- Email: [email protected]
Monte Carlo simulation of indium tin oxide current spreading layers in light emitting diodes
Thin Solid Films 515 (2007) 8660 – 8663 www.elsevier.com/locate/tsf
Monte Carlo simulation of indium tin oxide current spreading layers in light emitting diodes R.M. Perks a,⁎, J. Kettle b , A. Porch a , D.V. Morgan a a
b
Cardiff University School of Engineering, Queens Buildings, The Parade, Cardiff, CF24 3AA, United Kingdom Multidisciplinary Nanotechnology Centre, School of Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom Available online 5 April 2007
Abstract Transparent conductors such as indium tin oxide (ITO) are used in a range of optoelectronic devices. Such materials provide both the electrical interface with the semiconductor and a transparent window for the injection or extraction of photons. In AlGaInP surface emitting LED device structures, a particular problem is that of providing an efficient current spreading layer in order to ensure that electrons are injected across the whole of the active region. In this way, the light extracted can be maximised as it originates from the region below the transparent conductor rather than the contact metal. This paper describes a Monte Carlo simulation that can assist in the optimisation of current spreading and light transmission of ITO layers in LED devices. © 2007 Elsevier B.V. All rights reserved. Keywords: Light-emitting-diode; LED; Indium tin oxide; Monte Carlo; Semiconductor material; Optical transmittance; Sheet resistance; Mobility
1. Introduction Transparent, conducting thin films have been utilised in wide ranging applications; no more so than in optoelectronic devices [1,2]. The importance of effective upper surface current spreading in Light Emitting Diodes (LEDs), as well as the role that these transparent conductors play in the overall performance of such devices, has been widely reported for a range of LED material systems (see for example [3] for AlGaInP and [4] for GaN based devices). The material and geometrical properties of a current spreading layer are of fundamental importance in high efficiency, high power LED applications. For AlGaInP surface emitting LED device structures, a particular problem is that of providing an efficient current spreading layer in order to ensure that electrons are injected across the whole of the active region. In this way, the light extracted can be maximised as it originates from the region below the transparent conductor rather than the contact metal. This paper considers the performance of an LED (total light
⁎ Corresponding author. Tel.: +44 29 2087 6556; fax: +44 29 2087 4716. E-mail addresses: [email protected] (R.M. Perks), [email protected] (J. Kettle), [email protected] (A. Porch), [email protected] (D.V. Morgan). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.04.006
output) as a function of the three basic properties of the ITO current spreading layer, namely carrier (electron) concentration, n, carrier mobility, μ, and layer thickness, t. The LED device schematic is shown in Fig. 1. 2. Simulation and modelling of LED current spreading layers In 2004, Porch et al. [5] considered the material properties of transparent conducting thin films. This work described the ‘window of transparency’ in terms of the electrical properties of a given semiconductor (indium tin oxide (ITO) and related materials in this case). Specifically, this window is defined by two boundaries; namely the material band gap at short wavelengths (Eg = 3.75 eV for ITO) and the plasma edge at long wavelengths. The existence of the latter absorption edge is due to the substitutional n-type doping that arises during the growth of ITO thin films (Sn4+ in place of In3+ within the In2O3 lattice). The Mott criterion [6] sets this doping level for ITO at greater than 1019 cm− 3. Here, a degenerate free electron gas exists in the conduction band above the filled valence band. In this context, a simple Drude model can be used to illustrate the effect of n, μ, and ITO thickness, t, on both the sheet resistance of the current spreading layer as well as its optical transparency. As was concluded in [5], it is an increased mobility that gives
R.M. Perks et al. / Thin Solid Films 515 (2007) 8660–8663
Fig. 1. Schematic of the device simulated in this work and reported elsewhere [2,9].
