CHAPTER 2 PHYSICS OF LEDS

CHAPTER 2 PHYSICS OF LEDS 2.1 LIGHT EMITTING DIODE A light-emitting diode (LED) is simply a two terminal p-n junction diode, which emits light when forward bias is applied across the terminals. When an appropriate voltage is applied to the p-n junction, electrons are capable to recombine with holes in the active region and emits energy in form of photons. This phenomenon of emission of photons by electrons is called 'electroluminescence'. In 1907, H. J. Round first discovered the phenomenon of Electroluminescence in silicon carbide [67]. The wavelength of emitted light (color of light) are allied by the band gap energy of that semiconductor. Basically, light emitting chip consists of semiconducting material, doped with different types of impurities to obtain a p-n junction. In case of indirect band gap semiconductors (silicon or germanium), electrons and holes recombines non-radiatively, therefore, the direct bandgap semiconducting materials are generally used for the fabrication of HB-LEDs for lighting applications. 2.1.1 INTRODUCTION OF p-n JUNCTION DIODE p n junction is interface between p-types and n-type semiconducting material, which is building blocks of most of the electronic device The junction in between two type of material is generally non-conductive, which can further modulate by biasing. Under forward bias current can easily flow, whereas in reverse bias a little or no current flow across the junction of semiconducting material, which make this junction suitable for rectification and switching application. In the close proximity of an un-biased p-n junction as shown in Figure. 2.1, the electrons from n-type material diffuses towards p-side and recombine with holes, also holes from p-side diffuses toward n-side and recombine with electrons. Therefore, area near the p-n junction is depleted by free carriers, which is called 'depletion region'. In this region, no 27

free charge carriers are present, but small amount of charges due to ionized acceptors and donors are present there. So, a space charge region is created at interface due to donors from n-side and acceptors from p-side, which produce electric field and oppose the further diffusions of charges. The electric field generated across the junction, is given as [68]: 2.1 2.2 where N A and N D are the concentration of acceptor and donor atoms, respectively (all dopants are suppose to ionized, n= N D and p= N A ), n i represents intrinsic carrier concentration of the semiconductor and V D is diffusion voltage. The diffusion voltage or build in potential, forms a barrier at interface, so the free majority charge carriers (electron on n-side and holes on p-side) faces a barrier in order to reach other side of the neutral region containing opposite type conductivity. Figure. 2. 1: P-N junction under (a) zero bias, (b) forward bias [68] Width of depletion region, charge and diffusion voltage in depletion region are related by Poisson equation 2.3 [69]: 2.3 28

where, V represents diode potential and ℇ represents dielectric permittivity of given semiconductor. Depletion region is a non-conductive region, as a result, this region show high resistance and high resistance and high potential drop. So, external bias increases or decreases this V D, and as a result the reverse and forward bias, increases or decreases the barrier height respectively. 2.1.1.1 FORWARD BIAS Under forward bias the p-type material is connected with positive terminal, and the n-type is connected with the negative terminal of battery, and more holes from p-region and electrons from n-region pushes toward the junction. In this charge carriers are injected into the region containing same type material, as a result depletion width decreases and current flow increases. This extra charge carriers diffuse into the regions containing opposite type of conductivity, where they can eventually recombine with opposite type of carriers and emit photons [70]. 2.1.1.2. REVERSE BIAS In reverse bias, the p-type of junction is connected to negative terminal of power supply, so, holes at p-type and electrons at n-type material are pulled away from junction, and as a result the width of depletion region increases, which further increases the barrier voltage and causes a high resistance to flow of the charge carriers. This increase in resistance across p n junction causes low current to pass across the p n junction and the junction behaves like an insulator or dielectric. The strength of insulating region (electric field) increases with reverse-bias voltage and thus property of junction can be used in fabrication of variable capacitor. And above a certain critical value, the junction breaks down, and large current starts to flow across the junction, either by Zener or avalanche breakdown processes [70]. Both breakdown mechanism are non-destructive and reversible, as the amount of electric field can't reach up to the levels, at which the semiconducting material show any overheating or thermal damage. Shockley formulate the current voltage (I V) characteristics for a biased p-n junction as [71]: 29

2.4 where, D n, D p and τ n, τ p are the diffusion constants and minority-carrier lifetimes of electron and hole, respectively. A is cross-sectional area of junction and η is diode ideality factor. Ideality factor, η of any diode is the measure of, how easily a diode can follow an ideal diode equation. It is taken as 1 for Ge and 2 for Si [72]. At particular reverse biasing the junction current start saturating, the reverse biasing diode current start saturating, Is (reverse saturation current) which is represented by the preceding factor of exponential function in equation 2.5. Thus, the Shockley equation can be rewritten as [68]: 2.5 The I-V characteristics of p-n junction diode is shown in Figure. When the forward-bias conditions is applied and if diode voltage, V >> kt /e, then [exp (ev/kt) 1] exp (ev/kt). So, the Shockley equation under forward bias can be rewritten as [68]: ) 2.6 Figure. 2. 2: I-V characteristic curves [73] 30

