4. SEMICONDUCTOR DEVICES II PREVIOUS LECTURE Introduced some basic semiconductor devices. pn junction Formed by combining p-type and n-type doped semiconductors. Ec EF Ev n-type p-type Considered effect of applying external bias Vext. rectifying I-V behaviour I V INTRODUCTION TO LIGHT-EMITTING DEVICES Many semiconductor devices are based on pn junction. These include devices that involve emission or absorption of electromagnetic radiation e.g. light emitting diodes, solar cells, … Absorption solar panel Emission LED In order to understand such devices, need to consider how electromagnetic radiation interacts with semiconducting material. Visible (and near-visible) wavelengths. (photon energies ph g) 4.1 ABSORPTION Band diagram of semiconductor (in real space). c Eg Eph v x i.e. plotted over extent of semiconductor Earlier, saw how thermal energy can excite an electron out of valence band across Eg into conduction band. Can also do this by shining light onto the semiconductor. Absorption of photon and Excitation of electrons across Eg occurs if Eph Eg [Eph = energy of incident photons = (hc/)] Can also plot band diagram as function of wavevector k (Unit 3) i.e. in reciprocal space In case of direct gap semiconductors: minimum in conduction band lies directly above maximum in valence band in -k diagram conduction band g ph valence band k Incident photon, energy ph If ph < g, photon does not have enough energy to promote an electron from valence to conduction band. If ph g, photon can promote an electron across gap from valence to conduction band. i.e. absorption of a photon If ph > Eg, electron excited into conduction band (and hole in valence band) will have some excess energy (and momentum). Can find these using conservation of energy and momentum. E Eph E=0 k=0 k Before: electron in VB + incoming photon After: electron in CB Momentum: Energy: k ph k v k c 2 k v2 2 k c2 E E ph 2mv g 2mc Wavevector in conduction band - kc Wavevector in valence band - kv Wavevector of incident photon - kph mc*, mv* - effective masses in conduction and valence bands 2 simultaneous eq’ns for kv and kh. Can solve! Can also simplify since for optical (and near-optical) photons: k ph kc , kv so can usually neglect momentum of photon. i.e. k 0 . Vertical transition. ph [See Workshop Q.5] 4.2 EMISSION OF ELECTROMAGNETIC RADIATION Essentially the reverse of the absorption process. Recombination of electron in conduction band with hole in valence band; energy released emitted as photon of well-defined frequency. For process to occur, semiconductor must have direct gap. E g g k Fig.1 ph k Fig.2 Electrons excited into conduction band by some process e.g. forward biasing of material Holes excited in valence band. These rapidly thermalise to occupy states near band edges. i.e. energy transferred to lattice vibrations [Fig.1] Probablility of recombination greatest for states near band edges. Energy released in recombination event is g i.e. ph = g [Fig.2] Both energy and momentum conserved ( k 0) 4.3 LIGHT EMITTING DIODES - LEDs LEDs make use of emission process in semiconductors. Consist of pn junction of a direct gap semiconductor, operated in forward bias. Basic operation 1. Electrons from n-region diffuse across depletion layer into narrow region just inside p-side. 2. Here, they recombine with holes, emitting photons. 3. Wavelength of light determined by energy gap g. Eg hc III-V compounds Many of these are direct gap semiconductors For GaAs: g = 1.42 eV = 870 nm (near infrared) For GaP: g = 2.24 eV = 550 nm (red region) Ternary III-V compounds Alloys between Gp III elements (Al, Ga , In) and Gp V elements (P, As, Sb), containing 3 elements e.g. GaAsxP1-x 0x1 g 2.24 eV 1.42 eV x = 0 x x=1 (GaAs) (GaP) g can be tailored by varying x to give required Quaternary III-V compounds e.g. GaxIn1-xAsyP1-y 0x1 0y1 These types of semiconducting materials allow fabrication of red , yellow and green LEDs. I-V Characteristic Can also estimate g from I-V characteristic. Recall that in ideal case, can show that I V In