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Download 15.The Doping of Semiconductors
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Transcript
The Doping of Semiconductors The addition of a small percentage of foreign atoms in the regular crystal lattice of silicon or germanium produces lattice dramatic changes in their electrical properties, producing n-type and p-type semiconductors. Pentavalent impurities: Impurity atoms with 5 valence electrons produce n-type semiconductors by contributing extra electrons. Trivalent impurities: Impurity atoms with 3 valence electrons produce p-type semiconductors by producing a "hole" or electron deficiency. P- and N- Type Semiconductors N-Type Semiconductor The addition of pentavalent impurities such as antimony, arsenic or phosphorous contributes free electrons, greatly increasing the conductivity of the intrinsic semiconductor. Phosphorous may be added by diffusion of phosphine gas. P-Type Semiconductor The addition of trivalent impurities such as boron, aluminum or gallium to an intrinsic semiconductor creates deficiencies of valence electrons, called "holes". It is typical to use B2H6 diborane gas to diffuse boron into the silicon material. Bands for Doped Semiconductors The application of band theory to n-type and p-type semiconductors shows that extra levels have been added by the impurities. In n-type material there are electrons energy levels near the top of the band gap so that they can be easily excited into the conduction band. In p-type material, extra holes in the band gap allow excitation of valence band electrons, leaving mobile holes in the valence band. Silicon Lattice Silicon atoms form covalent bonds and can crystallize into a regular lattice. The illustration below is a simplified sketch; the actual crystal structure of silicon is a diamond lattice. This crystal is called an intrinsic semiconductor and can conduct a small amount of current. The main point here is that a silicon atom has four electrons which it can share in covalent bonds with its neighbors. These simplified diagrams do not do justice to the nature of that sharing since any one silicon atom will be influenced by more than four other silicon atoms, as may be appreciated by looking at the Silicon Crystal Structure after Kittel The above illustration shows the arrangement of the silicon atoms in a unit cell, with the numbers indicating the height of the atom above the base of the cube as a fraction of the cell dimension. Silicon crystallizes in the same pattern as diamond, in a structure which Ashcroft and Mermin call "two interpenetrating face-centered cubic" primitive lattices. The lines between silicon atoms in the lattice illustration indicate nearest-neighbor bonds. The cube side for silicon is 0.543 nm. Germanium has the same diamond structure with a cell dimension of .566 nm. Intrinsic Semiconductor A silicon crystal is different from an insulator because at any temperature above absolute zero temperature, there is a finite probability that an electron in the lattice will be knocked loose from its position, leaving behind an electron deficiency called a "hole". If a voltage is applied, then both the electron and the hole can contribute to a small current flow. The conductivity of a semiconductor can be modeled in terms of the band theory of solids. The band model of a semiconductor suggests that at ordinary temperatures there is a finite possibility that electrons can reach the conduction band and contribute to electrical conduction. The term intrinsic here distinguishes between the properties of pure "intrinsic" silicon and the dramatically different properties of doped n-type or ptype semiconductors. Valence Electrons The electrons in the outermost shell of an atom are called valence electrons; they dictate the nature of the chemical reactions of the atom and largely determine the electrical nature of solid matter. The electrical properties of matter are pictured in the band theory of solids in terms of how much energy it takes to free a valence electron. Germanium In solid state electronics, either pure silicon or germanium may be used as the intrinsic semiconductor which forms the starting point for fabrication. Each has four valence electrons, but germanium will at a given temperature have more free electrons and a higher conductivity. Silicon is by far the more widely used semiconductor for electronics, partly because it can be used at much higher temperatures than germanium. Silicon In solid state electronics, either pure silicon or germanium may be used as the intrinsic semiconductor which forms the starting point for fabrication. Each has four valence electrons, but germanium will at a given temperature have more free electrons and a higher conductivity. Silicon is by far the more widely used semiconductor for electronics, partly because it can be used at much higher temperatures than germanium. Doping The property of semiconductors that makes them most useful for constructing electronic devices is that their conductivity may easily be modified by introducing impurities into their crystal lattice. The process of adding controlled impurities to a semiconductor is known as doping. The amount of impurity, or dopant, added to an intrinsic (pure) semiconductor varies its level of conductivity. Doped semiconductors are often referred to as extrinsic. Dopants The materials chosen as