2.1.2 LIGHT EMISSION FROM p-n JUNCTION Under forward bias, extra charge carriers present in the material diffuses into the other regions, where they recombine with opposite type of charge and emit photons. In an ideal device, the charge carriers are injected into active region (depletion region) of device and emit a photon either by spontaneous or stimulated emission. The energy of emitted photons equal to band gap energy E g, where kt<<e g. 2.7 where, E g is band gap of semiconducting material and λ is emitted wavelength. So, the wavelength of emitted light were depend on the band gap of material. There are several factors which effect this emission wavelength and intensity. 1. Distribution of charge carriers in active region 2.Generation and recombination of carriers 3. Direct and in-direct band gap materials 2.1.2.1 DISTRIBUTION OF CARRIERS IN ACTIVE REGION The active region of LED can be fabricated in two ways. 1. Homo-junctions and 2. Hetero-junctions 2.1.2.1.1 HOMOJUNCTION DEVICES In a homojunction devices, semiconductor interface occurs between similar band gap semiconducting material. When an electron and hole go through the space charge region they recombine, and a photon is emitted. So the depletion region plus diffusion length is total active region for light emission. The minority charge carriers are distributed over quite large distance in materials and their concentration decrease continuously as these charges diffuses further into the adjacent region. So, the recombination occurs over a large region of material. Also the minority carrier concentration is changing continuously, as a result number of radiative recombination decreases, which comes into conclusion that homo-junctions are not suitable for fabrication of high efficient LEDs. 31

2.1.2.1.1 HETEROJUNCTION DEVICE In 2000, Nobel Prize in physics was awarded to Herbert Kroemer and Zhores I. Alferov for fabricating semiconductor hetero-structures, which are currently used in highspeed semiconductor and opto-electronics devices [74-75]. In heterojunction semiconductor, two dissimilar semiconductors containing different band gap are sandwiched together, which make it suitable for fabrication of quantum wells in optoelectronic device. These quantum well devices show superior light emission as compared to homo-junctions. In a quantum well heterostructure, a narrow band gap semiconductor is sandwiched between two wide band gap semiconductor to create a energy well. Narrow band gap acts as well and wide band gap acts as barrier. All charge carriers in this structure are confined in quantum well region, and this well region is called active region of device. Also the confined carriers are not able to diffuse into the adjacent region due to presence of the high energy barrier layer. The thickness of active region/quantum well (where charge carriers confined and then recombines) is order of de-broglie wavelength of electron [76]. Therefore, fabrication of double hetero-structures requires a brilliant growth techniques to obtain a extremely thin and high carrier concentrations layer. Generally these quantum well structures are grown by epitaxial layer MOCVD and MBE techniques. Figure. 2.3 shows a band diagram of double hetero-structure based on quantum well structure. In this structure extremely thin (10 nm) low band gap material GaAs (1.43 ev) is sandwiched between two layer of AlGaAs, that forming a well spatially. Barrier Layer AlGaAs QW GaAs Figure. 2. 3: Double Hetero-structure 32

2.1.2.2 GENERATION AND RECOMBINATION OF CARRIER When an electron excite from valence band to conduction band, under influence of potential, light, or current etc, a electron-hole pair is created in the material. This process of creation of electron-hole pair is called generation process. But there is restoring process which go parallely with generation and dismisses electron-hole pair is called 'recombination process' [77]. 2.1.2.2.1 GENERATION When electromagnetic radiation falls on a semiconductor, it is divided into three parts, absorbed, transmitted and reflected [77]. The photon absorbed by semiconducting material cause electron excitation from valence band to conduction band, and electron-hole pairs are generated. 2.1.2.2.2 RECOMBINATION Recombination is reverse process of generation. Excited electron comes back in valence band from conduction band either by radiative process by spontaneous emission or stimulated emission of photon or by non radiative process by emission of photon. Generated charge carriers spend some time in excited state and then returns to ground state. The time spend by carrier in excited state is called lifetime of that carrier ( ), and this depends on excess carrier concentration and recombination rate. Two cases are commonly studied here [11]: (i) Low level injection (ii) High level injection The carrier generated in this process due to electromagnetic radiation is for less than majority carrier concentration. In low level injection assumption, lifetime of carrier are generally calculated for minority carriers. The process, by which carrier recombine inside semiconductor are categorized into two parts. 1. Radiative 2. Non-radiative Non-radiative recombination, which generally involve emission of phonon are further classified into four types. 33