rise to a lower sheet resistance without detriment to the transparency. A higher carrier concentration would pull the plasma edge towards shorter wavelengths, thus narrowing the transmission window. The effect of varying n, μ and t on the optical transmission of an ITO thin film on top of a bulk dielectric substrate (characterised by its refractive index alone) can be calculated using a simple thin film multiple reflection (TFMR) model, within which the Drude model is used to describe the dielectric function of the ITO layer. Since the light emitted from the LED is incoherent, light intensities (rather than amplitudes) are added to calculate the power reflection and transmission coefficients (R and T, respectively). Fig. 2 shows the optical transmission of an ITO layer as a function of layer thickness for normal incidence, incoherent light, at free space wavelengths of 380 and 790 nm (the extremes of visible light) as well as at 590 nm (the centre of the emission peak of AlGaInP devices [7]). Here, the substrate is refractive index matched to the ITO layer; thus the maximum transmission is limited by Fresnel reflection at the ITO – air interface. We have chosen a carrier concentration of n = 2 × 1020 cm− 3 (set sufficiently above the Mott criterion) and an electron mobility of 50 cm2V− 1 s− 1 to represent a technologically achievable optimal current spreading layer [8]. As the ITO layer thickness is increased, the transmittance decreases as expected due to the onset of free electron absorption, an effect which is more pronounced for longer wavelengths. This result, however, considers the optical properties of the ITO layer in isolation and not the current spreading properties. In order to fully appraise the ITO layer in LED applications, both the optical and electrical properties must be considered simultaneously. We have therefore incorporated the TFMR model into a Monte Carlo simulation described in more detail below. Recent work by Kettle et al. [9] and Perks et al. [10] describe Monte Carlo simulations of photon trajectories within LED structures. This combines the simple Transmission Line Model (TLM) of a current spreading layer with a Monte Carlo ray tracing simulation of light propagation through a multi layer
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light emitting device. This combination weights the probability of photon generation in the active region of an LED according to the radial current distribution; and furthermore, maps that spatial distribution of light emission from the active region through the device to the LED surface, taking into account light polarization, internal reflections and absorption. The spatial intensity distribution of the LED emission, as derived by the simulation, has been shown to agree well with measured LED emission profiles obtained with a charge coupled device (CCD) camera [9]. This earlier work has highlighted the effectiveness of the transmission line model of Morgan et al. [2] as well as the role of device geometry in influencing device efficiency. It is this aspect of device efficiency (or total light output) and how it relates specifically to the carrier concentration, mobility and thickness of the ITO layer, that will be explored next. For a device structure, we consider the AlGaInP material system with an ITO current spreading layer above the active region (see Fig. 1), the properties of this layer being characterised by its resistivity, optical absorption and refractive index. The statistical average of a large number of photon trajectories (108) is obtained, giving a measure of total light output from the device. Photons originate at random positions within the active region at random polarizations, weighted according to the radial current distribution (as defined by the TLM). Those photons that emerge from the confines of the device are counted towards the total light output. A probability of escape is determined for the polarization of the photon based on the transmission coefficient of both parallel and perpendicular components. Photons that remain inside through internal reflection or absorption at the metal contact, substrate or in the ITO layer itself, are not counted towards light output. Furthermore, this may be interpreted as a measure of external efficiency since the total number of photons generated in the
Fig. 2. Transmission as a function of ITO film thickness calculated for an ITO layer with n = 2 × 1020 cm− 3 and mobility μ = 50 cm2 V− 1 s− 1.
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R.M. Perks et al. / Thin Solid Films 515 (2007) 8660–8663
The results of this analytical approach to current spreading using the transmission line model of Morgan et al. [2], the TFMR model of Porch [5] and the Monte Carlo simulation of Kettle et al. [9], can now be extended to calculate the design curves for the optimisation of current spreading layers in LED devices. These calculations are summarised in the data shown in
Figs. 3 and 5; and are best understood in terms of a series of plots of total light output for a range of ITO layer thickness t, carrier concentrations n and layer mobilities μ. The product of these three quantities (nμt) may be regarded as a figure of merit for a given current spreading layer. However; it does not give an indication of the extent to which free electron absorption will dominate, hence the need for the overall simulation. Fig. 3 shows a series of individual curves for total light output as a function of carrier concentration. Each curve is at a different ITO layer thickness ranging from 1 nm at the front to 1μm at the rear. The data shown here has been calculated for the device structure shown in Fig. 1 at a constant drive current of Id = 20 mA and an ITO layer mobility of 50 cm2V− 1s− 1. Taking, for example, the rear curve at an ITO layer thickness of 1 μm, the variation in total light output may be explained as follows. At low carrier concentrations (n = 2 × 1016cm− 3), the LED has a modest light output (around 1000 arbitrary units (AU)) where the majority of the current injected into the device flows though the active region immediately below the p-contact with minimal lateral current spreading. The material, as defined by these parameters, displays poor current spreading characteristics. If this rear curve is now followed from left to right as the carrier concentration increases to n = 2 × 1020 cm− 3, the total light output reaches a maximum value (at around 36000 AU). At this point, the current spreading properties of the material are optimal for the given thickness. By further increasing the carrier concentration beyond this optimal value, a sharp fall off in total light output is observed. This is entirely due to the onset of free electron absorption in the ITO layer. Increasing carrier concentration beyond n = 4 × 1021 cm− 3, the LED output would appear almost completely extinguished by the now opaque current spreading layer. The dotted line on this figure defines a ridge of maximum output and represents an optimally designed layer, in terms of both n and t for a given mobility. Whilst, in technological terms, the ability to vary material thickness might be more practical
Fig. 4. Relationship between optimum thickness for a given carrier concentration. This data (squares) was derived from the ridge at maximum light output shown in Fig. 3. The solid line is a fit to the data points.
