Contact Metal - Semiconductor
1) Level of Firm turning out of two arranges puttinges to contact:
An electron flow will be had from the having system andgreater F towards the other system sinchè the system does not possess an only level of Firm, it can be demonstrated simply observing that in the case of thermal equilibrium the current that slides in a back is equal to the current that slides in the opposite back, and can mutual be described like product of the density of full states in a system for the density of empty states in the other system and.
2) Difference between the energy of Firm of a metal and the energy of Firm of a semiconductor:
In a metal it is had that the level of Firm is dipped between the states allowed, under andF is all occupied while to of over they are all empty ones, in a semiconductor instead andf is comprised to the inside of the forbidden band and its varied position respect to it in function of the drogaggio.
3) Level of empty:
Draft of the minimal energy that an electron would have to possess for sottrarsi to the infuence of the origin atom.
4) Function job:
It is the difference of energy qj between the empty level of and the energy of Firm of the considered material.
5) Affinity electronic:
It is the difference of energy between the empty level of and the band of conduction of a semiconductor or an insulator.
6) Relation between the functions job and the transfer of electrons:
If jM < jS has an electron flow from the metal to the semiconductor otherwise if jM > jS has a flow in opposite sense, in 1° the case obtains a ohmmico contact, in 2° the case instead a rectifying contact.
7) Approximation of Depletion:
to) the concentration of minority bearers it comes neglected
b) the concentration of majority bearers is null to the inside of the region of depletion while in bulk it he is equal to the concentration of donori if we are considering a n-doped
8) Describe the splice metal-n_doped in the case jM > jS:
Since the level of Firm of the metal is inferior regarding that one of the semiconductor, an electron flow will be had from these last towards the metal therefore bands will be folded towards the high to indicate the electron emptying in the zone of Depletion and therefore the removal of the band of conduction from the level of Firm.
It loads : in the region with Depletion the donori have lost an electron therefore of Ionian are positi to you the fixed ones, for the approximation of Depletion their value is constant and equal to Nd in all the region therefore loads total stored in the region is Q = qNdxd , in the metal it will be had loads equal and opposite but disposed on a sheet to contact with the splice.
Field and: is obtained from the
law of Gauss as integral with the density of it loads divided for the
permittività ands of the semiconductor, for the property of sampling of the d it will be had that on
the edge of the metal the field is 
and
decreases until being worth 0 in x = xd .
It upgrades them of Built-In j : Is the potential
difference them between the base of the band of valence in the bulk
and the same one on the splice, is obtained as integral changed of
sign of the electric field between the splice and xd in particular such field has the
shape of a triangle rectangle of base xd and height andmax therefore 
, from it pu² to
extract the amplitude of the region of Depletion 
that replaced in the expression of it loads stored in
such region gives 
9) Effect of the polarization for the splice metal-n_doped in the case jM > jS :
Applying a positive polarization to the metal it is had that the present electrons in it come become lean and therefore the level of Firm trasla towards the bottom of an amount qVto , having per² to remain immutato the value of the barrier of upgrades them qjB is like if the bands of the bulk traslassero towards the high reducing in such a way upgrades them of Built-In j therefore in short is had that the electron flow from the semiconductor to the metal is facilitated while that from the metal to the semiconductor remains unchanged, is in regimen of direct polarization.
Applying a negative polarization to the metal it is had
that it comes filled up of Firm electrons and therefore its level of
traslaverso the high regarding that one of the semiconductor, also in
this case naturally qjB must remain constant therefore will have an elevation of
the tension of Built-In and therefore the electron flow will be
hindered from the semiconductor to the metal while the flow in
opposite back will remain substantially unchanged, is in regimen of
inverse polarization, loads stored in the region of Depletion 
increases in how much V <
0 while the ability differentiates them to unit of 
surface diminishes.
10) ideal Equation of the diode valve:
In conditions of thermal equilibrium it is had that |JMS| = | JSM| and JSM is
proporziona them through one constant of K proportionality to present
the free electron densityn s
in band of conduction to the edge with the splice therefore 
where Nd is the free electron concentration in the Bulk and f it is upgrades them of
Built-In. Applying one tension Vto we have that the electron flow can come hindered or
facilitated in a back while substantially remains immutato in the
opposite back, that is has 
dove 
.
