P. E. Russell: [email protected]QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Nanoscience and Nanotechnology Lecture 19 QuickTime™ and a TIFF (Uncompressed) decompressor are needed to see this picture. Only 7 lectures remaining! (including this one) Review of traditional microelectronics Course notes are at: http://www.phys.appstate.edu/nanotech/NanoCourseLecturePPTs2008/
Nanoscience and Nanotechnology Lecture 19. Only 7 lectures remaining! (including this one) Review of traditional microelectronics Course notes are at: http://www.phys.appstate.edu/nanotech/NanoCourseLecturePPTs2008/. Review of basic semiconductor Physics. - PowerPoint PPT Presentation
Welcome message from author
This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
When considering the Physics and Engineering of traditional semiconductors, we are mainly concerned with ‘bulk’ properties; and consider surfaces as defects.
This approach is the opposite of the nanotechnology approach, where the goal is to use the special properties of materials and devices at the nm scale, where surface atoms control properties.
. 5.1: ( ) Fig a A simplified two dimensional illustration of a Si atom with four , hybrid orbitalsψhyb. . ( ) Each orbital has one electron b A simplified two
. ( ) dimensional view of a region of the Si crystal showing covalent bonds c The .energy band diagram at absolute zero of temperature
Fig. 5.3: (a) A photon with an energy greater than Eg can excite anelectron from the VB to the CB. (b) When a photon breaks a Si-Sibond, a free electron and a hole in the Si-Si bond is created.
. 5.7: ( ) . ( ) ( Fig a Energy band diagram b Density of states number of states ). ( ) - per unit energy per unit volume c Fermi Dirac probability function
( ). ( ) probability of occupancy of a state d The product ofg(E) andf(E) is ( the energy density of electrons in the CB number of electrons per unit
). energy per unit volume The area undernE(E) . vsE is the electron .concentration in the conduction band
Fig. 5.9: Arsenic doped Si crystal. The four valence electrons of Asallow it to bond just like Si but the fifth electron is left orbiting theAs site. The energy required to release to free fifth-electron into theCB is very small.
Fig. 5.11: Boron doped Si crystal. B has only three valence electrons.When it substitutes for a Si atom one of its bonds has an electronmissing and therefore a hole as shown in (a). The hole orbits aroundthe B- site by the tunneling of electrons from neighboring bonds asshown in (b). Eventually, thermally vibrating Si atoms providesenough energy to free the hole from the B- site into the VB as shown.
Fig. 5.12: Energy band diagram for a p-type Si doped with 1 ppm B.There are acceptor energy levels just above Ev around B- sites. Theseacceptor levels accept electrons from the VB and therefore create holesin the VB.
Band diagram for b doped (p-type) Si
Small ionization energy allows thermal ionization at room temperature
Fig. 5.12: Energy band diagram for a p-type Si doped with 1 ppm B.There are acceptor energy levels just above Ev around B- sites. Theseacceptor levels accept electrons from the VB and therefore create holesin the VB.
Band diagram for b doped (p-type) Si
Small ionization energy allows thermal ionization at room temperature
Note that the electron from the valance band becomes fixed charge (in energy and position)
Fig. 5.13: Energy band diagram of an n-type semiconductor connectedto a voltage supply of V volts. The whole energy diagram tilts becausethe electron now has an electrostatic potential energy as well
For an n-type semiconductor (e.g. Arsenic doped) only the electrons are mobile. The ionized dopant atoms do not move.
Thus we have added both ‘mobile” and ‘fixed’ or ‘localized’ charge!
Fig. 5.14: (a) Below Ts, the electron concentration is controlled bythe ionization of the donors. (b) Between Ts and Ti, the electronconcentration is equal to the concentration of donors since theywould all have ionized. (c) At high temperatures, thermally generatedelectrons from the VB exceed the number of electrons from ionizeddonors and the semiconductor behaves as if intrinsic.
. 5.7: ( ) . ( ) ( Fig a Energy band diagram b Density of states number of states ). ( ) - per unit energy per unit volume c Fermi Dirac probability function
( ). ( ) probability of occupancy of a state d The product ofg(E) andf(E) is ( the energy density of electrons in the CB number of electrons per unit
). energy per unit volume The area undernE(E) . vsE is the electron .concentration in the conduction band
(The intrinsic case is shown here.)