Fig. 5. Total light output, as a function of carrier concentration, plotted at incremental values of mobility from 20 to 100 cm2 V− 1 s− 1 (lines — front to rear). Circles represent the ridge at maximum light output.
Fig. 3. A series of individual curves (lines) for total light output as a function of carrier concentration, each curve describing a different ITO layer thickness and calculated for the device structure shown in Fig. 1. The circles highlight the ridge at maximum light output. The projection of this ridge line onto the horizontal plane is presented in Fig. 4.
active region is governed primarily by the injected or drive current Id and the effective current spreading of the ITO layer. 3. Results and discussion
R.M. Perks et al. / Thin Solid Films 515 (2007) 8660–8663
than varying carrier concentration, the potential gains in terms of LED performance, through optimising thickness for a given carrier concentration, are far greater. If this ridge is followed through the series of curves from the rear to the front (for decreasing ITO layer thickness) an optimal thickness may be therefore found for any given carrier concentration. This is highlighted by the design curve (for both n and t) shown in Fig. 4. This curve tends towards higher carrier concentrations for thin layers since the attenuation of the ITO layer is derived from the product of free electron absorption (governed by n) and layer thickness t. Since the simulations are run at discrete values of carrier concentration, there is a degree of uncertainty associated with the exact position of the peak intensity. Therefore, the graphs were imported into a spreadsheet program and curve fitted so that the position of the peaks could be determined manually. This was accurate to within approximately 20% of the actual value. Fig. 5 considers a similar set of curves in which the layer thickness is fixed at 250 nm and the mobility is varied. Here, the total light output, as a function of carrier concentration, is plotted at incremental values of mobility from 20 to 100 cm2 V− 1 s− 1 (front to rear). A consistent trend is observed where again, an optimal carrier concentration exists. The dotted line highlights the ridge of maximum output. What is significant, however, is the emergence of saturation in the total light output as mobility is increased. One of the key conclusions of Porch et al. [5] relates to the role of mobility in optimising the spreading layer sheet resistance. This work concluded that a reduced sheet resistance can be achieved by maximising the mobility (and hence increasing the figure of merit term (nμt)) without the penalty of reduced light output arising from free electron absorption (governed by n and t). It is worth noting at this stage, however, that in practical terms, the upper limit of ITO mobility is set at around 100 cm2 V− 1 s− 1 due to ionized impurity scattering [11]. A trend towards near perfect current spreading could be achieved if the dependence of carrier effective mass on carrier concentration could be minimised through impurity reduction via post deposition processes. For the carrier concentration and thickness concerned, no further material improvements are likely to be achieved. Further enhancements to device performance are thus limited to geometrical considerations as summarised in Schubert [12]. 4. Conclusions In summary, we have used a Monte Carlo ray tracing model to study the performance of ITO as a current spreading layer on
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AlGaInP LEDs. By using a simple thin film multiple reflection model, the optical absorption of ITO has been calculated. Furthermore, the effects of carrier concentration, layer thickness and mobility on total light output from the LED have been calculated. Whilst some of the results obtained have been consistent with previously published work, the saturation in device efficiency as a function of mobility has been highlighted. This trend towards optimal current spreading in ITO represents a material limit; subsequent improvements in efficiency are thus limited to geometrical considerations. More importantly, however, is the realisation that there is a complex interrelationship between n, μ and t. An optimised current spreading layer may be defined by a trajectory through a three dimensional parameter space with orthogonal axes of n, μ and t. By incorporating TLM and TFMR models into a Monte Carlo simulation, the inter-relationship between material and geometrical factors have been studied. Acknowledgements The authors would like to acknowledge the Multidisciplinary Nanotechnology Centre, School of Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom, for the PhD studentship for Mr Jeff Kettle. References [1] A. Porch, D.V. Morgan, R.M. Perks, M.O. Jones, P.P. Edwards, J. Appl. Phys. 96 (8) (2004) 4211. [2] D.V. Morgan, I.M. Al-Ofi, Y.H. Aliyu, Semicond. Sci. Technol. 