Engineering 2000 Chapter 8 Semiconductors ENG2000: R.I. Hornsey Semi: 1
Overview We need to know the electrical properties of Si To do this, we must also draw on some of the physical properties and we return to our ideas about atomic bonding These will enable us to understand the difference between: insulators conductors metals As a start, we can try to answer a seemingly unrelated question why is a diamond transparent? ENG2000: R.I. Hornsey Semi: 2
Why is a diamond transparent? The process required to answer this question brings out several points which we can then apply to Si So, transparent to what? We usually mean visible light but we have to a bit more specific photons pf a particular energy E photon = hc/λ visible light: 400nm < λ < 700nm giving E photon 4 x 10-19 J = 2.5eV (recall, 1eV = 1.6 x 10-19 J) ENG2000: R.I. Hornsey Semi: 3
So we can now say that diamond does not absorb photons with energies corresponding to visible light. So what would happen if a photon was absorbed? Since the nucleus of the atoms is very small compared to the overall diameter, we would expect the photon to be absorbed by transferring the energy to the electrons Electrons tightly bound to the nucleus cannot readily change states so the photon energy is mostly given to the outer electrons ENG2000: R.I. Hornsey Semi: 4
Since the same electrons are also involved with bonding we ll get to that soon photon are only absorbed if they have enough energy to break the bonds So a very simplistic picture of the variation of light absorption with photon energy might look like: % absorbed E bond E photon ENG2000: R.I. Hornsey Semi: 5
The idea we have formed is that an electron can be moved between two states: loose and bound E bond For diamond, E bond is approximately 7eV which is a wavelength of about 180nm (x-ray) The source of energy to provide E bond does not have to be optical, it could be thermal electrical Once the electron is freed from the bond, it could move if a voltage was applied. The diamond could then conduct electricity ENG2000: R.I. Hornsey Semi: 6
If we try to obtain E bond from thermal excitation, the energy available is of the order of kt k = Boltzmann constant = 1.38 x 10-23 J/K T = absolute temperature in K (kt = 25.9meV at room temperature) Since this is much less than E bond, we can assume that diamond is a good insulator Important assumptions we made above include material is a perfect crystal electrons are in bonds that can be broken electrons can become loose enough to conduct We can now look at some of these issues in a bit more detail and for Si now rather than diamond [By the way, the reasons why gases and liquids are transparent are not the same... ] ENG2000: R.I. Hornsey Semi: 7
Energy levels Recall the silicon COVALENT BONDING that arose from the sharing of the outer electrons A simple but incorrect view of the energy levels would now be: 4 3 2 1 original electron shared electron We might now also imagine that we can create a loose electron by supplying enough energy to move an electron from 3 to 4 This is essentially a good picture; we will refine it further in a little while ENG2000: R.I. Hornsey Semi: 8
More on bonding If this picture of the energy levels is really true then we would get optical absorption only at a single wavelength because the electron can only be at an existing allowed energy level Since optical absorption occurs for a large range of photon energies above the critical value, the upper level must in fact be a band of energy You can imagine that any of the photon energy left over after breaking the bond gives the loose electron some energy which will later be released as heat ENG2000: R.I. Hornsey Semi: 9
Band diagram A better picture of the allowed energies of the electrons would therefore be: energy x E G E C E V This is a vital and standard representation it is called the BAND DIAGRAM of a material. ENG2000: R.I. Hornsey Semi: 10
The forbidden region between the bands the energy required to free the electron from the bond is formally called the BAND GAP, E G, of the material Since we presume that the free electrons can move can contribute to electrical conduction the upper band is known as the CONDUCTION BAND, E C The lower band is called the VALENCE BAND, E V, because it arises from the valence (outer) electrons of the atom ENG2000: R.I. Hornsey Semi: 11