We can determine n and p (the electron and hole concentrations) if we know g(E) and f(E) and…
Fig. 5.8. Energy band diagrams for (a) intrinsic (b) n-type and (c) p-typesemiconductors. In all cases, np = ni
2
Mass action law np=ni2: in equilibrium
Valid for both intrinsic and extrinsic semiconductors!
Mass action law np=ni2 = NcNvexp(-Egap/kT)
Where Nc is the density of states near conduction band edgeNv is the density of states near valence band edgeIf more electrons are added by doping, then fewer holes will exist due to recombination, keeping the product np constant!
In addition to carrier creation, we will have carrier recombination, i.e. if an electron excited to the CB is located (spatially) near a hole in the VB, the electron will reduce its energy by filling the hole (allowed electron state).
The electron and hole annihilate each other (as free charge carriers) via recombination.
Carrier RecombinationThe recombination rate R will be proportional to both the electron and hole concentrations (and hence to their product) Rnp
What about the carrier generation rate G?G will depend on the number of electrons available for excitation at Ev i.e. Nv and empty states at Ec i.e. Nc.And the probability of an electron making the transition i.e. exp[-Eg/kT] so: G NvNc exp[-Eg/kT] In equilibrium G = R, generation and recombination rates are equal. (more on this later)
Ge 0.66 4.13 1.04×1019 6.0×1018 2.4×1013 3900 1900 0.12 a
0.56 b
0.23 a
0.40 b
16
Si 1.10 4.01 2.8×1019 1.04×1019 1.45×1010 1350 450 0.26 a
1.08 b
0.38 a
0.56 b
11.9
GaAs 1.42 4.07 4.7×1017 7×1018 1.8×106 8500 400 0.067 ,a b 0.40 a
0.50 b
13.1
Use effective mass related to conductivity, rather than for density of states.
Table 5.1 Selected typical properties of Ge, Si and GaAs at 300 K. Effective mass related to conductivity (labeled a) is different than that for density of states (labeled b).
We have been assuming that there are many more empty states than there are electrons in the conduction band, and/or many more filled states than holes in the valence band; i.e. that Boltzmann statistics rather than Fermi-Dirac apply.
This is the non-degenerate semiconductor case;
i.e when n<<Nc and p<<Nv
What is the other possibility? Degeneracy!Occurs when doping concentration is very large; usually 1019 or 1020 cm-3 (out of 1023 cm-3)
Fig. 5.50: (a) In GaAs the minimum of the CB is directly above the maximumof the VB. GaAs is therefore a direct band gap semiconductor. (b) In Si, theminimum of the CB is displaced from the maximum of the VB and Si is anindirect band gap semiconductor. (c) Recombination of an electron and a holein Si involves a recombination center.
Si is not direct gap!This is most important in optoelectronic applications (laser, LED, photo…)More on this later.
Fig. 5.23: Recombination and trapping. (a) Recombination in Si via arecombination center which has a localized energy level at Er in thebandgap, usually near the middle. (b) Trapping and detrapping ofelectrons by trapping centers. A trapping center has a localizedenergy level in the band gap.
Cases where midgap states exist (due to impurities and/or defects)
Be sure you understand that midgap states can act as Trap sites or Recombinationsites
How can there be allowed states in the forbidden gap?
Allowed states (such as the charge carrier trap states and recombination centers of figure 5.23) are localized states within the forbidden band gap energy range of a defect-free material. The states are created by the perturbation of the normal periodic lattice by a point (or other) defect.
The trap states are localized in space to the area of the defect, and in energy to a specific energy within the band gap; determined by the type of defect creating the state.
Examples of defects creating midgap states include vacancies, interstitial and substitutional impurities, dislocations, stacking faults, etc.
How can there be allowed states in the forbidden gap?
These allowed individual states created by the perturbation of the normal periodic lattice act as:
Recombination sites if near midgap,Or asTrapping sites for electrons if near the CB edge, Or asTrapping sites for holes if near the CB edge.
Note that trapping just removes the charge carrier from the free carrier pool for a brief time; with the overall effect of having many traps being a reduction in charge carrier density available for conduction at any given time.
