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2 AN ABSTRACT OF THE THESIS OF Rodney Austin Snyder for the degree of Honors Baccalaureate of Science in Physics and Mathematics presented on May 22, Title: Thermoelectric Characterization of Silicon Wafers and Cu 12 Sb 4 S 13 Variant Thin Films. Abstract Approved: Janet Tate The Van der Pauw method for transport measurements of conductivity and carrier concentration were tested on indium-tin-oxide (ITO) films and silicon wafers, and then implemented on Cu 10- xag x Zn 2 Sb 4 S 13 thin films. ITO was used as a test case for high temperature transport measurements because it a well characterized semi-metal. The mobility of ITO as a function of temperature is m µt a for a = This proportionality is consistent with scattering dominated by phonon. Silicon was measured as a test case because it is a well characterized semiconductor that can be controllably doped n and p-type. Rectangular wafers were measured: 620-μm thick, <100>-oriented n-type Si and <111> 650-μm thick, <111>-oriented p-type Si. For p-type Si, ρ = 21 mωcm and p = 6.25x10 18 cm -3, for n-type Si, ρ = 14 mωcm and n = 9.5x10 17 cm -3. The power factors for n- and p-doped silicon were measured at W/mK 2. The room-temperature resistivity and Seebeck coefficient of thin film variants of the mineral tetrahedrite Cu 12 Sb 4 S 13 were measured. In bulk form, tetrahedrite has shown promise as a good thermoelectric material. Thin films of Cu 10-x Ag x Zn 2 Sb 4 S 13 with a thickness of 360 nm were produced by e-beam deposition. The Seebeck coefficients ranged from 10 to 113 μv/k and the resistivity from 8 to 50 mωcm. Together, these values yield power factors S 2 /ρ ranging from 10-7 to 10-4 W/mK 2, approaching the range of their bulk counterparts. Key Words: Transport measurements, resistivity, carrier concentration, Van der Pauw method, thermoelectric, thin film, tetrahedrite, ITO, silicon Corresponding address: snyderro@onid.oregonstate.edu

4 Thermoelectric Characterization of Silicon Wafers and Cu 12 Sb 4 S 13 Variant Thin Films By Rodney Austin Snyder A PROJECT Submitted to Oregon State University University Honors College In partial fulfillment of the requirements for the degree of Honors Baccalaureate of Science in Physics and Mathematics (Honors Associate) Presented May 22, 2014 Commencement June 2014

5 Honors Baccalaureate of Science in Physics and Mathematics project of Rodney Austin Snyder presented on May 22, APPROVED: Mentor, representing Physics Committee Member, representing Physics Committee Member, representing Physics Chair, Department of Physics Dean, University Honors College I understand that my project will become part of the permanent collection of Oregon State University, University Honors College. My signature below authorizes release of my project to any reader upon request. Rodney Austin Snyder, Author

6 ACKNOWLEDGEMENTS The work that was accomplished through this project could not have been accomplished without the help of a large number of people. First and foremost, I would like to thank Dr. Janet Tate for constantly pushing me and teaching me what it means to be a physicist. Dr. Tate has been a tremendous influence on the scientist I will become. I would also like to greatly thank Chris Reidy. His help was invaluable with repairing equipment, preparing samples, and providing general guidance in the lab. Thanks to Jason Francis for being my initial bridge into the research group and teaching me the basics. I am very grateful for Mark Warner and Larry Nelson for helping repair equipment when it broke and being patient enough to teach me along the way. Thanks to Dr. Doug Keszler, Dr. John Wager, Greg Angelos, Jaesoek Heo for providing the motivation and the samples for the tetrahedrite research. Thanks to Dan Speer for taking the Seebeck coefficient measurements for this project and working with my inconsistent schedule. I would like to thank Josh Mutch for helping keep the continuity in the lab going and taking measurements when he was asked. Thanks to Aaron Kratzer for taking thickness data on the ITO for this project. Funding for this project was provided by the Center for Sustainable Materials Chemistry. Thank you for all of your support!

