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From: Thanh Lam, process engineer
Date: October 2, 2017
To: Mr. Amir Khusrau, subsidiary president
Subject: Bandgap Measurement
Due to some experiences of malfunctioning devices that was made using the new gallium arsenide and gallium phosphide wafer, this experiment focuses on testing and verifying the bandgap of the new wafers that processed by the subsidiary.
This experiment will verify the bandgap of the new semiconductor with the correct semiconductor that have the bandgap of 1.42 eV. Gallium arsenide wafer is the one that will be put under optical absorption experiment to observe it output voltage. A sample small sample of gallium arsenide will be place between the Tungsten lamp and the photodetector. The signal from the photodetector will be output to the Transimpedance amplifier so it will convert the current to the output voltage. The data for this experiment are the photodetector voltage with the sample and without the sample for various wavelength. The bandgap can be calculated from finding the x-intersection from the graph of 𝛼^2 vs. Energy of photon, where 𝛼 is the optical absorption coefficient that can be calculated from the normalized transmissivity.
The bandgap energy for the sample of gallium arsenide is 1.33 eV. In comparison with the expected value of 1.42 eV, the percent difference is calculated to be 6.55%. This shows that the photon can be absorbed by the material and get excited into the conduction band. Furthermore, wafers may not be the main reason that cause some of the devices from the company to work improperly.
Introduction
Due to some improperly working devices, the company suspect that the gallium arsenide and gallium phosphide wafers that was processed by the subsidiary is the cause. Thus, it is necessary to run an optical absorption test to find the bandgap measurement that verify the expected value of 1.42 eV for GaAs and 2.2 eV for GaP.
The differences between a semiconductor with a metal and insulator are the bandgap energy and it properties. Bandgap energy is what make semiconductor to have a unique property of conducting electric current through absorption of light and heat. Comparing to metal and insulator, the bandgap energy for semiconductor is not too small or too big. It is within a medium range of energy where the energy of photon can excited the electron from the valance band onto the conduction band as shown in Figure 1.
Figure 1: Optical absorption generates electron – hole pairs [2] In order for the electron from the valence band to successfully jump to the conduction band, the energy of the photon must be equal or greater than the energy of the bandgap. If the photon energy is smaller than the bandgap energy then the photon will just pass through the material. The photon have must energy equivalent to bandgap energy because bandgap energy is
the wavelength. Furthermore, the transmissivity can be calculated from the proportionality of light intensity and it can be described as:
𝑇(𝜆)^ = (^) 𝐼𝐼 0 𝑡((𝜆𝜆)), (3)
where 𝑇(𝜆) is the transmissivity, 𝐼𝑡 is the amount of light that is transmitted through the sample (cd), 𝐼 0 is the light intensity before it enter the sample (cd).
This experiment will be measuring the photodetector voltage with the sample and another set of the photodetector voltage without the sample for various wavelength. The transmissivity can be calculated from the equation:
𝑇𝑟𝑎𝑤 = (^) 𝑃𝑉𝑃𝑉𝑤𝑖𝑡𝑤𝑖𝑡ℎ𝑜𝑢𝑡ℎ^ 𝑠𝑎𝑚𝑝𝑙𝑒 𝑠𝑎𝑚𝑝𝑙𝑒 , (4)
where 𝑇𝑟𝑎𝑤 is the transmissivity, 𝑃𝑉𝑤𝑖𝑡ℎ 𝑠𝑎𝑚𝑝𝑙𝑒 is the measured photodetector voltage with
sample (mV), 𝑃𝑉𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑠𝑎𝑚𝑝𝑙𝑒 is the measured photodetector voltage without sample (mV).
The transmissivity of normalization is related with the optical absorption coefficient through the equation:
𝑇𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑(𝜆) = 𝑒−𝛼𝐿, (5) where 𝑇𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑(𝜆) is the quotient of 𝑇𝑟𝑎𝑤 over 𝑇𝑟𝑎𝑤,𝑚𝑎𝑥, 𝛼 is the optical absorption coefficient (𝑐𝑚−1), L is the thickness of the sample (cm).
Experimental Procedure
In order to measure the photodetector voltage from the transimpedance amplifier, the chopper must set in front of the lamp so it flashing the light for a certain amount of frequency. This will set the reference signal for the transimpedance amplifier since the amplifier small signal that output from the photodetector. When a white light pass through the sample, it consists of many wavelength so it necessary to put monochromator in front of the photodetector. The purpose of monochromator is to set a specific wavelength so the photodetector will only read that specific wavelength of light. The monochromatic can be set manually for each specific wavelength as shown in Figure 2.
Figure 2: Monochromator was set at the wavelength of 900nm. There was five pieces of equipment and one sample of gallium arsenide that need for this experiment: Tungsten lamp source, Monochromator (Bausch & Lomb NO. 33-86-77), one light chopper, a photodetector and one lock-in amplifier (SR510). The setup for these equipment is shown in figure 2 and figure 3.