15 (1) (2000) 67. [3] T. Gessman, E.F. Schubert, J. Appl. Phys. 95 (5) (2004) 2203. [4] X. Guo, E.F. Schubert, Appl. Phys. Lett. 78 (21) (2001) 3337. [5] A. Porch, D.V. Morgan, R.M. Perks, M.O. Jones, P.P. Edwards, J. Appl. Phys. 95 (9) (2004) 4734. [6] P.P. Edwards, M.J. Sienko, Phys. Rev. B 17 (6) (1978) 2575. [7] J. Kettle, R.M. Perks, P. Dunstan, Electron. Lett. 42 (19) (2006) 1122. [8] M. Buchanan, J.B. Webb, D.F. Williams, Appl. Phys. Lett. 37 (2) (1980) 213. [9] J. Kettle, R.M. Perks, Electron. Lett. 42 (9) (2006) 553. [10] R.M. Perks, A. Porch, D.V. Morgan, J. Kettle, J. Appl. Phys. 100 (Art. No. 083109) (2006). [11] J.R. Bellingham, W.A. Phillips, C.J. Adkins, J. Mater. Sci. Lett. 11 (1992) 263. [12] E.F. Schubert, Light Emitting Diodes, Cambridge University Press, ISBN 0-521-53351-1, (2003) Chapter 7.
Monte Carlo simulation of indium tin oxide current spreading layers in light emitting diodes R.M. Perks a,⁎, J. Kettle b , A. Porch a , D.V. Morgan a a
b
Cardiff University School of Engineering, Queens Buildings, The Parade, Cardiff, CF24 3AA, United Kingdom Multidisciplinary Nanotechnology Centre, School of Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom Available online 5 April 2007
Abstract Transparent conductors such as indium tin oxide (ITO) are used in a range of optoelectronic devices. Such materials provide both the electrical interface with the semiconductor and a transparent window for the injection or extraction of photons. In AlGaInP surface emitting LED device structures, a particular problem is that of providing an efficient current spreading layer in order to ensure that electrons are injected across the whole of the active region. In this way, the light extracted can be maximised as it originates from the region below the transparent conductor rather than the contact metal. This paper describes a Monte Carlo simulation that can assist in the optimisation of current spreading and light transmission of ITO layers in LED devices. © 2007 Elsevier B.V. All rights reserved. Keywords: Light-emitting-diode; LED; Indium tin oxide; Monte Carlo; Semiconductor material; Optical transmittance; Sheet resistance; Mobility
1. Introduction Transparent, conducting thin films have been utilised in wide ranging applications; no more so than in optoelectronic devices [1,2]. The importance of effective upper surface current spreading in Light Emitting Diodes (LEDs), as well as the role that these transparent conductors play in the overall performance of such devices, has been widely reported for a range of LED material systems (see for example [3] for AlGaInP and [4] for GaN based devices). The material and geometrical properties of a current spreading layer are of fundamental importance in high efficiency, high power LED applications. For AlGaInP surface emitting LED device structures, a particular problem is that of providing an efficient current spreading layer in order to ensure that electrons are injected across the whole of the active region. In this way, the light extracted can be maximised as it originates from the region below the transparent conductor rather than the contact metal. This paper considers the performance of an LED (total light
⁎ Corresponding author. Tel.: +44 29 2087 6556; fax: +44 29 2087 4716. E-mail addresses: [email protected] (R.M. Perks), [email protected] (J. Kettle), [email protected] (A. Porch), [email protected] (D.V. Morgan). 0040-6090/$ - see front matter © 2007 Elsevier B.V. All rights reserved. doi:10.1016/j.tsf.2007.04.006
output) as a function of the three basic properties of the ITO current spreading layer, namely carrier (electron) concentration, n, carrier mobility, μ, and layer thickness, t. The LED device schematic is shown in Fig. 1. 2. Simulation and modelling of LED current spreading layers In 2004, Porch et al. [5] considered the material properties of transparent conducting thin films. This work described the ‘window of transparency’ in terms of the electrical properties of a given semiconductor (indium tin oxide (ITO) and related materials in this case). Specifically, this window is defined by two boundaries; namely the material band gap at short wavelengths (Eg = 3.75 eV for ITO) and the plasma edge at long wavelengths. The existence of the latter absorption edge is due to the substitutional n-type doping that arises during the growth of ITO thin films (Sn4+ in place of In3+ within the In2O3 lattice). The Mott criterion [6] sets this doping level for ITO at greater than 1019 cm− 3. Here, a degenerate free electron gas exists in the conduction band above the filled valence band. In this context, a simple Drude model can be used to illustrate the effect of n, μ, and ITO thickness, t, on both the sheet resistance of the current spreading layer as well as its optical transparency. As was concluded in [5], it is an increased mobility that gives