7 TABLE OF CONTENTS Page 1. Introduction Summary and goals Transport Properties Tetrahedrite properties Measurement Principles Bulk Measurements Conductivity Carrier Concentration and Mobility Thin Film Measurements Resistivity Carrier Concentration and Mobility The Van der Pauw Geometry Experimental Apparatus Masks and contacts Lakeshore 7504 Hall Measurement System High Temperature Hall Oven Materials Indium-Tin-Oxide (In 2 O 3 :Sn) Silicon Silver Tetrahedrite (Cu 10-x Ag x Zn 2 Sb 4 S 13 ) Experimental Results Indium-Tin-Oxide (In 2 O 3 :Sn) Silicon Silver Tetrahedrite (Cu 10-x Ag x Zn 2 Sb 4 S 13 ) Conclusions Bibliography... 32

8 LIST OF FIGURES Page Figure 2.1. A block of material with conductivity σ with length l and cross sectional area A [3] Figure 2.2. The set up for mobility measurements and the forces that are present [4] Figure 2.3. A semi-infinite uniform lamina with resistivity ρ and thickness d situated above the x-axis. Points P, Q, R, and S are on the edge of the film with P and Q separated by distance a, Q and R by b, and R and S by c Figure 2.4. A lamina with current i MO flowing into M and out of O. The potential difference is measured between points P and N [6] Figure 2.5. A CAD of a circular Van der Pauw geometry with bridges between the sample and contact points to act as virtual contacts. All dimensions are in mm Figure 3.1. An unpatterned sample mounted on the measurement chip Figure 3.2.The Hall measurement system block diagram Figure 4.1. The crystal structure for mineral tetrahedrite with 58 atoms in the unit cell [7,8] Figure 5.1. IV curves for adjacent contacts with average resistance 48 Ω Figure 5.2. The resistivity of ITO increased with temperature as expected for a metal Figure 5.3. The log μ vs log T plot from room temperature to 300 C. The mobility ranged from 33 to 25 cm 2 /Vs. The power law dependence is accurate with the slope of the line giving a = Figure 5.4. IV curves for n-type silicon with average resistance of 214 Ω Figure 5.5. IV curves of p-type silicon with average resistance 94.3 Ω Figure 5.6. The blue lines show compare the n-type results to the experimental results while the black lines show where the p-type results fit. These results fit the experimental standards closely [7] Figure 5.7. IV curves for Cu 9 Ag 1 Zn 2 Sb 4 S 13 with an average resistance of 1.90 kω. This was the least uniform sample of the set Figure 5.8. IV curves for Cu 8 Ag 2 Zn 2 Sb 4 S 13 with average resistance of 1.55 kω Figure 5.9. IV curves for Cu 7 Ag 3 Zn 2 Sb 4 S 13 with average resistance of 478 Ω

9 LIST OF FIGURES (Continued) Page Figure The resistivity and Seebeck Coefficients of the silver tetrahedrite films as a function of silver concentration Figure The power factor of silver tetrahedrite as a function of silver concentration Table 6.1. the thermal transport properties of silver tetrahedrite in thin film and bulk

10 1 1. Introduction 1.1 Summary and goals The purpose of this project is to measure the carrier density, carrier type, conductivity, and Hall mobility of thin films as a function of temperature. Transport measurements of this type elucidate the mechanism of charge conduction. Mobility is limited by various scattering mechanisms (phonon, impurity scattering), each of which have a characteristic temperature dependence. Indium-tin-oxide (ITO) thin films and silicon wafers are measured to validate the measurement techniques used. Semiconductors of the tetrahedrite subgroup are characterized as a thermoelectric with the information from the ITO and silicon measurements in mind. 1.2 Transport Properties The conductivity σ and carrier concentration n are useful material properties in physics. The conductivity determines the amount of current that is the result of an applied electric field. (1) J is the current density and E is the magnitude of the electric field. This is Ohm s law which is a good approximation in the event that scattering is frequent. The conductivity of a material is independent of its size and shape.

