to extract an electron from the metal equals qΦM, where ΦM is the work function. This model is frequently used when analyzing metals as it is a good approximation as the binding energy of the valence electrons is small and so the attractive force between nucleus and valence electron. However, this model does not work well for semiconductors since the effect of the periodic potential due to the atoms in the crystal has been ignored.

image02.png

Figure 2.1
The free electron model of a metal

If the binding energy increases we have to introduce a non translational invariant potential. The first idea should be a potential that varies periodically with the lattice constant. For simplicity let us consider a one dimensional lattice with lattice constant a. We assume point symmetry at the origin, then the potential U is then given by

image08.pngimage08.pngimage18.pngimage18.png

        How does this influence the behavior of the electrons? We get the answer by regarding electrons as waves passing the crystal. Bragg reflection occurs for wavelengths in the range of the lattice constant. The diffraction condition in reciprocal space is given as

image28.pngimage28.pngimage37.pngimage37.png

Where image03.pngimage03.png is the wave vector with direction of wave propagation and magnitudeimage04.pngimage04.png. The one dimensional equation reduces to

image05.pngimage05.pngimage06.pngimage06.png

with image07.pngimage07.png as the one dimensional reciprocal lattice vector. Equation 2.1.3 gives us the borders of all the Brillouin zones. No wave Ψ = A exp(ikx) with wave vector matching 2.1.3 can pass undisturbed through the sample. Diffraction will cause an equal distribution of waves in both directions. The result is a standing wave. Let us have a look at waves with wave vector k = 2π/a (n = 1). There are two possible standing wave solutions, the time independent amplitudes can be written as

image09.pngimage09.pngimage10.pngimage10.png

image11.pngimage11.pngimage12.pngimage12.png

Let us have a look where these two solutions concentrate the electron charge density. The distribution of charge density ρ = ΦΦ is given by the following equations:

image13.pngimage13.pngimage14.pngimage14.png

image15.pngimage15.pngimage14.pngimage14.png

Solution Φ− concentrates the charge density between the atoms where the periodic potential approaches a minimum. Solution Φ+ results in charge concentration near the cores where the periodic potential is highest. The reason for the band gap in periodic structures is to be found in this difference in potential energy of the two wave solutions. Calculations in three dimensions follow the same approach. The derivation of the band gap in real lattices is a complicated task that can just be solved by numerical calculations.

In this experiment, the wavelength dependent optical absorption for semiconductor samples; Gallium Phosphate (GaP) and Gallium Arsenide (GaAs), were measured.

The experimental assembly provides electromagnetic radiation in the wide range of 380nm to 1080nm. This range makes several interaction processes with matter possible. In the long wavelength limit radiation can excite free charge carriers to oscillate causing reflection. In short wavelength limit radiation has enough energy to interact with inner shell electrons. The typical band gap energy of semiconductors is found in between these extremes. Light cannot be absorbed when electrons would acquire the amount of energy to find themselves in the forbidden zone between the bands. Just photons with energy high enough manage to catapult electrons over the gap. We should therefore find a strong increase of absorption probability when the energy of a photon exceeds the energy of the band gap. This is displayed as changes in output signal intensity. The bandgap energy image16.pngimage16.png of each semiconductor crystal can be found using the following equation:

image17.pngimage17.pngimage19.pngimage19.png

Where image20.pngimage20.pngplancks constant, image21.pngimage21.png speed of light in a vacuum and image22.pngimage22.png the wavelength where the absorption becomes non-zero. By plotting the transmission constant (the ratio of image23.pngimage23.png, where image24.pngimage24.pngis the intensity reading without a sample) against the corresponding wavelength, the x-axis intercept of the from the absorption edge region gives image25.pngimage25.png.

