Question: Where do Electrons escape from?
About the article "Photoelectric effect", section "Three-step model".

Candidate passages:
In a semiconductor it is sometimes useful to think of the current as due to the flow of positive "holes" (the mobile positive charge carriers that are places where the semiconductor crystal is missing a valence electron).
This is the case in a p-type semiconductor.
A semiconductor has electrical conductivity intermediate in magnitude between that of a conductor and an insulator.
This means a conductivity roughly in the range of 10−2 to 104 siemens per centimeter (S⋅cm−1).
In the classic crystalline semiconductors, electrons can have energies only within certain bands (i.e.
ranges of levels of energy).
Energetically, these bands are located between the energy of the ground state, the state in which electrons are tightly bound to the atomic nuclei of the material, and the free electron energy, the latter describing the energy required for an electron to escape entirely from the material.
The energy bands each correspond to a large number of discrete quantum states of the electrons, and most of the states with low energy (closer to the nucleus) are occupied, up to a particular band called the "valence band".
Semiconductors and insulators are distinguished from metals because the valence band in any given metal is nearly filled with electrons under usual operating conditions, while very few (semiconductor) or virtually none (insulator) of them are available in the "conduction band", the band immediately above the valence band.
The ease with which electrons in the semiconductor can be excited from the valence band to the conduction band depends on the band gap between the bands.
The size of this energy bandgap serves as an arbitrary dividing line (roughly 4 eV) between semiconductors and insulators.
With covalent bonds, an electron moves by hopping to a neighboring bond.
The Pauli exclusion principle requires the electron to be lifted into the higher anti-bonding state of that bond.
For delocalized states, for example in one dimension – that is in a nanowire, for every energy there is a state with electrons flowing in one direction and another state with the electrons flowing in the other.
For a net current to flow, more states for one direction than for the other direction must be occupied.
For this to occur, energy is required, as in the semiconductor the next higher states lie above the band gap.
Often this is stated as: full bands do not contribute to the electrical conductivity.
However, as the temperature of a semiconductor rises above absolute zero, there is more energy in the semiconductor to spend on lattice vibration and on exciting electrons into the conduction band.
The current-carrying electrons in the conduction band are known as "free electrons", although they are often simply called "electrons" if context allows this usage to be clear. 
 CH4, for the central C neutral counting: C contributes 4 electrons, each H radical contributes one each: 4+4(1) = 8 valence electrons ionic counting: C4- contributes 8 electrons, each proton contributes 0 each: 8 + 4(0) = 8 electrons.
Similar for H: neutral counting: H contributes 1 electron, the C contributes 1 electron (the other 3 electrons of C are for the other 3 hydrogens in the molecule): 1 + 1(1) = 2 valence electrons.
ionic counting: H contributes 0 electrons (H+), C4- contributes 2 electrons (per H), 0 + 1(2) = 2 valence electrons conclusion: Methane follows the octet-rule for carbon, and the duet rule for hydrogen, and hence is expected to be a stable molecule (as we see from daily life) H2S, for the central S neutral counting: S contributes 6 electrons, each hydrogen radical contributes one each: 6+2(1) = 8 valence electrons ionic counting: S2- contributes 8 electrons, each proton contributes 0: 8+2(0) = 8 valence electrons conclusion: with an octet electron count (on sulfur), we can anticipate that H2S would be pseudotetrahedral if one considers the two lone pairs.
SCl2, for the central S neutral counting: S contributes 6 electrons, each chlorine radical contributes one each: 6+2(1) = 8 valence electrons ionic counting: S2+ contributes 4 electrons, each chloride anion contributes 2: 4+2(2) = 8 valence electrons conclusion: see discussion for H2S above.
Notice that both SCl2 and H2S follow the octet rule - the behavior of these molecules is however quite different.
SF6, for the central S neutral counting: S contributes 6 electrons, each fluorine radical contributes one each: 6+6(1) = 12 valence electrons ionic counting: S6+ contributes 0 electrons, each fluoride anion contributes 2: 0+6(2) = 12 valence electrons conclusion: ionic counting indicates a molecule lacking lone pairs of electrons, therefore its structure will be octahedral, as predicted by VSEPR.