1. Surface recombination 2. Auger transitions 3. Tunneling 4. Impact ionization 2.1.2.2.1 RADIATIVE RECOMBINATION Consider n 0 and p 0, the concentration of electron and hole in equilibrium condition. According to law of mass action [78]: 2.8 where n i is intrinsic carrier concentration. Excess carrier can be generated by absorption of light. n = +Δn (for electrons), p = +Δp (for holes) 2.9 where, Δn and Δp are the electron and hole excess carrier concentrations respectively. The increase and decrease of carrier concentration dependents up on recombination rate (R). And the recombination rate depends on number of charge carrier in conduction band (n) and number of empty state in valence valence band (p). So the recombination rate is given by bimolecular recombination equation [79]: R=Bnp 2.10 where, B is the constant of proportionality. In quantum well, charge carriers are confined in a spatial region due to presence of barrier layer. Suppose the thickness of quantum well is L and carrier densities in conduction band and valence band are n QW and p QW, respectively, so the effective carrier concentration is n QW /L and p QW /L for electrons and holes, respectively, then the bimolecular recombination equation for quantum well structure can be re-written as: 2.11 This equation shows an additional advantage of quantum wells. If thickness of quantum well is decreased, then carrier concentration increases and carrier lifetime decreases, as a result the number of radiative recombination increases. So, quantum wells 34

structure shows higher radiative recombination rate and is necessarily used for fabrication of efficient LEDs. 2.1.2.2.2 NON-RADIATIVE RECOMBINATION In non-radiative recombination electron and hole pair recombines non radiatively, and the energy liberated in this process goes to lattice (phonons). So, instead of emission of light, energy is used in heating of device. Thus, this type of recombination is not suitable for LEDs applications. Generally, two type of non radiative recombination process are studied for LEDs structure: SRH and Auger recombination's. 2.1.2.2.2.1 SHOCKLEY-READ-HALL (SRH) RECOMBINATION Shockley-Read-Hall non-recombination process occurs through trap centers, where electron present in transition level between bands, passes through a localized state. These states are created in between the band gap of material, due to impurities present in the lattice. This type of carrier capturing site inside the band gap is called deep-level traps [79]. Generally, phonon transitions occurs in the presence of these trap stats within the forbidden gap of the semiconductor and this process was first formulated by Shockley, Read and Hall. The rate of recombination R SRH is given by [11]: 2.12 2.13 2.14 where, and are the lifetimes of electron and hole. 2.1.2.2.2.2 AUGER RECOMBINATION Auger recombination is three particle recombination phenomenon, where, filling of an inner shell vacancy in the atom is attend by another electron/hole in same atom. When a core-electron is removed, it leaves a vacancy, and an electron present in higher energy shell fall into the vacancy, and as a result, energy is released. During recombination process, generally energy is released in form of photon, but sometimes emitted energy is directed to another excited electron, which jumps further deep into the conduction band. This excited 35

electron in deep conduction band is called an 'Auger electron' which will released its excess energy in term of phonons and fall to back to edge of conduction band. Auger recombination rate can be determined using equation [80]: 2.15 where, and are Auger coefficient for electrons and holes. 2.1.2.3 DIRECT AND IN-DIRECT BANG GAP MATERIALS 2.1.2.3.1 INDIRECT BAND GAP MATERIALS In case of indirect band gap materials as shown in Figure. 2.4, the edge of conduction band is shifted towards k vector in momentum space and the therefore no direct transition is possible. In such type of materials, an additional doping or level is required for radiative transition. This impurity form a shallow donor state near the edge of conduction band, and will capture the free electrons to provide the required momentum shift for the carrier recombination. This phenomenon of recombination of carriers through donor states is called an indirect recombination and generally this type of recombination's are nonradiative. Therefore, LED fabricated from non-direct band gap material show no/low photon emission. Figure. 2. 4: Indirect band gap material 36

2.1.2.3.2 DIRECT BANDGAP MATERIALS In the direct band gap materials as illustrated in Figure. 2.5, the minima of conduction band exists just above the maxima of valance band, so there is no net change in momentum when electron transit from VB to CB or CB to VB. So, the free electron present at the bottom of conduction band is able to recombine radiatively with the free holes present at the top of valance band, which results in spontaneous emission of photon, by the principle of energy conservation. Therefore, the direct bandgap semiconductors are generally used for the fabrication of light emitting device with higher efficiencies [81]. Figure. 2. 5: Direct band Gap Material 2.1.3 QUANTUM WELL LEDs LEDs based on quantum well structure are also called heterojunction/super-lattice LEDs. If the heterostructure are fabricated with sufficiently thin layers, then the quantum interference effects also appear prominently, in motion of the electrons. The most simplest quantum well structure consist of a thin layer of narrower band gap material inserted between two thicker layers of wider band gap semiconducting material as shown in Figure. 2.6. These type of structures are the key components for fabricating optoelectronic devices, in which the active region increase the power of electro-optical interactions by confining the charge carriers. In case of quantum well LEDs, the thickness of the active region is 37

comparatively less than de Broglie wavelength of electron in semiconducting material [82]. Thus, the carriers are confined in higher concentration in a very small region of quantum wells, so, the recombination probably increases and as a result the emission intensity increases. Periodic arrangement of quantum well structure as shown in Figure. shows further increase in emission intensity, because more carriers are captured in and, thus increase change of radiative recombination and this intensity further increases. Barrier Layer Quantum Well Figure. 2. 6: Quantum Well Structure 2.1.4 EFFICIENCIES Output efficiency of an optical device is given by: η Power = 2.16 Where P is the optical power emitted into the free space and IV represents the electrical power inputed to device. In case of an ideal LED, active region (quantum well) emits one photon, for every injected electron, so ideally every charge quantum particle should produce one light quantum particle, so an ideal active region in an LED has unit quantum efficiency [83]. But practically scenario is different. The quantum efficiency of LED can be classified into three types. 1. Internal Quantum Efficiency 2. External Quantum Efficiency 3. Extraction Quantum Efficiency 38

