Surfaces and Interfaces of Electronic Materials

Preface

This textbook is intended for students as well as professional scientists and engineers interested in the next generation of electronics and, in particular, in the opportunities and challenges introduced by surfaces and interfaces. As electronics technology improves with higher speed, higher sensitivity, higher power, and higher functionality, surfaces and interfaces are becoming more important than ever. To achieve higher performance at the macroscopic level, one requires even more refined control of these junctions at the microscopic and, in fact, the atomic scale. With each advance, new techniques have been developed to measure and alter physical properties with increasing refinement. In turn, these studies have revealed fundamental phenomena that have stimulated designs for new device applications. This synergy between characterization, processing, and design spans several academic disciplines including physics, chemistry, materials science, and electrical engineering.

Several excellent physics-based books are available that provide extensive mathematical analyses focused on specific effects that are also described here. However, the field of electronic surfaces and interfaces encompasses a wide range of chemical and materials science phenomena that impact electronic properties. Rather than follow advanced treatments of specific effects, this book describes at an intermediate level the full range of physical phenomena at surfaces and interfaces, the variety of techniques available to measure them, and the physical issues to be addressed in order to advance electronics to the next level of performance. The author hopes to convey the excitement of this field and the intellectual challenges ahead. He also wishes to thank many of his colleagues for paving the way for this book with their valuable discoveries and insights. Particular thanks are due to Prof. Eli Burstein, who introduced him to the physics of metal–semiconductor interfaces, Dr Charles B. Duke, whose theoretical studies of semiconductor surface structure and tunneling provided a framework on which the experimental program was built, and Prof. Giorgio Margaritondo, who helped launch his soft X-ray photoemission spectroscopy work on interfaces and introduced him to the international world of synchrotron radiation science. Finally, his deepest gratitude goes to his wife, Janice, for her patience, understanding, love, and support during the year in which this book was written.

Chapter 1

Introduction

1.1 Surface and Interfaces in Everyday Life

Surfaces and interfaces are all around us. Their properties are important in our daily lives and are basic to many of today’s advanced technologies. This is particularly true for the semiconductor materials that are used throughout modern electronics. The aim of this book is to present the physical principles underlying the electronic, chemical, and structural properties of semiconductor interfaces and the techniques available to characterize them. Surfaces and interfaces are a cross-disciplinary field of science and engineering. As such, this book emphasizes the principles common to physics, electrical engineering, materials science, and chemistry as well as the links between fundamental and practical issues.

Surfaces and interfaces play a central role in numerous everyday phenomena. These include (i) triboelectricity, the transfer of charge between two materials brought into contact – such as the static electricity built up on a comb after combing one’s hair; (ii) corrosion, the oxidation of structural materials used in, for example, buildings, bridges, and aircraft; (iii) passivation, the prevention of such chemical or biological processes using special protective layers; (iv) colloid chemistry, the wetting of surfaces and the dispersion of particles within fluids as emulsions or colloids, for example, paints and time-release capsule medicines; (v) tribology, the friction between sliding objects in contact and their interface lubrication; (vi) cleaning and chemical etching, the removal of surface layers or adsorbed species; (vii) catalysis, the reduction in energetic barriers to speed up or improve the yield of chemical reactions, for example, refining oil or burning coal; and (viii) optical interference, the rainbow of colors reflected off thin oil layers or the internal reflection of light between stacks of materials only a few wavelengths of light thick. On a much larger scale are (ix) electromagnetic interfaces between the earth’s atmospheric layers that bounce short-wave radio signals around the world and that alter the reflection or absorption of sunlight contributing to global warming.

1.2 Surfaces and Interfaces in Electronics Technology

Surfaces and interfaces are fundamental to microelectronics. One of the most important microelectronic devices is the transistor, all functions of which depend on the boundaries between electronic materials. Figure 1.1 illustrates the three aspects of this dependence. Here, current passes from a source metal to a drain metal through a semiconductor, in this case, silicon (Si). A gate metal between the source and the drain is used to apply voltages that attract or repel the charge carriers involved in the current flow. The result is control or gating of the current flow by this third electrode. This basic device element is at the heart of the microelectronics industry.

Figure 1.1 Source–gate–drain structure of a silicon transistor.

The surfaces and interfaces are the key to the transistor’s operation, shown in Figure 1.1. Thus, the contact between the metal and Si is a metal silicide. Barriers can form between metals and semiconductors that impede charge movement and introduce voltage drops across their interfaces. This barrier formation is a central topic of this book. Microelectronics researchers found that promoting a chemical reaction to form silicides, such as TiSi2 between Ti and Si, reduces such transport barriers and the contact resistivity ρc at these metal–semiconductor interfaces. This is illustrated, for example, in Figure 1.2a. Such interfacial silicide layers form low resistance, planar interfaces that can be integrated into the manufacturing process. A challenge of this approach is to achieve very thin, low ρc contacts without allowing reactions to extend far away from the junction.

