ECEstream: Semiconductors

Fermi Level

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"Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. This concept comes from Fermi-Dirac statistics. Electrons are fermions and by the Pauli exclusion principle cannot exist in identical energy states. So at absolute zero they pack into the lowest available energy states and build up a "Fermi sea" of electron energy states. The Fermi level is the surface of that sea at absolute zero where no electrons will have enough energy to rise above the surface. The concept of the Fermi energy is a crucially important concept for the understanding of the electrical and thermal properties of solids. Both ordinary electrical and thermal processes involve energies of a small fraction of an electron volt. But the Fermi energies of metals are on the order of electron volts. This implies that the vast majority of the electrons cannot receive energy from those processes because there are no available energy states for them to go to within a fraction of an electron volt of their present energy. Limited to a tiny depth of energy, these interactions are limited to "ripples on the Fermi sea".</div>
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At higher temperatures a certain fraction, characterized by the Fermi function, will exist above the Fermi level. The Fermi level plays an important role in the band theory of solids. In <b>doped semiconductors</b>, p-type and n-type, the Fermi level is shifted by the impurities, illustrated by their band gaps. The Fermi level is referred to as the electron chemical potential in other contexts.</div>
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In metals, the Fermi energy gives us information about the velocities of the electrons which participate in ordinary electrical conduction. The amount of energy which can be given to an electron in such conduction processes is on the order of micro-electron volts (see copper wire example), so only those electrons very close to the Fermi energy can participate. The Fermi velocity of these conduction electrons can be calculated from the Fermi energy.</div>
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This speed is a part of the microscopic Ohm's Law for electrical conduction. For a metal, the density of conduction electrons can be implied from the Fermi energy.</div>
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The Fermi energy also plays an important role in understanding the mystery of why electrons do not contribute significantly to the specific heat of solids at ordinary temperatures, while they are dominant contributors to thermal conductivity and electrical conductivity. Since only a tiny fraction of the electrons in a metal are within the thermal energy kT of the Fermi energy, they are "frozen out" of the heat capacity by the Pauli principle. At very low temperatures, the electron specific heat becomes significant.</div>
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Fermi Level

"Fermi level" is the term used to describe the top of the collection of electron energy levels at absolute zero temperature. Th...

Band Theory of Solids

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A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electrons in the materials. Instead of having discrete energies as in the case of free atoms, the available energy states form bands. Crucial to the conduction process is whether or not there are electrons in the conduction band. In insulators the electrons in the valence band are separated by a large gap from the conduction band, in conductors like metals the valence band overlaps the conduction band, and in semiconductors there is a small enough gap between the valence and conduction bands that thermal or other excitations can bridge the gap. With such a small gap, the presence of a small percentage of a doping material can increase conductivity dramatically.<br />
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An important parameter in the band theory is the Fermi level, the top of the available electron energy levels at low temperatures. The position of the Fermi level with the relation to the conduction band is a crucial factor in determining electrical properties.</div>
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<b style="text-align: justify;"><b>ENERGY BANDS FOR SOLIDS</b></b></h3>
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<b>Insulator Energy Bands</b></h4>
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Most solid substances are insulators, and in terms of the band theory of solids this implies that there is a large forbidden gap between the energies of the valence electrons and the energy at which the electrons can move freely through the material (the conduction band).</div>
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Glass is an insulating material which may be transparent to visible light for reasons closely correlated with its nature as an electrical insulator. The visible light photons do not have enough quantum energy to bridge the band gap and get the electrons up to an available energy level in the conduction band. The visible properties of glass can also give some insight into the effects of "doping" on the properties of solids. A very small percentage of impurity atoms in the glass can give it color by providing specific available energy levels which absorb certain colors of visible light. The ruby mineral (corundum) is aluminum oxide with a small amount (about 0.05%) of chromium which gives it its characteristic pink or red color by absorbing green and blue light.</div>
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While the doping of insulators can dramatically change their optical properties, it is not enough to overcome the large band gap to make them good conductors of electricity. However, the doping of semiconductors has a much more dramatic effect on their electrical conductivity and is the basis for solid state electronics.</div>
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<b>Semiconductor Energy Bands</b></h4>
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For intrinsic semiconductors like silicon and germanium, the Fermi level is essentially halfway between the valence and conduction bands. Although no conduction occurs at 0 K, at higher temperatures a finite number of electrons can reach the conduction band and provide some current. In doped semiconductors, extra energy levels are added.</div>
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The increase in conductivity with temperature can be modeled in terms of the Fermi function, which allows one to calculate the population of the conduction band.</div>
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<b>Conductor Energy Bands</b></h4>
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In terms of the band theory of solids, metals are unique as good conductors of electricity. This can be seen to be a result of their valence electrons being essentially free. In the band theory, this is depicted as an overlap of the valence band and the conduction band so that at least a fraction of the valence electrons can move through the material.<br />
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<b>Silicon Energy Bands</b></h4>
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At finite temperatures, the number of electrons which reach the conduction band and contribute to current can be modeled by the Fermi function. That current is small compared to that in doped semiconductors under the same conditions.</div>
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<b>Germanium Energy Bands</b></h4>
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At finite temperatures, the number of electrons which reach the conduction band and contribute to current can be modeled by the Fermi function. That current is small compared to that in doped semiconductors under the same conditions.</div>
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Band Theory of Solids