        Semiconductors can be classified into two types, namely direct gap and indirect gap

materials. GaAs is a direct gap semiconductor. The absorption spectrum for a direct gap material is shown in Figure 2(a).  Note that there is a very sharp absorption edge that starts at an energy equal toimage19.pngimage19.png. For an indirect semiconductor such as GaP, the energy gap is more complicated, resulting in a secondary absorption edge, as shown in Figure 2(b).  Indirect gap semiconductors include Si and Ge

image26.png

Figure 2.2

Optical absorption in pure insulators at absolute zero.


  1. Experimental Method

A Source of variable wavelength, monochromatic, light is obtained using a 100 W Quartz-Halogen (QTH) bulb in a housing that allows the light to be focused on the entrance slit of a grating monochromator. The lamp is powered by a FARNELL B30/10 power supply. This monochromator uses a diffraction grating in order to allow the wavelength of light that is brought to focus at the exit slit can be analyzed by rotating the grating.

image27.png

Figure 3.1

Grating monochromator showing how the initial beam of white

 light is split up using the rotating grating

The light emerging from the monochromator is detected by a Si-Based photodetector, between the monochromator and the detector. The intensities of the detected signals are very small and can be comparable to the noise amplitude so a lock-in amplifier in combination with an optical chopper was used to allow detection. The chopper modulates the light intensity passing through the monochromator, and the phase sensitive detector circuitry only amplifies signals with a narrow bandwidth about the modulating frequency. Stray light, not passing through the chopper will not give a detectable signal from the lock-in amplifier.

The power supply was turned to the 0-6V scale and the fine control was set to minimum before it was switched on.  The power supply was then switched and set to the

6-12V  range, allowing several minutes to heat up. The voltage was then increased by increasing the fine control, rotating it to approximately 75% full scale. The light was focused on the entrance slit of the monochromator, through the chopper blades.

        The chopper was then switched on and set to a frequency of 410Hz.The lock-in amplifier and DC voltmeter was then switched on and set to the following criteria: Sensitivity to 100mv, input A was used. The filter was set to BP (Bandpass) and MAN, and the line reject filter was set to F. The tuning display will show the chopper frequency. The output time constant was set to 300ms with a slope of 6dB and the output mode NORM.

        The wavelength on the monochromator was then switched to 1080nm and readings were taken (using no sample) every 20nm from 1080nm to 380nm and the response plotted. The photodetector housing was removed and the GaAs sample was mounted over it. Readings were then taken over the same range, again every 20nm. The GaAs sample was then replaced by the GaP sample and the experiment was carried out again. The Transmission constants were then plotted against wavelength as previously stated in the introduction. From these plots, the approximate positions for the absorption edges were indentified and more detailed measurements were carried out over these regions. These graphs were used in collaboration with image19.pngimage19.png to find the bandgap energies of each of the two semiconductors.

  1. Results and Discussion

A full set of measurements were taken for both semiconductors over the given range however when these results were plotted, the formed graphs did not follow the suspected relationship. This was due to the output frequency gradually going out of phase when the wavelength and samples were changed causing massive errors. There results were then ignored and the experiment was re-started.

Readings were then taken for both samples and the response frequency(no sample) over the range previously stated(1080nm to 380nm) making sure the output signal was always in phase, using the lock-in amplifier, every time the wavelength was altered. The tables of these results can be found in Figure 7.1 of the appendix.

The results were then plotted in order to indentify the position of the absorption edges.

image29.png

Figure 4.1

Graph of GaAs Transmission constant against wavelength


image30.png
Figure 4.2

Graph of GaP Transmission constant against wavelength

From these graphs it was clear that the absorption edges for GaAs and GaP were between wavelengths (800-1000)nm and (500-650)nm respectively. The absorptions edges were then analyzed by taking readings over these wavelength regions in smaller increments for the corresponding semiconductors. Tables of these results may be found in figure 7.2 and figure 7.3 in the appendix. The following graph for the absorption edge of GaAs was obtained.( Graph of GaP can be found in figure 7.4 the appendix)

image32.pngimage31.pngimage00.png

Figure 4.3

Graph of GaAs absorption edge

Using the linest function in excel, the gradient and intercept were found to be;

Gradient

Intercept(nm)

12.89069791

884.6134

1.663956093

0.940558

Figure 4.4

Linest table for GaAs Absorption edge

Were the intercept representsimage33.pngimage33.png. Therefore by using image19.pngimage19.png the value of the bandgap energy for GaAs was found to be 1.404eV. This process was repeated for the GaP sample and its corresponding bandgap was found to be 2.33eV.

