Mate Lab Report 2

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San Jose State University *

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153

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Electrical Engineering

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Apr 3, 2024

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From: Van Luong Nguyen, Electrical Engineer Date: March 9, 2022 To: Mr. Mark Benjamin, Manager Subject: Testing of doped germanium sample for dopant concentration amount Dear Mark, The germanium semiconductor sample from the supplier requires testing when considering such a large quantity purchase of germanium wafers. Meaning the quality could be a faulty point, but we would need to know whether the doped germanium product should have a dopant concentration of to carriers per to be determine of good quality. 5?10 14 5?10 15 𝑐𝑚 3 To conduct testing of the germanium product we must detect the dopant concentration which is where we utilize the Hall Effect. By applying a voltage to a sample of doped germanium wafers, making sure to observe the resulting magnetic field. With the Hall voltage and current across the sample being measured using a Hall console across three magnetic field strengths in forward bias and reverse bias. The measured dopant concentration is about . This value is 7. 62?10 14 𝑐???𝑖𝑒??/𝑐𝑚 3 between the expected range of and . Based on these sample 5?10 14 5?10 15 𝑐???𝑖𝑒??/𝑐𝑚 3 results, the doped germanium wafers from the prospective supplier is of a high enough quality to proceed with a bulk order and SemiTech we should pursue this deal. Van Luong Nguyen

Introduction The purpose for this experiment was to test the quality of the germanium sample to determine if it meets the dopant concentration range of between to carriers per 5?10 14 5?10 15 . The test were done in a laboratory as to find if the given sample provided by the supplier 𝑐𝑚 3 will meet the standard dopant values. Testing of the quality of the semiconductor would be defined by the conductivity and draft mobility of the sample. These two factors are directly related to the carriers concentration. Thus the Hall Effect would need to be used in this experiment by placing the germanium wafers in an electric field and a magnetic field as displayed in Figure 1. Figure 1: Hall-voltage Circuit With the sample of germanium being placed in the magnetic field perpendicular to the current, thus developing the electric field. This phenomenon is used to measure the amount and type of carriers within a semiconductor. With the fact that both types of carriers (holes and electrons) produce conductivity, though the carrier type can’t be determined just from electrical measurements. As that would be subjected to the influence of a magnetic field on a moving

charge to determine. This effect occurs due to the charged particle being subjected to the Lorentz force as the sample creates a voltage potential. Using this equation to calculate the draft velocity: (1) 𝑉 ? = ? ? (𝑒*𝑝*?*?) The n represents the number of carriers or dopant concentration of the sample, is the current in ? 𝑋 the x-direction, represents the magnetic field in the z-direction, q represents the charge of the ? ? electron which is , t represents the thickness of the sample which is 0.01 cm, and 1. 6?10 −19 𝑉 ? would be the voltage potential created by the carrier. According to the right hand rule, the force is on the -y direction. Given that the carrier is in equilibrium, the forces should be in the inversed direction and would have the same magnitude. Which means (2) 𝑒 ? (𝑉 ? /?) = 𝑒 ? 𝑉 ? ? ? ? From equation 1 and 2: (3) 𝑉 ? = ? ? ? ? ? 𝑒 ? 𝑝 ? ? We would also need to utilize Ohm’s Law to get resistance and resistivity as well as conductivity. In these following equations: (4) 𝑅 = 𝑉/? (5) 𝑝 = 1/σ = (𝑅 ? ?)/𝐿 Where p refers to resistivity, is the conductivity, A is the cross section area, and L is the length σ of the sample. After we would need to calculate the hole mobility μ from the two value of conductivity and hole concentration with the equation: (6) σ = µ ? 𝑒 ? 𝑝

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Experimental Procedure The sample that the supplier sent was .2 cm long, .1 cm wide, and had a thickness of 0.01 cm. It was held by the Hall console, which was used to measure the current passing through the sample. There was a probe that we would have in the near the middle of the sample to get the most direct, but to also have it not touch the sample. It was also used to control the level of the magnetic field and to have it applied perpendicular to the direction of the current. The current through the sample and the Hall voltage was measured in forward bias of 300, 600, 900 Gauss as well as in reverse bias of -300, -600, -900 Gauss equivalently. The probe would be zeroed out and calibrated before the beginning of each gauss measurement. The experimental equipment is shown below in Figure 2:

Figure 2: Testing Equipment used to control and measure Hall voltage and current Results The given data in terms of the germaniun wafer sample measurements has a length of .2 cm, width of .1 cm, and has a thickness of .01 cm. The gathered data is what was measured throughout the testing of the sample of germanium. Magnetic Field sample current (mA) hall voltage (mV) 3.00E-06 5 14 3.00E-06 3 9 3.00E-06 1 4 6.00E-06 5 26 6.00E-06 3 16 6.00E-06 1 6