R.M. Perks et al. / Thin Solid Films 515 (2007) 8660–8663
Fig. 1. Schematic of the device simulated in this work and reported elsewhere [2,9].
rise to a lower sheet resistance without detriment to the transparency. A higher carrier concentration would pull the plasma edge towards shorter wavelengths, thus narrowing the transmission window. The effect of varying n, μ and t on the optical transmission of an ITO thin film on top of a bulk dielectric substrate (characterised by its refractive index alone) can be calculated using a simple thin film multiple reflection (TFMR) model, within which the Drude model is used to describe the dielectric function of the ITO layer. Since the light emitted from the LED is incoherent, light intensities (rather than amplitudes) are added to calculate the power reflection and transmission coefficients (R and T, respectively). Fig. 2 shows the optical transmission of an ITO layer as a function of layer thickness for normal incidence, incoherent light, at free space wavelengths of 380 and 790 nm (the extremes of visible light) as well as at 590 nm (the centre of the emission peak of AlGaInP devices [7]). Here, the substrate is refractive index matched to the ITO layer; thus the maximum transmission is limited by Fresnel reflection at the ITO – air interface. We have chosen a carrier concentration of n = 2 × 1020 cm− 3 (set sufficiently above the Mott criterion) and an electron mobility of 50 cm2V− 1 s− 1 to represent a technologically achievable optimal current spreading layer [8]. As the ITO layer thickness is increased, the transmittance decreases as expected due to the onset of free electron absorption, an effect which is more pronounced for longer wavelengths. This result, however, considers the optical properties of the ITO layer in isolation and not the current spreading properties. In order to fully appraise the ITO layer in LED applications, both the optical and electrical properties must be considered simultaneously. We have therefore incorporated the TFMR model into a Monte Carlo simulation described in more detail below. Recent work by Kettle et al. [9] and Perks et al. [10] describe Monte Carlo simulations of photon trajectories within LED structures. This combines the simple Transmission Line Model (TLM) of a current spreading layer with a Monte Carlo ray tracing simulation of light propagation through a multi layer
8661
light emitting device. This combination weights the probability of photon generation in the active region of an LED according to the radial current distribution; and furthermore, maps that spatial distribution of light emission from the active region through the device to the LED surface, taking into account light polarization, internal reflections and absorption. The spatial intensity distribution of the LED emission, as derived by the simulation, has been shown to agree well with measured LED emission profiles obtained with a charge coupled device (CCD) camera [9]. This earlier work has highlighted the effectiveness of the transmission line model of Morgan et al. [2] as well as the role of device geometry in influencing device efficiency. It is this aspect of device efficiency (or total light output) and how it relates specifically to the carrier concentration, mobility and thickness of the ITO layer, that will be explored next. For a device structure, we consider the AlGaInP material system with an ITO current spreading layer above the active region (see Fig. 1), the properties of this layer being characterised by its resistivity, optical absorption and refractive index. The statistical average of a large number of photon trajectories (108) is obtained, giving a measure of total light output from the device. Photons originate at random positions within the active region at random polarizations, weighted according to the radial current distribution (as defined by the TLM). Those photons that emerge from the confines of the device are counted towards the total light output. A probability of escape is determined for the polarization of the photon based on the transmission coefficient of both parallel and perpendicular components. Photons that remain inside through internal reflection or absorption at the metal contact, substrate or in the ITO layer itself, are not counted towards light output. Furthermore, this may be interpreted as a measure of external efficiency since the total number of photons generated in the
Fig. 2. Transmission as a function of ITO film thickness calculated for an ITO layer with n = 2 × 1020 cm− 3 and mobility μ = 50 cm2 V− 1 s− 1.
