Why do holes have mass

For example, the light absorption and refractive index in the dielectric is purely determined by the conduction electrons for a short wavelengths when a photon energy is larger than the dielectric band gap. The hole is the electron. The is not an atom, or a nuclear, or any type of a positively- charged particle or any kind of a void.

The hole is a negatively- charged electron, which at condition in a solid behaves exactly as a positively- charged particle. A good example is a metal, in which the electrons of an energy higher than the Fermi energy are "electrons" and the electrons of an energy lower than the Fermi energy are "holes".

When the electrical field is applied, an electrons, which move along field, accelerate and gain energy. In contrast, the electrons, which move in the opposite direction, slow down and loss energy. The change of the electron energy changes the number of electrons moving in each direction.

The dependence of the number of electrons on an electron energy is called the electron energy distribution See here. As a result of applying of the electrical field, the energy distribution of electrons moving along the field shifts up and the energy distribution of electrons moving opposite to the field shifts down. The total positive charge of all nucleases precisely equal to the total negative charge of all electrons. There is an energy band to the close unoccupied states and the conduction electrons cannot be scattered to those states.

As I have explains above , in order to transport the Charge and the Spin, the conduction electrons should be able to change their direction distribution. In one direction it should be more electrons and in the opposite direction should be less. In the absence of unoccupied states the conduction electrons are unable to do that and therefore unable to do any transport.

This reason id the same to the reason why the conduction electrons cannot make any current in a dielectric. As a result of replacing a few of atoms of Si by atoms of phosphorous in the crystal of Si, the number of conduction electrons in Si slightly increases and the subtle balance between equal number of conduction electrons and their quantum states is broken. Since there are no available unoccupied states, these additional conduction electrons occupies the upper states conduction band of a higher energy, there is a huge number of unoccupied quantum states there.

Therefore, these additional conduction electrons, which are provided by the phosphorous, are able to transport the Charge and the Spin. As a result of replacing a few of atoms of Si by atoms of boron in the crystal of Si, the number of conduction electrons in Si slightly decreases and the subtle balance between equal number of conduction electrons and their quantum states is broken. There are more available quantum states than the conduction electrons and some of quantum states become unoccupied.

Since there are unoccupied states, the conduction electrons are are able to transport the Charge and the Spin. This main band is called the valence band and the unoccupied quantum states are called the holes.

As a result, a tiny region at contact in the p-Si becomes negatively- charged and a tiny region in n- Si becomes positively- charged. Electrons travel in the conduction band between the two materials. Since the conduction band is formed by the uppermost shell, farthest from any of the nucleus, and since proton resides inside nucleus and hence more energy is required to move an proton than an electron.

Holes are absence of electrons in covalent bond and hole movements are actually movement of electrons to fill up an adjacent hole in the covalent bond. Thus, the electrons moving this way are still under the influence of nuclear forces that scatter them. In contrast, free electrons or just commonly referred to as electrons move within the semiconductor material freely, without going from a covalent bond vacancy to another.

Meaning, free electrons are less influenced by the scattering due to nuclear forces and hence the higher mobility.

The movement of holes is not movement of electrons to fill up an adjacent hole in the covalent bond. The movement of a hole is as "free" as the movement of an electron. In fact, both the electrons and the holes are the same delocalized electrons.

For example, in a metal the electrons and holes can be only distinguished by their energy. The energy of an electron is above the Fermi energy and the energy of a hole is below the Fermi energy. Of cause, an electron and a hole interact differently with electrical field. The mean-free path of a hole may reach several micrometers typically in a semiconductor it is nm at room temperature.

If you see an electron as a wave, the mean-free path of an electron is just the size of the electron. Therefore, the size of a hole may be a micrometer. The distance between covalent bonds is about 0. It means that simultaneously an electron or a hole is filling up or interacts with a million of covalent bonds. Surely, the movement of holes is not movement of an electron to fill up adjacent holes in the covalent bonds. Besides, in order to jump from one covalent bond to other covalent bond an electron needs to interact with a phonon.