forward bias I = I0[exp{eV/kT} – 1] So for large V, we should get an exponential increase. In practice, I increases linearly with V for large V. Once I is high enough, the series resistance of the diode limits the exponential increase and Ohmic behaviour is observed. [Could be due to contact resistance between metal and semiconductor, resistivity of the semiconductor, or series resistance of connecting wires]. So actually get something like: I Ohmic Region V g/e Once pn junction is forward biased by value greater than Eg/e, large numbers of electrons injected from n to p, and holes from p to n I becomes large and limited by series resistance. Can extrapolate linear region back to I = 0 to obtain estimate for g. In terms of energy bands c zero bias Eg F v n p modest forward bias V eV large forward bias V eV large numbers of electrons flow from n to p (and holes from p to n) when eV > g and I is limited by series resistance 4.4 INJECTION LASER Essentially a pn junction with very heavy doping levels ( 0.1%). On n-side concentration of electrons in conduction band is very high F effectively moves into bottom of conduction band Similarly, for p-side F effectively moves into top of valence band So in zero bias F n p Under forward bias ph n p If bias is high enough, large numbers of electrons are injected into states near conduction band edge on p-side. If enough electrons injected, can get population inversion (more electrons near conduction band edge than near valence band edge on p-side). electron-hole recombination photon emission photon can cause recombination of electron in conduction band, with associated stimulated emission of second coherent photon (consequence of population inversion) Both stimulating and stimulated photons can cause further stimulated emission [Can enhance this by sandwiching active p-region between mirrors] So can build up narrow coherent beam of monochromatic radiation [ph g] . High energy density possible. Light Amplification by Stimulated Emission of Radiation 4.5 QUANTUM WELL DEVICES Single layer pn junction laser requires high threshold current densities reliability problems. Alternative Approach Could consider making laser from a stack of thin active layers, separated by confining layers. Each thin active layer can be regarded as quantum well, in which electrons are confined in 2-D. Example of a low dimensional structure. Consider thin layer of GaAs sandwiched between 2 layers of AlxGa1-x As. g(AlxGa1-xAs) g(GaAs) d AlxGa1-xAs GaAs AlxGa1-xAs z g(GaAs) – 1.42 eV 1.42 eV < g(Al1-xGaxAs) < 2.16 eV Assuming d << lateral (in-plane) dimensions: electrons in GaAs layer confined in potential well quantisation of electron motion in z-direction If approximate the potential step to be infinite, can compare with particle in 1-D box. Solving Schrodinger eq’n for this gives [as in Unit 2] h2n2 Ecz 8me* d 2 n - integer [Ecz - quantised energy of electrons in conduction band of GaAs] Including (unrestricted) in-plane motion of electron 2 k //2 h2n2 Ec 2me* 8me* d 2 [k// - in-plane component of wavevector k] Similarly for quantised states in valence band: 2 k //2 h2n2 Eg Ev 2mh* 8mh* d 2 D() E1/2 z k (a) D() (b) (c) (a) quantised energy levels in quantum well (b) -k curves, including in-plane motion (c) Density of states D() In 2-D me* D(E) = 2 [Unit 2] So D() of 2D electrons within each bound state in well is independent of steps in D() As potential well gets wider, energies of bound states become more closely spaced steps harder to see D() approaches parabolic 3-D form i.e. D() E1/2 If quantum well structure is to form a light emitting device e.g. laser , what is wavelength of emitted light? Photon emission occurs as result of electron-hole recombination between bottom of conduction band and top of valence band (direct gap material). i.e. for k// =0, and n = 1 So E ph h2 h2 Eg * 2 * 2 8me d 8mh d hc Hence can be tuned by altering well width d. In practice, normally use sequence of wells in a multiquantum well (MQW) structure, rather than a single well. AlxGa1-xAs GaAs