Lecture 3: Semiconductors and recombination. Prof Ken Durose, University of Liverpool

Transcription

1 Lecture 3: Semiconductors and recombination Prof Ken Durose, University of Liverpool

2 Outline semiconductors and 1. Band gap representations 2. Types of semiconductors -Adamantine semiconductors (Hume -Rothery 8-N coordination rule -Others -Solid solutions recombination 3. Doping and point defects 4. Generation and recombination

3 1. Band gap and its representation Shockley Queissler limit and band gap

4 Energy of an electron (ev) 1.1 Band gap origins E C E g E t E F Diagram from M J Cooke Semiconductor devices E V (Recall the Pauli exclusion principle) x (m) Energy vs space representation of a band diagram. E t is a trap energy level x-homocontrol.png

5 1.1 Band gap origins Electrons in a periodic potential (e.g. Kronig-Penney model) Diagram from AK Dekker Solid State Physics

6 1.2 E-k reduced zone representation (textbook) E E Direct gap e.g. III-V s and II-VI s k k Indirect gap e.g. Si

7 1.2 E k band diagram (GaAs)

8 1.2 N(E) vs E density of states E E g N(E) NB there is a very low DOS at the band edge and so photons of energy E g are not the most likely to be absorbed

9 2 Types of semiconductor + solid solutions Ib IIb III IV V VI VII B C N O F Al Si P S Cl Cu Zn Ga Ge As Se Br Ag Cd In Sn Sb Te I Hume-Rothery 8-N Co-ordination rule: The co-ordination number in a compound is 8-N, where N is the average valency number. We will use this rule to go looking for semiconductors like silicon, valency 4 i.e. isoelectronic variants of Si. Si and Ge are gpiv semiconductors and are tetrahedrally co-ordinated, they have the structure of diamond. Adamantine = diamond like

10 2 Types of semiconductor + solid solutions III-V semiconductors Ib IIb III IV V VI VII B C N O F Al Si P S Cl Cu Zn Ga Ge As Se Br Ag Cd In Sn Sb Te I GaP, GaAs, GaSb, InP, InAs, InSb etc

11 2 Types of semiconductor + solid solutions II-VI semiconductors Ib IIb III IV V VI VII B C N O F Al Si P S Cl Cu Zn Ga Ge As Se Br Ag Cd In Sn Sb Te I ZnO, ZnS, ZnSe, ZnTe, CdO, CdS, CdSe, CdTe etc

12 2 Types of semiconductor + solid solutions I-III-VI semiconductors the chalcopyrite family Ib IIb III IV V VI VII B C N O F Al Si P S Cl Cu Zn Ga Ge As Se Br Ag Cd In Sn Sb Te I CuInSe 2, CuGaSe 2, CuInSe 2 etc

13 2 Types of semiconductor + solid solutions I-II-IV-VI semiconductors the kesterite family Ib IIb III IV V VI VII B C N O F Al Si P S Cl Cu Zn Ga Ge As Se Br Ag Cd In Sn Sb Te I Cu 2 ZnGeSe 4, Cu 2 ZnSnS 4, Cu 2 ZnSnSe 4 etc

14 Solid solutions GaP Eg ~ 2.3eV GaAs Eg ~ 1.4eV Ternary semiconductor Ga(As x P 1-x ) Eg in the range eV Lattice parameter (a 0 ) varies also NB To vary Eg and a o independently, you need a quaternary system, such as Ga x In 1-x As y P 1-y

15 Vegards law - linear variation of lattice parameter with x a[a x B 1-x C] = a[bc] - x * {a[bc] a[ac]} a a[bc] a[ac] Psst! It might not be linear in Practice... but it often is. 0 x 1

16 Vegard s law for band gap Eg Ideal obeys Vegard s law i.e. is linear Eg[AB] Eg[AC] 0 x 1 Non - ideal bowed Bowed curve represented by a bowing parameter b Eg[AxB1-xC] = x * Eg[AC] + (1-x) * Eg[BC] - b * x * (1-x).