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R.M. Perks et al. / Thin Solid Films 515 (2007) 8660–8663
The results of this analytical approach to current spreading using the transmission line model of Morgan et al. [2], the TFMR model of Porch [5] and the Monte Carlo simulation of Kettle et al. [9], can now be extended to calculate the design curves for the optimisation of current spreading layers in LED devices. These calculations are summarised in the data shown in
Figs. 3 and 5; and are best understood in terms of a series of plots of total light output for a range of ITO layer thickness t, carrier concentrations n and layer mobilities μ. The product of these three quantities (nμt) may be regarded as a figure of merit for a given current spreading layer. However; it does not give an indication of the extent to which free electron absorption will dominate, hence the need for the overall simulation. Fig. 3 shows a series of individual curves for total light output as a function of carrier concentration. Each curve is at a different ITO layer thickness ranging from 1 nm at the front to 1μm at the rear. The data shown here has been calculated for the device structure shown in Fig. 1 at a constant drive current of Id = 20 mA and an ITO layer mobility of 50 cm2V− 1s− 1. Taking, for example, the rear curve at an ITO layer thickness of 1 μm, the variation in total light output may be explained as follows. At low carrier concentrations (n = 2 × 1016cm− 3), the LED has a modest light output (around 1000 arbitrary units (AU)) where the majority of the current injected into the device flows though the active region immediately below the p-contact with minimal lateral current spreading. The material, as defined by these parameters, displays poor current spreading characteristics. If this rear curve is now followed from left to right as the carrier concentration increases to n = 2 × 1020 cm− 3, the total light output reaches a maximum value (at around 36000 AU). At this point, the current spreading properties of the material are optimal for the given thickness. By further increasing the carrier concentration beyond this optimal value, a sharp fall off in total light output is observed. This is entirely due to the onset of free electron absorption in the ITO layer. Increasing carrier concentration beyond n = 4 × 1021 cm− 3, the LED output would appear almost completely extinguished by the now opaque current spreading layer. The dotted line on this figure defines a ridge of maximum output and represents an optimally designed layer, in terms of both n and t for a given mobility. Whilst, in technological terms, the ability to vary material thickness might be more practical
Fig. 4. Relationship between optimum thickness for a given carrier concentration. This data (squares) was derived from the ridge at maximum light output shown in Fig. 3. The solid line is a fit to the data points.
Fig. 5. Total light output, as a function of carrier concentration, plotted at incremental values of mobility from 20 to 100 cm2 V− 1 s− 1 (lines — front to rear). Circles represent the ridge at maximum light output.
Fig. 3. A series of individual curves (lines) for total light output as a function of carrier concentration, each curve describing a different ITO layer thickness and calculated for the device structure shown in Fig. 1. The circles highlight the ridge at maximum light output. The projection of this ridge line onto the horizontal plane is presented in Fig. 4.