11) Barrier of Schottky:
Draft of the obstacle to the electron flow from a metal towards a semiconductor drugged in uniform way, it is equal to the difference of energy between the level of Firm of the metal and the band of conduction to the interface of the semiconductor with oxide.
12) Equation of the current in the contact of Schottky:
The concept that stà to the base is that one as an
example to integrate the equation of Drift & relative Diffusion to
n_doped 
a long the region of loads spaces them,
in particular being 
and 
is obtained multiplying for 
and integrating between 0 and xd 
is obtained and replacing the
conditions to the contour for f and n 
is obtained in which for 
is obtained where Js depends on the square root
of the Vto therefore it
comes thought constant inasmuch as Jx depends esponenzialmente on Vto.
13) Barrier of Mott:
Draft of a system constituted from a metal and a
semiconductor that in proximity of the splice weakly is drugged in
order then to become heavy drugged beyond xd with xd small so that no line of electric field you finish in it
and therefore to its inside the field is constant, it derives some
that it upgrades only defined them for 0 < x < xd is 
and replaced in 
the can easy be integrated.
14) ohmmico Contact of Tunnel:
We suppose of having a metal to contact with a n_doped
heavy drugged so that the region of loads spaces them 
becomes of the order of the nm, applying a positive
tension to the metal if of it it lowers the level of Firm regarding
that one of the semiconductor therefore will become the passage for
effect possible Tunnel from the semiconductor to the metal.
Applying instead a negative tension it is had that the level of
Firm of the metal is raised regarding that one of the semiconductor
and therefore is possible the electron passage for effect Tunnel from
the metal to the semiconductor.
15) ohmmico Contact of Schottky:
If jM < jS has an electron flow from the metal to the semiconductor, therefore there will be a region dictates of accumulation in which many free bearers while in the metal a d will be had of loads positive, in virtue of this greater one n° of electrons are present have themselves that the n_doped he becomes drugged mainly and therefore the bands are folded towards the bottom so that the band of Firm conduction is approached the level of and the band of valence mainly if it removes some.
The presence of the free bearers to contact with the splice involves
16) Contact neutro:
Draft of a contact lacking in tension of Built-In and in which to the splice the same free electron density is had that is had in the bulk.
17) Length of spread:
It is the length for which the concentration of the electrons that they diffuse reduces to 1/e of the value that has to the interface in short measure qualitatively the length of the region of loads spaces them.
18) States of surface and they classification:
Up to now we have supposed that the states available of a system are only those contents in the band of valence and the band of conduction, in truth that is true in the bulk in fact in surface will only have that the ties are incomplete and therefore they will have richiudere between of they or on atoms of impurità giving place to a distribution of the states various from that is had in the bulk, and in particular we will have of the states comprised to the inside of gap.con a peak in correspondence of 1/3 of the same one. The states of surface are said to be:
to) neutral donors if when occupied from an electron and cargos positively when they are empty
b) empty neutral accepters if when and cargos negatively when occupied from an electron
moreover holding account that microscopically the amplitude of the transition region is of tens of reticular plans, the fast states of surface are had that are those to contact with the bulk and therefore they fastly catch up the thermal equilibrium with the same one and the states of surface discs of a valve that are found in intermediate zones of the transition region and therefore employ more time to catch up the thermal equilibrium with the bulk.
19) Effects of surface on the contact metal-semiconduttore:
The states of surface and the impurità suppose allotted in an amplitude layer d place between the semiconductor and the metal, to its heads has one fallen of upgrades them and the passage of electrons is possible for effect Tunnel, if the states of surface are of type accepter they embezzle electrons to the n_doped and therefore the band of conduction on the edge goes away from the level of Firm. In virtue of how much as soon as said it is clearly that in presence of a n_doped with of the states of type surface accepter the metal in order to realize a rectifying contact is not necessary.