One might conclude that this molecule would be highly reactive - but the opposite is true: SF6 is inert, and it is widely used in industry because of this property.
TiCl4, for the central Ti neutral counting: Ti contributes 4 electrons, each chlorine radical contributes one each: 4+4(1) = 8 valence electrons ionic counting: Ti4+ contributes 0 electrons, each chloride anion contributes two each: 0+4(2) = 8 valence electrons conclusion: Having only 8e (vs. 18 possible), we can anticipate that TiCl4 will be a good Lewis acid.
Indeed, it reacts (in some cases violently) with water, alcohols, ethers, amines.
Fe(CO)5 neutral counting: Fe contributes 8 electrons, each CO contributes 2 each: 8 + 2(5) = 18 valence electrons ionic counting: Fe(0) contributes 8 electrons, each CO contributes 2 each: 8 + 2(5) = 18 valence electrons conclusions: this is a special case, where ionic counting is the same as neutral counting, all fragments being neutral.
Since this is an 18-electron complex, it is expected to be isolable compound.
Ferrocene, (C5H5)2Fe, for the central Fe: neutral counting: Fe contributes 8 electrons, the 2 cyclopentadienyl-rings contribute 5 each: 8 + 2(5) = 18 electrons ionic counting: Fe2+ contributes 6 electrons, the two aromatic cyclopentadienyl rings contribute 6 each: 6 + 2(6) = 18 valence electrons on iron.
conclusion: Ferrocene is expected to be an isolable compound.
Examples of electron counting.
These examples show the methods of electron counting, they are a "formalism", and don't have anything to do with "real life" chemical transformations.
Most of the 'fragments' mentioned above do not exist as such; they cannot be kept in a bottle: e.g.
the neutral C, the tetraanionic C, the neutral Ti, and the tetracationic Ti are not "free" species, they are always bound to something, for neutral C, it is commonly found in graphite, charcoal, diamond (sharing electrons with the neighboring carbons), as for Ti which can be found as its metal (where it shares its electrons with neighboring Ti atoms!
), C4- and Ti4+ 'exist' only with appropriate counterions (with which they probably share electrons).
So these formalisms are only used to predict stabilities or properties of compounds! 
In atoms with a single electron (hydrogen-like atoms), the energy of an orbital (and, consequently, of any electrons in the orbital) is determined exclusively by formula_12.
The formula_23 orbital has the lowest possible energy in the atom.
Each successively higher value of formula_12 has a higher level of energy, but the difference decreases as formula_12 increases.
For high formula_12, the level of energy becomes so high that the electron can easily escape from the atom.
In single electron atoms, all levels with different formula_7 within a given formula_12 are (to a good approximation) degenerate, and have the same energy.
This approximation is broken to a slight extent by the effect of the magnetic field of the nucleus, and by quantum electrodynamics effects.
The latter induce tiny binding energy differences especially for s electrons that go nearer the nucleus, since these feel a very slightly different nuclear charge, even in one-electron atoms; see Lamb shift.
In atoms with multiple electrons, the energy of an electron depends not only on the intrinsic properties of its orbital, but also on its interactions with the other electrons.
These interactions depend on the detail of its spatial probability distribution, and so the energy levels of orbitals depend not only on formula_12 but also on formula_7.
Higher values of formula_7 are associated with higher values of energy; for instance, the 2p state is higher than the 2s state.
When formula_32, the increase in energy of the orbital becomes so large as to push the energy of orbital above the energy of the s-orbital in the next higher shell; when formula_33 the energy is pushed into the shell two steps higher.
The filling of the 3d orbitals does not occur until the 4s orbitals have been filled.
The increase in energy for subshells of increasing angular momentum in larger atoms is due to electron–electron interaction effects, and it is specifically related to the ability of low angular momentum electrons to penetrate more effectively toward the nucleus, where they are subject to less screening from the charge of intervening electrons.