Figure 1.2 Expanded view of a (a) interface between metal and semiconductor with reacted layer, (b) gate–semiconductor interface with trapped charge in insulator and at insulator–semiconductor junction, and (c) dopant or impurity atom diffusion into semiconductor.

The second important interface appears at the gate–semiconductor junction, shown in Figure 1.2b. Here, the earliest transistor experiments [1] showed the presence of fixed charges at this interface that prevented control of the source–drain current. This gate interface may involve a metal in direct contact with the semiconductor or, more commonly, a stack of metal-on-insulator-on semiconductor to apply voltage bias without introducing additional current. Atomic sites within the insulator and its semiconductor interface can immobilize charge and introduce dipoles across the insulator–semiconductor interface. This localized charge produces a voltage drop that offsets applied voltages at the gate metal, opposing the gate’s control of the source–drain current flow. Minimizing the formation of these localized charge sites has been one of the prime goals of the microelectronics industry since the invention of the transistor.

The third important microelectronic interface involves diffusion of atoms into and out of the semiconductor. Atomic diffusion of atoms into the semiconductor that donate or accept charge is used to control the concentration of free charge carriers within specific regions of a device. Acceleration and implantation of ionized atoms is a common process to achieve such doped layers that extend into semiconductor surfaces, here illustrated in Figure 1.2c. In addition, atomic diffusion can occur between two materials in contact that are annealed at high temperature. High-temperature annealing is often used to heal lattice damage after implantation or to promote reactions at particular device locations. However, such annealing can introduce diffusion and unintentional doping at other regions of the device. Outdiffusion of semiconductor constituents is also possible, resulting in native point defects that can also be electrically active. Balancing these effects requires careful design of materials, surface and interface preparation, thermal treatment, and device architectures.

Microelectronic circuits consist of many interfaces between semiconductors, oxides, and metals. Figure 1.3 illustrates how these interfaces form as silicon progresses from its melt-grown crystal boule to a packaged chip. The Si boule formed by pulling the crystal out of a molten bath is sectioned into wafers, which are then oxidized, diffused, or implanted with dopants, and overcoated with various metal and organic layers. Photolithography is used to pattern and etch these wafers into monolithic arrays of devices. The wafer is then diced into individual circuits that are then mounted, wire bonded, and packaged into chips.

Figure 1.3 Integrated circuit manufacturing process flow.

Within each circuit element, there can be many layers of interconnected conductors, insulators, and their interfaces. Figure 1.4 illustrates the different materials and interfaces associated with a 0.18−μm transistor at the bottom of a multilayer Al–W–Si-oxide dielectric assembly [2]. Reaction, interdiffusion, and formation of localized states must all be carefully controlled at all of these interfaces during the many patterning, etching, and annealing steps involved in assembling the full structure. Figure 1.4 also shows that materials and geometries change to compensate for the otherwise increasing electrical resistance as interconnects between layers shrink into the nanoscale regime. This continuing evolution in microelectronics underscores the importance of interfaces since the material volume associated with these interfaces becomes a larger proportion of the entire structure as circuit sizes decrease.

Figure 1.4 Multilayer, multimaterial interconnect architectures at the nanoscale. Feature size of interconnects at right is 45 nm [2].

Many other conventional electronic devices rely on interfaces for their operation. Figure 1.5a illustrates the interface between a metal and semiconductor within a solar cell schematically as an energy E versus distance × band diagram. The Fermi levels EF in the metal (solid line) and the semiconductor (dashed line) align at a constant energy, whereas the conduction band EC and the valence band EV in the semiconductor bend near the interface. Incident photons of energy hν at this interface create electrons and holes that separate under the field set up by these bent bands. This charge separation results in photoinduced current or voltage between the metal and the semiconductor.

Figure 1.5 Interfaces in conventional electronics: (a) solar cell, (b) gas sensor, (c) optoelectronic emitter, and (d) photoemissive cathode.

Figure 1.5b shows what appears to be a transistor structure except that, unlike Figure 1.1, there is no gate. Instead, molecules on this otherwise free surface adsorb on the surface, exchanging charge and inducing a field analogous to that of a gate. Figure 1.5c illustrates a circuit that generates photon, microwaves, or acoustic waves. The contacts that inject current or apply voltage to the generator layer are key to its practical operation. Unless the resistance of such contacts is low, power is lost at these contacts, reducing or totally blocking power conversion inside the semiconductor. Figure 1.5d illustrates an interface involving just a semiconductor surface that emits electrons when excited by incident photons. Chemical treatment of selected semiconductors enables these surfaces to emit multiple electrons when struck by single photons. Such surfaces are useful as electron pulse generators or photomultipliers.