        The experiment was repeated to clarify our readings and try and reduce our errors. A table of these results and bandgap plots can be found in the appendix.

From these sets of results, the bandgaps for GaAs and GaP were found to be 1.409eV and 2.34eV respectively. By using the law of averages, we can combine our two results to form:

Semiconductor

Bandgap Energy (eV)

GaAs

1.41

GaP

2.33

Figure 4.5

Table of Finalised Bandgap Energies

 These values coincide with published values for GaAs and GaP at 300k of 1.43eV and 2.26eV respectively

  1. Conclusion

We conclude that transmission spectra of a given semiconducting sample are just sufficient to calculate its energy band gap value. We have verified this method for two semiconducting materials, GaAs and GaP and found this an accurate and fastest for energy band gap determination. Measurements of the transmission constants of both the GaAs and the GaP semiconductor samples gave, using the accepted value for the speed of light and Planck’s constant, energy values of (1.41 and 2.33)eV respectively which are consistent with accepted values of (1.43 and 2.26)eV for the bandgap energies measured at 300K.

  1. References

[1] O.S. Heavens, Optical Properties of Thin Solid Films, Butterworth, London, 1955.

[2] F. Tepehan, N. Ozer, Solar Energy Materials and Solar Cells 30 (1993) 353.

[3] T.P. Sharma, S.K. Sharma, V. Singh, C.S.I.O. Communication 19 (3±4) (1992) 63.

[4] V. Kumar, V. Singh, S.K. Sharma, T.P. Sharma, Optical Materials 11 (1998) 29.

[5] V. Kumar, T.P. Sharma, Optical Materials 10 (1998) 253.

[6] S.K. Sharma, V. Kumar, S. Sirohi, S.K. Kaushish, T.P.Sharma, C.S.I.O. Communications 4 (3) (1996) 189.

[7] J. Tauc (Ed.), Amorphous and Liquid Semiconductor, Plenum Press, New York, 1974, p. 159.


  1. Appendix

Lambda

Vo

VGaAs

VGaP

TGaAs

TGaP

1080

530

141

109

0.266038

0.20566

1060

575

158

136

0.274783

0.236522

1040

620

169

156

0.272581

0.251613

1020

651

191

165

0.293395

0.253456

1000

677

197

173

0.29099

0.255539

980

700

203

178

0.29

0.254286

960

717

207

181

0.288703

0.252441

940

731

210

181

0.287278

0.247606

920

742

212

183

0.285714

0.246631

900

753

208

184

0.276228

0.244356

880

758

34

185

0.044855

0.244063

860

764

31

185

0.040576

0.242147

840

769

30

184

0.039012

0.239272

820

774

29

185

0.037468

0.239018

800

780

30

186

0.038462

0.238462

780

778

31

185

0.039846

0.237789

760

772

27

184

0.034974

0.238342

740

780

27

185

0.034615

0.237179

720

782

27

184

0.034527

0.235294

700

787

23

184

0.029225

0.233799

680

785

21

183

0.026752

0.233121

660

790

20

183

0.025316

0.231646

640

789

19

180

0.024081

0.228137

620

787

18

176

0.022872

0.223634

600

790

22

175

0.027848

0.221519

580

798

27

158

0.033835

0.197995

560

789

16

127

0.020279

0.160963

540

782

15

49

0.019182

0.06266

520

769

17

26

0.022107

0.03381

500

740

18

26

0.024324

0.035135

480

690

17

26

0.024638

0.037681

460

630

18

25

0.028571

0.039683

440

547

19

25

0.034735

0.045704

420

429

17

26

0.039627

0.060606

400

96

18

25

0.1875

0.260417

380

51

18

25

0.352941

0.490196

Figure 7.1

Table of results showing the intensities of the output signal and transmission constants


