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Magnetoresistance of N-Type Magnesium Germanide Soo Nyong Lee Iowa State University

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Magnetoresistance of N-Type Magnesium Germanide Soo Nyong Lee Iowa State University Iowa State University Capstones, Theses and Retrospective Theses and Dissertations Dissertations 1968 Magnetoresistance of n-type magnesium germanide Soo Nyong Lee Iowa State University Follow this and additional works at: https://lib.dr.iastate.edu/rtd Part of the Condensed Matter Physics Commons Recommended Citation Lee, Soo Nyong, "Magnetoresistance of n-type magnesium germanide " (1968). Retrospective Theses and Dissertations. 4607. https://lib.dr.iastate.edu/rtd/4607 This Dissertation is brought to you for free and open access by the Iowa State University Capstones, Theses and Dissertations at Iowa State University Digital Repository. It has been accepted for inclusion in Retrospective Theses and Dissertations by an authorized administrator of Iowa State University Digital Repository. For more information, please contact [email protected]. This dissertation has been microfilmed exactly as received 69-9870 LEE, Soo Nyong, 1936- MAGNETORESISTANCE OF N-TYPE MAGNESIUM GERMANIDE. Iowa State University, Ph.D., 1968 Physics, solid state University Microfilms, Inc., Ann Arbor, Michigan MAGNETORESISTANCE OF N-TYPE MAGNESIUM GERMANIDE by Soo Nyong Lee A Dissertation Submitted to the Graduate Faculty in Partial Fulfillment of The Requirements for the Degree of DOCTOR OF PHILOSOPHY Major Subject: Physics Approved: Signature was redacted for privacy. In Charg of Major Work Signature was redacted for privacy. Signature was redacted for privacy. Iowa State University Ames, Iowa 1968 ii TABLE OF CONTENTS ABSTRACT iii INTRODUCTION 1 A. Magnetoresistance 1 B. Properties of Mg^Ge 3 C. Purpose of This Investigation 8 THEORY 9 A. Magnetoconductivity Tensor Components 9 B. Experimental Approach 14 C. Energy Surfaces of the Many-Valley Type 17 EXPERIMENTAL PROCEDURE 28 A. Preparation of Samples 28 B. Measurements 35 EXPERIMENTAL RESULTS 52 A. Hall Coefficient and Resistivity 52 B. Magnetoresistance 65 DISCUSSION 91 A. Conduction Band Model 91 B. Hall Coefficient 93 C. Energy Separation Between A- and C-Minima 97 D. Resistivity 99 E. Hall Mobility F. Magnetoresistance iii VI. CONCLUSION AND RECOMMENDATIONS 105 A. Conclusion 106 B. Future Work 107 VII. LITERATURE CITED 109 VIII. ACKNOWLEDGMENTS 114 IX. APPENDIX 115 iv LIST OF FIGURES Figure 1. Crystal structure of MgoGe. Eight Mg atoms are at ±1/4/ ±1/4, ±1/4. Four Ge atoms are at 0,0,0; 0,1/2,1/2; 1/2,0,1/2; 1/2,1/2,0. 4 Figure 2. Sample orientations. Magnetoresistance coef­ ficients were measured along <ÏÏ2>, 45°, <111> and 135° directions. 15 Figure 3. Constant energy ellipsoids for a many valley semiconductor. 20 Figure 4. Method for growth of single crystals of MggGe. 30 Figure 5. Orientations of a magnetoresistance sample. 32 Figure 6. Orientation of single crystals. 34b Figure 7. Arrangement of the probes attached to the sam­ ple. Probes 1 and 2 are current probes, 3 and 4 are for resistance and magnetoresistance measurements, and 3, 4, and 5 are for Hall voltage measurements. 36 Figure 8. Sample holder with spring contact probes. 38 Figure 9. Modified sample holder with resistance probe distance of 1.27 mm. 41 Figure 10. Overall view of sample holder. Two teflon wheels guide the sample holder in an axial rotation. 42 Figure 11. Block diagram of the magnetoresistance apparatus. 45 Figure 12. Measurement of Hall voltage. 49 Figure 13. Temperature dependence of Hall coefficients. C-samples show Hall coefficient maxima just before the onset of intrinsic conduction. 55 Figure 14. Temperature dependence of resistivities. Sample Bl shows the sharpest shape in the extrinsic region. For C-samples the resistivity suddenly decreases near 250K with increasing temperature indicating that electrons move up into a higher" band where they have a higher mobility. 58 V Figure 15, Field dependence of Hall coefficients. The Hall coefficients are nearly independent of the magnetic field up to 7k gauss. 61 Figure 16, Temperature dependence of Hall mobilities. For A-samples the Hall mobility varies as T-1.6 at high temperatures indicating that acoustic mode scattering is dominant. The purer samples C and D show quite low mobility values at low temperatures and all samples show similar mobility values above 300K. 62b Figure 17, Hall mobility as a function of carrier concen­ tration. The data points 7B1, 7B3 and llBl are taken from the earlier report by Redin et al. (48). The Hall mobilities at 77K for six additional samples/ JlA/ J8A, J8B, JMPl and PlD, are also shown in the figure. The solid line shows the Hall mobilities at 77K, the dashed line shows the Hall mobilities at 300K. The large variation in Hall mobilities at 77K disappears at 300K. 64b Figure 18, Effect of Mg distillation on electrical prop­ erties of MggGe. 67 Figure 19. Angular dependence of the magnetoresistance coefficients at 77K. A, B, C, and D samples show distinctive differences in their angu­ lar dependence. 