Surfaces and interfaces have an even larger impact on electronics as devices move into the quantum regime. Figure 1.6 illustrates four such quantum electronic devices schematically. Figure 1.6a illustrates the energy band diagram of a quantum well, one of the basic components of optoelectronics. Here, the decrease in bandgap between EC and EV of one semiconductor sandwiched between layers of a larger bandgap semiconductor localizes both electrons and holes in the smaller gap material. This joint localization enhances electron–hole pair recombination and light emission. The quantum well is typically only a few atomic layers thick so that the allowed energies of electrons and holes inside the well are quantized at discrete energies. This promotes efficient carrier inversion and laser light emission. Imperfections at the interfaces of these quantum wells can reduce the quantized light emission by introducing competing channels for recombination that do not involve the quantized states in the well.

Figure 1.6 Four quantum electronic devices. (a) Charge localization, recombination, and photon emission at a quantum well; (b) carrier confinement and transport at a semiconductor inversion layer; (c) tunneling transport at an avalanche detector; and (d) carrier confinement in three dimensions at quantum dots.

Figure 1.6b shows a schematic energy band diagram of a semiconductor with bands that bend down at the surface, allowing EF to rise above EC. The high concentration of electrons is confined to within a few tens of nanometers or less at the surface. This phenomenon is termed a two-dimensional electron gas (2DEG) layer. It forms a high carrier concentration, high mobility channel at the surface that is used for high-frequency, high-power devices, often termed high electron mobility transistors (HEMTs). Again, imperfections at the semiconductor interface can produce local electric fields that scatter charges, reduce mobility, and alter or even remove the 2DEG region.

Figure 1.6c illustrates a structure consisting of alternating high- and low-bandgap semiconductors characteristic of a cascade laser or of a very high frequency transistor. In either case, charge must tunnel through the ultrathin (monolayers) "barrier" layers into quantized energy levels. Once again, the perfection of these interfaces is crucial for the charge to tunnel efficiently between layers. Finally, Figure 1.6d represents a real-space pair of quantum dots encapsulated by other media. Such quantum dots with sizes of only a few nanometers also have quantized energy levels that yield efficient laser emission. Again, optical emission is impacted if imperfections and recombination are present at their interfaces.

The materials that comprise all electronics consist of metals, semiconductors, and/or insulators. It is instructive to realize that these three materials differ primarily in terms of the energy separation between their filled and empty electronic states. For metals, this bandgap is 0. For insulators, it can be quite large, typically 5 eV or more. Semiconductors lie between these two regimes with intermediate bandgaps ranging from a few hundred meV or milli-electron volts to several electron volts.

These bandgaps and Fermi levels in the energy band diagrams of Figures 1.5 and 1.6 point to another key aspect of interfaces – the alignment of energy levels between the constituents. This chapter emphasizes that contacts and charge transport between metals, semiconductor, and insulators are essential to all electronic applications. How their energy levels align is a fundamental issue that is still not well understood. The question is, does this matter? The interface band structure determines how much energy difference exists between materials and thereby what barriers exist to charge movement between them. The question is, what affects this phenomenon? There are three primary factors: (i) the constituents of the junctions, (ii) the conditions under which they form the interface, and (iii) any subsequent thermal or chemical processing. Therefore, to understand how surfaces and interfaces impact electronics, it is important to know their properties at the microscopic level and how these factors shape these properties.

Surface and interface science continues to have enormous practical value for electronics. It has helped develop the semiconductor industry into the high-performance, high-value-added industry that it is today. Surface and interface tools are essential for monitoring, controlling, and ultimately designing micro- and optoelectronic clean room processes. They are also central to controlling properties of contacts. As such, they are integral to designing the next generation of electronic device materials and fabrication processes.

Problems

1. As electronics shrinks into the nanoscale regime, the actual numbers of atoms become significant in determining the semiconductor’s physical properties. Consider a 0.1-µm Si field effect transistor with a 0.1 µm × 0.1 µm cross section and a doping concentration of 10¹⁷ cm−3. How many dopant atoms are there in the channel region? How many dopant atoms are there altogether?

2. Assume the top channel surface has 0.01 trapped electron per unit cell. How many surface charges are present? How much do they affect the channel’s bulk charge density?

3. What fraction of atoms is within one lattice constant of the channel surfaces?

4. Figure1.4 illustrates the complexity of the transistor chip structure. Describe three interface effects that could occur in these structures that could degrade electrical properties during microfabrication.

5. Name three desirable solar cell properties that could be affected by interface effects.

6. Name three interface effects that could degrade quantum well operation.

References

1. Bardeen, J. (1947) Phys. Rev., 71, 717.

2. Lammers, D. (2007) Semiconductor International, www.semiconductor.net/article/CA6513618.html (accessed 18 December 2007).

Chapter 2

Historical Background

2.1 Contact Electrification and the Development of Solid-State Concepts

The history of electrical contacts extends far back in time past the Greco–Roman era. Contact electrification or, more precisely, triboelectricity was well known in ancient times in the form of static electricity. Thus, the rubbing of cat’s fur with amber was an early example of charge transfer between solids. However, systematic observation of this electrical phenomenon began much later when, in 1874, Braun used selenium to form a rectifier, which conducted electricity unequally with positive versus negative applied voltage [1]. See Henisch’s Rectifying Semiconductor Contacts [2] for a detailed review of early literature on semiconductor interface phenomena.