suitable dopants depend on the atomic properties of both the dopant and the material to be doped. In general, dopants that produce the desired controlled changes are classified as either electron acceptors or donors. A donor atom that activates (that is, becomes incorporated into the crystal lattice) donates weakly-bound valence electrons to the material, creating excess negative charge carriers. These weakly-bound electrons can move about in the crystal lattice relatively freely and can facilitate conduction in the presence of an electric field. (The donor atoms introduce some states under, but very close to the conduction band edge. Electrons at these states can be easily excited to conduction band, becoming free electrons, at room temperature.) Conversely, an activated acceptor produces a hole. Semiconductors doped with donor impurities are called n-type, while those doped with acceptor impurities are known as p-type. The n and p type designations indicate which charge carrier acts as the material's majority carrier. The opposite carrier is called the minority carrier, which exists due to thermal excitation at a much lower concentration compared to the majority carrier. For example, the pure semiconductor silicon has four valence electrons. In silicon, the most common dopants are IUPAC group 13 (commonly known as group III) and group 15 (commonly known as group V) elements. Group 13 elements all contain three valence electrons, causing them to function as acceptors when used to dope silicon. Group 15 elements have five valence electrons, which allow them to act as a donor. Therefore, a silicon crystal doped with boron creates a p-type semiconductor whereas one doped with phosphorus results in an n-type material. Carrier concentration The concentration of dopant introduced to an intrinsic semiconductor determines its concentration and indirectly affects many of its electrical properties. The most important factor is doping that directly affects is the material's carrier concentration. In an intrinsic semiconductor under thermal equilibrium, the concentration of electrons and holes is equivalent. That is, n = p = ni Where n is the concentration of conducting electrons, p is the electron hole concentration, and ni is the material's intrinsic carrier concentration. Intrinsic carrier concentration varies between materials and is dependent on temperature. Silicon's ni, for example, is roughly 1×1010 cm-3 at 300 kelvins (room temperature). In general, an increase in doping concentration affords an increase in conductivity due to the higher concentration of carriers available for conduction. Degenerately (very highly) doped semiconductors have conductivity levels comparable to metals and are often used in modern integrated circuits as a replacement for metal. Often superscript plus and minus symbols are used to denote relative doping concentration in semiconductors. For example, n + denotes an n-type semiconductor with a high, often degenerate, doping concentration. Similarly, p − would indicate a very lightly doped ptype material. It is useful to note that even degenerate levels of doping imply low concentrations of impurities with respect to the base semiconductor. In crystalline intrinsic silicon, there are approximately 5×1022 atoms/cm³. Doping concentration for silicon semiconductors may range anywhere from 1013 cm-3 to 1018 cm-3. Doping concentration above about 1018 cm-3 is considered degenerate at room temperature. Degenerately doped silicon contains a proportion of impurity to silicon in the order of parts per thousand. This proportion may be reduced to parts per billion in very lightly doped silicon. Typical concentration values fall somewhere in this range and are tailored to produce the desired properties in the device that the semiconductor is intended for. Effect on band structure Band diagram of a p+n junction. The band bending is a result of the positioning of the Fermi levels in the p+ and n sides. Doping a semiconductor crystal introduces allowed energy states within the band gap but very close to the energy band that corresponds with the dopant type. In other words, donor impurities create states near the conduction band while acceptors create states near the valence band. The gap between these energy states and the nearest energy band is usually referred to as dopant-site bonding energy or EB and is relatively small. For example, the EB for Boron in silicon bulk is 0.045 eV, compared with silicon's band gap of about 1.12 eV. Because EB is so small, it takes little energy to ionize the dopant atoms and create free carriers in the conduction or valence bands. Usually the thermal energy available at room temperature is sufficient to ionize most of the dopant. Dopants also have the important effect of shifting the material's Fermi level towards the energy band that corresponds with the dopant with the greatest concentration. Since the Fermi level must remain constant in a system in thermodynamic equilibrium, stacking layers of materials with different properties leads to many useful electrical properties. For example, the p-n junction's properties are due to the energy band bending that happens as a result of lining up the Fermi levels in contacting regions of p-type and n-type material. This effect is shown in a band diagram. The band diagram typically indicates the variation in the valence band and conduction band edges