11 2 The carrier concentration n is the density of carriers in a material. The carrier concentration, as well as the sign of the carriers, is determined from the Hall voltage. The Hall voltage is a potential difference that is created perpendicular to the current as a result of an applied magnetic field. The relation of these quantities is (2) where q is charge of the carriers (±1.9x10-19 C) and d is the thickness of the material. The carrier concentration and conductivity are related by the mobility μ [1] (3) The mobility of a material is a measure of how quickly a carrier can move through the material. The drift velocity v d is the average speed of carriers moving through the lattice (4) High motilities allow for devices to react rapidly. This is beneficial for making devices such as transistors which need to switch between states quickly. For this project, tetrahedrite samples will be characterized. This class of materials was chosen due to their high thermopower (S), or Seebeck coefficient in bulk. The power factor can be calculated from the thermopower and conductivity (5) The thermopower and conductivity both have a key role in the figure of merit (6) where κ is the thermal conductivity. A large figure of merit (ZT > 1) leads to a high thermoelectric efficiency which reduces the amount of power wasted in devices. The

12 3 electrical conductivity between materials can vary by several orders of magnitude, which has a large impact of ZT. Doping the sample can increase the number of carriers but also might distort the lattice and lower the conductivity. A balance between a uniform lattice and a large number of carriers must be achieved to produce a large conductivity. 1.3 Tetrahedrite materials The mineral tetrahedrite is a chalcogenide with chemical formula (CuFe) 12 Sb 4 S 13. Synthetic variants of the parent structure have been explored as semiconductors with the potential to be good thermoelectrics. These variants have direct substitutions onto the copper sites of Cu 12 Sb 4 S 13 with other transition metals including zinc, manganese and iron. Silver has been recently been substituted as well. Some of these compounds have a large thermoelectric figure of merit. Substitutions with manganese have promise as thermoelectrics thanks to a lower thermal conductivity than the parent structure [2]. Silver tetrahedrite, Cu 10-x Ag x Zn 2 Sb 4 S 13, has Seebeck coefficients between 500 and 650 W/K 2 m in the bulk which is up from a maximum of 300 W/K 2 m in other derivatives. The large Seebeck coefficient of silver tetrahedrite inspired a study of thin films of the material.

13 4 2. Measurement Principles The techniques used to measure conductivity and carrier concentration differ between bulk materials and thin films. For bulk materials, conductivity is measured using the dimensions of the block and finding the resistance with a two contact approach. The carrier concentration is measured using the Hall effect directly. In thin films, the method to find the conductivity and the carrier concentration are outlined by Van der Pauw and require a more complicated four contact approach. 2.1 Bulk Measurements Understanding the bulk measurements can give valuable insight into thin film measurements. The conductivity can be solved for analytically in bulk materials while the conductivity needs to be found computationally in thin films Conductivity In bulk materials, the measurement of the conductivity starts by placing low resistance Ohmic contacts on the ends of a block of the material with length L and contact size A as depicted in figure 2.1.

14 5 Figure 2.1. A block of material with conductivity σ with length l and cross sectional area A [3]. Ohmic contacts are defined by a linear relationship between the current and voltage across the contacts and as shown in equation 7. (7) The conductivity can be found by applying a current across the material and measuring the potential difference. The conductivity is found from equation 8. (8) Carrier Concentration and Mobility The carrier concentration of a bulk material is found by placing Ohmic contacts onto the ends and sides of a block with thickness d. A current is applied to the ends and a magnetic field is then applied perpendicular to both the surface and the current as shown in figure 2.2.

6 Figure 2.2. The set up for mobility measurements and the forces that are present [4]. The carriers feel a resulting Lorenz force (9) where is the drift velocity.

15 6 Figure 2.2. The set up for mobility measurements and the forces that are present [4]. The carriers feel a resulting Lorenz force (9) where is the drift velocity. The electric field can be written in terms of its components, (10) E applied is the electric field that drives the current, and in a material with frequent scattering, does not accelerate the carriers. E H is the Hall field which occurs due to charges building up on the edge of the sample shown in figure 2.2. The Hall voltage V H is the voltage that is present when the Lorenz force is zero. In this case, (11) Since the drift velocity and the magnetic field are perpendicular to each other by design, (12) Substituting in the current in terms of the drift velocity and noting that the electric field must be constant across the material gives

