Semiconductor electronics

1) Effect of the approach of two atoms:

Every atom possesses of the electrons which can only possess determine levels to you of energy, when two atoms are approached have that every level of energy comes splittato in two various levels one to energy lower saying level than valence and one to energy higher saying level than conduction. If we have N atoms, they are come to constitute two bands ciascuna constituted from N levels on which can lodge 2N electrons in how much for the principle of exclusion of Pauli, on a same level of energy you can be 2 electrons purchè have spin opposite.

If draft of a metal we have ourselves that only half of the only band is filled up while in the case of a semiconductor the valence band is full while the conduction band is empty.

 

2) Gap:

The gap is a comfort in order to describe the current in the band of ambient valence in fact to temperature has that some electrons pass from the band of valence to the conduction band, leaving of the free places in valence band and a movement to chain of electrons is had in order to fill up them, wanting to describe the current would have to describe the movement of a n° highest of electrons instead if we consider gaps, will have to describe the movement of n° the much smallest one than bearers.

 

3) intrinsic Semiconductor:

It is a semiconductor for which the n° of electrons in conduction band he is equal to the gap number in valence band, the reported largenesses to it have of customary pedice i.

 

4) N-Doped:

It is a semiconductor drugged with impurità pentavalenti (…like phosphorus) which is gone to replace in the reticulum to silicon atoms, therefore they will form ciascuna 4 covalenti ties and therefore there will be an electron to which enough applying one small energy for sottrarlo to the donore that therefore becomes one ione positive. In the band chart therefore we will have a Donor-Level situated to 0,05eV from the conduction band and to ambient temperature all the electrons supplied from the donori will be already found in conduction band. For this type of semiconductor the majority bearers are the electrons.

 

5) P-Doped:

It is a semiconductor drugged with impurità trivalenti (…like Boron) which is gone to replace in the reticulum to silicon atoms, therefore they will form ciascuna 3 covalenti ties and therefore there will be an incomplete tie that will recall electrons from near atoms obtaining therefore one ione negative. In the band chart we will have a Acceptor-Level situated to 0,05eV over the valence band and to ambient temperature this level will be already filled up from coming from electrons from the band of valence in which therefore there will be of the gaps that concur the flow of one current, therefore they are the majority bearers.

 

6) thermal Equilibrium:

It is a situation in which every process it is balanced from its inverse one, that is is a dynamic equilibrium

 

7) Law of action of mass:

np = n^{the 2}

where n it is the electron concentration in conduction band, p it is the gap concentration in valence band and n it is the electron concentration in band of valence for an intrinsic semiconductor, it is constant and varied only with the temperature.

 

8) Function of Firm distribution of Dirac:

It is a distribution function that holding account of the principle of exclusion of Pauli supplies the probability that an electron to one given temperature possesses an energy and, it is: , in particular it is worth ½ for the energy of Firm. It is observed that for T=0K the states with smaller energy of and_f are all full loads while the states with greater energy of and_f are all empty ones.

 

9) Density of states to the edge of the band of conduction and the band of valence:

The Fermi-Dirac distribution of for if it does not say a lot, it must be associated to a distribution that describes the density of states is in valence band that in conduction band, in truth us enough to consider the edge of both the bands in how much as an example for the conduction band it will be popolata from little electrons in how much is over the level of Firm, the two density is pertanto e , they only differ for the effective mass and therefore N_c @ N_v .

 

10) electron Concentration in conduction band:

Being a lot little the electrons in conduction band, we think all to them concentrates to you on the edge where the density of states is N_c , and the Fermi-Dirac function is reduced to a exponential , therefore .

 

11) gap Concentration in valence band:

Being a lot little the gaps in valence band, we think all to them concentrated on the edge where the density of states is N_v , and the Fermi-Dirac function is reduced to a exponential , therefore .

 

12) degenerated Semiconductor:

Draft of a drugged semiconductor a lot heavy, for a p-type will be had that the level of Firm and_f is to the inside of the valence band while for n-type a level of Firm is to the inside of the conduction band, speaks about semiconductor degenerated in how much the states is concurred is many neighbors to the level of Firm like happens for the metals.

 

13) Nearly-levels of Firm:

The level of Firm is only defined in the case of thermal equilibrium, if instead the semiconductor is subordinate as an example to cancellation incident is in a condition not equilibrium and two levels of Firm are had, one for the electrons and one for lacune the moreover the law of action of mass more is not verified but it turns out to be function beyond that of the temperature also of the difference of energy between the two levels of Firm

 

14) Fotogenerazione:

It is had that if a photon with at least equal energy to the value of the energy-gap records on a semiconductor, it yields energy to an electron that therefore is moved from the band of valence to the conduction band, naturally generates in valence band ugual a gap number.

 

15) Effects of the heavy-doping:

One is had reduction of energy-gap between band of valence and the band of conduction.

 

16) Speed of drift:

The electrons in a crystal are subject to a thermal speed having randomica direction, it is much elevating and very to superire sispetto to the speed of drift that it is that one in the direction of an electric field and junior clerk.

 

17) Mobility:

It is the constant of proportionality between the speed of drift of the bearers and the electric field and that it determines it, its value it is where t_cn it is the time of scattering medium and is independent from the field applied.

The dependency of mobility from the temperature is

The reasons of this dependency are from searching themselves in the scattering in fact are had:

to)       there is a transfer of energy you give to bearers al due reticulum alle vibrations that it carries out to cause della temperature, these vibrations can be understandings like hits with delle particles calls fononi, it is had that al to grow della temperature they increase the vibrations therefore increase it hits and it diminishes mobility to it like T^{- n} with n that assumes values comprised between 1,66 and 3, of usual 2,5.

b)       Scattering with impurità ionizzate, whose effect on mobility becomes to growing of the temperature in how much the bearers less important moves more fastly and therefore they little remain in order time in the pressed ones of the impurità.

c)       Scattering from undesired collisions with impurità or defects of the crystal.

Everyone of these processes is characterized from one constant of time t_i , mobility turns out to be dominated from the process that has the smaller constant of time, well it is had that to the low temperatures mobility increases to growing of the temperature in how much predominates the effect a) while to the high temperatures predominates the effect b) and therefore mobility diminishes to growing of the temperature.

 

18) Limiting velocity:

To growing of the electric field applied, one has an increase of the speed of the bearers, but this until catching up the limiting velocity beyond which it begins the effect of a new mechanism of scattering.

 

19) Current of spread:

In the semiconductors which have the not highest conductivity, it finds importance also the spread current, than it is established laddove exists a difference of concentration of bearers between two zones of the semiconductor, is observed that in the metals where the conductivity is highest, this current does not come considered.