Three decades later, Einstein explained the photoelectric effect at metal surfaces using wave packets with discrete particle energies [3]. This established not only the particle nature of light but also the concept of work function, one of the building blocks of energy band theory. Notably, his work on the photoelectric effect, rather than his many other achievements, was the basis for Einstein’s 1921 Nobel Prize. In 1931, Wilson presented a theoretical foundation for semiconductor phenomena which was based on the band theory of solids [4, 5]. Siemens et al. [16] and Schottky et al. [7] subsequently showed that the semiconductor interior was not a factor in contact rectification. In 1939, Mott [8], Davidov [9, 10], and Schottky [11–13] all published theories of rectification. Each of their models involved a band-bending region near the interface. Mott proposed an insulating region between the metal and the semiconductor that accounted for current–voltage measurements of copper oxide rectifiers. Davidov advanced the importance of thermionic work function differences in forming the band-bending region. Schottky introduced the idea that the band-bending region could arise from stable space charge in the semiconductor alone rather than requiring the presence of a chemically distinct interfacial layer. Bethe’s theory of thermionic emission of carriers over the energy barrier [14], based in part on Richardson’s earlier work on thermionic cathodes [15], provided a description of charge transport across the band-bending region that described the rectification process for most experimental situations. These developments laid the groundwork for describing semiconductor charge transfer and barrier formation. See [2, 16–20] for more extensive reviews of metal–semiconductor rectification, with particular emphasis on current transport and tunneling.

2.2 High-Purity Semiconductor Crystals

A major roadblock to experimental studies was the need for semiconductors with high purity. Without sufficiently high crystal perfection and purity, the intrinsic semiconductor properties were masked by the effects of impurities and lattice imperfections. By the 1940s, large high-purity semiconductor single crystals had become available using crystal-pulling and zone-refining techniques [21–26]. Two such crystal-growth techniques – Czochralski and float zone – are illustrated in Figure 2.1.

Figure 2.1 Pulling of an Si crystal from the melt (the Czochralski method): (a) silicon crystal being pulled with a seed crystal from molten silicon [25]. (b) Float-zone process with impurity segregation away from the molten zone. (c) Cutout of Czochralski crucible interior, (d) Ingot sectioning into wafers [26].

2.3 Development of the Transistor

By the mid-1940s, companies such as Bell Telephone had begun efforts aimed at producing amplifiers based on semiconductors rather than on vacuum tubes. A key event in this industrial research occurred when Bardeen, Shockley, and Pearson discovered that electric charges immobilized on the semiconductor surface were interfering with the gate modulation of the charge and current inside the semiconductor. Bardeen correctly interpreted this observation in terms of electronic states that were localized at the semiconductor interface [27]. By reducing the density of these states and their effect on the field effect pictured in Figure 2.2, Bardeen, et al. [28] were able to demonstrate the transistor action [29]. For this discovery, they received the 1956 Nobel Prize in Physics. And the interface concepts inherent in the transistor continue to drive the electronics revolution.

Figure 2.2 (a) Bardeen (center), Brattain (right), and Shockley (left) [28]. (b) A point contact transistor with three gold contacts on germanium crystal [29].

By the early 1950s, the semiconductor employed for transistors changed from germanium to silicon, due in large part to the latter’s native oxide, the dielectric separating a gate metal from a semiconductor, being more resistant to water vapor in air [22]. By 1958, Jack Kilby [30] had invented the first integrated circuits by creating arrays of transistor circuits on silicon wafers. The 1950s and early 1960s saw the development of many types of semiconductor devices such as photodiodes, sensors, photomultipliers, and light emitters. Their reliability and usefulness required not only high crystal purity but also refined methods to form their electrical contacts. This requirement led to the development of high-vacuum technology – pumps, chambers, and gauges to be discussed in following chapters.

By the mid-1960s, there was significant interest in understanding the variation of band bending and Schottky barrier formation at metal–semiconductor interfaces. The pioneering work of Mead and Spitzer resulted in barrier measurements by several techniques for metals on semiconductors. These contacts were formed in medium vacuum, ∼10−6 Torr and, to minimize contamination, they cleaved the semiconductor crystals in streams of evaporating metal atoms [31]. Mead and Spitzer interpreted the systematic differences they observed across classes of semiconductors in terms of different bonding between ionic versus covalent crystal lattices.