The differences So now we can formally state the differences between insulators, semiconductors and conductors The terms insulator, semiconductor and conductor are based on everyday experience the energy to get an electron into the conduction band is usually gained from thermal energy An insulator is therefore a material for which the band gap is large compared with kt e.g. diamond with E G = 7eV A semiconductor is a material for which the band gap is medium! e.g. Si (1.1ev), Ge (0.7eV), GaAs (1.4eV) ENG2000: R.I. Hornsey Semi: 12
And a conductor has essentially no energy gap A metal is not bonded covalently and we don t think of it as having a band gap at all while it is possible to think in terms of energy bands, the conduction and valence bands of a metal overlap, allowing free transition of electrons HOWEVER, we have not yet determined the origin of the energy bands... There are several levels of explanation, from handwaving to a full quantum-mechanical treatment! we will look at the handwaving argument! ENG2000: R.I. Hornsey Semi: 13
Formation of bands The easiest way to think of the formation of bands is due to interactions between the shared electrons in the covalent bonds A conceptual picture would look something like: [note: it doesn t have to be the same electron in the same bond they can swap over provided there is no net movement] ENG2000: R.I. Hornsey Semi: 14
[Don t worry about the handwavyness of these pictures this is the way everyone thinks of things! The real situation is very complex and only weird people like chemists do the whole treatment] Now, the electrons in the bonds interact due to electrostatic (Coulomb) forces The strength of the interactions depends on the electrons separations which are not constant. Therefore the energy level associated with these bonds broadens into a band all the levels for all the atoms in the material are slightly different from each other, but lie in a defined range ENG2000: R.I. Hornsey Semi: 15
The same is true for all of the atomic levels they all form bands, including the loosely bound outer levels we think of as being free Obviously, the amount of interaction between electrons in different atoms depends on how close the atoms are to each other ENG2000: R.I. Hornsey from Callister Semi: 16
In fact, the band gap etc of semiconductors can be changed by STRAINING the material i.e. changing the inter-atomic distance This is an important area of advanced semiconductor research for materials such as SiGe alloys ENG2000: R.I. Hornsey Semi: 17
Electrons and holes When the electron is excited to the conduction band by whatever means it leaves behind a space This is called a HOLE: E C E G E V hole ENG2000: R.I. Hornsey Semi: 18
In our bonding picture, this looks like: e - hole Just like electrons in the conduction band, holes in the valence band are mobile and act just like positive particles (with +e of charge) except that they cannot exist outside a material a hole is the absence of an electron Si ENG2000: R.I. Hornsey Semi: 19
Electrical conduction in a semiconductor therefore involves the movement of both holes and electrons electrons in the conduction band holes in the valence band We can picture the motion of a hole as follows: http://www.vislab.usyd.edu.au/photonics/devices/semic/images/car_hole_an.gif ENG2000: R.I. Hornsey Semi: 20
e - + hole Si http://www.vislab.usyd.edu.au/photonics/devices/semic/movies/electron_hole_move.mov ENG2000: R.I. Hornsey Semi: 21
Intrinsic semiconductor A pure semiconductor is known as intrinsic material because its properties are intrinsic to the Si One very important property of an intrinsic semiconductor is that electrons and holes can only be created in pairs termed electron-hole pairs (EHPs) And therefore must be present in equal numbers Mathematically, this is expressed as n = p = n i n = concentration (or density) of electrons (# / cm3) in conduction band p = concentration (or density) of holes (# / cm3) in valence band n i = intrinsic carrier concentration ENG2000: R.I. Hornsey Semi: 22
Recombination The opposite of electron-hole pair generation is also important to maintain the steady-state balance i.e. equilibrium When an electron and hole meet, they can recombine with the release of energy usually heat in Si, but could be light in other materials This is shown the band diagram as: E C E G E V ENG2000: R.I. Hornsey Semi: 23