A useful way to visualize the difference between conductors, insulators and semiconductors is to plot the available energies for electro...

Intrinsic Semiconductor

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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".</div>
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If a voltage is applied, then both the electron and the hole can contribute to a small current flow.</div>
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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.</div>
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The term intrinsic here distinguishes between the properties of pure "intrinsic" silicon and the dramatically different properties of doped n-type or p-type semiconductors.<span class="Apple-tab-span" style="white-space: pre;"> </span></div>
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Intrinsic Semiconductor

A silicon crystal is different from an insulator because at any temperature above absolute zero temperature, there is a finite probabilit...

Semiconductor Current

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The current which will flow in an intrinsic semiconductor consists of both <b>electron</b> and <b>hole</b> current. That is, the electrons which have been freed from their lattice positions into the conduction band can move through the material.</div>
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In addition, other electrons can hop between lattice positions to fill the vacancies left by the freed electrons. This additional mechanism is called hole conduction because it is as if the holes are migrating across the material in the direction opposite to the free electron movement.<span class="Apple-tab-span" style="white-space: pre;"> </span></div>
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The current flow in an intrinsic semiconductor is influenced by the density of energy states which in turn influences the electron density in the conduction band. This current is highly temperature dependent.<br />
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<b>Electrons and Holes</b><br />
In an intrinsic semiconductor like silicon at temperatures above absolute zero, there will be some electrons which are excited across the band gap into the conduction band and which can produce current. When the electron in pure silicon crosses the gap, it leaves behind an electron vacancy or "hole" in the regular silicon lattice. Under the influence of an external voltage, both the electron and the hole can move across the material. In an n-type semiconductor, the dopant contributes extra electrons, dramatically increasing the conductivity. In a p-type semiconductor, the dopant produces extra vacancies or holes, which likewise increase the conductivity. It is however the behavior of the p-n junction which is the key to the enormous variety of solid-state electronic devices.<br />
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Semiconductor Current

The current which will flow in an intrinsic semiconductor consists of both electron and hole current. That is, the electrons which have...

Silicon and Germanium

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<span style="text-align: justify;">Solid state electronics arises from the unique properties of silicon and germanium, each of which has four valence electrons and which form crystal lattices in which substituted atoms (dopants) can dramatically change the electrical properties.</span><br />
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<b>Silicon</b></div>
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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.</div>
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<b>Germanium</b></div>
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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.</div>
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<b>Silicon Lattice</b><br />
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.<br />
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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 unit cell.<br />
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<b>Valence Electrons</b></div>
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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.</div>
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Silicon and Germanium

Solid state electronics arises from the unique properties of silicon and germanium, each of which has four valence electrons and which form...