wavelength

Vo

VGaAs

T

800

240

9

0.0375

805

239

10

0.041841

810

239

9

0.037657

815

239

10

0.041841

820

238

10

0.042017

825

236

11

0.04661

830

235

11

0.046809

835

235

10

0.042553

840

236

11

0.04661

845

235

10

0.042553

850

235

10

0.042553

855

234

10

0.042735

860

234

11

0.047009

865

234

11

0.047009

870

234

11

0.047009

875

233

11

0.04721

880

233

12

0.051502

881

233

12

0.051502

882

233

12

0.051502

883

232

12

0.051724

884

233

12

0.051502

885

232

13

0.056034

886

232

14

0.060345

887

231

26

0.112554

888

232

48

0.206897

889

231

83

0.359307

890

232

121

0.521552

891

232

144

0.62069

892

231

160

0.692641

893

231

169

0.731602

894

231

176

0.761905

895

231

187

0.809524

900

231

198

0.857143

905

232

200

0.862069

910

231

202

0.874459

915

231

203

0.878788

920

230

203

0.882609

925

230

204

0.886957

930

229

203

0.886463

935

228

203

0.890351

940

227

203

0.894273

945

227

203

0.894273

950

226

202

0.893805

955

225

200

0.888889

960

224

200

0.892857

965

224

198

0.883929

970

223

199

0.892377

975

222

197

0.887387

980

222

196

0.882883

985

222

197

0.887387

990

219

196

0.894977

995

218

195

0.894495

Figure 7.2

Table of results showing the transmission constants for the absorption edge analysis of GaAs

wavelength

Vo

VGaP

T

650

245

185

0.755102

645

244

184

0.754098

640

244

182

0.745902

635

244

182

0.745902

630

245

185

0.755102

625

243

179

0.736626

620

244

183

0.75

615

243

184

0.757202

610

242

183

0.756198

605

243

182

0.748971

600

242

178

0.735537

595

243

175

0.720165

590

242

169

0.698347

585

240

165

0.6875

580

239

166

0.694561

575

234

165

0.705128

570

234

165

0.705128

565

236

157

0.665254

560

236

150

0.635593

555

235

146

0.621277

554

235

144

0.612766

553

234

139

0.594017

552

324

135

0.416667

551

235

132

0.561702

550

234

126

0.538462

549

234

120

0.512821

548

234

116

0.495726

547

235

107

0.455319

546

235

92

0.391489

545

234

86

0.367521

544

234

84

0.358974

543

235

83

0.353191

542

234

76

0.324786

541

235

59

0.251064

540

235

43

0.182979

535

233

22

0.094421

530

232

14

0.060345

525

228

13

0.057018

520

226

12

0.053097

515

222

13

0.058559

510

220

11

0.05

505

216

10

0.046296

Figure 7.3

Table of results showing the transmission constants for the absorption edge analysis of GaP