2.4 The Surface Science Era

The advent of ultrahigh vacuum technology (UHV) with chamber pressures of 10−10 Torr or less in the late 1960s marked the birth of surface science as we know it today. Researchers using surface science techniques began measuring the surface properties of semiconductors in the early 1970s. They interpreted the localized states of Bardeen [27], Tamm [32], and Shockley [33] as intrinsic surface states, that is, localized states intrinsic to the semiconductor alone and related to the bonding at the outer layer of semiconductor atoms. Kurtin et al. [34] pointed out a pronounced transition between ionic and covalent semiconductors that they interpreted by differences in lattice disruption between classes of compound semiconductors. Theoretical calculations of such disrupted lattices supported the appearance of localized states with energies in the semiconductor bandgap. Such gap states could, in principle, pin the Fermi level in a narrow range of similar energy positions. On the other hand, the examination of the atomic arrangements on semiconductor surfaces revealed that the atoms typically rearranged or reconstructed to minimize their bond energy. In general, this reconstruction moves the energies of such states out of the bandgap, where they have no effect on Fermi-level stabilization inside the gap. Early surface science experiments that had reported observing such states with energies inside semiconductor bandgaps were later reinterpreted in terms of surface artifacts. Indeed, these events highlighted the importance of surface preparation and the role of factors that were extrinsic to the semiconductor itself.

Another intrinsic state model invoked wavefunction tunneling from metals into semiconductor bandgaps. Theoretical methods based on this concept also introduced localized charge states at the metal–semiconductor interface [35–38] and could also account for differences between barriers of semiconductors with different bond ionicity [39].

By the mid-1970s, the refinement of monolithic electronic circuitry on silicon wafers had involved the material science or microelectronic metallurgy of the various electronic material interfaces. A key aspect of this metallurgy involved understanding and predicting the interfacial reactions at silicon–metal interfaces [40, 41].

Researchers involved in manufacturing microelectronics realized that small variations in interface chemical composition could introduce significant variability in electronic device properties. At this stage of microelectronic development, highly reproducible interface conditions, rather than atomically pristine ones, were paramount in satisfying manufacturing tolerances.

During this period, Andrews and Phillips found that chemical reactions at metal–silicon interfaces displayed systematic variations with Schottky barrier heights [42, 43]. Brillson demonstrated that chemical reaction and diffusion occurred on an atomic scale at interfaces between metals and compound semiconductors [44–46]. Detection of this interface chemistry became possible with the development of UHV surface science techniques that were sensitive to properties of the outer few monolayers. The systematics of Schottky barrier behavior with this interface chemistry led to the concept of a thermodynamic heat of interface reaction that could account for the qualitative transition in Schottky barriers between reactive and unreactive interfaces. This concept could be extended to interfacial layers of only a few atomic layers. Such interlayers could, in fact, alter the interface chemistry and, thereby, the barrier formation of a macroscopic metal–semiconductor contact [47–49].

Spicer et al. introduced another widely discussed concept of Schottky barriers, namely, the formation of defects at the semiconductor surface by the adsorption of metal or other adsorbate atoms [50, 51]. This model accounted for the nearly complete insensitivity of GaAs Schottky barriers to different metals. Technologically such effects were of high interest since GaAs and other III–V compound semiconductors possessed higher mobility than Si and were, therefore, more suitable for high-frequency applications. However, by the late 1980s, many researchers had shown that a wide range of Schottky barriers could be achieved with GaAs and other compound semiconductors [52–55], with high-quality crystalline materials and careful interface preparation.

The 1980s also saw the invention and development of the scanning tunneling microscope (STM), which permits the observation of atomic distributions on surfaces. Extensions of this instrument would permit local measurements of work function, capacitance, and barrier heights on a scale of nanometers. By the 1990s, one of these techniques, atomic force microscopy (AFM), was being used to probe insulating materials as well as semiconductors. Another STM extension, ballistic electron energy microscopy (BEEM), revealed heterogeneous electronic features across semiconductor surfaces that could account for multiple barrier heights within the same macroscopic contact.

These Schottky barrier developments also provided new insights into the heterojunction band offsets that are critical to micro- and optoelectronic device operation. As with metal–semiconductor contacts, researchers realized the importance of interfacial bonding and growth techniques in controlling band alignment between the two semiconductors.

2.5 Advances in Crystal Growth Techniques

Concurrent with the development of new surface science, techniques and insights were advances in crystal growth techniques. Besides the crystal pulling and float-zone methods illustrated in Figure 2.2, other techniques pictured in Figure 2.3 include horizontal Bridgman from a melt in a crucible (a and b), liquid phase epitaxy (LPE) (not shown) involving a melt above a single crystal substrate, and molecular beam epitaxy (MBE) (c) [56]. The epitaxial techniques, particularly MBE, are capable of producing atomically abrupt layers (d). Figure 2.3e illustrates the layers of a laser diode, a man-made structure enabled by atomic control of semiconductor growth.

