MODULE 1.2 CARRIER TRANSPORT PHENOMENA

Transcription

1 MODULE 1.2 CARRIER TRANSPORT PHENOMENA

2 Carrier Trasort Pheoeo Carrier drift: obility, coductivity ad velocity saturatio Carrier Diffusio: diffusio curret desity, total curret desity The Eistei relatio

3 Carrier Trasort Pheoeo Desities of charged articles are iortat to uderstad the electrical roerties of a seicoductor aterial. Net flow of the electros ad holes i a seicoductor geerate currets. The rocess bywhich these charged articles ove is called trasort. Two basic trasort echaiss i a seicoductor crystal are: Drift:- the oveet of charge due to electric fields, Diffusio:-the flow of charge due to desity gradiets. Teerature gradiets i a seicoductor ca also lead to carrier oveet, but sice device size is sall, this effect is igored. Carrier trasort deteries the curret-voltage characteristics of seicoductor devices. First, seicoductor i equilibriu is discussed

4 Carrier Drift Electric field alied roduces a force o electros ad holes, so that they are accelerated. This et oveet of charge due to a electric field is called drift, which give rise to drift curret. Av. theral eergy of Theral velocity, v th electro or 3k BT * hole 3 k 2 The carriers udergo collisio with vibratig atos ad charged doat ios after travellig a distace resultig i scatterig of the carriers. 2.3x10 5 B T / sec 1 * v 2 2 th c c average tie betwee collisios ea free ath sec, so v th 10 5 c x

5 v(t) Drift velocity, v d Carrier Drift O alicatio of a electric field, E, ad a force, F = qe/ * acts o the carrier betwee collisios. Whe the charged article collides with a ato i the crystal, the article loses ost of its eergy. The article will agai begi to accelerate ad gai eergy util it is agai ivolved i a scatterig rocess. This cotiues over ad over agai. Throughout this rocess, the article will gai a average drift velocity which, for low electric fields, is directly roortioal to the electric field. Average For v d sall, q tie betwee collisio is,, q v(t) q Average et velocity of carrier due to drift field,,,., t t v d

6 Mobility: For 0, v d q,,, v sat Velocity Saturatio, q,, obility v d Drift velocity saturates at high fields For For electros, holes, v v d d,, q q E

7 2 /V-sec Electro & hole obilities: At low doig levels, the obility is liited by collisio with lattice, i.e., hoos For Silico µ At high doig levels, obility is liited by scatterig by doat ios µ 1E+19 1E+21 1E+23 1E+25 1E+27 at/ 3 µ > µ for sae doig level, sice holes have higher effective ass tha electros. μ,, 2 /V-sec (c 2 /V-Sec) μ, 2 /V-sec (c 2 /Vsec) Ge Si GaAs (3900) (1400) (8500) (1900) (470) (400)

8 Electro & hole obilities:

9 Drift Curret : Curret due to drift of carriers i resece of a electric field the will be give by: drift J Electro Drift Flow v d Electro drift curret desity drift J Hole Drift Flow J drift qv d v d q Hole drift curret desity J drift qv d q J drift drift drift J J q( ) J drift 1 where q( ) coductivity

10 (i) High te.:- (itrisic) carriers are high σ is high (ii) id te.(rt):- (extrisic), colete ioisatio Carriers are cost. So σ is cost. (iii) Low te. :- (freeze out zoe) Carriers less. So σ is also less

11 Resistivity of Silico :

12 Scatterig Mechaiss: Mobility of carriers is affected by scatterig echaiss. Scatterig echais is of two tyes hoo ad iurity [A] Electros ove freely ad uerturbed i a erfect eriodic otetial i a solid. But the theral vibratios cause a disrutio of the otetial fuctio, resultig i a iteractio betwee the electros or holes ad the vibratig lattice atos. This affect the velocity ad obility of the carriers which is called to as hoo scatterig. [B]Iurity atos are added to the seicoductor to cotrol or alter its characteristics. These iurities are ioized at roo teerature so that a coulob iteractio exists betwee the electros or holes ad the ioized iurities. This coulob iteractio roduces scatterig or collisios ad also alters the velocity of the charge carrier:- iurity scatterig.

13 Scatterig Mechaiss: Phoo scatterig icreases with teerature = collisio tie of carriers due to hoo scatterig 1/(hoo desity x theral velocity) 1/(T*T 1/2 ) T -3/2 Iurity scatterig icreases with cocetratio of iurity atos ad defects. As te. icreases, carriers osses high theral vel., so easily ass by the iurities 3/2 I = coll. tie of electro due to iurities ad defects T Total Scatterig effect = (Na N d ), qt, 1 T 1 P 1 I 1, 1 T 1 I

14 Mobility vs. Teerature Mobility is deteried by Lattice scatterig (doiat at high T) At sall doat coc., μ decreases with icreasig T, Idicatig the doiace of hoo scatterig Iurity scatterig (doiat at low T) At very high doat coc., ad low teerature, iurity Scatterig doiate, so μ icreases with icreasig T