Optical & electronic properties of nanomaterials 1. Finite vs infinite quantum well: Within a GaAs crystal, a 7 nm wide single quantum well of Ino.3Gao.7As is formed. The band gap minimum of the well is 0.21 eV below the upper band gap edge of GaAs (1.49 eV). a) Calculate, how many electron states exist within the quantum well, using the equation for the energy Eigenstates for an infinite quantum well and the effective mass for electrons in GaAs (which is 6.7% of the free electron mass). b) Compare this calculation to the fact, that 2 energy states exist in practice (see Lecture 11 notes, slide 7) and draw a conclusion. energy (eV) Optical Absorption in a Quantum Well 0.8 0.7 0.6 0.5 -0.5 -0.6 -0.7 150 K 8x8 k.p GaAs GaAs band gap 1.49 eV 0 20 7 nm In Ga 40 0.7 60 distance (nm) GaAs 2 electron states in the well Transition energies for k=0 e1-hh1: 1.21 eV e1-lh1: 1.32 eV e2-hh2: 1.36 eV band gap: 1.49 eV 4 hole states in the well 80 (c) 100 www.nextnano.de 120 cb vb (hh) vb (lh) e1 e2 hh1 hh2 hh3 Ih1 absorption (1/m) 600000 500000 400000 300000 200000 100000 0 GaAs In 3 GaAs GaAs 03 Absorption of 7 nm In GaAs quantum well GaAs band gap 1.49 eV steps are typical of 2D system e1-hh1 1.21 eV e2-hh2 1.36 eV e1-lh1 1.32 eV continuum (3D system) proportional to square root of energy -x-polarized -z-polarized 150 K 1.05 1.10 1.15 1.20 1.25 1.30 1.35 1.40 1.45 1.50 1.55 1.60 1.65 8x8 k.p energy (eV) (c) www.nextnano.de