Figure 2.3 (a) Crystal growing from the melt in a crucible by solidification from one end of the melt (horizontal Bridgman method) or (b) melting and solidification in a moving zone. (c) Crystal growth by molecular beam epitaxy (MBE) by evaporation cells inside a high-vacuum chamber directing beams of Al, Ga, and As and dopants on to a GaAs substrate [56]. (d) Scanning electron micrograph of the cross section of an MBE-grown crystal having alternating layers of GaAs (dark lines) and AlGaAs (light lines). Each layer is four monolayers (4 × a/2 = 11.3 Å) thick. (e) A laser diode composed of multiple GaAs and AlGaAs layers that produce coherent, monochromatic light with current injection through the layer stack. This man-made structure of atomically ordered layers is made possible by epitaxial growth techniques.

(Courtesy IEEE Spectrum.)

2.6 Future Electronics

The next generations of electronics will demand even greater understanding and control of surfaces and interfaces. As devices become ultrasmall, for example, less than 100 nm dimensions, they will require ultrashallow junctions, abruptness at least below quantum-scale dimensions, lower densities of localized states, and atomic-scale optimization of electronic properties and chemical stability. Ultrahigh speed device structures will require the elimination of deep and shallow interface traps. Ultrastable contacts must function under very high temperature and possibly chemically corrosive conditions.

The history of the past six decades in microelectronics illustrates the synergy between science and technology as semiconductor discoveries led to devices, which stimulated the development of new techniques that advanced both scientific understanding and device architectures. This interplay of semiconductor growth, characterization methods, and device designs has steadily raised our understanding and control of electronic materials. There are a number of excellent books that treat the history of semiconductors, their applications, and their extension into the quantum mechanical regime at much greater depth; for example, see [57, 58].

The aim of Chapters 1 and 2 has been to motivate the study of surfaces and interfaces. Their properties alter charge densities, band structure, and electronic states on a scale of hundred of nanometers down to atomic layers. These microscopic properties manifest themselves as major changes in device features. As semiconductor structures shrink well below the micron scale, surfaces and interfaces, in fact, dominate the electronic and optical properties. In turn, atomic and nanoscale techniques are available to characterize the electronic, chemical, and geometrical properties of electronic materials structures. The chapters to follow describe the electrical and optical properties that depend on surfaces and interfaces along with the techniques developed to measure them. How these properties and techniques will contribute to the next generation of electronics comprises the concluding portion of this book.

Problems

1. (a) The first transistor was made with Ge. Why? (b) From Figure 2.2b, speculate on how low resistance contacts were made.

2. Si emerged as the material of choice for microelectronics. (a) Give five reasons why. (b) What feature of the Si/SiO2 is the most important for device operation and why?

3. Give one example each of how surface and interface techniques have enabled modern complementary metal-oxide-semiconductor (CMOS) technology (a) structurally, (b) chemically, and (c) electronically.

4. (a) Give two reasons and two examples why GaAs, InP, and many other III–V compound semiconductors are used for quantum-scale optoelectronics. (b) Give reasons why they are advantageous for high-speed transistors.

5. (a) Which would you choose for quantum well lasers, GaAs or GaP, and why? (b) Which would you choose for high-power, high-frequency transistors, GaAs or GaN?

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Chapter 3

Electrical Measurements

3.1 Schottky Barrier Overview

Electrical contacts to semiconductors are central to solid-state device performance. The potential barrier set up by band bending at the semiconductor interface is at the heart of all modern electronics. This barrier is equal to the energy difference between the Fermi level EF of a metal relative to the band edge of the semiconductor’s majority charge carrier, and it determines the ohmic or rectifying behavior of the electrical contact.

Figure 3.1a illustrates the current–voltage behavior of an ohmic metal–semiconductor contact. Here, the resistance R = V/I is the same for both forward and reverse bias. The steep slope pictured here indicates a low resistance. Such ohmic contacts are required for devices and circuits in which the contact introduces no voltage drop. Ohmic contacts are essential in delivering all the applied voltage to the desired circuit element without loss of voltage or energy to intermediate components. Examples include contacts to (i) laser diodes to produce light emission with the lowest possible applied voltage, (ii) metal-oxide-semiconductor field effect transistor (MOSFET) capacitors to perform computer operations with minimum possible energy generation, and (iii) high power, high electron mobility transistors (HEMTs) for radio frequency (RF) wave generation to minimize resistive heating.

Figure 3.1 Current versus voltage plots of (a) symmetric or ohmic contact and (b) asymmetric or rectifying contact.

Figure 3.1b illustrates the current–voltage behavior of a rectifying metal–semiconductor contact. Here, the resistance is low in the forward direction and high in the reverse direction. This asymmetric behavior is extremely useful for active electronics since the built-in voltage of the band bending can control circuit current and voltage in numerous ways. Examples include (i) a current rectifier that blocks alternating current in one direction, (ii) a solar cell that generates voltage with illumination, (iii) a photodetector that generates current with illumination, and (iv) a laser diode that generates light with applied voltage. The utility of these bent bands is magnified by the exponential dependence of carrier density on applied voltage so that small applied voltages can have disproportionately large electrical effects.

