LED access resistances W the output window size p-layer series access resistance d p n-layer series access resistance d n The n-layer series access resistance R = ρ s n where the resistivity of the n-layer is ρ n, the thickness is d n and the contact area is A The p-layer series access resistance (for rectangular W x W window) n R d n A W 2 1 / ρ ρ W d = 2d s p p p p p 1
I-V characteristics of real LEDs The I-V characteristic of the p-n junction: qv j I= IS exp 1 kt V j is the voltage drop across the p-n junction itself. In addition, there is a voltage drop across the series access resistances: V s-n = I R s-n ; V s-p = I R s-p ; where d R n s n = ρ n A R s p p ρ 1 2d p The total voltage drop across the LED: V = V j + V sn + V sp ; The LED current is controlled by the junction voltage V j : V j = V - V sn -V sp ; qv ( I Rs ) The real LED I-V: I= IS exp 1 kt R s is the total access series resistance. R s = R s-n +R s-p + R contact 2
High efficiency heterostructure LEDs All the LEDs considered in above lectures utilized the p-n junctions formed of the same material on the n- and p-sides. In these, so-called homojunctions, the potential barriers controlling the electron and hole currents are only due to the difference in the material doping (impurity concentrations on the n- and p-sides). Major issues in regular (homojunction) LEDs: 1.Very high concentration of electrons and holes is hardly achievable due to diffusion (the characteristic length of injected carrier distribution is L n or L P. 2.The access regions of LED absorb the light generated at the p-n junction; thinning the access regions increases access resistance. 3.To achieve high injection levels, very high doping is needed. This worsen material quality and reduces efficiency; it also further increases the absorption. 3
In the heterojunctions, the potential barriers for electrons and for holes can be different Example: undoped AlGaAs/GaAs heterostructure creates different barriers for the electrones and for the holes at the hetero-interface barrier for electrons For GaAs, E G = 1.42 ev; For AlAs, E G = 2.18 ev For Al x Ga 1-x As, E G = 1.424 + 1.247 x (x < 0.45) barrier for electrons 4
p-n heterojunctions In the p-n heterojunction, the potential barriers for electrons and holes are determined by both the composition and the doping difference p-n homojunction from materials 2 p-n homojunction from materials 1 5
Double heterojunction (DH) LED structure Typical AlGaAs/GaAs DH LED structure could be i (undoped) region as well AlGaAs (barrier) GaAs (LED active region) AlGaAs (barrier) 6
Dramatic increase in the extraction efficiency: DH LEDs with wide-bandgap cladding layers Zero bias E g2 > E g1 n E g2 > E g1 p E g1 Forward bias 7
DH LEDs Homojunction and DH LEDs under forward bias Typically, W DH << L n, L P After F.Schubert, Light-Emitting-Diodes-dot-org 8
DH LEDs At very high forward bias: Є C Є Fn Є Fp Є V n, p p(x) regular LED n(x) regular LED 9
DH LEDs The active region of DH LEDs forms a so-called quantum well In the quantum well, electrons and holes are strongly confined. Therefore, the recombination rate, R ~ n x p, increases significantly 10
Advantages of DH LEDs 1. Both n- and p- regions are made out of widebandgap materials (ε G > hν), therefore there is no absorption in these regions: they form optical windows 2. n- and p- regions can be highly doped. 3. Injected electrons and holes are confined in a very narrow active region (quantum well) where the n x p product is extremely high. Therefore, the radiative recombination rate, R, is high. 11
DH LEDs confinement issue Effect of electric field on electron hole confinement and recombination No electric field Electric field applied hν ε G Under electric field applied the electrons and holes are partially separated. This decreases the recombination efficiency and creates so-called red-shift of the emission. The QW thickness in DH-LEDs must be kept small enough. 12
Multiple Quantum Well LEDs The total number of energy states in the quantum well is limited. Therefore, at high injection currents, all the states available can be occupied by electrons. This will saturate the optical power. Increasing the QW thickness is not practical as it reduces the confinement. Multiple Quantum Well (MQW) structure overcomes this problem 13