In the case if such jumping between the covalent bonds were the mechanism of the hole transport, the hole mobility would be very small.

It would be even smaller than mobility in a material with hopping conduction. In a metal the electron mobility and the hole mobility is the same. Only reason for a difference in the mobilities in a semiconductor is different spatial symmetry of the envelop function for an electron and a hole. Thank you Vadym Zayets for the detailed explanation considering spin-orbit interaction. However, I have a little doubt in my mind. As you pointed out, both are delocalized electrons having only difference in spatial symmetry,how would you explain the effective mass of electrons is smaller than hole in accordance with your explanation?

The mobility of electrons and holes is different, because the electrons and holes have different spatial symmetry. The electrons have s-orbital -like symmetry of the envelop wave function. The holes have p-orbital -like symmetry of the envelop wave function.

There are two reasons why the difference in the spatial symmetry causes the different mobility. They may sound different, but they explain the same fact. The first reason, why the mobility is different, is that it takes a longer time for an electron to circle around the p-orbital than around the s-orbital. A delocalized electron simultaneously moves along the crystal lattice and rotates around millions of atomic nuclei. It might sound strange that it is possible to rotate around several objects simultaneously.

Since an electron is a wave, it is possible. For example, when light is diffracted by a diffraction grating , each photon is reflected from each of million steps of the grating simultaneously. Any wave can interact with many objects simultaneously. It is not forbidden. There are many experimental proofs that delocalized electrons have a non-zero orbital moment.

For example, their g-factor is different from 2, they experience the center-symmetrical spin-orbit interaction and the existence of the split-off valence band is other proof. The non-zero orbital moment literally means that the delocalized electron is orbiting around atomic nuclei. The second reason, why the mobilities effective masses are different for holes and electrons in a semiconductor, is that the magnitudes of the s-like and p-like envelope functions are different in the vicinity of the atomic nucleus.

The electrons of different symmetry interact differently with the nucleus. Therefore, the amplitude of the lattice periodic potential is different for electrons and holes in a semiconductor. This causes the different effective masses. Mobility is proportional to the average time between two consecutive scattering events collisions and is inversely proportional to the effective mass.

Electrons and holes are scattered by different types of crystal imperfections, which include phonons, impurities, defects, etc. In current MOSFET transistor, the channel electrons and holes are scattered mainly by impurity and interface charges Coulomb scattering , interface roughness, and phonons. The average time between collisions also known as the mean free time is given by the Mathiessen's Rule. I have a question that mobility of holes in oxides having 2p orbital e. I have followed your answers on difference in mobility of electrons and holes but still didn't get answer to this question.

Could you please explain it to me. For example, the mobility of the holes and electrons in a metal is absolutely identical. Whether it is a hole and an electron are only distinguished by the electron energy in respect to the Fermi energy. The energy of a hole is smaller than the Fermi energy, the energy of an electron is greater. Generally the energy of an electron of p-symmetry is smaller than an electron of s-symmetry and the energy of an electron of d-symmetry is smaller than an electron of p-symmetry as it follows the electron arrangement in a free atom it is not always the case.

You can look in more details about this topic in the following my paper V. Zayets, ", JMM , pp 53—65 You can download it here. Secondly, the mobility of the electron depends more on crystal symmetry than atomic symmetry s-,p-,d-. You can understand it as follows.

The mobility of an electron depends on the length of the electron. The longer length of the electron, the greater its mobility. The length of an electron depends how well the electron function of neighbor atoms are overlap. Within oversimplify view, more they overlap, longer the electron length is. I do not now details about band structure of gallium oxide and copper oxide.

A possible explanations is as follows. The oxide are mainly ionic crystals. The oxygen takes one or two s- or p- from Ga ore Cu. Therefore, s- or p- electrons becomes localized and they do not participate in the conductivity. In contrary, d- or p- electrons are still near its host atom, their neighbor-atom wave functions can overlap and they become delocalized conduction electrons. Of course, everything depends on crystal symmetry. Additionally, the wavefunction could be elongated due the Coulomb's repulsion from neighbor oxygen.