The internal quantum efficiency is defined as the ratio of number of photons emitted from the active region to the number of electron injected into LED per second [83]. 2.17 Where P int represents the optical power emitted from active region and I represents the injection current. Every photons emitted from active region (quantum well) should escape from LED die, and in case of ideal LED, all the photons emitted from active region, will escape to free space so the extraction quantum efficiency of ideal LED is unity. Meanwhile, in case of real LED, all the photons emitted in active region, will not escape to free space. Some of the photons will never escape or leave semiconductor surface, because, of refractive index fulfill, absorption, reflection coefficient R and T of material and interface. So the extraction quantum efficiency of light is different from internal quantum efficiency and is defined as the ratio of number of photons emitted into free space per second to the number of photons emitted from active region [83]: 2.18 where, P represents the optical power emitted into the free space. Extraction quantum efficiency hinders the output performance of LEDs and it should not exceeds beyond 50% limit for commercial device. The external quantum efficiency is defined as the ratio of number of photons emitted into free space per second to the number of electrons injected into LED [83]: 2.19 2.2 TECHNOLOGY COMPUTER AIDED DESIGN (TCAD) FOR OPTIMIZING LED S STRUCTURE To cope with today the development cost and competition in the semiconductor industries, TCAD methodologies are most extensively used for designing and analysis. TCAD will reduce the experimental cost, time and as well as resources. A lots of best tools are present in market which can be used now, to study and design more efficient LEDs. 39

Various problems in LEDs are now successfully solved using these simulation software's. These tools can be used to simulate band diagram, electron and holes transport in-side the structure, emission spectra, I-V curves, non radiative and radiative carrier recombination rate, electric field distribution etc. inside LEDs structure. Simulation software can also used to model one dimensional drift-diffusion equation, which can account for specific features of III-nitride materials like: strong piezoelectric effect, existence of spontaneous polarization, accepter activation low efficiency and very high threading dislocation densities. ATLAS from M/s SILVACO, APSYS, SiLENSe, MEDICI from M/s Synopsis, BIPOLE3 (Bipsim), G-PISCES (Gateway Modeling) and. DESIS (ISE Integrated System Engineering) are some software's, which are most commonly used for designing III-Nitride LEDs. Atlas from M/s Silvaco is powerful tools for simulation of III-V group based LEDs. Two types of simulation models are generally use to study the LED structure: physical and empirical model. ATLAS from M/s SILVACO is a physical-based device simulator. It predict the electrical characteristics, which are associated with specified physical structures and bias conditions. Whereas empirical models provide efficient approximation and interpolation. They do not provide insight, or predictive capabilities, or encapsulation of theoretical knowledge. Physically-based simulation has become very important mainly for two reasons. (i) it is quicker and cheaper than performing experiments. (ii) it provides device insight, which is difficult or impossible to measure. A physical based simulation software is generally used to solve a set equation, to obtain the current voltage (I-V) characteristics under different biasing condition. The set of equation solved by simulator software consist of Poisson s Equation, Maxwell equation, carrier continuity equations and transport equations [84]. 2.2.1 POISSON S EQUATION Poisson s Equation relating the electrostatic potential to space charge density is given by [84]: 2.20 where ε is the local permittivity, V is the electrostatic potential, and ρ is the local space 40

charge density. ATLAS, takes intrinsic Fermi potential (V i ) as a reference potential. The local space charge density includes the contributions of all mobile and fixed charges, such as electrons, holes, and ionized impurities. The electric field in region is calculated by: 2.21 2.2.2 CARRIER CONTINUITY EQUATIONS The continuity equations for charge carriers are defined using equations [84]: 2.22 where p and n are the hole and electron concentration, q is electron's charge on, 2.23 and holes. are the generation rate, current density and recombination rate for electrons and 2.2.3 THE TRANSPORT EQUATIONS Generally, carriers are charge particles, and motion of these particle leads to current in device. The current density and charge transport equation are normally found by approximating and simplifying Boltzmann Transport Equation, which result in transport models like drift-diffusion model and Energy Balance Transport Model. The choice of generation and recombination models also play an important role in selecting these transport models. Drift-Diffusion charge transport model is simplest model and is generally used to study the transport of carrier inside semiconductor. The drift-diffusion transport approximation is not much valid in case of smaller feature sizes [84]. So, advanced energy balance transport equation is generally used for the simulation of deep sub-micron devices. ATLAS from M/s SILVACO features both the drift-diffusion transport equation and advanced energy balance transport equation. The feature size of LED die is around 1x1 mm 2 so, drift-diffusion model are generally used for studying the carrier transport inside these LED devices. 2.2.3.1 DRIFT-DIFFUSION TRANSPORT EQUATION Carriers generally/commonly diffuses from high concentration regions to low 41