P-N Junction

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<span style="font-family: inherit;">One of the crucial keys to solid state electronics is the nature of the P-N junction. When p-type and n-type materials are placed in contact with each other, the junction behaves very differently than either type of material alone. Specifically, current will flow readily in one direction (forward biased) but not in the other (reverse biased), creating the basic diode. This non-reversing behavior arises from the nature of the charge transport process in the two types of materials.</span></div>
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<span style="font-family: inherit;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjcVV66qMXdTqD3OyJj6ujeP9VyTAB2H7FWfhf6dFebOUc_Lh9eAZ0WK6bBcVrGXbLQAczcywYm7_Ixolj1yFL9zkYGAtU4Adp9Nqd4ruqlz-YUjxyTONqwUimVue0RlCbHsN-nI1u6GVOq/s1600/pn+junction.gif" /></span></div>
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<span style="font-family: inherit;">The open circles on the left side of the junction above represent "holes" or deficiencies of electrons in the lattice which can act like positive charge carriers. The solid circles on the right of the junction represent the available electrons from the n-type dopant. Near the junction, electrons diffuse across to combine with holes, creating a "depletion region". The energy level sketch above right is a way to visualize the equilibrium condition of the P-N junction. The upward direction in the diagram represents increasing electron energy.</span></div>
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<b style="text-align: justify;"><span style="font-family: inherit;">DEPLETION REGION</span></b></h3>
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<span style="font-family: inherit;">When a p-n junction is formed, some of the free electrons in the n-region diffuse across the junction and combine with holes to form negative ions. In so doing they leave behind positive ions at the donor impurity sites.</span></div>
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<b><span style="font-family: inherit;">Details of Depletion Region</span></b></h4>
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<span style="font-family: inherit;">In the p-type region there are holes from the acceptor impurities and in the n-type region there are extra electrons.</span></div>
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<span style="font-family: inherit;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEg9YbtTaNfzIH7hFB-pGqhexEVXJlIZzUugRyT2wSLvFh2TC3XXiJMuLmVGECzuZoFa44x1g44z2J6bCqYT_8VHnqWZ_xWg8dvUTirzJlTvRk75JJjME71rDsNwYTR7yc2fIfPVmyINCzhyphenhyphen/s1600/depletionregion1.gif" /></span></div>
<span style="font-family: inherit; text-align: justify;">When a p-n junction is formed, some of the electrons from the n-region which have reached the conduction band are free to diffuse across the junction and combine with holes.</span><br />
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<span style="font-family: inherit;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEi9QdL2uthvRW8LL_MtVU4DyXpbci6AW4mZAYc_gpsOZOAJWKR4_4S5WzOFSfMXOlXFygKCHwkKwzu0fZ4FZ_bG1CiDMAFFqxfm_sPkMuVT-IyJxdnUhl7Iv8sGrOUrY0RPRkCkst5NJMxM/s1600/depletion+region2.gif" /></span></div>
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<span style="font-family: inherit;">Filling a hole makes a negative ion and leaves behind a positive ion on the n-side. A space charge builds up, creating a depletion region which inhibits any further electron transfer unless it is helped by putting a forward bias on the junction.</span></div>
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<span style="font-family: inherit;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEjlq7E1WEM-ZGE6wHjjgCBr5QYXUPQhnsOhcmLmmMQDrPbrRtuepP7-lP2BnJv66-Bs8vSG353cRQ5P0Y-ujQ_lepsHZcog6l7Ak9jDyanT6LBkjbTDyzSq2CPXoHVC4Qpk5DETTJu8ZF7L/s1600/depletion+region3.gif" /></span></div>
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<span style="font-family: inherit;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEgIgHxnNRldxwl_Cr-xNCZ1i77SeHtkzxLZlEsDbzr5HY4XN4lRem0pidXyBPIes698zphI1mbQwNhIoSwmyhsSD34_nYu9RhTO7lUFSahc66AKWt5cSjjp6IEED9Y7CHrLN3xcTZDGq9Ku/s1600/depletion+region4.gif" /></span></div>
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<b><span style="font-family: inherit;">BIAS EFFECT ON ELECTRONS IN DEPLETION REGION</span></b></h3>
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<b><span style="font-family: inherit;">Equilibrium of P-N Junction</span></b></h4>
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<span style="font-family: inherit;">For a p-n junction at equilibrium, the Fermi levels match on the two sides of the junctions. Electrons and holes reach an equilibrium at the junction and form a depletion region. The upward direction in the diagram represents increasing electron energy. That implies that you would have to supply energy to get an electron to go up on the diagram, and supply energy to get a hole to go down.</span></div>
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<span style="font-family: inherit;"><img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEhZxX3VCcTYxwip234w77LnatOKJ6rFbFzEpBPnZFAtdPgsGasUazsmt5j7FjDc96ZKGkruvfWPm0ykgr6Vvnmo7jvmtDMqSipEu8NOBb-gsJe7cXDenQJ_3reTMNvj9F_pueBgkLpio1Tj/s1600/p-n+junction+at+equilbrium.gif" /></span></div>
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<b><span style="font-family: inherit;">Reverse-Bias of P-N Junction</span></b></h4>
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<span style="font-family: inherit;">To reverse-bias the p-n junction, the p side is made more negative, making it "uphill" for electrons moving across the junction. The conduction direction for electrons in the diagram is right to left, and the upward direction represents increasing electron energy.</span></div>
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<b><span style="font-family: inherit;">Forward-Bias of P-N Junction</span></b></h4>
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<span style="font-family: inherit;">To forward bias the p-n junction, the p side is made more positive, so that it is "downhill" for electron motion across the junction. An electron can move across the junction and fill a vacancy or "hole" near the junction. It can then move from vacancy to vacancy leftward toward the positive terminal, which could be described as the hole moving right. The conduction direction for electrons in the diagram is right to left, and the upward direction represents increasing electron energy.</span></div>
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P-N Junction