9.00E-06 5 38 9.00E-06 3 24 9.00E-06 1 8 -3.00E-06 5 -10 -3.00E-06 3 -6 -3.00E-06 1 -2 -6.00E-06 5 -23 -6.00E-06 3 -13 -6.00E-06 1 -4 -9.00E-06 5 -35 -9.00E-06 3 -22 -9.00E-06 1 -7 Table 1: Collected Measurements utilizing equipments. Bz for Magnetic Field, Ix for Sample Current, Vy is for Hall Voltage With this table we calculate the resistance using Ohm’s Law, with it being in which instance 𝑉? ?? 9.00E-06 at sample current 5 would result in a value of . 38 5 = 7. 6Ω Bz (V*s/cm^2) Ix*Bz 3.00E-06 1.50E-05 3.00E-06 9.00E-06 3.00E-06 3.00E-06 6.00E-06 3.00E-05 6.00E-06 1.80E-05 6.00E-06 6.00E-06 9.00E-06 4.50E-05 9.00E-06 2.70E-05 9.00E-06 9.00E-06 -3.00E-06 -1.50E-05 -3.00E-06 -9.00E-06 -3.00E-06 -3.00E-06 -6.00E-06 -3.00E-05

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-6.00E-06 -1.80E-05 -6.00E-06 -6.00E-06 -9.00E-06 -4.50E-05 -9.00E-06 -2.70E-05 -9.00E-06 -9.00E-06 Table 2: Magnetic Field in (V*s/cm^2) and Magnetic field(Bz) times Current (Ix) This value of Ix*Bz would be used with the Hall voltage to get the value of p through the Hall Effect. By plotting the Magnetic Field and Sample Current vs. Hall Voltage to confirm the carrier concentration of the sample. Graph 1: Hall Effect in Semiconductor This is done through equation 3, with the slope for the fitted line means . Then to 1 (𝑒 ? 𝑝 ? ?) = 819388 => 𝑝 = 1 (819388)(1.6*10 −19 )(.01) = 7. 62 * 10 14 𝑐???𝑖𝑒??/𝑐𝑚 3

calculate the mobility we would need equation 6 with . µ = σ/(𝑒 ? 𝑝) = .0263 (1.6*10 −19 )(7.62*10 14 ) = 215. 71 𝑐𝑚 2 /𝑉 * ? Discussion of Results The germanium semiconductor condutivity is a determining factor when considering if the sample is of great quality. This being that the conductivity is needed to get the dopant concentration amount to see if the sample value fits between and carriers per 5?10 14 5?10 15 . From the test we have as sample carrier concentration value of . 𝑐𝑚 3 7. 62?10 14 𝑐???𝑖𝑒??/𝑐𝑚 3 Thus deeming the sample to be in range of the reference dopant concentration which would make these germanium sample to be of good quality. Based on this, the doped germanium sample is fit for use and the bulk order from the prospective supplier should be pursued. According to the Electrical properties, the hole mobility of germanium is around . This means there was a significant difference between the theoretical and 1900 𝑐𝑚 2 /𝑉 * ? experimental value for mobility. A possible source of error present in this experiment was the couple beginning test in which the direction and calibration of the equipment was not understood fully at the time which may have changed future readings. With the measurements being a mess at the beginning we had to retest again under different pretense setting to prevent the same error. The values were more accurate the second time around, but the constant use after 2 whole sets of testing could have result in it being off a bit.

Conclusion The purpose of this experiment was to determine the quality of the doped germanium wafers to consider a possible bulk order by SemiTech from the supplier through the utiliziation of the Hall Effect to compare the dopant concentration of the sample to an accepted value for a good quality sample. With the accepted values being between and carriers per 5?10 14 5?10 15 with our value for carrier concentration being would confirm 𝑐𝑚 3 7. 62 * 10 14 𝑐???𝑖𝑒??/𝑐𝑚 3 that our sample of doped germanium is of great quality. This would mean that pursuing a bulk purchase of germanium wafers from the supplier would be worth it as it meets quality standards for similar quality germanium wafers.

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References 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 4, pp. 1-8 Kasap, S., “Electrical and Thermal Conduction in Solids: Mainly Classic Concepts,” in Principles of Electronic Materials and Devices , 3 rd ed., McGraw-Hill, 2006, Boston, Chapter 2.5 and 2.7 B.G. Streetman, Solid State Electronic Devices (1995), Chapter 3.4.5. Velasquez Luna, J. (2018). MatE 153 Protocol Hall Effects. Retrieved March 9, 2022 MatE 153 Hall Effect in Semiconductors-1. Retrieved March 9, 2022

Mate Lab Report 2

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