69 Figure 20. Dependence of the magnetoresistance upon magnetic field. The magnetoresistance varies as the square of the magnetic field at low fields. 72 Figure 21. Magnetoresistance of MggGe. 73 Figure 22. Magnetoresistance as a function of carrier concentration for 77K, 165K and 250K. The magnetoresistance increases sharply near n=1.5xlO^^ cm~^ with decreasing carrier concentration. 74 Figure 23. Seitz coefficients b+ c and d are plotted as functions of carrier concentration. A-sam­ ples and Bl sample show the symmetry relation of <100> ellipsoids (b + c= -d and d < 0). 83 vi Figure 24. Temperature dependence of the anisotropy parameter K for A-samples and Bl sample. 85b Figure 25. Temperature dependence of the ratio Hall mobility to conduction mobility for A-samples and Bl sample. ^ 89 Figure 26. The temperature dependence of the Hall and conduction mobilities. At high temperatures the acoustic mode scattering is dominant, but at low temperatures ionized impurity scattering is important. 90 Figure 27. Conduction band model for Mg^Ge. 92 Figure 28. The quantities x= n^j^ and y=it:p-c plotted as a function of temperature for different samples. 95 vii LIST OF TABLES Table 1. Values of anisotropy factors for conductivity coefficients in case of single ellipsoid. 23 Table 2. Anisotropy factors for systems of ellipsoids having cubic symmetry. 24 Table 3. Inverse Seitz coefficients for systems of ellipsoids having cubic symmetry. 25 Table 4. Dimensions and characteristics of n-type Mg^Ge samples. 53 Table 5. Galvanomagnetic coefficients. 75 Table 6. Temperature dependence of Hall and conduction mobilities. 87 viii ABSTRACT The electrical resistivity. Hall coefficient and weak field magnetoresistance were measured from 5OK to 350K for a number of n-type Mg^Ge samples having carrier concentra­ tions at 300K from 1.0 x 10^^ cm~^ to 8.7 x 10^^ cm~^. Our data suggests the possibility of a triple conduction band for MggGe. The highest band is characterized by <100> ellipsoids. At 77K the electron Hall mobility = 2000 cm /volt-sec and the anisotropy parameter K = = 1.6. This band seems to be deformed near the bottom edge so that 9 for electrons near the bottom of the band jXjj = 4000 cm /volt- sec and K = 3.5 at 77K. The next highest band minima also lie along <100> directions, but the mobility of the charge carriers in this band is only one-tenth that of the charge carriers in the highest band. The energy separation of the two bands is estimated to be 0.03 + 0.005 eV. The lowest band minima appeared to be located either in the <110> or <111> directions, or near these directions. The effective — • M masses of the electrons are estimated to be m=0.63 m^ and m* = 0.25 m^ for the higher part of the highest band. The conduction effective mass of the electrons in the second * highest band is estimated to be m = 0.75 m^. The conduction —1 52 mobility varied as T" * at temperatures above 150K for most samples indicating acoustic mode scattering was dominant at the higher temperatures. 1 I. INTRODUCTION A. Magnetoresistance When a magnetic field is applied to a conductor its resistance changes. This effect is called magnetoresistance. The study of this effect provides a knowledge of the band structure and the scattering mechanisms which are important for understanding the transport properties of semiconductors. The magnetoresistance was first studied by Gantz (17) and extensively investigated by Harding (23), Wilson (60) and Davis (11) in the 1930's. The theory was developed on isotropic materials with the magnetic field perpendicular to the current. Davis (11) extended the theory to include anisotropic materials and arbitrary directions of the magnetic field. However, the theory was so general that the solution could not be expressed in a closed form. In 1950, Seitz (50) derived in closed form a general equation for the magneto­ resistance which applied to semiconducting crystals possess­ ing cubic symmetry. This equation initiated many important studies of the magnetoresistance in semiconductors. The study of magnetoresistance became a useful tool for investigating the band structure and the scattering mechanism in many semiconductors (4). Conduction band min­ ima in electron energies for n-type Ge were found by this method to consist of <111> ellipsoids (46, 42, 22, 20) with 2 an anisotropy in mobility ) of about 20 both at room temperature, 300K, and at liquid helium temperature, 4.2K (6, 22, 33). These facts were confirmed by cyclotron resonance experiments (13). The conduction band of Si was found to have <100> minima by magnetoresistance studies (45, 20, 5, 29) with mobility anisotropies of about 5 at room temperature and at 80K. Similar mobility anisotropies were later obtained by cyclotron resonance at low temperatures (12, 13, 47). Early magnetoresistance measurements on III - V semi­ conductors indicated that a spherical energy surface at k = 0 in the Brillouin zone where k is the wave-vector.
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