versus some spatial dimension, often denoted x. The Fermi energy is also usually indicated in the diagram. Sometimes the intrinsic Fermi energy, Ei, which is the Fermi level in the absence of doping, is shown. These diagrams are useful in explaining the operation of many kinds of semiconductor devices. Preparation of semiconductor materials Semiconductors with predictable, reliable electronic properties are necessary for mass production. The level of chemical purity needed is extremely high because the presence of impurities even in very small proportions can have large effects on the properties of the material. A high degree of crystalline perfection is also required, since faults in crystal structure (such as dislocations, twins, and stacking faults) interfere with the semiconducting properties of the material. Crystalline faults are a major cause of defective semiconductor devices. The larger the crystal, the more difficult it is to achieve the necessary perfection. Current mass production processes use crystal ingots between four and twelve inches (300 mm) in diameter which are grown as cylinders and sliced into wafers. Because of the required level of chemical purity and the perfection of the crystal structure which are needed to make semiconductor devices, special methods have been developed to produce the initial semiconductor material. A technique for achieving high purity includes growing the crystal using the Czochralski process. An additional step that can be used to further increase purity is known as zone refining. In zone refining, part of a solid crystal is melted. The impurities tend to concentrate in the melted region, while the desired material recrystalizes leaving the solid material more pure and with fewer crystalline faults. In manufacturing semiconductor devices involving heterojunctions between different semiconductor materials, the lattice constant, which is the length of the repeating element of the crystal structure, is important for determining the compatibility of materials. Semiconductors and doping Semiconductors are materials which are neither conductors or insulators, having conductivities intermediate to those of conductors like copper and insulators like wood or plastic. Common semiconductors are Silicon and Germanium. The reason semiconductors are important is that with some engineering they can sometimes both conduct and insulate depending on their connections. Thus they serve as the basis for switching and amplification, the fundamental actions of computer elements. A typical modern processor has several million transistors, one of the elements manufactured from semiconducting material which we will study here. Doping refers to the addition of impurities to a semiconductor. The addition of impurities adds charge carrying elements to the semiconductor. The two classes of doping are p-type and n-type which refer to the introduction of positive and negative charge carriers. For instance if one introduces a Phosphorus atom into a silicon lattice, the phosphorus atom would prefer to shed one of the electrons in its outer shell in order to fit in with the silicon lattice. This electron is then available to slide through the material, carrying current. This is an example of n-type doping. By doping the same lattice with Boron, the Boron site wishes to suck an electron out of the silicon lattice to fit neatly into the structure. The site which is now missing an electron represents a positive charge, and therefore the doping is p-type. Movement of this site constitutes a current. Doping becomes important when p-doped and n-doped materials are connected. This constitutes a diode which is the subject of the next page. Diodes Diodes are electric components which force current to flow in only one direction. They are formed by connecting p-type and n-type semiconductors as shown to the right. When current flows from the p-type to the n-type material, the positive holes and the negative electrons are forced into close contact at the boundary. At the boundary, the electrons fill the holes across the boundary while the terminals supply new holes and electrons. Thus, in the forward bias case a continual current flows. In the reverse bias case, the charge carriers are pulled apart. There is no longer an easy way for electrons to tunnel through the barrier as there are no longer many empty holes waiting on the opposite side. The circuit-diagram representation of a diode is direction current is allowed to flow. with the arrow representing the Rectifiers A rectifier is a simple device used for creating a DC source from an AC source. The figure below demonstrates a simple half-wave rectifier. Since the current only flows one way through the resistor the voltage drop can never be negative. The capacitor serves merely as an extra voltage source to even out the sine wave The figure below demonstrates the resulting voltage VS. The term half-wave refers to the fact that in the absence of the capacitor, a voltage exists only during the time when the primary source is positive. One can make a steadier source with a fullwave rectifier as shown below. For the full-wave rectifier the current flows from left to right through the resistor for all parts of the AC cycle. This results in a positive voltage at all times as shown in the figure below. The addition of capacitors would smooth out the resulting DC current even further.