concentration regions due to the concentration gradient and these diffusion produces an electric current called diffusion current. Macroscopic electric current which is associated with mobility is called drift current. When external voltage is applied on a semiconductor then the corresponding electric field due to V, can affect movement of carriers or in average electrons will drift along the direction opposite to the electric field. The current density expressions: J J n n n n p p p p 2.24 where n and p are quasi Fermi potentials, 1 n E q 1 p E q FN FP 2.25 The conduction and valence band edge energies are written as: E E C V q( ) 0 q( ) 0 g 2.26 where 0 is some reference potential, is the position dependent electron affinity and E g is the position dependent band gap. Now 0 can be written as, r ktl NCr 0 ln ; q q n E ktl N 0 ln q q n ir r g Vr ir 2.27 where n ir is the intrinsic carrier concentration of the arbitrarily selected reference material, and r is the index that indicates all of the parameters are taken from reference material. Fermi energies are expressed as, 42

n EFN EC ktl ln ktl ln n N n EFP EV ktl ln ktl ln p N C V 2.28 The final terms in above equations are due to the influence of Fermi Dirac statistics. These final terms are defined as follows: F1/2 ( nn ) n nn e F1/2 ( np ) p np e EFN EC 1 n nn F1/2 ktl Nc n E E p V FP 1 p F1/2 ktl Nv 2.29 where Nc and Nv are position dependent terms and γ n = γ p = 1 for Boltzmann statistics. By combining Equations 2.24 to 2.29 the following expressions for current densities are obtained, ktl ktl N C Jn ktl n n q nn ln n ln q q q nir kt L g ktl N J p ktl p n q p p ln p ln q q q n V ir 2.30 2.3 STUDY OF EFFICIENCY DROOP PROBLEM IN InGaN/GaN LEDs BY ATLAS The controversial efficiency droop is a major problem which limits the performance of high brightness (HB) GaN LEDs at high injection current [85-89]. Shen et al. found that auger recombination due to non-radiative recombination of charge carriers in quantum well is a major cause of the efficiency droop [90]. Justin et al. analyzed the emitted electrons from p-n junction in vacuum and observed that auger electrons were generated under electrical carrier injection in InGaN/GaN LEDs [91-93]. Few other reports considered polarization charges or field as a major cause of the efficiency droop [94-95]. 43

The non-uniform distribution of holes in quantum wells, junction heating and electron overflows over active layers were also suggested by various groups as the cause of efficiency droop [96-97]. In case of heterojunction LEDs, electron and hole mobilities play an important role which is normally reduced by doping. Polarization doping has been considered as an alternate way to dope semiconductors. By varying the indium composition in InGaN layer, different polarization doping profiles can be achieved. Till now, the polarization doping was considered only in AlGaN/GaN high electron mobility transistors for providing a high concentration of two-dimensional electron gas (2-DEG) at the AlGaN/GaN interface [98-99]. Although, some authors used this type of doping in InGaN/GaN LEDs, and reduced the effect of piezoelectric polarization at InGaN/GaN interface. However, studies are limited only to achieving low resistance and highly doped p-gan and only few reports are available on the effect of doping on reducing efficiency droop [100-101]. Under this scenario, polarization doped active layer structures are proposed to improve the efficiency degradation in InGaN/GaN LEDs, which reduce the inbuild polarization and increase the distribution of charge inside the quantum wells resulting in lowering of spatial separation between electron and hole wave functions. This also enhances the radiative recombination over active region and thus the efficiency of InGaN/GaN LEDs increases. Also, IQE, band gap, emission intensity, and internal field are studied by ATLAS from M/s Silvaco, Santa Clara, CA, USA [102-104]. So, we have studied the effect of polarization doping on efficiency droop, which is the major problem faced by researchers. And by polarization doping we found the improvement in internal quantum efficiency of InGaN/GaN LEDs. For determination of the band diagram, internal quantum efficiency, current-voltage characteristics, emission spectra etc., one can set up serial computations in Simulation software to cover some range of the bias as well as for a given bias. On the other hand, calculation of carrier wave functions, emission spectra and gain spectra can be done using the known band diagram. Information of band diagram and distribution of charge carrier provides a good basis for optimum development of LED structure for new light emitting diodes. Properties of semiconducting material which can be used in fabrication of heterostructure is obtained from simulation result, which can also be stored in the number of 44