Everything depends on crystal symmetry and atom arrangement. An electron of d-symmetry may have greater mobility that an electron of p-symmetry. My Research and Inventions click here to see all content or button bellow for specific topic. Holes and Electrons Spin and Charge Transport.

What do we know about holes in a solid? Is a hole a positive particle? Is there a real hole inside something? Classical model consider a hole literally as a hole or a void in the ocean of electrons it is an incorrect view!!!! Is it half-full? Energy distribution of electrons in a non-magnetic material, in which conduction electrons are not spin- polarized.

Band Current Simple example. Electron Current Hole Current Scattering of conduction electrons between different quantum states. Why is an electron is faster and a hole is slower??? Orbitals of Heavy Holes Shape of orbitals depends on direction of the orbital moment. If orbital moment and spin is unquenched, the orbital shape depends on spin direction as well. Direct-band semiconductor. Scattering electron current. Numbers n forward and n backward of forward- and backward- moving electrons vs.

Right part blue shows electrons n forward moving along the electrical field forward. Left part green shows electrons n backward moving opposite to the electrical field backward. The total number of electrons moving in each direction is calculated by an integration over all energies.

The "holes" are electrons, which energy is smaller than the Fermi energy E F shown in upper graph. In contrast, an electron moving opposite to electrical field loses the energy. As a result, the electron distribution of "electrons" and "holes" is shifted towards the electrical field. These electrons are mostly contribute to charge and spin transport Details see here Distribution of conduction electrons for their movement directions.

The length of a vector from axis origin to sphere is proportional to the number of electrons moving in the vector direction. Directional distribution of electrons is a sphere in an isotropic material. When an electrical field is applied along y- axis, the sphere moves along y-axis for an "electron" current and opposite to y-axis for an "hole" current.

It means that in case of "electron" current there are more electron moving along y-axis than opposite to y- axis. In case of "hole" current there are more electron moving opposite to y- axis than along y-axis.

They accelerate and gains energy. As a result, the distribution is shifted to a higher energy. They slow down and loss energy. As a result, the distribution is shifted to a lower energy. Energy of an "electron" is higher than E F. In electrical field E , the number of electrons, which moves along E , becomes larger and the number of electrons, which moves opposite to E , becomes smaller.

As a result, the sphere is sifted along the field E and therefore the electron current flows along E as in case a negatively- charged carrier.

Energy of a "hole" is smaller than E F. In electrical field E , the number of electrons, which moves along E , becomes smaller and the number of electrons, which moves opposite to E , becomes larger. As a result, the sphere is sifted opposite to the field E and therefore the electron current flows opposite to E as in case of a positively- charged carrier.

I truly appreciate your comments, feedbacks and questions I will try to answer your questions as soon as possible Comment Box is loading comments Holes and Electrons Spin and Charge Transport In a solid all positively-charged particles the protons are localized inside an atomic nuclear and they do not transport the charge and the spin.

Only negatively-charged particles the electrons transport the charge and the spin. However, some electrons with energies lower than the Fermi energy behave like positively-charged particles. Therefore, the collective movement of negatively-charged electrons are described as a movement of positively- charged particles called the holes.

The hole in a metal and a semiconductor is not real hole. It is not void or unfilled orbital. It is an electron, which has the properties similar to that of a positive particle in vacuum. The same content can be found in this paper V. Zayets JMMM Chapter 6. Content click on the chapter for the shortcut 1. Is any difference between holes in a semiconductors and holes in a metal? Are they of the same kind? What is the hole? Is it a void in the ocean of electrons?

Or it is an electron with special features? Simple facts about holes in a metal and a semiconductor 5. Since a metal has both the electrons and holes, is it possible to make a transistor using only metals similar to a semiconductor transistor a MOSFET transistor or a bipolar transistor? Does the hole has the spin? Are the holes really positively charged and the electrons negatively charged? Excitons Transport of electrons and holes in a metal and semiconductor Main part of page 1.