16 7 (13) Equation 13 gives a relationship between the carrier concentration n and the measureable quantities of the Hall voltage, the current applied the thickness of the sample and the magnetic field. The charge is C and the sign is determined by the sign of the Hall voltage. Once the carrier concentration and the conductivity are known, the mobility is found from The mobility is a positive quantity and the absolute value on the charge in equation 14 ensures that. (14) 2.2 Thin Film Measurements The Van der Pauw method is used to calculate the resistivity and the carrier concentration of thin films. Films must be arbitrarily thin, yet can be any shape as long as the contacts are made on the edge of the film. In this section, the mathematics and underlying assumptions for this method are outlined Resistivity The Van der Pauw method for calculating resistivity is a 4 contact approach for thin films. The method can be used with any arbitrary shape [5]. To prove this, first

17 8 consider a semi-infinite uniform lamina of thickness d starting at the x-axis with resistivity ρ as depicted in figure 2.3. Figure 2.3. A semi-infinite uniform lamina with resistivity ρ and thickness d situated above the x-axis. Points P, Q, R, and S are on the edge of the film with P and Q separated by distance a, Q and R by b, and R and S by c. Next, let a current I 0 flow into P from a point contact and out at infinity. The current density at a distance r from P is (15) The factor of πrd is a result of the conservation of current and calculated from the integral (16) The current density is uniform at a distance r away because there is no preference in the direction the current will flow as the lamina being uniform. The potential difference between points R and S is then

18 9 (17) Using Ohm s law, simplifies equation 17 to (18) Integrating this expression gives the potential difference in terms of defined quantities ( ) (19) Similarly, if a current of I 0 is flowing out of point Q from infinity, the potential difference is ( ) (20) Using superposition of the current into P and out of Q using results in the potential difference ( ) (21) Dividing by the current in P and out of Q and exponentiating both sides gives the expression (21) (22)

19 10 Similarly, it can also be shown that ( ) (23) Adding these expressions together yields [5] ( ) ( ) (24) This expression can be used to solve for the resistivity computationally. This result can be shown to hold for arbitrary lamina of finite size by first assuming that the upper part of the plane coincides with the complex z-plane with z=x+iy. With this assumption, a conformal mapping can be used to use an arbitrary shape [5] Carrier Concentration and Mobility The carrier concentration and mobility can also be measured for lamina of arbitrary shapes. This can be done provided that a. The contacts are small and Ohmic b. The contacts are on the edge c. The lamina is of uniform thickness d. The distribution of current streamlines is unchanged when a magnetic field is applied [6]. If the contacts are placed somewhere on the surface of the lamina, error is introduced as shown in section 2.3. For a lamina that fits all of these assumptions the Hall field at equilibrium is

20 11 (25) where J is the current density. Figure 2.4 shows the Hall field on a lamina at equilibrium. Note that the Hall field is perpendicular to the current at every point. Figure 2.4. A lamina with current i MO flowing into M and out of O. The potential difference is measured between points P and N [6]. The Potential between P and N is where V Ω is the potential difference between P and N without the magnetic field and V H is the Hall voltage. The Hall voltage between P and N is found by integrating the electric field on a path perpendicular to the current. Integrating in along this path eliminates the potential contribution from the current. As a result, integrating from P to N will yield the same Hall voltage as integrating from P to N. (26) (27) The carrier concentration is then found from

21 12 (28) 2.3 The Van der Pauw Geometry Samples with high symmetry are used to find the carrier concentration to reduce the size of the V Ω term. Disks are used to eliminate the V Ω term. If the contacts take up a width w on the edge of a disk with diameter D, the error introduced into the resistivity and mobility are [5] (29) (30) The pads in figure 2.5 make the effective contact size the width of the bridge between the pad and the sample.

22 13 Figure 2.5. A CAD of a circular Van der Pauw geometry with bridges between the sample and contact points to act as virtual contacts. All dimensions are in mm. If the current i flows into 3 and out of 1, and a magnetic field B is applied out of the page, the V Ω term vanishes from the carrier concentration expression yielding (31) This means that the potential difference between contacts 4 and 2 is the Hall voltage. In practice, the V Ω term is not completely eliminated due to non-uniformities in the sample. To reduce the error introduced from a non-zero V Ω term, the following set of averages are taken. First, let be the potential between contacts 1 and 2 with a positive (p) or negative (n) magnetic field applied and I 12 be the current into 1 and out of 2. The contact