output files allowing a post processing analysis. For the present research work, ATLAS from M/s SILVACO has been used to study the III-N LED structure. Many input parameter in current simulation are taken from ATLAS library. Band gap of InN is considered as 0.7 ev in current work and the other input material parameter for InGaN/GaN LED, used in the study are listed in table 2.1. The polarization value (spontaneous/ piezoelectric) in GaN and InGaN are used through interface charge density. 2.3.1 STRUCTURE AND PARAMETERS FOR DROOP STUDY Table. 2. 1:Input material parameters used in simulation of InGaN/GaN LEDs Parameters Units InN GaN AlN Band gap (300K), E g ev 0.7 3.42 6.2 Band gap bowing parameter for Ternary, b ev 3.8 NA 1.3 Varshni parameter, ev/k 0.245 0.909 1.799 Varshni parameter, K 624 830 1462 Dielectric constant, 15.3 8.9 85 * Effective Mass of electron, m 0 0.12 0.2 0.32 m e * Effective mass of holes, m 0 0.17 1 0.417 m h Lattice Constant, a Ǻ 3.548 3.189 3.112 Elastic Constant, C 33 GPa 200 392 382 Elastic Constant, C 13 GPa 94 100 127 Spontaneous polarization, P sp C/m 2-0.042-0.034-0.09 Piezoelectric const., E 33 C/m 2 0.81 0.67 1.5 Piezoelectric const., E 31 C/m 2-0.41-0.34-0.53 GaN layer with a doping of 2x10 18 cm -3, five pairs of In 0.16 Ga 0.84 N/GaN multi-quantum wells with 7 nm thick GaN barriers and 3 nm thick InGaN quantum wells, a 20 nm thick Al 0.15 Ga 0.85 N electron blocking layer (EBL) and 100 nm thick Mg doped p-gan layer with 45

The LED structure studied here (Figure. 2.7), consists of 200 nm thick Si doped n-a doping of 2x10 19 cm -3. In the proposed polarization doped LED structure, five pairs of In 0.16 Ga 0.84 N (3 nm)/gan (7 nm) layers were replaced by 5 pairs of polarization doped InGaN layers with thickness 10 nm. The drift diffusion and incomplete ionization models were used to calculate current densities and charges in the device. The higher activation energy of Mg dopant in GaN (170 mev) causes the hole densities to be smaller than the actual Mg density [105-106]. Hole and electron mobilities at different fields were approximated by Monte Carlo simulations and feed into the simulator by C operations. p-contact p-gan (100nm), 2x10 19 cm -3 Al 0.15 Ga 0.85 N (20nm) [In 0.16 Ga 0.84 N/GaN (3nm/7nm)] x5 n-gan (200nm), 2x10 18 cm -3 (a) p-contact Substrate n-contact p-gan (100nm), 2x10 19 cm -3 Al 0.15 Ga 0.85 N (20nm) [InGaN (10nm)]x5 Polarization Doped n-gan (200nm) 2x10 18 cm -3 Substrate (b) n-contact Figure. 2. 7: Schematic cross-sectional diagrams of (a) basic LED structure (b) polarization doped LED structure. Polarization charges due to spontaneous and piezoelectric fields in layers and interfaces were included in simulation by calculating the compressive and tensile strain in the layer. A strained wurtzite three-band Chuang model based upon Kronig Penney modeling was used for calculation of gain and radiative recombination rates in InGaN/GaN 46

LEDs [107-108]. Shockley Read Hall (SRH) and Auger based models were also used for calculation of non-radiative carrier lifetime of minority carriers in active region. The lifetime of minority carriers in active region was calculated by the following expression: = + + 2.31 where, and are values of radiative, Auger, and SRH recombination lifetimes of the minority carriers, respectively. Gummel and Newton Raphson algorithms were used to solve coupled equations having linear and quadratic convergence, respectively. The structural, optical and electrical properties of materials used in the simulation were taken from the published data [109-113]. The schematic cross sectional diagrams of InGaN/GaN LED structures used in this study are shown in Figure. 2.1. Although, it is very difficult to grow the polarization doped InGaN/GaN LED structures, there are large reports available on the growth of polarization doped AlGaN/GaN structures for HEMT's applications by metal organic chemical-vapor deposition (MOCVD) and molecular-beam epitaxy (MBE) [114-116]. In our case, the polarization doping in InGaN/GaN quantum well LEDs can be accomplished by varying the In content in InGaN quantum wells, which was previously demonstrated by using the graded growth technique in MOCVD [117-119]. 2.3.2 RESULTS AND DISCUSSION The emission intensity versus wavelength of LED structures A, B, C and D are shown in Figure. 2.8. The peak emission intensity of polarization doped LED structure B is higher (1.6x10 18 cm -2 s -1 ) than conventional LED structure A (2.0x10 16 cm -2 s -1 ) which is due to increase in active region length. In conventional LED structure, the ratio of active region over total region is 3:10 (thickness of InGaN layer is 3 nm and InGaN QW + GaN barrier is 10 nm), whereas in polarization doped structure (active region thickness is 10 nm), this ratio increased to 10:10. Emission peaks of doped LED structures B, C, and D shifted towards higher wavelength which can be due to variation of indium compositions in active region. This shift can be increased considerably by changing the doping profile. The red shift in peak emission wavelength and an increase in emission intensity can be used for the fabrication of InGaN/GaN HB blue/green LEDs and laser diodes. 47