17 Solid solutions in two III-V semiconductor series

18 3 Semiconductor doping Substitutional doping Intrinsic doping Vacancies Interstitials Complexes Ib IIb III IV V VI VII B C N O F Al Si P S Cl Cu Zn Ga Ge As Se Br Ag Cd In Sn Sb Te I

19 3 Substitutional doping Substitutional dopants in Si Everything is on a gpiv site P Si gpv on a gpiv site electron excess this is a donor B Si gpiii on a gpiv site electron deficient - this is an acceptor Substitutional doping in III-V compounds such as InP e.g. Cd In gpii on a gpiii site electron deficient = acceptor e.g. S P gpvi on a gpv site = donor C could occupy the gpiii or the gpv site amphoteric dopant

20 3 Substitutional doping.cont Substitutional doping in II-VI compounds such as CdTe On the gpii site e.g. Cu Cd gpia on a gpii site electron deficient = acceptor e.g. In Cd gpiii on a gpii site = donor On the gpvi site e.g. As Te gpv on a gpvi site electron deficient = acceptor e.g. Cl Te gpvii on a gpvi site = donor

21 3 Native defect or intrinsic defect doping - vacancies Metal i.e. cation vacancies e.g. Cd vacancies in CdTe Cd oxidation state 2+ Te oxidation state 2- If you heat CdTe it loses Cd when neutral Cd leaves it takes two electrons with it leaving a doubly +ve charged V Cd V Cd is a double acceptor Non-metal i.e. anion vacancies e.g. S vacancies in CdS Cd oxidation state 2+ S oxidation state 2- If you heat CdS it loses S when neutral S leaves it takes two electrons with it leaving a doubly -ve charged V S V S is a double donor heat + Cd(g) heat + S(g) CdTe CdTe with V Cd CdS CdS with V S

22 3 Native defect or intrinsic defect doping - interstitials Metal i.e. cation interstitials e.g. Cd interstitials in CdTe Cd oxidation state 2+ Te oxidation state 2- Add neutral Cd to CdTe as an interstitial to achieve its usual oxidation state it must lose two electrons. Cd i is assumed to be a donor Non-metal i.e. anion vacancies e.g. Te interstitials in CdTe Add neutral Te to CdTe as an interstitial to achieve its usual oxidation state it must gain two electrons. Te i is assumed to be an acceptor

23 e.g. the A-centre 3 Complex centres Add neutral Cd to CdTe as an interstitial to achieve its usual oxidation state it must lose two electrons. Cd Te single donor V Cd double acceptor [V Cd Cl Te ] single acceptor This is the A-centre

24 3 Energy levels in the gap of silicon Diagram from Solid State Electronic Devices, Streetman and Banerjee

25 3 Kroger Vink nomenclature for point defects If you need to get specific about point defects and their reactions and equilibria, then check out Kroger-Vink nomenclature 2%80%93Vink_notation

26 4 Generation and recombination Trapping Recombination Direct and indirect Recombination via trap states ( Shockley Hall Reed mechanism) Kinetics for recombination in direct gap materials

27 4.1 Recombination types Direct recombination (a) It is radiative Diagram from Intro to Electronic Devices Michael Shur Indirect recombination (b-d) is not usually radiative. (Auger recombination not shown is also indirect )

28 4.2 Trapping centres Diagram from Solid State Electronic Devices, Streetman and Banerjee Centres below the Fermi level at E r are full of electrons. For them to act as traps, either a) holes are temporarily trapped there then reemitted or b) electrons are temporarily trapped there then reemitted NB strictly this is what trapping is. However the term trap is used more widely than this as follows now

29 4.2 Recombination via traps a) holes are trapped b) electrons annihilate with the trapped holes overall there is one electron hole pair less plus some heat This is most often called Shockley Hall Read recombination Diagram from Solid State Electronic Devices, Streetman and Banerjee

30 4.2 Recombination via traps The recombination rate is maximised when the trap energy E t is mid-gap. These are killer traps or lifetime killers e.g. Au Si - Where E t is mid-gap, the diode factor has a value of n = 2 Treatment from Intro to Electronic Devices M Schur

31 4.3 Kinetics of direct recombination Symbols G = generation rate R = recombination rate n = negative carriers p = positive carriers n i = intrinsic carrier concentration At equilibrium Under steady state conditions (e.g. under illumination), there is additional generation: r = rate constant for recombination m 3 s -1

32 4.3 Kinetics of direct recombination For the case where there is additional generation of the recombination rate is written This can be simplified by substituting (subtract this from both sides)

33 4.3 Recombination in direct gap semiconductors Examples that bring out the important effects:

34 4.3 Recombination in direct gap semiconductors rp and rn have units of 1 s they are lifetimes -1 There is a numerical example in M J Cooke, page 69.

35 Example problem generation/recombination e 1 r p Example from M J Cooke Semiconductor Devices, p 69-70

36 Example problem cont Minority carrier density changes a lot Majority carrier density invariant Example from M J Cooke Semiconductor Devices, p 69-70

37 Books used to compile this lecture (including picture credits) Semiconductor Devices, M J Cooke Intro to Electronic Devices, M Shur Solid State Electronic Devices, B G Streetman and S K Banerjee Solid State Physics, AK Dekker