23 14 placement is seen in figure 2.5. Eight measurements are averaged to get the carrier concentration qn = 8 x 10-8 IB/[d(V C + V D + V E + V F )] (32) V C = V 24P - V 24N, with I 13 (33) V D = V 42P - V 42N, with I 31 (34) V E = V 13P - V 13N, with I 42 (35) V F = V 31P - V 31N. with I 24 (36) A similar set of averages are taken to eliminate errors from non-uniformity for resistivity measurements. Again, let V 12 be the potential between contacts 1 and 2 and I 12 be the current into 1 and out of 2. Next, let R 12,34 be V 34 /I 12 where the voltage between 3 and 4 with a current applied into 1 and taken out of 2. R 21,34 = V 34 /I 21, R 12,43 = V 43/ I 12, (37) R 32,41 = V 41 /I 32, R 23,14 = V 14/ I 23, (38) R 43,12 = V 12 /I 43, R 34,21 = V 21 /I 34, (39) R 14,23 = V 23 /I 14, R 41,32 = V 32 /I 41. (40) Using these values, R A and R B are defined as R A = (R 21,34 + R 12,43 + R 43,12 + R 34,21 )/4 (41) R B = (R 32,41 + R 23,14 + R 14,23 + R 41,32 )/4 (42) Using the defined quantities R A and R B, the resistivity is computed from a similar equation to the theoretical model [1] ( ) ( ) (43)

24 15 3. Experimental Apparatus The experiment can be broken down into three steps; making contacts, operation of the equipment, and interpretation of the results. Low resistance Ohmic contacts are necessary to ensure that the sample properties determinate rather than the contact barrier properties; making good contacts is a non-trivial manner. Important operational details and the experimental limits of the equipment are presented. Finally, the data analysis is discussed, including examination of current-voltage (IV) curves and assessment of resistivity averages in order to determine the quality of the contacts and validity of the measurements. 3.1 Masks and contacts The thin film samples are deposited through a shadow mask similar to that shown in figure 2.5. The diameter of the film is 5-10 mm with typical thickness nm. Metal pads are used to make electrical contact with the film. For room temperature measurements, indium pads are melted onto each of the four pads of the film or onto the very edge of the film if unpatterned. Indium melts at 170 C and the soldering iron temperature is kept as low as possible (about 200 C) to prevent oxidation of the indium. A dedicated soldering probe is used to prevent contaminating the indium. A small amount of indium is soldered onto thin wires (about 0.5 mm) at 200 C and then pressed onto the pads on the sample. For high temperature measurements, metal contacts are

16 evaporated onto the sample. The metal for the contacts must have a higher melting point than the maximum measurement temperature used; typically aluminum is used.

25 16 evaporated onto the sample. The metal for the contacts must have a higher melting point than the maximum measurement temperature used; typically aluminum is used. The contacts should have a thickness of at least 1μm to ensure that the spring-loaded contact pins used in the high temperature sample holder do not go through the metal and contact the substrate. Figure 3.1. An unpatterned sample mounted on the measurement chip 3.2 Lakeshore 7504 Hall Measurement System The block diagram for the Hall measurement system is shown in Fig 3.2. All of the measurement devices are interfaced by the computer and are run remotely.

26 17 Figure 3.2.The Hall measurement system block diagram There are restrictions on the currents and power in the system. The upper limit on the voltmeter is 5V and the upper limit of the ammeter is 2A. The magnet power supply can apply 50A safely to the electromagnet. The magnetic poles can be moved to adjust the field. The closer the poles are, the larger the magnetic field is. In practice, it is difficult to achieve a magnetic field much greater than 20kG. These limits put a practical limit on the

27 18 carrier densities that can be measured. The largest carrier concentration measured with this set up had a two-contact resistance of about 1 GΩ. In principle, the carrier concentration can be measured for any sample, but in practice, only highly symmetric samples can be measured. The resistance averages need to be close to each other. For samples with resistances near 1 kω, these averages should be within a factor of 5. For samples with resistances near 1 MΩ, these averages should be within 50%. The discrepancy in these averages is because a larger current can be applied to the lower resistive sample which causes the Hall voltage to be larger. The carrier concentration should be independent of the applied magnetic field, so fields from 15 kg to 20 kg are swept in increments of 1 kg with the field reversed after all of these measurements are taken. The whole process takes minutes which means that about 10 minutes pass between measurements at the positive and negative magnetic fields. The time delay can cause some samples to change, but this usually is not a problem unless the sample is highly reactive with oxygen at room temperature. The time delays during the measurement process can cause drift in the acquisition system. The system is turned on a few hours before the measurement to allow the system to normalize which minimizes this drift. 3.3 High Temperature Hall Oven The high temperature Hall oven is an attachment for the Hall measurement system that is designed to heat samples up to 450 C. The measurement procedure is similar to

