Doped semiconductors: donor impurities
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1 Doped semicoductors: door impurities A silico lattice with a sigle impurity atom (Phosphorus, P) added. As compared to Si, the Phosphorus 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 impurity atom. This type of impurity is called door. Note, that there is o hole created whe a free electro comes from the impurity atom.
2 Free electro cocetratio i door - doped 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 impurity (e.g. Phosphor) i Si is N D, the cocetratio of free electros, N D For Si ad other semicoductors, the typical dopig levels are: N D = cm cm -3 D = cm cm -3 (compare to i = cm -3 i itrisic Si) D >> i Dopig provides a flexible cotrol over semicoductor coductivity. The vast majority of microelectroic devices are based o doped semicoductors
3 Resistace of Door-Doped Silico sample How much would be the resistace of the (1 cm 1cm 1cm) Si sample doped with door impurities 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 doped Si crystal ca be sigificatly lower tha that of itrisic Si
4 Doped semicoductors: acceptor impurities A silico lattice with a sigle impurity 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 type of impurity is called acceptor. There is o correspodig free electro created from acceptor impurity
5 Hole cocetratio i acceptor - doped semicoductors If the cocetratio of acceptor impurity (B atoms) i Si is N A, the hole cocetratio p A N A For Si ad other semicoductors, the typical acceptor dopig levels are: N A = cm cm -3 p A = cm cm -3 (compare to i = cm -3 i itrisic Si); p A >> i The vast majority of microelectroic devices usig hole coductivity, are based o doped semicoductors I doped semicoductors, the cocetratio of itrisic electros ad holes ca be eglected as compared to those comig from door ad acceptor impurities.
6 Cocetratio temperature depedece i doped semicoductors, cm -3 Impurity electros N D Itrisic electros, itrisic holes T 100 K 200 K 300 K 400 K Typical depedece for -Si (i.e. door-doped) (for p-si (i.e. acceptor doped) the depedeces 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 temperature. 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 paret atom ad reaches reach the coductace bad The miimum eergy of the coductio bad is deoted as E C
9 Eergy Bad Gap (E g ) E c E v Bad-gap Forbidde Eergy regio Geerally o electro ca have the eergy betwee E c ad E v The bad-gap 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 temperature. Temperature 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 = (Electro Average Eergy + Hole Average Eergy) /2 (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 -type semicoductor Extra free electro Phosphorus (P) has 5 outer shell electros. I the -type 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 p-type semicoductor Extra electro vacacy or hole Boro (B) has 3 outer shell electros. I the p-type 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 Fp
14 Electro cocetratio: Carrier Cocetratio ad Fermi level: -type material N D N D - Door atoms cocetratio Fermi eergy level: EF EC Hole cocetratio i the -type material: p = 2 i p = 2 i
15 Hole cocetratio: Carrier Cocetratio ad Fermi level: p-type material p p N A N A - Acceptor atoms cocetratio Fermi eergy level: EF EV Electro cocetratio i the p-type material: p = p 2 i p p = 2 i
16 Compesatio If both door ad acceptor are added to a itrisic semicoductor the the semicoductor is said to be compesated If N D > N A, the free electro cocetratio: = N D -N A If N D < N A, the hole cocetratio: p= N A -N D
17 Drift Curret The electric curret due to electric field is called the Drift Curret. The electro curret desity (curret per uit area): J = qµ E drift, µ is the electro mobility ad is the electro cocetratio. E Similarly the hole curret desity: Jp,drift = qµ p pe µ p is the hole mobility ad p is the hole cocetratio. J,drift J p,drift
18 cot Drift Curret ad coductivity The total (electro + hole) drift curret desity: Coductivity: J drift = J = qµ,drift + J E + p,drift qµ p pe J = q( µ + µ p) E drift p Coductivity: = q( + p) J drift σ µ µ p 1 1 ρ = = σ q( µ + µ p) p =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. Abrupt 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, pdiff = dp qdp dx Electro Cocetratio D p is the diffusio coefficiet of holes Electro diffusio J,diff x Hole Cocetratio Hole diffusio J p,diff x
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