Perspective Cite This: ACS Energy Lett. 2018, 3, 655−662 Fundamental Limitations of Wide-Bandgap Semiconductors for Light-Emitting Diodes † † ‡ § † Jun Hyuk Park, Dong Yeong Kim, E. Fred Schubert, Jaehee Cho, and Jong Kyu Kim*, † Department of Materials Science and Engineering, Pohang University of Science and Technology, 77 Cheongam-Ro, Nam-Gu, Pohang, Gyeongbuk 37673, Republic of Korea ‡ Department of Electrical, Computer, and Systems Engineering, Rensselaer Polytechnic Institute, 110 Eighth Street, Troy, New York 12180, United States § School of Semiconductor and Chemical Engineering, Semiconductor Physics Research Center, Chonbuk National University, Jeonju 54896, Republic of Korea ABSTRACT: Fundamental limitations of wide-bandgap semiconductor devices are caused by systematic trends of the electron and hole effective mass, dopant ionization energy, and carrier drift mobility as the semiconductor’s bandgap energy increases. We show that when transitioning from narrow-bandgap to wide-bandgap semi- conductors the transport properties of charge carriers in pn junctions become increasingly asymmetric and characterized by poor p-type transport. As a result, the demonstration of viable devices based on bipolar carrier transport, such as pn junction diodes, bipolar transistors, light-emitting diodes (LEDs), and lasers, becomes increasingly difficult or even impossible as the bandgap energy increases. A systematic analysis of the efficiency droop in LEDs is conducted for room temperature and cryogenic temperature and for emission wavelengths ranging from the infrared, through the visible (red and blue), to the deep-ultraviolet part of the spectrum. We find that the efficiency droop generally increases with bandgap energy and at cryogenic temperatures. Both trends are consistent with increasingly asymmetric carrier-transport properties and increasingly weaker hole injection as the bandgap energy of LEDs increases, indicating that fundamental limitations of wide-bandgap semiconductor devices are being encountered. uring the past 100 years, inorganic light-emitting diodes (LEDs) have undergone a significant evolution, A strong asymmetry between n-type from the very first visible LED based on SiC to today’s and p-type properties, such as doping Dffi ff highly e cient white LEDs, that resulted from a series of concentration, carrier injection, e ec- breakthroughs and advances in epitaxial growth of high-quality tive mass, and carrier mobility, would crystals, the employment of heterostructures, and advances in device architecture such as improved light out-coupling.1 pose a fundamental challenge to the Semiconductor material systems used for LEDs covering the efficiency of LEDs. visible spectrum include III-phosphides (AlGaInP) that are capable of emitting red, orange, amber, and yellow light and III- In an LED, a light quantum (photon) is generated when an nitrides (AlGaInN) for emitting green, cyan, blue, and violet electron in the conduction band radiatively recombines with a light as well as ultraviolet (UV) radiation. LEDs are being used hole in the valence band. Because radiative transitions in a in areas as diverse as indicators, signage, displays, and general semiconductor are from the conduction band minimum to the lighting. Furthermore, using efficient GaInN-based blue LEDs valence band maximum, the energy of the photon is in combination with a phosphor has enabled bright and energy- approximately equal to the bandgap energy of the semi- saving white light sources.2,3 Tremendous progress has been conductor. Quantum wells, frequently composed of two alloy made, as demonstrated by white LEDs with a greater than 200 semiconductors whose bandgap is tuned by varying the alloy lm/W efficacy, far exceeding the efficacy of traditional composition, enable good confinement for electrons and holes incandescent and Hg-discharge-based fluorescent lighting to the active region while emitting the desired color for light. It ffi devices. The future of white LEDs looks bright and is is apparent that the e ciency of an LED hinges on electrons flourishing, considering emerging and advanced applications such as smart and adaptive lighting sources, visible light Received: January 1, 2018 communication, and purification and disinfection using light Accepted: February 13, 2018 sources that are pleasant, healthy, and energy efficient.3,4 Published: February 13, 2018 © XXXX American Chemical Society 655 DOI: 10.1021/acsenergylett.8b00002 ACS Energy Lett. 2018, 3, 655−662 ACS Energy Letters Perspective and holes being injected into the quantum well active region. In inducing spatial separation between the electron wave function other words, a strong asymmetry between n-type and p-type and hole wave function,6 which makes radiative recombination properties, such as doping concentration, carrier injection, inefficient. Inspection of the figure also reveals that there is a effective mass, and carrier mobility, would pose a fundamental significant problem in the UV where the LED efficiency challenge to the efficiency of LEDs. Indeed, there is a