Later chapters review many of the techniques employed to obtain low-resistance ohmic contacts. The control of rectifying, that is, Schottky barrier, contacts for particular semiconductors is a much greater challenge. The following sections introduce the basic concepts of Schottky barriers and the conventional techniques used to measure these barriers in the laboratory. We then describe the difference between the electrical properties expected on the basis of this classical framework versus the actual properties observed experimentally. This difference provides the central motivation for understanding charge transfer at surfaces and interfaces on an atomic scale and thereby controlling electronic properties macroscopically.

3.2 Ideal Schottky Barriers

Ideally, the band-bending region inside the semiconductor forms as a result of charge transfer between a metal and a semiconductor. This charge transfer depends in turn on the difference in Fermi level between the two materials. Thus, the expected band bending for a given semiconductor should depend on the metal’s work function. Figure 3.2 illustrates the band-bending scheme for metals on high and low work function at surfaces on n- and p-type semiconductors [1]. For the high work function metal and n-type semiconductor in Figure 3.2a, electrons flow from the semiconductor to the metal after contact, depleting a characteristic surface region in the semiconductor of electrons. With the two Fermi levels EFM and EFSC aligned, a double layer forms with a voltage drop of qVB equal to the contact potential difference between the metal and the interior of the semiconductor. The double layer consists of a surface space charge region, typically 10−4−10−6 cm thick, and an induced charge on the metal surface. The n-type depletion region in Figure 3.2a is a layer of high resistance. Thus, a voltage applied to this junction will fall mostly across the surface space charge region. The band bending depends on the difference in thermionic work function and in this simple model is expected to be

Figure 3.2 Schematic diagram of band bending before and after metal–semiconductor contact for (a) high work function metal and n-type semiconductor, (b) low work function metal and n-type semiconductor, (c) high work function and p-type semiconductor, and (d) low work function metal and p-type semiconductor [1].

(3.1) equation

where ΦM and ΦSC are the metal and semiconductor work functions, respectively, and the n-type Schottky barrier is

(3.2) equation

where χSC is the semiconductor electron affinity. Note that ΦSC and χSC differ by ECbulk–EF, the difference in energy between the conduction band edge EC and the Fermi level in the semiconductor bulk so that

(3.3) equation

For typically doped n-type semiconductors, EC−EF<0.1eV. Equation 3.1 also holds for p-type semiconductors, but , where EG is the semiconductor bandgap.

According to this band-bending model, the potential Φ within the semiconductor satisfies Poisson’s equation¹)

(3.4) equation

In Equation 3.3, ρ is the charge density in the surface space charge region of width w, × denotes the coordinate axis normal to the metal–semiconductor interface, and εs is the static dielectric constant of the semiconductor. Using the abrupt approximation such that ρ ≅ qN, the bulk concentration of ionized impurities within the surface space charge region, for x<W and , and dΦ/dx = 0 for x > w, one obtains [2]:

(3.5) equation

and a depletion layer width of

(3.6) equation

Here Nq = n, the bulk charge density. Thus, the abrupt metal–semiconductor junction contains a parabolic band-bending region. Analogous conclusions can be drawn from the low work function metal case shown in Figure 3.2b and the high versus low work function metals on a p-type semiconductor in Figures 3.2c and d respectively. Note that Figures 3.2b and c exhibit accumulated band-bending regions, which present no barrier to majority carrier transport across the interface.

3.3 Real Schottky Barriers

In reality, the conventional or classical picture of Schottky barrier formation described by Equation 3.1 and illustrated in Figure 3.2 does not agree with experimental measurements of metal–semiconductor interfaces. Figure 3.3 illustrates this disagreement for barrier heights of different metals on Si [3–6]. The correlation between ΦM − ΦSC (straight line) and the band bending for metals with different work functions [7] on the same semiconductor has typically not been strong. This weak dependence can be interpreted from Bardeen’s work [8] to mean that localized states at the interface can accumulate charge and generate dipoles that take up much of the metal–semiconductor potential difference. These surface or interface states can have several origins.

Figure 3.3 Plot of barrier heights ΦSB [3–5] as a function of metal work function [7] ΦM for metals on n-type Si. The circles are barrier heights for cleaved Si and the vertical lines cover the range of barrier values for chemically prepared surfaces after aging. The diagonal line is a plot of ΦSB = ΦM − χSi, where χSi = 4.05 eV [6]. The ΦM are selected values obtained by photoemission techniques.

Consider a rectification barrier with and without surface states. Figure 3.4 shows a metal and a semiconductor before and after contact. In Figure 3.4a, band bending is present even without a metal contact. This is due to negative charge that fills states localized at or near the surface at energies below the Fermi level EFSC. If the surface state density is relatively high, that is, ∼ 10¹⁴ cm−2, the presence of the metal does not alter EF + qVB appreciably. Instead, Figure 3.4b shows that most of the contact potential difference ΦM − ΦSC falls across an atomically thin interface dipole region instead of the semiconductor space charge region. The voltage drop Δχ across this dipole depends on the density of localized states that are filled with electrons as well as the dielectric constant of the layer across which this voltage drops. Assuming that this dipole layer is sufficiently thin that charge tunnels freely across it, the resultant abrupt interface is typically pictured without the dipole as in Figure 3.4c.