Figure. 2. 8: Emission intensity versus wavelength for conventional and polarization doped LED structures. The inset in the Figure. represents the emission intensity in log scale of LED structures A and B. Figure. 2. 9: Normalized IQE versus current densities for conventional and polarization doped LED structures. The inset show un-normalized IQE for doped and un-doped structures. The normalized IQE versus current density of conventional structure A and polarization doped LED structures B, C, and D are shown in Figure. 2.9. Polarization doped LED structures show improvement in efficiency droop which can be explained by studying 48

the band diagrams of LED structures A and B which are shown in Figure. 2.10 (a) and (b) for 0 ma/cm 2 and 290 ma/cm 2, respectively. For comparison, the band structure of p-n junction LED diode is also plotted in the Figure. 2.10 (a). Figure. 2. 10: The energy level diagram of a conventional LED structure A and polarization doped LED structure B at (a) 0 ma/cm 2 and (b) 290 ma/cm 2. In basic p-n junction LED, recombination occurs over a large region, whereas in quantum well structures, carriers are confined in higher concentration in a very small region (quantum wells). So, the probable number of recombination increases in quantum wells. In InGaN/GaN quantum wells, due to spontaneous and piezoelectric polarization, electron and hole wave functions are spatially separated (Stark effect) almost by the active layer length (3 nm) and it reduces the direct (radiative) recombination of carriers in active region. This 49

condition can be visualized as, recombination of carriers in indirect band gap semiconducting material (here momentum axis on the E-K diagram is replaced by position vector). The problem of indirect/spatial recombination of carriers increases if we forward bias the device. In polarization doped structure B, the spatial separation between conduction band minima and valence band maxima (electron and hole wave functions) has decreased to 35% of the active region length. This decrease in spatial separation increases the direct recombination of carriers in active layer which results in an increase in efficiency of the polarization doped structure. Moreover, due to polarization doping, a 2-DEG is accumulated just nearer to p-gan. So, the large number of electrons are accumulated just near to p-gan, which increases the radiative recombination from all quantum wells. Figure. 2.11 (a) and (b) shows the emission intensity of polarization doped structure (B) and conventional LED structure (A). In conventional LED structure A, most of the emission (1.8x10 16 cm -2 s -1 ) is from first quantum well, which is next to p-gan. However, very low emission is obtained from second (1.4x10 15 cm -2 s -1 ), third (7.3x10 13 cm -2 s -1 ), fourth (2.0x10 14 cm -2 s -1 ) and fifth (4.6x10 14 cm -2 s -1 ) quantum wells. In the polarization doped structure B, second (5x10 17 cm -2 s -1 ), third (4.2x10 17 cm -2 s -1 ), fourth (2.2x10 17 cm -2 s -1 ) and fifth (6.7x10 15 cm -2 s -1 ) quantum wells are emitting luminescence which is comparable to the emission from first (5.3x10 17 cm -2 s -1 ) quantum well. So, the net emission from polarization doped structure is higher than the conventional LED structure A. It was found that, for a conventional LED structure A, the IQE decreased to 90% at very low injection current density of 238 ma/cm 2, whereas for polarization doped LED structures B, C, and D, the efficiency decreased to 90% at 6330 ma/cm 2, 1753 ma/cm 2 and 362 ma/cm 2, respectively. It can be seen clearly that structure B shows the highest improvement in efficiency droop (25%) which is because of the large (15%) average Indium concentration in the quantum well, whereas the variation in indium composition is small (10% to 20%). In case of LED structures C and D, the average Indium composition is small (12.5% and 10%, respectively), but the variation is very large (from 5% to 20% and 1% to 20%, respectively). So, the efficiency droop can be seen at a low current density in structure D as compared to structures B and C. When the indium composition variation is 50

smaller in the quantum well, the effect of piezoelectric polarization is low and hence the efficiency is high. Figure. 2. 11: Emission intensity from different quantum well versus wavelength of: (a) conventional LED structure A and (b) polarization doped LED structure B. Figure. 2.12 shows the IQE of reverse polarization doped LED structures E, F and G. Similar type of improvement in efficiency droop was observed in reverse polarization doped LED structure, E. The IQE of structure E decreased to 90% at 260 ma/cm 2, whereas LED structure F, shows same efficiency variation as for conventional LED structure A. But, for the structure G, the efficiency decreased to 90% at a very low current density of 44 51

ma/cm 2. This controversial result of reduction of efficiency with reverse polarization doping in structure F and G is still unexplainable. Efficiency droop can be further improved by doping the electron blocking layer (EBL). Figure. 2. 12: Normalized Internal Quantum Efficiency for conventional and reverse polarization doped LED structures. Figure. 2.13 shows the IQE versus current density for polarization doped EBL structures H and I. The structure H shows improvement in efficiency droop. The efficiency of structure H is reduced to 80% at a current density of 1319 ma/cm 2, whereas for basic LED structure A, efficiency is reduced at 659 ma/cm 2. This improvement in efficiency droop can be explained on the basis of band diagram, shown in Figure. 2.14. In structure H, the electrostatic field is reduced at GaN/AlGaN interface due to linear grading of Al composition (0% 15%). Therefore, the efficiency of structure H increases, whereas in structure I, where Al composition is varied from 15% to 0%, the efficiency decreases to 80% at 506 ma/cm 2 which can be due to barrier tunneling. The EBL became triangular in this case. The improvement in efficiency droop in proposed structures are listed in Table I. Maximum improvement of 25.6 % is obtained in LED structure B whereas, structures with doped EBL show maximum improvement of 1%. 52