For this simple situation we can say that the rate of recombination, r i, is proportional to: n 0 ( the equilibrium electron concentration) p 0 ( the equilibrium hole concentration) Thus r i = const. x n 0 p 0 = const. x n i 2 n 0 p 0 = n i 2 is a fundamental equation for semiconductors rather confusingly known as the mass action law In steady state, this must also equal the rate of generation of e-h pairs, g i Recombination is a very important mechanism in many devices, including anything with a p-n junction in it It may take many forms and may emit useful things, like light in LEDs for example ENG2000: R.I. Hornsey Semi: 24
Conduction So, our picture of the energy bands now allows us to say that conduction can take place when electron-hole pairs are created which usually occurs under illumination photoconductivity or by temperature At room temperature, the number of e-h pairs (= n i ) is about 1.5 x 10 10 cm -3 for Si there are >10 22 Si atoms per cm 3! comparable for metals, where all electrons conduct But if kt 25meV and EG = 1.1eV, why are there any e-h pairs at all in the dark? because kt is the average thermal energy; some electrons have much more and this relatively small number that does the conduction ENG2000: R.I. Hornsey Semi: 25
The net result is that intrinsic Si is not a good conductor at room temperature unless it is illuminated. This appears in the values of the resistivity, a material property enabling resistance to be calculated by R = l/a: Si: ρ = 2.3 x 10 5 Ωcm diamond: ρ ~ 10 16 Ωcm metal: ρ = 2 x 10-6 Ωcm We need to find a way to control this... ENG2000: R.I. Hornsey Semi: 26
Doping Probably the most useful property of semiconductors is the ability to control the conductivity ( = 1/ ) In fact, what we will control directly is the carrier concentrations To do this, we somehow have to escape from the limitations of the intrinsic material The aim, therefore, is to gain extra charge carriers (electrons and/or holes) at room temperature This is achieved by adding impurities into the Si crystal lattice - which is called DOPING ENG2000: R.I. Hornsey Semi: 27
The resultant doped material is now known as EXtrinsic because the material s properties are now dependent on the impurities rather than its intrinsic properties Moreover, we can control the doping so that a material can have more electrons or more holes The equilibrium electron and hole concentrations are denoted by n 0 and p 0 as before n and p are now the instantaneous non steady state values ENG2000: R.I. Hornsey Semi: 28
N-type material A semiconductor with an excess of electrons is called n-type we will see later that this does not mean that there are no holes n-type extrinsic Si is obtained by adding in a material such as phosphorus (P), arsenic (As) or antimony (Sb) into the lattice. These are Group V elements each of these elements likes to bond with 5 bonds In the Si crystal, however, the dopant atoms are forced to bond with the 4 bonds preferred by Si atoms ENG2000: R.I. Hornsey Semi: 29
This leaves a spare bond, and hence an extra, free electron The bonding picture of this process looks like: e - P Therefore, we can add electrons to the conduction band - this type of dopant is called a DONOR Si ENG2000: R.I. Hornsey Semi: 30
It still takes a little energy to separate the electron from the donor atom, so the band diagram looks like: E C E C E G E D E G E D E V E V T = 0K T 50K Donors become positively ionised ENG2000: R.I. Hornsey Semi: 31
Activating dopants Because we still need this small energy (30-60meV), at T = 0K there will be no electrons in the conduction band At higher temperatures (> ~50K), most of the donors will be ionized when the donor atom contributes its electron to the conduction band, it becomes positively charged This is an important point to note; when the electron has left the donor, the principle of charge neutrality says that the remaining dopant is positively charged we cannot, therefore, gain charges but the electron is mobile while the ionized donor is fixed. ENG2000: R.I. Hornsey Semi: 32
P-type material The complement to n-type material is p-type, which has an excess of holes which are mobile in the valence band By analogy with n-type, we can dope Si to be p- type by adding an impurity element with only 3 bonds such dopants include boron (B), aluminium (Al), gallium (Ga) and indium (In) ENG2000: R.I. Hornsey Semi: 33
In the bonding picture, this is represented by: B hole Si ENG2000: R.I. Hornsey Semi: 34
