Can someone help me gain an understanding of why bandgap and electron effective mass in semiconductors are proportional to one another e. Ravindran, phy02e semiconductor physics, autum 20 17 december. The concept of effective mass follows from physicists love for simple relations such as ohms law current density conductivity x electric field intensity or newtons second. Design complex semiconductors and devices the goal of this course is to teach the fundamentals of quantum mechanics, a modern approach to physics on the nano scale.
Introduction the effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a parabola. The effective mass reflects the inverse of the band curvature. We report here a theory totally different in conception. The ek diagram for direct band gap semiconductors will be studied and the hole concept will be. An alternative to the ekdiagram is proposed as a mean of teaching the concept of hole to undergraduate students who have never studied quantum mechanics. The canonical definition given for the effective mass is that it is related to the curvature of the conduction and valence bands in the band structure energy dispersion in terms of kvector for electrons and holes respectively. Energyband and effective mass band gap electron hole. Generalized effective mass approach for cubic semiconductor nmosfets on arbitrarily oriented wafers anisur rahman, mark s. In most semiconductors the effective mass is a tensor quantity. In this presentation, the effective mass theory emt for the electron in the crystal lattice will be introduced.
The effective mass of a semiconductor is obtained by fitting the actual ek diagram around the. Seeger the physics of semiconductors grundmann basic semiconductors physics hamaguchi electronic and optoelectronic properties of semiconductors singh quantum well wires and dots hartmann. Energyband and effective mass free download as powerpoint presentation. Introduction of the concepts of hole and effective mass. Some background on the application of quantum mechanics to crystalline solids is given in order to discuss the concept of. Effective mass calculator emc implements calculation of the effective masses at the bands extrema using finite difference method not the band fitting method. In 3d, the second derivative is a tensor the effective mass is anisotropic, and 4 concept of effective mass. This diagram indicates diagramatically how the actual electron states are equally spaced in kspace. The important point is that the electron in a periodic potential is accelerated relative to the lattice in an applied electric or magnetic field as if its mass is equal to an effective mass. One way of directly determining the effective mass of electrons in a semiconductor is by cyclotron. In solid state physics, a particles effective mass often denoted m. Effectivemass theory of metalsemiconductor contact resistivity article pdf available in applied physics letters 1038 august 20 with 225 reads how we measure reads. Energy bands and effective mass semiconductors, insulators and metals semiconductors insulators metals the concept of effective mass the electrical properties of metals and insulators are. In most semiconductors the conduction bands have a parabolic dispersion relation, and so these electrons respond to forces electric field, magnetic field, etc.
Why effective mass of hole is greater than electron. Semiconductors types, examples, properties, application. The effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a parabola. Effective mass calculator for semiconductors github. The hole concept is useful to describe the properties at the valence bandtop. The effective mass concept if useful because it allows us to retain the notion of a freeelectron even when we have a periodic potential, as long as we use m to.
Effective mass theory freespace motion with a different mass 2. In a solid, the electron hole effective mass represents how electrons move in an applied field. Ravindran, phy02e semiconductor physics, 30 january 20. Chapter 11 density of states, fermi energy and energy bands. Introduction the effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a paraboloid. In general, electron in a flatter band has a larger m. Electrons strongly absorb microwaves of that frequency. Ghosh school of electrical and computer engineering 1285 electrical engineering building purdue university, west lafayette, in 47907 abstract. Optical conductivity and optical effective mass in a high.
The ek diagram for direct band gap semiconductors will be studied and. Very first thing is that in solids the energy is distributed in terms of energy band. This is given by the curvature of each of the bands. Fundamentals of semiconductors by peter y yu and manuel cardona, spriger, 1996. The effective mass is used in transport calculations, such as transport of electrons under the influence of fields or carrier gradients, but it also is used to calculate the carrier density and density of states in semiconductors. In such complex materials there is no single definition of effective mass but instead. To avoid any terminology confusion, this is asked in the context of solid state physics and semiconductors.
Band theory of solids in this 33 mins video lesson basic concepts, energy level splitting and energy bands, conductivity and band structure, conductorsmetals, semi. Why is the effective mass of electron different for metals. Seeger the physics of semiconductors grundmann basic semiconductors physics hamaguchi. Semiconductor materials, elemental and compound semiconductors, band model of semiconductors, carrier concentration in energy bands, fermi level and energy distribution of carriers inside band, extrinsic semiconductors, concept of effective mass, heavily doped semiconductors. These masses are related but, as explained in the previous sections. What is the rest mass of a hole in a semiconductor.
The electron near band bottom is like a free electron with m. And secondly the solid structure is generally expressed in reciprocal. Overview hole and effective mass intrinsic sm doped sm pn junction. The concept of electron and hole effective mass in semiconductors has been developed starting from the mobility of carriers be them electrons or holes. Most actual band structures for semiconductors have ellipsoidal energy surfaces which require longitudinal and transverse effective masses in place of the three principal effective masses figure 11. Learn how the mass of electrons varies along the band giving rise to the concept of holes. The concept of hole and effective mass intrinsic semiconductor doped semiconductor m.
Physics explains the theories, properties and mathematical approach governing semiconductors. In one dimension, an electron with wavevector k has group velocity. The concept of effective mass follows from physicists love for simple relations such as ohms law current density conductivity x electric field intensity or newtons second law of motion. Understand and design custom semiconductor materials with optical and electrical properties tailored to. We show that our calculated values compare acceptably. Effective mass in semiconductors 21 physical meaning of the band effective mass of course, for a free electron, in a 3d solid we would find that m is a secondorder tensor with 9 components. Comparing free ein vacuum in an electric field mo9. Lecture 1 introduction to semiconductors and semiconductor. Pdf effectivemass theory of metalsemiconductor contact. In three dimensions, constant energy surfaces are not necessarily. The effective mass of electrons and holes in the material.
Therefore, the densityofstates effective mass is expressed as 3 1 2 d l m t 11. In semiconductors, at finite temperatures, there are electrons in the conduction band. While this concept is simple enough the issue turns out to be substancially more complex due to the multitude and the occasional anisotropy of the minima and maxima. A particles effective mass is the mass it appears to carry in transport in. Nptel syllabus fundamental concepts of semiconductors. The effective mass of a semiconductor is obtained by fitting the actual ek diagram around the conduction band minimum or the valence band maximum by a paraboloid. The dynamics of the electron in free space and in the lattice will be compared. Effective mass defects in effectivemass theory emt the energy levels of the donor is. The physics of semiconductors by kevin f brennan, cambridge univ. Effective mass is defined by means of the ek diagram. Intrinsic and extrinsic semiconductors effective mass at k0, the e,k relationship near the minimum is usually parabolic.
The electron effective mass in the valence band is negative, but the hole behaves as if it has a positive mass. Semiconductors can be compounds such as gallium arsenide or pure elements, such as germanium or silicon. The effective mass may be anisotropic, and it may even be negative. It tells how fast the electrons will drift when an electric. To understand the concept of effective mass, firstly you need to know about band structure. Semiconductors are the materials which have a conductivity between conductors generally metals and nonconductors or insulators such ceramics. The concept of hole and effective mass intrinsic semiconductor no doping. Im not sure how this relates to the differing effective mass for metals and semiconductors, are saying the curvature of the dispersion graph for a semiconductor is different from that of a metal, and thats why the effective mass differs. Helloi feel that this is a graduatelevel question, so i hope that this question is not found to be insultingly easy. Bonding becomes more ionic elements compounds families of semiconductors semiconductor is insulator at 0 k, but because of its smaller energy gap diamond 5.