半導體雷射講義 (Part 3 – AlGaAs Quantum-Well Lasers and VCSELs) 教師: 郭艷光博士 國立彰化師範大學物理系所暨光電研究所 電子郵件: ykuo@cc.ncue.edu.tw 網頁: http://ykuo.ncue.edu.tw

Optoelectronic Semiconductor Materials The elementary and compound semiconductor materials are useful in electric and optical applications. We will discuss the fundamental characteristics of a few semiconductor materials that are important in optical applications. In this chapter, we will start with the AlGaAs because it possesses unique material properties. The AlAs and the GaAs have almost identical lattice constants, which indicates that the ternary AlxGa1-xAs compounds can be grown on the GaAs substrate with very little strain and hence a very small density of traps (caused by defects) at the interface can be expected. In addition to the AlGaAs, there are several semiconductor materials that have important application in the light emitting diodes (LED) and laser diodes (LD). We will focus on the InxGa1-xAsyP1-y/InP that is important in optical fiber communication (Chapter 4), the (AlxGa1-x)0.5In0.5P/GaAs that has important application in 570~670 nm (yellowish green to red) LED and LD (Chapter 5), and InxGa1-xN/Al2O3 that has important application in ultraviolet (UV) and visible LED and LD (Chapter 6). 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

The Problems of a Homojunction Semiconductor Laser In a traditional homojunction semiconductor laser, as in the case for every equilibrium p-n junction, the Fermi level is constant throughout the device with no current flow. When the junction is biased in the forward direction, the Fermi level splits because of the injection of minority carriers (electrons into the p region, holes into the n region) and there exists a region near the junction where there is simultaneously a high density of electrons and a high density of holes. Because of the much higher mobility of electrons compared to that of holes, most of the injection is by electrons into the p region. The electrons recombine with the majority holes after diffusing a distance, d ( 0.93 mm for GaAs). The (lateral) laser mode might extend over a larger distance than the diffusing distance d. In this situation, the central part of the laser mode experiences gain, whereas the edges experience loss. The simple p-n junction lasers have two major drawbacks: (1) the injected minority carriers are “free” to diffuse that dilutes the spatial distribution of recombination and thus the gain; (2) there is very little guiding and confinement of the electromagnetic wave being amplified. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Homojunction Semiconductor Lasers 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Band Gap and Refractive Index of AlxGa1-xAs The problems of the simple p-n junction lasers can be solved by the use of heterostructures to form the active portion of the laser. These are junctions between two dissimilar materials such as GaAs with AlxGa1-xAs, with x being the fraction of gallium being replaced by aluminum. For the AlxGa1-xAs, as the percentage of aluminum is increased (x), the band gap increases and the index of refraction decreases, and this asynchronous behavior is true for quaternary alloy combinations also. This fact is truly God’s gift to the semiconductor laser field, for it greatly alleviates the problems encountered by the homojunction lasers. The AlxGa1-xAs is a direct band gap semiconductor material when the aluminum composition, x, is smaller than ~0.45, and becomes an indirect band gap semiconductor material when x is greater than ~0.45. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

AlxGa1-xAs Semiconductor Materials Band gap is quite linear when 0  x  0.45. Refractive index is linear when 0  x  1. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Electronic and Optical Properties of DH Lasers p-type Layer Index n-type Layer ~0.2μm Undoped Active Layer Electrons Holes Band Gap Energy Light n1 n2 Conduction Band Mode Profile Valence Band Carrier Confinement Optical Confinement 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Double-Heterostructure Semiconductor Lasers Size of a Laser Diode  300 m (L)  200 m (W)  100 m (H) Laser Threshold: R1R2e2gL = 1 g = (1/2L) ln(1/ R1R2) If R1 = R2 = [(n-1)/(n+1)]2 = [(3.5-1)/(3.5+1)]2 = 0.3, Then g = [1/(230010-6)] ln[1/(0.30.3)]  4000 m-1 = 40 cm-1 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