One of the crucial keys to solid state electronics is the nature of the P-N junction. When p-type and n-type materials are placed in conta...

Doping of Semiconductors

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The addition of a small percentage of foreign atoms in the regular crystal lattice of silicon or germanium produces dramatic changes in their electrical properties, producing n-type and p-type semiconductors.</div>
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<b>Pentavalent impurities</b></div>
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Impurity atoms with 5 valence electrons produce n-type semiconductors by contributing extra electrons.</div>
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<b>Trivalent impurities</b></div>
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Impurity atoms with 3 valence electrons produce p-type semiconductors by producing a "hole" or electron deficiency.</div>
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<b><u>N-Type Semiconductors</u></b></div>
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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 (PH3).</div>
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<b>N-Type Band Structure</b></div>
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The addition of donor impurities contributes electron energy levels high in the semiconductor band gap so that electrons can be easily excited into the conduction band. This shifts the effective Fermi level to a point about halfway between the donor levels and the conduction band.</div>
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<img border="0" src="https://blogger.googleusercontent.com/img/b/R29vZ2xl/AVvXsEie4RdB1vp2vsIcOtDl7qRzBjShuqLU5Pe8HkTMMceIy3fTwi8ync4sptV1LY-3oZoiHyI7yAizH8-iLdnxmVsykS3SUC_GH9DmtXBemXsmsRTt7uKIXF-ro6bhqbZqhbRVb8vYSqtzrUld/s1600/N-type+band+structure.gif" /></div>
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Electrons can be elevated to the conduction band with the energy provided by an applied voltage and move through the material. The electrons are said to be the "majority carriers" for current flow in an n-type semiconductor.<br />
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<b><u>P-Type Semiconductor</u></b></div>
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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.</div>
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<b><u>P-Type Band Structure</u></b></div>
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The addition of acceptor impurities contributes hole levels low in the semiconductor band gap so that electrons can be easily excited from the valence band into these levels, leaving mobile holes in the valence band. This shifts the effective Fermi level to a point about halfway between the acceptor levels and the valence band.</div>
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Electrons can be elevated from the valence band to the holes in the band gap with the energy provided by an applied voltage. Since electrons can be exchanged between the holes, the holes are said to be mobile. The holes are said to be the "majority carriers" for current flow in a p-type semiconductor.</div>
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Doping of Semiconductors

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P-N Junction

Doping of Semiconductors

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