Semiconductors

1) Describe a semiconductor:

Medium valence 4 is a having material, for which to temperature 0K it is had that the 2 inferior bands completely are occupied while the third band is empty, therefore if not there is elevating gap of energy between 2ª and 3ª the band, are had that to ambient temperature a discreet electron number is already found in the conduction band.

 

2) Typology of gap in a semiconductor:

A gap is had directed when the maximum of the valence band is had for the same one k for which the minimum of banda.di the conduction is had while a gap is had indirect when the maximum of the valence band is had for a k various from the k for which the minimum of the conduction band is had. The silicon as an example has the gap indirect.

 

3) optical Absorption applied to the detection of the tipologia of the gap:

The optical absorption is a experiment that is carried out in order to characterize the tipologia of the gap of a semiconductor, in short bomb dropping gear a sheet with having photons various l, and measure to the escape the absorption of the sheet, looks at that the absorption is null sin when a photon with a k is not sended which a next energy to that one of the gap corresponds, dopodichè has a linear increase of the absorption sin when saturation phenomena are not taken place.

In the case of gap indirect, the absorption in function of the frequency of the photon incident would seem to have to begin a w beginning from higher regarding that for the gap the collision of a photon with an electron has headed in how much cannot any change the k and, for the same one k, the gap he is greater. In the crystal they are but always present of the fononi which are it characterizes to you from k elevates to you and little energy therefore a collision electron-photon-fonone can determine a not null absorption for the same one w of the fonone from which it begins the directed absorption of the gap.

 

4) not degenerate Semiconductor:

A semiconductor is not degenerate when ha , and therefore the 1 neighbor to the exponential in the function of distribution of Fermi-Dirac can itself be neglected.

 

5) electron Concentration in the band of conduction to the T temperature:

It is given from the integral where for the density of states in and, D(and) rigirano the aces and are observed according to that k and are for the conduction band a parabola that for the origin analogous to how much had been found for the D(and) of a free electron gas three-dimensional with the difference that in that case the parabola passed for the origin. was had while in our case holding account of the translation and considering the effective mass, will have while for f(and,T) uses the customary Fermi-Dirac function, after all therefore the integral is making the hypothesis of not degenerate semiconductor that is and-m > > KT one to the denominator can be neglected obtaining on which operating the change of variable and remembering that ottiene .

 

6) gap Concentration in the band of valence to the T temperature:

E' given from the integral where account must be held that:

to)       the probability f_p that there is a gap he is equal to the probability that not is an electron therefore f_p = 1-f_and(and,T).

b)       the band of valence with the rigirati aces has a parabolic shape similar to that one of the D(and) in the three-dimensional case for free electrons but ribaltata regarding the k, in it the effective mass of gap m must moreover be replaced_h after all has .

Carrying out the integral it is found .

 

7) Law of the action of mass:

It asserts that the product of the gap number for the present electron number in the band of conduction to one given temperature is constant.

It is demonstrated simply multiplying n(T) and p(T) and verifying that draft of an amount that varies alone with the temperature, is obtained in fact .

 

8) intrinsic Semiconductor and involuntary drogaggio:

It is a semiconductor in which the gap concentration is equal to the electron concentration, this in truth never is not verified in how much is always present of the impurities that can be behaved like gaps or electrons. In order to obtain an intrinsic semiconductor a controdrogaggio consisting in finding through measures of Hall effect is carried out the tipologia of the predominant bearers and to insert in the semiconductor bearers of the other type.

 

9) Value of upgrades them chemical in an intrinsic semiconductor:

An intrinsic semiconductor is considered for which , equals such value with the generic value and is obtained.

 

10) Mobility of the bearers:

It that is represents the coefficient of proportionality between the field applied and the speed of drift assumed from the bearers

but being also pertanto and remembering that ottiene

.

 

11) Property of transport in the pure semiconductors:

The conductivity electrical worker is , it has a minimum if n = p, in the case of an intrinsic or pure semiconductor for which it is had the it looks at therefore that then and quindi therefore if we make a diagram di according to sees that it is one straight with slope . From this curve for a semiconductor as the silicon looks at that the electron number in band of ambient conduction to temperature is small and therefore the high resistività, one becomes therefore necessary to resort to the drogaggio of the semiconductor.

 

12) Donore:

A pentavalente element inserted in a crystal well-known tetravalente semiconductor, possesses an electron which it cannot create covalenti ties and from a comparison with the electron in the hydrogen atom it finds that the beam of its orbit is of the 30 Angstroms and the ionization energy is of approximately 0,02eV therefore already to ambient temperature it could be embezzled to the relative donore.