image34.png

Figure 7.4

Graph of GaP Absorption Edge for Run 1

image35.png

Figure 7.5

Graph of GaP Absorption Edge for Run 2

image36.png

Figure 7.6

Graph of GaAs Absorption Edge for Run 2


wavelength

Vo

VGaAs

T

850

766

30

0.039164

855

766

30

0.039164

860

766

33

0.043081

865

766

33

0.043081

870

766

33

0.043081

875

766

34

0.044386

880

765

36

0.047059

881

765

36

0.047059

882

765

38

0.049673

883

764

39

0.051047

884

764

42

0.054974

885

764

48

0.062827

886

765

57

0.07451

887

762

67

0.087927

888

764

85

0.111257

889

762

102

0.133858

890

762

121

0.158793

891

764

136

0.17801

892

762

144

0.188976

893

762

157

0.206037

894

762

176

0.230971

895

762

191

0.250656

900

762

204

0.267717

905

764

216

0.282723

910

762

212

0.278215

915

763

218

0.285714

920

762

221

0.290026

Figure 7.7

Table of Transmission Constants of GaAs Absorption Edge for Run 2


wavelength

Vo

VGaP

T

580

239

178

0.74477

575

234

176

0.752137

570

234

176

0.752137

565

236

164

0.694915

560

236

160

0.677966

555

235

156

0.66383

554

235

146

0.621277

553

234

138

0.589744

552

234

139

0.594017

551

235

129

0.548936

550

234

125

0.534188

549

234

120

0.512821

548

234

112

0.478632

547

235

107

0.455319

546

235

92

0.391489

545

234

86

0.367521

544

234

83

0.354701

543

235

82

0.348936

542

234

76

0.324786

541

235

57

0.242553

540

235

48

0.204255

535

233

36

0.154506

530

232

30

0.12931

525

228

28

0.122807

520

226

26

0.115044

Figure 7.8

Table of Transmission Constants of GaP Absorption Edge for Run 2

This student written piece of work is one of many that can be found in our University Degree Physics section.

(?)
Not the one? Search for your essay title...
  • Join over 1.2 million students every month
  • Accelerate your learning by 29%
  • Unlimited access from just £6.99 per month

Related University Degree Physical Sciences Skills and Knowledge Essays

See our best essays

Related University Degree Physics essays

  1. Hooke's law lab report. Hookes law and the investigation of spring constant k

    * Method The equipments needed in the experiment are a spring; a number of weights which each of them is 100gram heavy; a meter ruler; a ring stand; clamps; notebook and pencil. They were placed as shown in the diagram.

  2. The aim of this experiment is to investigate the relationship between the current, voltage ...

    All parts of the hypotheses were confirmed to be correct and supported by the results we obtained. Conclusion Looking at the graphs and the table of results it is clear that the hypotheses stated in the beginning of the experiment are correct: > When current is passed through a fixed

  1. Qualitative analysis of Sprinting.

    An efficient pull and support phase is present in all successful sprinting (Kraini, G 1996). Elite sprinters stride length and frequency is a function of a superior pull and support phase. The pull and support phase is shown below figure 1 and 2.

  2. The purpose of this experiment was to demonstrate the uncertainty of experimental measurements. ...

    The equation of the line of best fit (regression) was obtained. The parameters obtained by fitting the program was significant because the acceleration of the puck on the horizontal plane (ax) is the slope of the x(t) graph, which was 0.355 m/s2.

  1. The objective of this laboratory was to measure the speed at which sound was ...

    Because sound is traveling through air (gases) in this case, the altitude affects the speed of sound because of the air pressure. At lower altitudes sound travels faster because of higher air pressure. At higher temperatures sound travels faster because as explained by the equipartition theorem of thermodynamics.

  2. Is there really an energy crisis?

    ethanol), gaseous fuels (methane), electricity, and heat6. It is cheap and widely available. Unlike wind power and solar power, biomass does not have the problem of storage since it is easy and inexpensive to store and transport. The major benefit of using biomass as a fuel is that it greatly reduces emissions of greenhouse gases, namely by reducing carbon dioxide.

  1. Free essay

    Measurement of gravity using a rigid pendulum

    The time for one torsional oscillation of the steel bar suspended from the torsion wire was found to be 7.65 � 0.1s, timing 5 oscillations 3 times. Likewise, the time taken for one torsional oscillation of the pendulum suspended by the same wire was measured to be 6.73 � 0.1s, measuring 5 oscillations 3 times.

  2. Double Slit Interference

    Figure 2 Procedure and Observations: Required Apparatus: 1. Track and Screen from the Basic Optics System 2. Diode Laser 3. Multiple Slit Disk 4. White Paper 5. Meter Stick Figure 3: The experimental setup First the optical bench was set up with the laser on one end of the optics bench and the white screen on the other end.

  • Over 160,000 pieces
    of student written work
  • Annotated by
    experienced teachers
  • Ideas and feedback to
    improve your own work