Fig. 5.23: Recombination and trapping. (a) Recombination in Si via arecombination center which has a localized energy level at Er in thebandgap, usually near the middle. (b) Trapping and detrapping ofelectrons by trapping centers. A trapping center has a localizedenergy level in the band gap.
Charge carrier pair is lost permanently due to recombination.
Trapping causes a temporary loss of a single charge carrier.
Carrier creation: Photoinjected charge carriersLet’s consider the case of n-type material
Consider an n-type semiconductor with a doping concentration of 5 x 1016 cm-3.
What are the carrier concentrations?Let’s define some terms;nno majority carrier concentration in the n-type semiconductor in the dark (only thermally ionized carriers) (i.e. the electron concentration in n-type)
pno minority carrier concentration in the n-type semiconductor in the dark (only thermally ionized carriers) (i.e. the hole concentration in n-type)
Note: the no subscript implies that mass action law is valid!
With light of Ephoton>Egap hitting the semiconductor, we get photogeneration of excess charge carriers.
Δnn excess electron concentration such that::Δnn = nn-nn0
And Δpn excess hole concentration such that::Δpn = pn-pn0Note that photogenerated carriers excited across the gap can only be created in pairs i.e. Δpn = Δnn and now (in light) nnpn≠ni
Fig. 5.26: Illumination of an n-type semiconductor results in excesselectron and hole concentrations. After the illumination, therecombination process restores equilibrium; the excess electronsand holes simply recombine.
Fig. 5.26: Illumination of an n-type semiconductor results in excesselectron and hole concentrations. After the illumination, therecombination process restores equilibrium; the excess electronsand holes simply recombine.
Carrier creation followed by recombination
Mostly majority carriers in the dark
Almost equalCarrier concnsIn light
The extra minority carriers recombine once the generation source is removed.
Diffusion current density = (charge) x fluxWhere Flux = ΔN/A Δt or #of charge carriers passing unit area per unit time
Ficks first law relates Flux to concentration gradientFlux =e= -De dn/dx for electrons
So the current density (due to diffusion) becomes: Diffusion current density = (charge) x flux
note: diffusion is away from high concentrationJDe= -ee for charge carriers due to diffusion, orJDe= eDe dn/dx for electrons and JDh= -eDe dp/dx for holes
Fig. 5.29: (a) Arbitrary electron concentration n(x,t) profile in asemiconductor. There is a net diffusion (flux) of electrons fromhigher to lower concentrations. (b) Expanded view of twoadjacent sections at xo. There are more electrons crossing xocoming from left (xo-l ) than coming from right (xo+l ).
Fig. 5.30: Arbitrary hole concentration p(x,t) profile in asemiconductor. There is a net diffusion (flux) of holes from higherto lower concentrations. There are more holes crossing xo comingfrom left (xo-l ) than coming from right (xo+l ).
Fig. 5.31: When there is an electric field and also a concentrationgradient, charge carriers move both by diffusion and drift. (Ex is theelectric field.)
Carrier motion: via diffusion (due to concn gradient) and drift (due to electric field)
Both diffusion and drift occur in semiconductors.
Note here that holes (minority carriers) drift and diffuse in the same direction; but electrons (majority carriers) do not!
JD, h = electric current density due to hole diffusion, e = electronic charge, h = hole flux, Dh = diffusion coefficient of holes, dp/dx = hole concentration gradient€
JD,h = eΓh = −eDh
dp
dx
Total Electron Current Due to Drift and Diffusion
Je = electron current due to drift and diffusion, n = electron concentration, e = electron drift mobility, Ex = electric field in the x direction, De = diffusion coefficient of electrons, dn/dx = electron concentration gradient
Fig. 5.32: Non-uniform doping profile results in electron diffusiontowards the less concentrated regions. This exposes positively chargeddonors and sets up a built-in field Ex . In the steady state, the diffusion ofelectrons towards the right is balanced by their drift towards the left.
Vo
Carrier diffusion due to doping level gradient.This is a common device fabrication step.
Diffusion occurs until an electric field builds up!
Fig. 5.32: Non-uniform doping profile results in electron diffusiontowards the less concentrated regions. This exposes positively chargeddonors and sets up a built-in field Ex . In the steady state, the diffusion ofelectrons towards the right is balanced by their drift towards the left.