decreases from >50% at the visible/UV boundary to values as pronounced trend in LED efficiency: As the bandgap energy low as 0.01−10% at 200−300 nm. The poor efficiency in the increases, i.e., as the wavelength becomes shorter, the external DUV is a clear indicator of a fundamental limitation quantum efficiency (EQE) of LEDs generally decreases; encountered with wide-bandgap semiconductors. furthermore, the efficiency droop problem becomes more First, we discuss a fundamental trend in asymmetric carrier severe. transport properties in semiconductors as the bandgap energy In this Perspective, we first discuss the fundamental trends of increases or the temperature decreases. The two-band Kane the asymmetric carrier transport properties in terms of electron model, based on the quantum-mechanical k · p perturbation and hole effective mass, dopant ionization energy, dopant theory,10 allows for the identification of general trends in the ionization, and carrier drift mobility as the semiconductor’s field of semiconductors.9 The model predicts a specific bandgap energy increases. We then show a wide range of dependence of the electron effective mass on the semi- ’ ff experimental results of high-quality GaAs infrared (IR) LEDs, conductor s bandgap energy, Eg. The electron e ective mass AlGaInP red LEDs, GaInN blue LEDs, and AlGaN deep- can be expressed as follows10 ultraviolet (DUV) LEDs. It is found that the efficiency droop ’ m 2 increases with the semiconductor s bandgap energy, consistent e =+ |⟨||⟩|ν 2 1 px c with increasingly asymmetric carrier-transport properties as well mmEeeg* (1) as increasingly weaker hole injection as the bandgap energy of LEDs increases. As the asymmetry in carrier transport increases, * ff where me is the free electron mass, me is the electron e ective the portion of electron current in the p-type semiconductor mass in the semiconductor, px is the momentum operator in the layer to the total LED current becomes larger due to increasing x direction, |c⟩ is the state at the conduction band minimum, fl 10 electron over ow, which results in the decrease of hole current and |ν⟩ is the light-hole state at the valence band maximum. in the p-type region and hence the hole injection into the Let us consider two limiting cases of the bandgap energy: multiple quantum well (MQW). Therefore, pn junction based First, consider a narrow-gap semiconductor or even a wide-bandgap semiconductor devices would be severely limited semiconductor with vanishingly small bandgap energy, i.e., Eg by fundamental p-type doping limitations. → 0. In this case, the right-hand side of eq 1 becomes very large Figure 1 shows reported EQEs of GaAs IR, AlGaInP and * fi so that me approaches zero. This trend is con rmed by GaInN visible, and AlGaN UV LEDs as a function of emission * − experimental values of me with narrow-direct-bandgap III V semiconductors (for example, InAs, with Eg = 0.354 eV, has an ff * e ective mass of me = 0.022me), and on the extreme side, graphene has a zero bandgap energy (Eg = 0.0 eV) as well as a ff * 11 zero e ective mass (me = 0.0me) near the Dirac point. Second, consider wide-bandgap semiconductors. For the limit of large-bandgap energies, the right-hand side of eq 1 * ≈ approaches 1.0, and thus, me me. This trend is consistent * − with experimental values of me of wide-direct-bandgap III V semiconductors: For example, AlN (Eg = 6.28 eV) has the largest electron effective mass among binary direct-gap III−V * 12 semiconductors (me = 0.33me). Accordingly, eq 1 predicts the theoretical trend that the electron effective mass increases as Eg increases, consistent with the well-known experimental * values of me of actual semiconductors. Figure 1. EQEs of AlGaInP- and GaInAs-based IR and GaInN- Additional guidance on the effective masses can be obtained based visible and AlGaN-based UV LEDs as a function of emission from the Kronig−Penney model that is based on quantum − wavelength, as reported in the technical literature.5 8 External mechanics considering the propagation of electrons in a one- quantum efficiencies of 780, 870, and 940 nm IR LEDs were dimensional potential,13 which allows valuable insight into the estimated through the operation current and light output power of carrier transport in semiconductors. Within the framework of commercially available unmounted LEDs. the Kronig−Penney model, electrons in lower-lying bands are necessarily subject to higher potential barriers and thus become − wavelength, i.e., bandgap energy of the semiconductor.5 8 In more spatially localized than electrons in higher-lying bands. the IR and visible regions, efficiencies are generally high, that is, The stronger localization manifests itself as a heavier electron greater than 50%. In the center of the visible region, a dip in the effective mass associated with lower bands. As a result, valence efficiency occurs that is known as the “green gap”. The green band carriers (holes) fundamentally have a heavier effective gap is well understood for both material systems, AlGaInP and mass than conduction band carriers (electrons).