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Acceptors |
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Doping defects that introduce an energy state in the band gap close to the valence band. |
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At medium temperatures – generally meaning room temperature – electrons from the valence band
will completely fill these states leading to a density of holes in the valence band that is about equal to the density of
the acceptor states.
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Conductivity s |
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A specific propery of any material, defined as the relation between electrical field E
and current density j |
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Generally, the conductivity s is a tensor of second order and may depend
on other parameters including the firld strength E. |
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As long as the current–field relationship is linear (demanding s
¹
s(E) ), the material exhibits ohmic
behavior. |
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s can always be expressed in terms of the density n of
carriers reponsible for conduction, their charge q, and their mobiltiy µ, via |
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Diffusion length |
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The diffusion length L always refers to minority carriers. It is the average distance a minority
carrier moves away from its point of origin, given by |
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With D = diffusion coefficient and t =
time for the movement (= life time for a minority carrier). |
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The diffusion length is a prime material parameter
that comes up in many formula, it can be rather large (up to mm) in indirect semiconductors and it is very
sensitive to certain lattice defects.
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Donors |
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Doping defects that introduce an energy state in the band gap close to the conduction band that is occupied
by an electron at low temperatures. |
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At medium temperatures these electrons will move to the conduction band leading to a density of electrons
in the conduction band that is about equal to the density of the donor states.
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Doping |
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Controlled introduction of lattice defects that introduce energy states for electrons in the band gap |
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Often done with substitutional atoms that are to the left or right of the element they replace in the periodic
table |
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But all defects – e.g. dislocations and grain boundaries – may have energy levels in the band
gap, too, and thus may introduce doping.
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Electrons in semiconductors |
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Mainly refers to the free electrons in the conduction band, contributing
to the conductivity. |
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In addition, this may also refer to electrons present on various additional states inside the band gap
(e.g., the energy levels of donors and/or acceptors). |
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However, although the valence band is mainly filled with electrons, one avoids considering them explicitly
– by just treating the empty valence band places (called holes; see below).
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Holes in semiconductors |
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States in the valence band not occupied by electrons. Quasiparticles; behave for all practical purposes
like free positively charged electrons.
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Intrinsic semiconductors |
| |
Undoped "perfect" semiconductors with properties exclusively governed by the crystal. The Fermi
energy is in the middle of the band gap; electron and hole densities are equal (= ni).
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Life time |
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Usually the average time t a minority carrier, after it was generated
by thermal fluctuations or other energy expenditures, "lives" before it disappears again by recombination. Refers
to thermal equilibrium in this case. |
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In more complicated circumstances – e.g. in space charge regions or in non-equilibrium conditions
– life times must be considered more carefully; a distinction between generation and recombination life time, e.g.,
might be necessary.
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Majority carriers |
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The kind of carrier – electrons or holes – being present in the larger density. |
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Majority carriers are electrons in the case of doping with donors, and holes in the case of doping with
acceptors.
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Mass action law |
| |
Traditional, albeit somewhat misleading name for the relation between the equilibrium
densities of electrons, ne , holes, nh, and the intrinsic density, ni,
in doped semiconductors: |
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Directly obtainable by using the Boltzmann approximation for
the occupation of the bands.
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Minority carriers |
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The kind of carrier – electrons or holes – being present in the smaller density. |
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Minority carriers are holes in the case of doping with donors, and electrons in the case of doping with
acceptors.
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n-type semiconductor; n-doped, n-doping |
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Semiconductors with the majority carriers being electrons. Doping thus was done with donors
.
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p-type semiconductor; p-doped, p-doping |
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Semiconductors with the majority carrierers being holes. Doping thus was done with acceptors
. |
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Do not mix up p-doped with P-doped ("P": phosphorous) in silicon!
P is a donor in Si; P-doped Si is an n-type semiconductor. |
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p-n junction |
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A transition from p-type to n-type within one piece of material. Electrically, a p-n
junction is a diode (i.e. it has rectifying properties). |
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The "ideal" p-n junction is a paradigm of semiconductor science. It is usually highly
idealized and considered to be - An abrupt
junction, i.e. the doping changes from p-type to n-type abruptly,
- with constant doping levels on both sides of the junction, being
- one-dimensional, and being
- "large", i.e. the p and n areas are much longer than the
diffusion length of the carriers.
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Real p-n junctions, especially in integrated circuits, do not even come close to these assumptions.
Nevertheless, the results of the ideal p-n junction contain almost everything needed to tackle the real junctions
and thus should be well understood.
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Perfect semiconductors |
| |
Ideally, a perfect crystal contains only those crystal defects necessary for device function – i.e.
doping atoms and perfect interfaces. What makes an interface perfect is hard to define; in case of doubt: the absence of
interface states in the band gap. |
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Si crystals are closer to being perfect then anything else (in the unanimated world, that is). Their
dislocation density is zero (which has not been possible to achieve for practically all other (large) crystals), the level
of unwanted point defects is in the (1 . . . 10) ppm region for O and C, respectively, and in the low
ppb if not ppt region for everything else. |
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There are, however, unavoidable remnants of the intrinsic point defects (vacancies and self-interstitals)
that were present in thermal equilibrium at high temperatures. They may occur in any forms of microclusters; not yet fully
understood. |
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© H. Föll (Semiconductors - Script)
2.2.1 Intrinsic Properties in Equilibrium 
With frame