 

13) Effect of the drogaggio with donori:

One be free having is created little inferior energy to the minimal energy of the conduction band, this state is popolato from all electrons disappears had to you to the donori, for they enough KT = 0,02eV in order to pass in conduction band, that is already to ambient temperature.

 

14) Accepter:

A trivalente element inserted in a crystal well-known tetravalente semiconductor, creates three covalenti ties therefore an electron of the semiconductor remains in the ready crystal to catch a whichever wandering electron in order to form a covalent bond.

 

15) Effect of the drogaggio with accepters:

One be free having is created little advanced energy to the energy of the valence band, therefore already to ambient temperature the passage of the electron from the band of valence to the free state is had, with consequent creation of one gap in the valence band.

 

16) electron Concentration in band of conduction in function of the energy of the donori:

For a type semiconductor n it is had that the electron concentration n(T) in the valence band is being the concentration of ionizzati donori. Advancing the hypothesis that has confronting this amount with the generic electron concentration in the band of conduction to the temperature T it obtains and replacing it is had .

 

17) gap Concentration in band of valence in function of the energy of the accepters:

With the same made considerations in order to gain the electron concentration in conduction band it is found

 

18) Resistività in function of the temperature for a drugged semiconductor:

Supposing that the semiconductor is drugged of type n, we have that the conductivity is therefore depends on the temperature is through the time of relaxation t but in heavier way through the exponential that appears in the it that is has allora that, expressing the according to is one straight with slope . To growing of the temperature a saturation effect is had for which all the donori are pass to you in conduction band and therefore the semiconductor is like if it were intrinsic and one straight with slope is had .

 

19) Splice p-n:

Creating the splice between a semiconductor of type p and a semiconductor of type n a gradient of concentration of charges is had which it gives place to a spread procedure for which electrons affluiranno towards the zone p and will be recombined leaving in the semiconductor of type n (..a ridosso of the splice) a region of loads positive while of gaps affluiranno towards the zone n and will be recombined leaving in the semiconductor of type p (..a ridosso of the splice) a region of loads negative. As the spread process goes ahead the distribution of charges gives to place to a more and more intense electric field whom it prevents that the spread process continues, to this point will be had upgrades them chemical equal in both the semiconductors.

They will be however present also in this case of the currents in how much the thermal agitation generates in both the semiconductors of the braces gap-electron one of which is facilitated from the electrostatic field to cross the splice.

 

20) Position to the equilibrium of the bands of the semiconductor of type n regarding the bands of the semiconductor of tipo p:

Gap between band of valence and the band of conduction it is approximately the same one, they but they must have in common the same one upgrades them chemical, than for the type semiconductor n it is found to half between and_d and the band of conduction while for the type semiconductor p it is found to half between the top of the valence band and and_to . It can be had upgrades them chemical single constant if the bands of the zone p are found to higher energies regarding the bands of the zone n.

 

21) Currents in one splice p-n:

J_nr is the recombination electron current that slides from the zone n towards the zone p

J_ng is the current of thermal electron generation that slides from the zone p towards the zone n

J_pr is the recombination gap current that slides from the zone p towards the zone n

J_pg is the current of thermal gap generation that slides from the zone n towards the zone p

To the equilibrium e is had:

 

22) Property of the splice like rectifier:

Applying a tension to the splice it is had that it is moved to us towards the new equilibrium in which upgrades them chemical is not the same one in the two semiconductors but on one side it will be higher than an amount eV regarding the other side, this determines a lowering or an elevation of the barrier of upgrades them that it leaves invariate the currents of generation e while varies the currents of recombination of an equal amount to the factor of Boltzmann and analogous for gaps is had therefore the current density total is .

After all therefore ha .

 

23) inverse Polarization:

Applying to a positive tension on the cathode (..regione n) is had that to growing of V stretches to J₀.

In the representation to bands it is had that it upgrades them chemical in the region p knows them of eV regarding the value that it had in polarization absence, and since it must itself be always found to half between the level and of the accepters and the top of the valence band it has that the bands of the aontanano zone p from the bands of the zone n increasing the barrier of upgrade them.

 

24) direct Polarization:

Applying to a negative tension on the cathode (..regione n) is had that to growing of V stretches esponenzialmente to infinite.

In the representation to bands it is had that it upgrades them chemical in the region n knows them of eV regarding the value that it had in polarization absence, and since it must itself be always found to half between the level of the donori and the base of the conduction band it has that the bands of the zone n are approached the bands of the zone p reducing the barrier of upgrade them.