Doped semiconductors: donor impurities

Transcription

1 Doed semicoductors: door imurities A silico lattice with a sigle imurity atom (Phoshorus, P) added. As comared to Si, the Phoshorus has oe extra valece electro which, after all bods are made, has very weak bodig. Very small eergy is required to create a free electro from a imurity atom. This tye of imurity is called door. Note, that there is o hole created whe a free electro comes from the imurity atom.

2 Free electro cocetratio i door - doed semicoductors Whe door atoms are itroduced ito the semicoductor material, they are all ioized. Each door atom creates oe free electro. If the cocetratio of door imurity (e.g. Phoshor) i Si is N D, the cocetratio of free electros, N D For Si ad other semicoductors, the tyical doig levels are: N D = cm cm -3 D = cm cm -3 (comare to i = cm -3 i itrisic Si) D >> i Doig rovides a flexible cotrol over semicoductor coductivity. The vast majority of microelectroic devices are based o doed semicoductors

3 Resistace of Door-Doed Silico samle How much would be the resistace of the (1 cm 1cm 1cm) Si samle doed with door imurities with cocetratio cm -3? σ = qµ ; L 1 R = ρ = A σ L A = cm -3 µ = 1000 cm 2 /(V s) q = C σ = C cm cm 2 /(V s) σ = 3.2 (Ohm cm) -1 ρ = Ohm cm R = (Ohm cm) 1 cm /(1cm 1cm) = Ohm The resistace of a doed Si crystal ca be sigificatly lower tha that of itrisic Si

4 Doed semicoductors: accetor imurities A silico lattice with a sigle imurity atom (Boro, B) added. Boro has oly three valece electros, oe electro less tha the Si atom. Havig oly three valece electros - ot eough to fill all four bods - it creates a excess hole that ca be used i coductio. This tye of imurity is called accetor. There is o corresodig free electro created from accetor imurity

5 Hole cocetratio i accetor - doed semicoductors If the cocetratio of accetor imurity (B atoms) i Si is N A, the hole cocetratio A N A For Si ad other semicoductors, the tyical accetor doig levels are: N A = cm cm -3 A = cm cm -3 (comare to i = cm -3 i itrisic Si); A >> i The vast majority of microelectroic devices usig hole coductivity, are based o doed semicoductors I doed semicoductors, the cocetratio of itrisic electros ad holes ca be eglected as comared to those comig from door ad accetor imurities.

6 Cocetratio temerature deedece i doed semicoductors, cm -3 Imurity electros N D Itrisic electros, itrisic holes T 100 K 200 K 300 K 400 K Tyical deedece for -Si (i.e. door-doed) (for -Si (i.e. accetor doed) the deedeces are similar

7 Mobile charge carriers eergy I semicoductors, the mobile charge carriers are the free electros ad holes Boud electro E c E v Atom valece bad Itrisic material at low temerature. There are o free electros or holes o free carriers. The mobile charge eergy does ot make sese.

8 Coductace bad eergy Hole coductace bad Free electro E c E v Atom Whe the electro i the valece bad acquires sufficiet extra eergy, it ca be detached from its aret atom ad reaches reach the coductace bad The miimum eergy of the coductio bad is deoted as E C

9 Eergy Bad Ga (E g ) E c E v Bad-ga Forbidde Eergy regio Geerally o electro ca have the eergy betwee E c ad E v The bad-ga is the eergy differece betwee E c ad E v : E g =E c -E v

10 Mobile charge carriers eergy coductace bad Hole E c Free electro E v Atom valece bad Itrisic material at high temerature. Temerature geerates free electros ad holes i equal cocetratios. The eergy of free electros is close to E C ; the eergy of holes is close to E V

11 Average free carrier Eergy Fermi eergy coductace bad The average eergy of all the mobile charges i semicoductor: E ave Average [(Electro Average Eergy + Hole Average Eergy)] (E C + E V )/2. E F E c E v The average eergy of all the mobile charges i semicoductor is called Fermi eergy E F. I itrisic semicoductor: E F (E C + E V )/2. valece bad The eergy of free electros is close to E C ; the eergy of holes is equal to E V

12 -tye semicoductor Extra free electro Phoshorus (P) has 5 outer shell electros. I the -tye material most of the mobile charges are free electros. Therefore, the average eergy of mobile charges is close to E C : E F E C E C E V E F

13 -tye semicoductor Extra electro vacacy or hole Boro (B) has 3 outer shell electros. I the -tye material most of the mobile charges are holes. Therefore, the average eergy of mobile charges is close to E V : E F E V E C E V E F

14 Electro cocetratio: Carrier Cocetratio ad Fermi level: -tye material N D N D - Door atoms cocetratio Fermi eergy level: EF EC Hole cocetratio i the -tye material: = 2 i = 2 i

15 Hole cocetratio: Carrier Cocetratio ad Fermi level: -tye material N A N A - Accetor atoms cocetratio Fermi eergy level: EF EV Electro cocetratio i the -tye material: = 2 i = 2 i

16 Comesatio If both door ad accetor are added to a itrisic semicoductor the the semicoductor is said to be comesated If N D > N A, the free electro cocetratio: = N D -N A If N D < N A, the hole cocetratio: = N A -N D

17 Drift Curret The electric curret due to electric field is called the Drift Curret. The electro curret desity (curret er uit area): J = qµ E drift, µ is the electro mobility ad is the electro cocetratio. E Similarly the hole curret desity: J,drift = qµ E µ is the hole mobility ad is the hole cocetratio. J,drift J,drift

18 cot Drift Curret ad coductivity The total (electro + hole) drift curret desity: Coductivity: J drift = J = qµ,drift + J E +,drift qµ E J = q( µ + µ ) E drift Resistivity: = q( + ) J drift σ µ µ 1 1 ρ = = σ q( µ + µ ) =σ E

19 Diffusio Curret Diffusio is due to cocetratio differece betwee two regios of a semicoductor The carriers will move from higher cocetratio regio to the lower oe. Abrut cocetratio chage Cocetratio x Gradual cocetratio chage Cocetratio x

20 cotiued Diffusio Curret The electro diffusio curret desity:, J diff D is the diffusio coefficiet of electros = d qd dx The hole diffusio curret desity: J, diff = d qd dx Electro Cocetratio D is the diffusio coefficiet of holes Electro diffusio J,diff x Hole Cocetratio Hole diffusio J,diff x

21 Total Currets i semicoductors with both electric field ad cocetratio gradiets Electro curret desity d J = J, drift + J, diff = qµ E + qd dx Total electro curret I = J A Hole curret desity: d J = J, drift + J, diff = qµ E qd dx Total hole curret I = J A Total curret desity: J = J + J Total curret: I= J A= ( J + J ) A A is the samle cross-sectio area