Figure. 2. 13: Normalized IQE for conventional and polarization doped EBL LED structures. Figure. 2. 14: Energy level diagrams for conventional and polarization doped EBL LED structures at 0 ma/cm 2. 2.3.3 ELIMINATION OF EFFICIENCY DROOP IN HB-LED STRUCTURE InGaN/GaN LEDs show large efficiency droop, which can be reduce by polarization doping. By doping active region of LEDs, the efficiency droop can be reduced by 25%, whereas by doping the EBL, the efficiency droop can be further reduced to 1%. 53

This improvement in efficiency droop can be directly correlated with the length of the active region, average Indium composition and variation of Indium composition in active region. In these structures, a high density electron gas is accumulated nearer to top p-gan layer which resulted as an increment in the emission intensity from second, third, and fourth quantum wells. It is observed that problem of efficiency droop in InGaN/GaN LED can be reduced up to a certain limit, but cannot be eliminated completely. So, here we search together for an alternate material which show similar light emission and put with no efficiency droop. ZnO is also a wide and direct band gap semiconductor, contains large exciton binding energy and wurtzite crystalline symmetry. The structural, optical and electrical properties of ZnO are similar to GaN, so, GaN can be easily replaced by in InGaN/GaN by ZnO. Hence, in further research, we studied the ZnO/GaN hybrid material based LED system to see and solve the problem of efficiency droop in GaN LED. 2.3.4 ZnO/GaN BASED HYBRID LED STRUCTURE The proposed hybrid LED structure as shown in Figure. 2.15 consist of 200 nm Al doped n-zno layer (n ~ 1.0x10 17 cm -3 ), 7 nm Cd doped ZnO layer (quantum well), 5 nm ZnO layer barrier layer, 30 nm Al doped electron blocking GaN layer layer and 500 nm Mg doped p-gan layer (p ~ 1.0x1019 cm -3 ). Simulation parameters used in this study are taken from literature. The electron mobility and hole mobility are taken as 40 cm 2 /v/sec and 5 cm 2 /v/sec respectively and operational temperature is set to 300 K and others. Figure. 2. 15: Schematic cross-sectional diagrams of GaN/ZnO based hybrid LED structure. 54

Emission Intensity (a.u.) Normalized IQE (a) (b) 1.0 InGaN/GaN 0.8 0.6 0.4 0.2 10-6 10-3 10 0 Current Density(A/cm 2 ) 10 3 (c) (d) 4.0x10 16 3.5x10 16 InGaN/GaN 3.0x10 16 2.5x10 16 2.0x10 16 1.5x10 16 1.0x10 16 5.0x10 15 0.0 2.6 2.8 3.0 Energy (ev) Figure. 2. 16: (a) Internal quantum efficiency of CdZnO/ZnO LED structure, (b) Internal quantum efficiency of InGaN/GaN LED structure, (c) emission intensity of CdZnO/ZnO LED structure, and (d) emission intensity of InGaN/GaN LED structure. Internal Quantum Efficiency of CdZnO/ZnO and InGaN/GaN LED structure, are shown in Figure. 2.16 (a) and (b). InGaN/GaN LEDs with simulation structure as shown in Figure. 2.16 (b) shows a sharp droop in efficiency at 1A/cm 2 current density, but in CdZnO/ZnO hybrid LED as shown in Figure. 2.16 (a), no efficiency droop is seen even at high current density 6x10 3 A/cm 2 current density [120]. Figure. 2.16 a, b, c and d shows the IQE and emission intensity of CdZnO/ZnO, and InGaN/GaN LED structure, respectively. It 55

is found that the emission intensity of CdZnO/ZnO LED structure ( 10 22 Ev/cm 2 /sec) is also larger in comparison to InGaN/GaN LED structure ( 10 16 Ev/cm 2 /sec). So, CdZnO/ZnO hybrid structure show no efficiency droop and high emission intensity as comparison to InGaN/GaN LED, so in next part of our research work, we have studied CdZnO/ZnO structure for fabrication of HB-LED. 2.3.5 CONCLUSION In this chapter, we studied the physics of LEDs, TCAD tools and problem of efficiency droop in InGaN/GaN LEDs. ATLAS from M/s Silvaco was used for studying the efficiency droop problem and it is observed that the polarization doping can reduce droop to certain limit but not completely. So, in search of novel material for LED, we ended here with GaN/ZnO hybrid material system, which show similar type of light emission with no efficiency droop. This hybrid system can be tuned further to change the emission wavelength and output intensity. So, ZnO based hybrid material can be used as an alternate material for fabrication of intense and high efficient LEDs. 56