active region is governed primarily by the injected or drive current Id and the effective current spreading of the ITO layer. 3. Results and discussion
R.M. Perks et al. / Thin Solid Films 515 (2007) 8660–8663
than varying carrier concentration, the potential gains in terms of LED performance, through optimising thickness for a given carrier concentration, are far greater. If this ridge is followed through the series of curves from the rear to the front (for decreasing ITO layer thickness) an optimal thickness may be therefore found for any given carrier concentration. This is highlighted by the design curve (for both n and t) shown in Fig. 4. This curve tends towards higher carrier concentrations for thin layers since the attenuation of the ITO layer is derived from the product of free electron absorption (governed by n) and layer thickness t. Since the simulations are run at discrete values of carrier concentration, there is a degree of uncertainty associated with the exact position of the peak intensity. Therefore, the graphs were imported into a spreadsheet program and curve fitted so that the position of the peaks could be determined manually. This was accurate to within approximately 20% of the actual value. Fig. 5 considers a similar set of curves in which the layer thickness is fixed at 250 nm and the mobility is varied. Here, the total light output, as a function of carrier concentration, is plotted at incremental values of mobility from 20 to 100 cm2 V− 1 s− 1 (front to rear). A consistent trend is observed where again, an optimal carrier concentration exists. The dotted line highlights the ridge of maximum output. What is significant, however, is the emergence of saturation in the total light output as mobility is increased. One of the key conclusions of Porch et al. [5] relates to the role of mobility in optimising the spreading layer sheet resistance. This work concluded that a reduced sheet resistance can be achieved by maximising the mobility (and hence increasing the figure of merit term (nμt)) without the penalty of reduced light output arising from free electron absorption (governed by n and t). It is worth noting at this stage, however, that in practical terms, the upper limit of ITO mobility is set at around 100 cm2 V− 1 s− 1 due to ionized impurity scattering [11]. A trend towards near perfect current spreading could be achieved if the dependence of carrier effective mass on carrier concentration could be minimised through impurity reduction via post deposition processes. For the carrier concentration and thickness concerned, no further material improvements are likely to be achieved. Further enhancements to device performance are thus limited to geometrical considerations as summarised in Schubert [12]. 4. Conclusions In summary, we have used a Monte Carlo ray tracing model to study the performance of ITO as a current spreading layer on
8663
AlGaInP LEDs. By using a simple thin film multiple reflection model, the optical absorption of ITO has been calculated. Furthermore, the effects of carrier concentration, layer thickness and mobility on total light output from the LED have been calculated. Whilst some of the results obtained have been consistent with previously published work, the saturation in device efficiency as a function of mobility has been highlighted. This trend towards optimal current spreading in ITO represents a material limit; subsequent improvements in efficiency are thus limited to geometrical considerations. More importantly, however, is the realisation that there is a complex interrelationship between n, μ and t. An optimised current spreading layer may be defined by a trajectory through a three dimensional parameter space with orthogonal axes of n, μ and t. By incorporating TLM and TFMR models into a Monte Carlo simulation, the inter-relationship between material and geometrical factors have been studied. Acknowledgements The authors would like to acknowledge the Multidisciplinary Nanotechnology Centre, School of Engineering, Swansea University, Singleton Park, Swansea, SA2 8PP, United Kingdom, for the PhD studentship for Mr Jeff Kettle. References [1] A. Porch, D.V. Morgan, R.M. Perks, M.O. Jones, P.P. Edwards, J. Appl. Phys. 96 (8) (2004) 4211. [2] D.V. Morgan, I.M. Al-Ofi, Y.H. Aliyu, Semicond. Sci. Technol. 15 (1) (2000) 67. [3] T. Gessman, E.F. Schubert, J. Appl. Phys. 95 (5) (2004) 2203. [4] X. Guo, E.F. Schubert, Appl. Phys. Lett. 78 (21) (2001) 3337. [5] A. Porch, D.V. Morgan, R.M. Perks, M.O. Jones, P.P. Edwards, J. Appl. Phys. 95 (9) (2004) 4734. [6] P.P. Edwards, M.J. Sienko, Phys. Rev. B 17 (6) (1978) 2575. [7] J. Kettle, R.M. Perks, P. Dunstan, Electron. Lett. 42 (19) (2006) 1122. [8] M. Buchanan, J.B. Webb, D.F. Williams, Appl. Phys. Lett. 37 (2) (1980) 213. [9] J. Kettle, R.M. Perks, Electron. Lett. 42 (9) (2006) 553. [10] R.M. Perks, A. Porch, D.V. Morgan, J. Kettle, J. Appl. Phys. 100 (Art. No. 083109) (2006). [11] J.R. Bellingham, W.A. Phillips, C.J. Adkins, J. Mater. Sci. Lett. 11 (1992) 263. [12] E.F. Schubert, Light Emitting Diodes, Cambridge University Press, ISBN 0-521-53351-1, (2003) Chapter 7.