28 19 that as room temperature measurements, but there are additional procedures associated with heating. To prevent the sample from being oxidized, the chamber is evacuated to 10-4 Torr and flushed out with an inert gas, high purity argon. During high temperature measurements, the magnetic field is not swept through a range of fields, so measurements are only two minutes apart for each field. The entire range of temperatures is swept through in about 2 hours with cooling taking an additional 3-4 hours depending on the peak temperature. The Hall oven interfaces with the software for the Lakeshore system so that the process can be automated. The mobility and resistivity can be measured as a function of temperature. Due to the diameter of the sheath of the oven, the poles of the magnet are spaced further apart which limits the magnetic field to 10kG as opposed to 20kG for room temperature measurements. As a result, low mobility samples are difficult to measure, but the resistivity can still be measured. The stability of the sample at high temperatures is important to note as the lattice of the sample may shift at a lower temperature than the bulk material. These shifts can be the result phase transitions or some elements evaporating off of the film.

29 20 4. Materials 4.1 Indium-Tin-Oxide (In 2 O 3 :Sn) Indium-tin-oxide (ITO), a well characterized semiconductor, has been measured to determine the accuracy of the high temperature Hall oven. ITOcan vary from being a weak metal to a semiconductor. The sample measured for this calibration was a thin film 162 nm thick with metallic properties. 4.2 Silicon Silicon is a well-known semiconductor that can be easily and controllably doped n and p-type. Silicon wafers are cheap and commercially available. The resistivity of doped silicon can vary from 10-4 to 10 4 Ωcm and the carrier concentration can range from to cm -3 [7]. Rectangular samples of <100> 620μm n-type silicon and <111> 650μm p-type silicon were measured to determine the accuracy of the apparatus. The nominal resistivities were Ωcm < ρ < 0.02 Ωcm for p-type silicon and 0.01 Ωcm < ρ < Ωcm for n-type silicon. 4.3 Silver Tetrahedrite (Cu 10-x Ag x Zn 2 Sb 4 S 13 ) Tetrahedrite materials are a class of materials with the same crystalline structure as Cu 12 Sb 4 S 13 which is shown in figure 4.1. These materials have been shown to have a

30 21 large Seebeck coefficient in bulk materials, which makes them interesting as a thermoelectric [12]. 360 nm thin films of Cu 10-x Ag x Zn 2 Sb 4 S 13 were produced by Greg Angelos in the Wager lab by e-beam deposition with the silver and zinc going onto the copper site of the films. The x value of silver was varied between 1 and 3. The tetrahedrite films were rectangular rather than patterned which has no impact on measuring the resistivity. Figure 4.1. The crystal structure for mineral tetrahedrite with 58 atoms in the unit cell [8,9]

31 Voltage (mv) Experimental Results 5.1 Indium-Tin-Oxide (In 2 O 3 :Sn) The transport properties of indium-tin-oxide (ITO) were measured as a function of temperature from room temperature to 300 C. A 10 kg magnetic field was used for carrier concentration measurements. ITO is very conductive so contact was made directly to the sample without metal pads being evaporated on. The IV curves in figure 5.1 show that the contacts are Ohmic terminal resistance ITO thin film 0 1-2: R = 46.5 Ω : R = 50.7 Ω : R = 50.7 Ω : R = 44.3 Ω Current (ma) Figure 5.1. IV curves for adjacent contacts with average resistance 48 Ω. The room temperature resistivity was 145μΩcm while the mobility was 33cm 2 /Vs which are consistent with the literature [10]. The resistivity of ITO rises with temperature, figure 5.2, which is consistent with ITO being a weak metal. In a metal, most of the states near the Fermi energy are already filled at room temperature. This

32 Resistivity μω cm 23 means that the temperature dependence of the mobility is dominated by the resistivity since the carrier concentration is fairly constant. The mobility decreased as temperature increased. The log μ-log T plot in Fig. 5.3 is a straight line, which indicates the powerlaw assumption m µt a is accurate with the slope of the line giving a = This temperature dependence is consistent with piezoelectric acoustic phonon scattering [11] Resistivity vs. Temperature ITO Temperature C Figure 5.2. The resistivity of ITO increased with temperature as expected for a metal.