Since the dopant atom is missing a bond, it can accept an electron which is the same as adding a hole. This type of dopant is therefore called an acceptor Again, it takes a little energy to force the electron from the valence band onto the acceptor atom, so the band diagram at T > 0K is: E C E a - E v = 30-60meV E G E A Acceptors become negatively ionised E V T 50K ENG2000: R.I. Hornsey Semi: 35
The type of doping described above for Si is known as substitutional doping because the dopant atom substitutes for a Si atom Typical dopant concentrations are 10 16-10 20 cm -3 At room temperature, almost all dopants are ionized so doping changes the carrier concentration by 6 10 orders of magnitude The terminology for carriers in n-type or p-type materials is n-type p-type electrons majority minority holes minority majority ENG2000: R.I. Hornsey Semi: 36
Conductivity Once they are able to move, electrons and holes can contribute to electrical conduction The current they can carry depends on So how many carriers how fast they move how much charge they carry J n = nqv n J p = pqv p where J = current density (A/cm 2 ), and q is the electronic charge note: v n and v p are in opposite directions because the charges are opposite ENG2000: R.I. Hornsey Semi: 37
Mobility At low electric fields, the carrier velocity is proportional to the applied field v = The constant of proportionality (as defined above) is called the MOBILITY Hence: v n = n v p = + p So the total current density is Where J = q( n n + p p ) = = is the electrical conductivity for Si, µ n = 1350 cm 2 /Vs, µ p = 480 cm 2 /Vs ENG2000: R.I. Hornsey Semi: 38
Electron drift The electrons have two components of velocity Thermal velocity is very high ~10 7 cm/s but has no net direction and contributes nothing to a current The net drift imposed by the applied electric field is what leads to the current flow drift velocity is of the order of 1 cm/s ENG2000: R.I. Hornsey Semi: 39
Temperature dependence Like many energy-activated processes, the variation of n i with temperature is exponential n i = const e E G 2kT The variation of n i with temperature is shown on the next slide Followed by n(t) for an extrinsic material ENG2000: R.I. Hornsey Semi: 40
Intrinsic carrier concentration, n i (cm -3 ) -3 ) m (c n a tio tr c e n o n C sic in tr I n 600 C 400 C 200 C 27 C 0 C L L L L 10 18 10 15 10 12 10 9 1.45 10 10 cm -3 10 6 2.4 10 13 cm -3 2.1 10 6 cm -3 Ge Si 10 3 GaAs 1 1.5 2 2.5 3 3.5 4 1000/T (1/K) Fig. 5.16: The temperature dependence of the intrinsic concentration. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) http://materials.usask.ca ENG2000: R.I. Hornsey Semi: 41
At very high temperatures, n i increases beyond N a ln(n) Intrinsic slope = -E g /2k provided N d >> n i the number of carriers is dominated by N d dopants are activated as T > 50-100K so carrier concentration increases ln(n d ) T i Extrinsic T s Ionization slope = - E/2k n i (T) 1/T Fig. 5.15: The temperature dependence of the electron concentration in an n-type semiconductor. From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) http://materials.usask.ca ENG2000: R.I. Hornsey Semi: 42
Charge neutrality Earlier on, we said that when a donor gives up its electron to the conduction band it becomes positively charged More generally, we can say that whatever we do with doping n, p or both the material must remain electrically neutral Thus in all circumstances p 0 + N D + = n 0 + N A A result of this is that a material doped equally with donors and acceptors at the same time becomes intrinsic again! ENG2000: R.I. Hornsey Semi: 43
Application to p-n diode hole electron zero bias hole flow recombination zone + forward bias electron flow depletion zone + reverse bias ENG2000: R.I. Hornsey Semi: 44
Diode I-V characteristic Current Ge Si GaAs ~0.1 ma 0 0.2 0.4 0.6 0.8 1.0 Voltage Fig.6.4: Schematic sketch of the I-V characteristics of Ge, Si and GaAs pn Junctions From Principles of Electronic Materials and Devices, Second Edition, S.O. Kasap ( McGraw-Hill, 2002) http://materials.usask.ca ENG2000: R.I. Hornsey Semi: 45
Summary We have scratched the surface of how semiconductors work the picture is much more complex than we have assumed and these complexities are actually important in how practical devices are made We have learned how to distinguish conductors, insulators and semiconductors in terms of their band structure And we now know control the carrier concentrations and hence the conductivity The next step, were we to take it, would be to use the band diagrams for different pieces of semiconductor to design devices such as transistors ENG2000: R.I. Hornsey Semi: 46