AlxGa1-xAs Double-Heterostructure Semiconductor Lasers 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Quantum-Well Semiconductor Lasers A double-heterostructure laser consists of an active layer sandwiched between two higher-gap cladding layers. The active layer thickness is typically in the range of 0.1-0.3 m. If the double-heterostructure laser with an active-layer thickness of ~10 nm is fabricated, the carrier (electron or hole) motion normal to the active layer is restricted. As a result, the kinetic energy of the carriers moving in that direction is quantized into discrete energy levels similar to the quantum-mechanical problem of the one-dimensional potential well. Quantum-well lasers have many advantages: 1) laser wavelength can be varied by changing the well width, 2) lower threshold current, 3) higher quantum efficiency, and 4) narrower linewidth. If there is only one quantum well in the active layer, we call it a Single Quantum-Well (SQW) structure; if there are a few quantum wells in the active layer, we call it a Multiple Quantum-Well (MQW) structure. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Manipulating the Laser Wavelength by Varying the Thickness of the Quantum Well Lz   l  2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Eigenfunction and Eigenenergy in a Quantum-Well Structure For finite well: En becomes smaller 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Confined State Energy as a Function of Lz for GaAs/Al0.2Ga0.8As The region of band gap is not shown in this figure. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Quantum Size Effect on Density of States Previously, by assuming that all dimensions were huge compared to the deBroglie wavelength, we derived the density of states for a bulk semiconductor material: When the dimension is comparable to the deBroglie wavelength, the quantum size effect (QSE) becomes easily observable and the density of states changes to reflect the quantization of momentum perpendicular to the thin layer. It can be shown that the density of states is a constant independent of energy provided E is larger than the first allowed state E1, which in turn must be larger than the normal band edge of the semiconductor. Hence by choosing the the dimension of the quantum well Lz, one can “design” the energy state and thus “engineer” the band gap. Similar quantum effects occur in the valance band. Since it has both light hole (lh) and heavy hole (hh) (i.e., different effective masses) the positions of the subbands are also different. Transitions can occur between an electron state in the conduction band to either a light hole or a heavy hole state in the valance band. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Allowed Momentum Vectors in a Thin Semiconductor 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Density of States in a Quantum Well of Thickness Lz 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Density of States for Different Thickness Lz 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Strained Quantum-Well Lasers Quantum-well lasers have also been fabricated using an active layer whose lattice constant differs slightly from that of the substrate and cladding layers. Such lasers are known as strained quantum-well lasers. The strained quantum-well lasers show many desirable properties such as (i) a very low threshold current density and (ii) a lower line width both under continuous wave (CW) operation and under modulation (pulse operation). The origin of the improved device performance lies in the band-structure changes induced by the mismatch-induced strain. The figure shown in the next page shows the band structure of a semiconductor under compressive and tensile strain. Strain splits the heavy-hole and the light-hole valance bands at the G point of the Brillouin zone where the band gap is minimum in direct band gap semiconductors. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Band Structure of a Direct Band-Gap Semiconductor Under Stress 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Vertical-Cavity Surface-Emitting Laser (VCSEL) The major difference between a vertical-cavity surface-emitting laser (VCSEL) and an edge-emitting laser (EEL) lies in the fact that a VCSEL emits light in the direction along the axis of crystal growth. The VCSELs have symmetrical laser beams that have small divergent angles. Hence, when compared to the EEL, the light emitted by a VCSEL may be coupled into an optical fiber more effectively. VCSELs are of advantage in the application of 2D arrays for communication. There is no need for the VCSEL wafers to be cleaved and coated for device performance testing, which saves a lot of time in device characterization. Light emitting diodes (LED) have been used in some short-distance optical fiber communication systems. If the LED light source were replaced by a VCSEL, the operating distance and data transmission rate would be greatly enhanced. Since the packaging for both LED and VCSEL are almost identical, the substitution of a LED by a VCSEL in an optical fiber communication system is very cost effective. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Schematic Cross Section of a Surface-Emitting Laser 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Surface-Emitting Lasers with Distributed Bragg Reflectors (High-resistance region) (High-reflection mirror) (R < 1.0)  Laser Cavity (Laser power << 10 mW) p-spacer n-spacer Quantum-well region (R  1.0) CONTACT (for externally applied driving current) 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Reflectivity as a Function of the Number of DBR Pairs Pair number   R  n (= n1- n2)   R  2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Structures of GaAs-AlGaAs Surface-Emitting Lasers 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

InGaAs-GaAs SEL Structures with Transparent Substrates 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Multiple Interference of a Single-Layer Thin Film The reflectivity is maximum when where m is an odd integer. 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Schematic of a Bottom Emitting VCSEL Design 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Reflectivity Spectrum of a 20-Pair AlAs/GaAs DBR 0.98 mm 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Refractive Index Dispersion for AlGaInP, AlAs and GaAs 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Semiconductor DBR Mirrors Used in AlGaInP LEDs (Absorptive) 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

Reflectivity Spectra for Transparent and Lossy DBRs Transparent DBR Reflectivity can never approach to 1.0. Lossy DBR 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光

850-nm VCSEL 2003/09/15 半導體雷射講義-3 / 國立彰化師範大學物理系所暨光電研究所 / 郭艷光