Figure 5: Energy of photon vs. the log scale of photodetector voltage with and without sample. Finding the bandgap for this gallium arsenide sample will require the plot of photon energy versus the optical absorption coefficient square. In order to calculate the optical absorption coefficient, the raw transmissivity need to be calculated as shown in equation (4).
𝑇𝑟𝑎𝑤 = (^) 𝑃𝑉𝑃𝑉𝑤𝑖𝑡ℎ𝑜𝑢𝑡 𝑠𝑎𝑚𝑝𝑙𝑒𝑤𝑖𝑡ℎ 𝑠𝑎𝑚𝑝𝑙𝑒 = 0.381𝑉 0.04𝑉 = 0.105 𝑓𝑜𝑟 𝑤𝑎𝑣𝑒𝑙𝑒𝑛𝑔𝑡ℎ 𝑜𝑓 900𝑛𝑚
The transmissivity for wavelength at 900nm is also max transmissivity of this whole data; thus, the normalized transmissivity can be calculated by dividing max transmissivity by every other transmissivity. A sample calculation will use the transmissivity of wavelength 898nm to calculate for normalized transmissivity.
𝑇𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑 = (^) 𝑇𝑟𝑎𝑤,𝑚𝑎𝑥𝑇𝑟𝑎𝑤 = 0.0980.105 = 0.
-1.
-0.
0
1
2
3
1.375 1.38 1.385 1.39 1.395 1.4 1.405 1.41 1. Photodetector Voltage (mV) log scale Ephoton (eV)
Photodetector voltage vs. Ep
log(PV with sample) log(PV without sample)
From knowing the normalized transmissivity, the optical absorption coefficient can be calculated from the equation (5). Given that the thickness of gallium arsenide sample to be 0. inch. The conversion of this thickness to cm will be:
𝐿 = 0.011𝑖𝑛 ∗ 2.54𝑐𝑚𝑖𝑛 = 0.028 𝑐𝑚 𝑇𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑(𝜆) = 𝑒−𝛼𝐿
𝛼 = ln(𝑇𝑛𝑜𝑟𝑚𝑎𝑙𝑖𝑧𝑒𝑑−𝐿 (𝜆))= −0.028 𝑐𝑚 ln(0.929) = 2.63 𝑐𝑚−
After taking the square of the optical absorption coefficient, 𝛼, the curve of the 𝛼^2 𝑣𝑠. 𝐸𝑝 is shown in Figure 6.
Figure 6: The graph of the optical absorption coefficient versus energy of photon.
The bandgap energy of this sample will be the x – interception of the linear line that tangent with the curve as shown in Figure 7.
0
5000
10000
15000
20000
25000
30000
35000
40000
45000
1.375 1.38 1.385 1.39 1.395 1.4 1.405 1.41 1.
α^2 (cm^
Ephoton (eV)
(α^2) vs Ephoton
smaller than the expect value so this is not likely to the device that made from this sample. It is important that the energy of photon is equal or bigger than the energy of the bandgap for the excitation of carrier to occur. If the sample bandgap energy is smaller than that of the expected values then photon energy that used to excite the electron for the expected bandgap would be more than sufficient for bandgap with the energy of 1.33 eV.
The result from this experiment may not be accurate because the source of light does not only came from the Tungsten lamp. Since the light of the room is on, the light intensity of the room may contribute the absorption and this will increase the transmissivity. Furthermore, the environment of this experiment must be dust free in order to improve the transmissivity when light pass through the transparent semiconductor. The third error is the technical issue with the lock-in amplifier since one of the button that control the sensitivity of the phase is broken. It is more difficult to record a maximum voltage that output by the amplifier.
Conclusion
Due to many improperly working devices, the company suspected that the wafers from the subsidiary were label incorrectly and delivered wrong shipment. The expected value of bandgap energy for gallium arsenide is 1.42 eV, while the experimented sample of gallium arsenide shows a bandgap energy of 1.33 eV. The percent difference for this experiment is around 6.55% and this shows that the calculated values is not too far off from the expected value given that there are many errors in the experiment. This shows that the shipment of the wafer was right because the calculated values is very close to the expected values. Since the subsidiary only process gallium arsenide with the bandgap of 1.42 eV and gallium phosphide with the bandgap of 2.2 eV, the sample from the experiment cannot be gallium phosphide because the calculated values does not exceed 1.42 eV. Base on this result, the company should do the same
experiment on the sample of gallium phosphide in case the subsidiary does not miss label the wafer.
References
[1] Laboratory Notes Materials Engineering 153 Electronic, Optical and Magnetic Properties, Department of Biomedical, Chemical and Materials Engineering, San Jose State University, San Jose CA 2014, Chapter 07, pp. 01-07.
[2] Kasap, S., “Optical Absorption” in Principles of Electronic Materials and Devices, 3rd ed., McGraw-Hill, 2006, Boston, pp.427-431.