Why is the mobility of electron higher than that of hole? The reason why the electron mobility is higher than the hole mobility There is no any real holes in the electron gas!!!! Above the Fermi energy E F the slope is positive and the half-filled states are called the electrons.

Below the Fermi energy E F the slope is negative and the half-filled states are called the holes. More details is here or V. Zayets, JMMM Similar to a glass of wine, when a quantum state is filled only by one electron, it is called: - half-filled or the electron -half-empty or the hole. The spin of the hole is absolutely identical to the spin of the electron click on image to enlarge it.

In the equilibrium the spacial charge distribution is very smooth and the total charge equals to zero everywhere. The spacial charge distribution the is the sum of charges of local and conduction electrons, holes, nuclears and dopants.

Due to a thermo fluctuation some electrons may move slightly from right to left. At the left it will be more electrons. It is region of the charge accumulation, which is negatively charged. At the right, there is a region of the charge depletion, which is positively charged. Mean-free path of states, which filled by two , one or none electrons. The electron is the half-filled state with energy above the Fermi energy.

When the half-filled state moves left, the right space is occupied by "empty" state. Length mean-free path of half-filled state is substantially shorter than the length of the "empty" state.

As result, there is a sharp noticeable negatively-charged region of charge accumulation and there is a broad unnoticeable region of charge depletion. Therefore, the electron can be a negatively charged particle. The hole is the half-filled state with energy below the Fermi energy. When the half-filled state moves left, the right space is occupied by full-filled state. Length mean-free path of half-filled state is substantially shorter than the length of the full-filled state. As result, there is a sharp noticeable positively-charged region of charge depletion and there is a broad unnoticeable region of charge accumulation.

Therefore, the hole can be considered a positively charged particle. Energy distribution of states, which filled by one and two electrons. This is an important consideration for ships, submarines, torpedoes, fish, etc, that end up having considerably more inertia than their own mass, and end up accelerating slower with the engine on.

One time I did mathematics for realistic barrel falling into water in computer game; the apparent 'increase' of the mass, in combination with the conservation of momentum, rather accurately describes a large part of the deceleration of object when it is entering water.

Sign up to join this community. The best answers are voted up and rise to the top. Stack Overflow for Teams — Collaborate and share knowledge with a private group. Create a free Team What is Teams? Learn more. Why does a semiconductor hole have a mass? Ask Question. Asked 9 years, 4 months ago. Active 7 years ago. Viewed 8k times. Improve this question. Ron Maimon 1. Add a comment. Active Oldest Votes. Improve this answer.

Ron Maimon Ron Maimon 1. Alfred Centauri Alfred Centauri Constantin Negut Constantin Negut 21 1 1 bronze badge. Re: electron mass hole silicon can we assign degree of freedom to a hole?

Re: why effective mass of hole greater than electron flatulent said:. A hole is an imaginary particle that is used to make the math work. KerimF Advanced Member level 4. Re: why effective mass of hole greater than electron To me, the whole theory is imaginary though necessary for the math work. Actually, the energy due to electrical, magnetic or gravity field But the particles by which these waves can travel, are surely not the ones of the atomic universe.

World scientists will have to wait many years before introducing the concept theory that relates to the universes below and above the two already perceived ones; our universe and the universe which form its masses the atomic one For those who are curious, the particles of the first universe below the atomic one are the particles forming its masses; the masses of electrons, nucleus Obviously these sub-particles, in turn, are also formed by moving particles in the space of a lower sub-universe In other words, our existence is made by a universe formed by a huge space and particles called stars and planets I forgot the universe above ours I guess most of you now have already imagined it by applying the same concept.

Last edited: Jul 10, For a hole to move, requires a series of electrons to vacate position ahead of it. So its "mass" is going to look like all those reluctant valence electrons' mass that had to be plowed out of the way time shared. Similar threads E. Elementary Electronic Questions. Why is mobility of holes less than electrons? Part and Inventory Search. Welcome to EDABoard.