Thus, in atoms of higher atomic number, the formula_7 of electrons becomes more and more of a determining factor in their energy, and the principal quantum numbers formula_12 of electrons becomes less and less important in their energy placement.
The energy sequence of the first 24 subshells (e.g., 1s, 2p, 3d, etc.)
is given in the following table.
Each cell represents a subshell with formula_12 and formula_7 given by its row and column indices, respectively.
The number in the cell is the subshell's position in the sequence.
For a linear listing of the subshells in terms of increasing energies in multielectron atoms, see the section below.
"Note: empty cells indicate non-existent sublevels, while numbers in italics indicate sublevels that could exist, but which do not hold electrons in any element currently known."
To allow conduction, semiconductors are doped with impurities which donate mobile electrons (or holes).
However, these electrons are slowed down through collisions with the impurities (dopants) used to generate them in the first place.
HEMTs avoid this through the use of high mobility electrons generated using the heterojunction of a highly-doped wide-bandgap n-type donor-supply layer (AlGaAs in our example) and a non-doped narrow-bandgap channel layer with no dopant impurities (GaAs in this case).
The electrons generated in the thin n-type AlGaAs layer drop completely into the GaAs layer to form a depleted AlGaAs layer, because the heterojunction created by different band-gap materials forms a quantum well (a steep canyon) in the conduction band on the GaAs side where the electrons can move quickly without colliding with any impurities because the GaAs layer is undoped, and from which they cannot escape.
The effect of this is to create a very thin layer of highly mobile conducting electrons with very high concentration, giving the channel very low resistivity (or to put it another way, "high electron mobility").
This layer is called a two-dimensional electron gas.
As with all the other types of FETs, a voltage applied to the gate alters the conductivity of this layer. 
An electron can be "bound" to the nucleus of an atom by the attractive Coulomb force.
A system of one or more electrons bound to a nucleus is called an atom.
If the number of electrons is different from the nucleus' electrical charge, such an atom is called an ion.
The wave-like behavior of a bound electron is described by a function called an atomic orbital.
Each orbital has its own set of quantum numbers such as energy, angular momentum and projection of angular momentum, and only a discrete set of these orbitals exist around the nucleus.
According to the Pauli exclusion principle each orbital can be occupied by up to two electrons, which must differ in their spin quantum number.
Electrons can transfer between different orbitals by the emission or absorption of photons with an energy that matches the difference in potential.
Other methods of orbital transfer include collisions with particles, such as electrons, and the Auger effect.
To escape the atom, the energy of the electron must be increased above its binding energy to the atom.
This occurs, for example, with the photoelectric effect, where an incident photon exceeding the atom's ionization energy is absorbed by the electron.
The orbital angular momentum of electrons is quantized.
Because the electron is charged, it produces an orbital magnetic moment that is proportional to the angular momentum.
The net magnetic moment of an atom is equal to the vector sum of orbital and spin magnetic moments of all electrons and the nucleus.
The magnetic moment of the nucleus is negligible compared with that of the electrons.
The magnetic moments of the electrons that occupy the same orbital (so called, paired electrons) cancel each other out.
The chemical bond between atoms occurs as a result of electromagnetic interactions, as described by the laws of quantum mechanics.
The strongest bonds are formed by the sharing or transfer of electrons between atoms, allowing the formation of molecules.
Within a molecule, electrons move under the influence of several nuclei, and occupy molecular orbitals; much as they can occupy atomic orbitals in isolated atoms.
A fundamental factor in these molecular structures is the existence of electron pairs.
These are electrons with opposed spins, allowing them to occupy the same molecular orbital without violating the Pauli exclusion principle (much like in atoms).
Different molecular orbitals have different spatial distribution of the electron density.
For instance, in bonded pairs (i.e.
in the pairs that actually bind atoms together) electrons can be found with the maximal probability in a relatively small volume between the nuclei.
On the contrary, in non-bonded pairs electrons are distributed in a large volume around nuclei.