33 Log of Mobility (cm 2 /Vs) Hall Mobiltiy of ITO Log Temperature (K) Figure 5.3. The log μ vs log T plot from room temperature to 300 C. The mobility ranged from 33 to 25 cm 2 /Vs. The power law dependence is accurate with the slope of the line giving a = Silicon Figure 5.4 and 5.5 show the IV curves for n-type and p-type silicon respectively. The resistances for each set of contacts are within 25% of the average which is better than required for good data at this resistance range. The resistivity was Ωcm for the p- type silicon and Ωcm for n-type. The carrier concentration at 20kG was n = 9.5x10 17 cm -3 and p = 6.25x10 18 cm -3. These values are compared to the theoretical model and are plotted in Fig The Seebeck coefficients for the n-type and p-type silicon were 800 μv/k and 650 μv/k respectively. The Seebeck coefficients were measured by Dan Spear in the Tate lab. The power factor, σs 2, was calculated from these results and was W/K 2 m for both n-type and p-type silicon.

34 Voltage (V) Voltage (V) terminal resistance n-type Si : R = 250 Ω 2-3: R = 207 Ω 3-4: R = 176 Ω : R = 221 Ω Current (ma) Figure 5.4. IV curves for n-type silicon with average resistance of 214 Ω terminamal resistance p-type Si 1-2: R = 82.4 Ω 2-3: R = 87.6 Ω 3-4: R = 106 Ω Current (ma) Figure 5.5. IV curves of p-type silicon with average resistance 94.3 Ω.

35 26 Figure 5.6. The blue lines show compare the n-type results to the experimental results while the black lines show where the p-type results fit. These results fit the experimental standards closely [7]. 5.3 Silver Tetrahedrite (Cu 10-x Ag x Zn 2 Sb 4 S 13 ) The resistivity and Seebeck coefficients were measured for the atomic concentration of silver; x = 1, 2, and 3. The resistivities ranged from 8 to 50 mωcm and the Seebeck coefficients from 10 to 113 μv/k. These results are summarized in figure Figures 5.7, 5.8 and 5.9 show the IV curves for the resistivity measurements.

36 Voltage (V) Voltage (V) terminal resistance Cu 9 Ag 1 Zn 2 Sb 4 S : R = 1.98 kω 2-3: R = 0.80 kω 3-4: R = 2.33 kω 4-1: R = 2.87 kω Current (ma) Figure 5.7. IV curves for Cu 9 Ag 1 Zn 2 Sb 4 S 13 with an average resistance of 1.90 kω. This was the least uniform sample of the set terminal resistance Cu 8 Ag 2 Zn 2 Sb 4 S : R = 1.40 kω : R = 1.47 kω : R = 1.67 kω : R = 1.66 kω Current (ma) Figure 5.8. IV curves for Cu 8 Ag 2 Zn 2 Sb 4 S 13 with average resistance of 1.55 kω.

37 Voltage (V) terminal resistance Cu 9 Ag 1 Zn 2 Sb 4 S : R = 572 Ω : R = 393 Ω : R = 410 Ω 4-1: R = 535 Ω Current (ma) Figure 5.9. IV curves for Cu 7 Ag 3 Zn 2 Sb 4 S 13 with average resistance of 478 Ω. The average resistances for Cu 7 Ag 3 Zn 2 Sb 4 S 13 and Cu 8 Ag 2 Zn 2 Sb 4 S 13 were within 25% of the average while the Cu 9 Ag 1 Zn 2 Sb 4 S 13 had resistances within a factor of 3 of the average resistance. The Cu 9 Ag 1 Zn 2 Sb 4 S 13 sample was less uniform than the other samples so the contacts were placed with less symmetry. This resulted in a larger discrepancy in resistance values from a shorter distance between some contacts. However, the break in symmetry here does not impact the ability to measure resistivity with high precision.