Figure 3.4 Schematic energy band diagram of a metal and a semiconductor with a high density of surface states: (a) before contact, (b) after contact, and (c) as pictured conventionally with interface dipole not shown [1].

Thus is not equal to but rather

(3.7) equation

For high enough densities of interface states, small movements of the Fermi level within this energy range of states produce large changes of localized state occupation. As a result, most of the potential difference between metal and semiconductor produces changes in the interface dipole rather than in the surface space charge region. The barrier height ΦSB and band bending qVB are then relatively independent of metal work functionΦM. The Fermi level at the surface is then termed pinned by surface states within a narrow range of energy in the semiconductor bandgap.

The earliest direct evidence of this Fermi level pinning was the field effect experiment associated with the transistor development [8]. Here the presence of states at the interface reduces the effect on an applied gate voltage on the Fermi level movement within the surface space charge region, thereby preventing large changes in carrier concentration that can move within the transistor’s channel.

Figure 3.5 illustrates this field effect experiment [9] and the resultant Fermi level changes with bias and surface states. In Figure 3.5a, a condenser plate applies a gate voltage V to the Si surface while current A yields conductivity of the surface space charge region. Surface conductivity is given by

(3.8) equation

where e is electron charge and μ is carrier mobility. Electrons in the conduction band are denoted as short dashes. Without surface states or bias, the bands in Figure 3.5b are flat and EF lies above midgap for an n-type semiconductor. With applied bias and no surface states in Figure 3.5c, a positive bias increases the electron charge density inside the semiconductor surface, causing the bands to bend down as EF moves closer to EC. The increased charge density results in increased conductivity σ and current density J = σ , where is applied electric field. With surface states present as in Figure 3.5d, this voltage-induced band bending and the addition of majority carriers are reduced. The control of carriers in the surface space charge region by an applied voltage is essential to the operation of all active electronic devices such as the transistor.

Figure 3.5 Experimental configuration for field effect measurements of Shockley and Pearson [9]. Surface conductivity of Si slab measured by current is monitored as a function of gate voltage (a) for (b) no bias, (c) bias with no surface states, and (d) bias with surface states.

3.4 Schottky Barrier Height Measurements

3.4.1 Current–Voltage (J–V) Technique

There are several methods used to measure barrier heights between metals and semiconductors. They differ in (i) how difficult measurements are to perform and (ii) the factors that can complicate their interpretation. The most straightforward method is the current–voltage or J–V technique. Thermionic emission-diffusion theory yields a forward J–V characteristic given by

(3.9) equation

where

probability of electron emission over the semiconductor potential maximum into the metal without electron–optical phonon scattering, fq = ratio of total J with versus without tunneling and quantum-mechanical reflection, vR = recombination velocity, vD = effective diffusion velocity with thermionic emission, m∗ is the carrier’s effective mass, m0 is the free electron mass, T is temperature, and V is the applied voltage.

For V > 2 kBT/q in the forward direction, A∗∗ can be approximated by A∗, and ΦSB consists of a barrier height extrapolated to zero field, ΦSB0 minus a term ΔΦ due to the combined effects of applied electric field and image force [10]. The effect is given by

(3.10) equation

and illustrated in Figure 3.6. Here, the applied electric field = V/W, where W is the width of the surface space charge region and any dipole layer. Depending on N and S, the contact’s depletion region width W is typically <1000 Å so that voltages of only 1 V can produce field gradients of 10⁵V cm−1 or higher. As an example, ΔΦ = 0.03 eV with S = 16 0, for example, Ge, and = 10⁵V cm−1. While the ΔΦ term is only several tens of millivolts, it can nevertheless affect the J–V behavior for nonzero voltages.

Figure 3.6 Schematic energy band diagram between a metal surface and a semiconductor. The effective barrier is lowered from ΦSB0 to ΦSB when an electric field is applied to the interface. (After Sze [10].)

The forward current density in Equation 3.9 extrapolated logarithmically to zero applied forward bias has an intercept at

(3.11) equation

so that the barrier ΦSB0 can be extracted from a plot of ln J versus applied forward voltage. The slope of the J–V plot in Figure 3.7 also provides the "ideality factor" n of the contact, defined by [10]

Figure 3.7 Forward current density versus applied voltage for a metal–semiconductor contact.

(3.12)

In general, the second and third terms of Equation 3.12 are much less than one so that n ≈ 1. However, a variety of physical processes can increase n. These include tunneling through the barrier [11, 12], intermediate layers with new dielectric and transport properties [12, 13], and recombination or trapping at states near the