38 Power Factor (W/K 2 m) Resistivity (mωcm) Seebeck Coefficient (μv/k) X Resistivity Seebeck Coefficient Figure The resistivity and Seebeck Coefficients of the silver tetrahedrite films as a function of silver concentration. 1.E+00 1.E-01 1.E-02 1.E-03 1.E-04 1.E-05 1.E-06 1.E Cu 10-X Ag X Zn 2 Sb 4 S 13 Power Factor X Figure The power factor of silver tetrahedrite as a function of silver concentration.

39 30 6. Conclusions For this thesis project, a system for high temperature transport measurements was developed. The high temperature system that was installed can measure samples up to 450 C in a magnetic field of 1 T. High temperature Hall measurements were conducted on indium-tin-oxide to test the procedure. The procedure was shown to work by finding that m µt a is accurate with the slope of the line giving a = -0.3 for ITO. The procedure will be implemented in future projects. The silicon measurements showed that the system worked by verifying the properties of a well-known material. Results with our system agree closely to the known experimental results [7]. Silicon measurements showed that the power factor is a good measure for a thermoelectric, but more information is needed to get the complete picture. The thermal conductivity is an import material property to know when evaluating a new thermoelectric material. Measuring the thermal conductivity of a material is difficult and beyond the scope of this project. `The transport properties of Cu 10-x Ag x Zn 2 Sb 4 S 13 thin films were measured and compared to the bulk forms. In bulk, the Seebeck coefficients were between 450 and 650 μv/k and the resistivities were between 0.05 and Ωm [12]. When the samples were made into thin films, the Seebeck coefficients and resistivities of the samples decreased sharply. These sharp decreases resulted in a larger power factor in some of the samples when comparing them to their bulk counterparts. However, since the Seebeck

40 31 coefficient decreased so much, the samples no longer had the property that made interesting in the first place. This result is summarized in table 6.1. Variant # (X) Resistivity (mω cm) Seebeck Coefficient (µv/k) Power Factor (W/m K 2 ) Thin Films Bulk Table 6.1. the thermal transport properties of silver tetrahedrite in thin film and bulk. The carrier concentration and mobility were impossible to measure due to the non-uniformity of the films. Patterned samples are being prepared and will be characterized as soon as they are done. The film variant of Cu 8 Ag 2 Zn 2 Sb 4 S 13 had a high level of impurities that could have resulted in figure 5.10 having no trend in the Seebeck coefficient. Further tests on the new samples will need to be done to confirm this.

41 32 Bibliography 1. US Department of Commerce, N. The Hall Effect. at < 2. Heo, J., Laurita, G., Muir, S., Subramanian, M. A. & Keszler, D. A. Enhanced Thermoelectric Performance of Synthetic Tetrahedrites. Chem. Mater. 26, (2014). 3. Resistivity Geometry by Omegatron is licensed by under CC by Hall Effect at < 5. A Method of Measuring Specific Resistivity and Hall Effect of Discs of Arbitrary Shape, L. J. Van der Pauw, Philips Research Reports, Vol 13, No 1, A Method of Measuring the Resistivity and Hall Coefficient on Lamellae of Arbitrary Shape, L. J Van der Pauw, Philips Research Reports, Semiconductors on NSM at < 8. Johnson M L, Burnham C W, American Mineralogist, 70 (1985) p , Crystal structure refinement of an arsenic-bearing argentian tetrahedrite 9. Kiyoaki Tatsuka, N. M. Tetrahedrite stability relations in the Cu-Fe-Sb-S system.american Mineralogist 62, (1977). 10. Ray, Swati, Ratnabali Banerjee, et al. "Properties of tin doped indium oxide thin films prepared by magnetron sputtering." Journal of Applied Physics. (1983) 11. Electrical Characterization of GaAs Materials and Devices, David Look, Wiley (1992) 12. Jaeseok Heo. Design Meets Nature: New Multi-functional Tetrahedrites as PV and TE Materials.

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DEPOSITION OF THIN TiO 2 FILMS BY DC MAGNETRON SPUTTERING METHOD

Chapter 4 DEPOSITION OF THIN TiO 2 FILMS BY DC MAGNETRON SPUTTERING METHOD 4.1 INTRODUCTION Sputter deposition process is another old technique being used in modern semiconductor industries. Sputtering