Modeling the Optical Response of Phonon-dressed
Contents
1. HOME rhosts file on all computers listed in the hostfile The HOME host1 E le eae rhosts file should contain the names of the comput host2 Example COM ers and your user name host3 Example COM A i host4 Example COM E For a user with user name tcaduser the HOME The simulation will be running on the 4 machines listed oscar sie above and will be started from host1 Example COM host1 Example COM tcaduser host2 Example COM tcaduser host3 Example COM tcaduser host4 Example COM tcaduser 2 Set the environment variable SILVACO_ MPI HOSTS to the full path name of the hostfile my hosts 3 In order to be able to connect to remote hosts with out being asked for a password for every simulation use RSA authentication Run shell ssh keygen t rsa Accept the default value for the file in which to store the key HOME ssh id_rsa and enter a passphrase If you prefer not to use a passphrase you can skip that part You can refer to the ssh documentation for more detailed information Next copy a file generated by ssh keygen shell cd HOME ssh shell cp id_rsa pub authorized_keys In order for RSA authentication to work you need to have the HOME ssh directory on all comput ers specified in the hostfile my hosts This might be already taken care of if your home directory is on a common filesystem If not copy the HOME ssh directory to your home directory on all computers in the hostfile There will be fou2. the donor trap density in the GaN buffer deter mines the substrate leakage current and the acceptor trap density in GaN buffer affects the threshold voltage and the maximum drain current The ALPHA parameter on the THERMCONTACT statement has an impact on the negative differential resistance at high current operation as well as the maximum drain current Figure 5 shows the breakdown characteristics and the im pact generation rate distribution calculated by using slow transient simulation 3 An increase of the gate current in cluding the base current is observed near breakdown and the value is of the same order as the drain current In addi tion it should be noticed that impact ionization occurs near the drain side edge of p GaN region These results indicate that breakdown voltage is dominated by the hole current into the base electrode through the p GaN layer Super HFET Wg 1mm Data from Super_IdVg10V log Drain Current A Figure 3 Simulated Id Vg characteristics of the GaN Super HFET The Simulation Standard Page 10 Super HFET Wg 1mm Data from multiple files Drain Current A MEN A 0 0 0 8 0 8 0 0 08 90980 A 8 Figure 4 Simulated Id Vd characteristics of the GaN Super HFET Conclusion We have successfully demonstrated Atlas device simu lation of a GaN based Super HFET using the polariza tion junction conc
3. 0 5 W cm in 4 steps SOLVE Bl lE7 LIL STEPSIO NSTEP 7 1 MULL Adding the Imult option will make the lit step a multi plier enabling a logarithmic sweep where the intensity is swept from 1e 7 W cm to 1 W cm in 7 steps 3 Wavelength Sweep SOLVE BEAM 2 LAMDA1 0 6 WSTEP 0 05 WFINAL 1 1 This will sweep the beam 2 wavelength from 0 6 um to 1 1 um in 50 nm increments 4 Transient Analysis To perform a transient optoelectronic simulation users should first perform a steady state simulation SOLVE Bl L B2 0 0 VGATE 1 2 The Simulation Standard Then the transient simulation can be initiated In this case a 1 us simulation It is evident that beam 1 has been switched off and beam 2 intensity is increased SOLVE B1 0 B2 1 TSTEP 1E 11 TSTOP 1E 6 This instantaneous change in intensity is a bit unrealis tic Users can also specify a ramp time for the change in intensity SOLVE B1 2 B2 1 5 RAMP LIT RAMPTIME 1E 9 ISTEP 1E 11 TSTOP 1E 7 Transient Simulation With Intensity Ramp Light intensity beam 1 W cm2 Light intensity beam 2 W cm2 sof H N Transient time s Figure 9 Beams 1 and 2 light intensities vs time on a lin log scale Light intensity is ramped over a 1 ns ramp time Beam 1 intensity is increased from 1 W cm to 2 W cm and Beam 2 intensity is increased from 0 5 W cm2 to 1 5 W cm Additional Information For additional in
4. We var we computed spectra for a ied the phonon cloud sizes from 1 on site vibron to 4 and noticed only small changes in the spectra which is expected due to the fact that g suppresses hopping expo nentially As was discussed in Section I two additional parameters are needed a band gap and a Stokes shift Here we used a band gap of 2 87 eV and an additional Stokes shift of 0 15 eV These parameters alone correctly reproduce the absorption spectrum below the peak and emission spectrum above the peak in particular the vi bronic structure peaks along the spectral backbone as shown in Figure 2 However high energy modes and the background dielec tric add additional featureless profile to the measured spectrum These are often modeled as highly broad ened extra energy levels We model these as Voigt line shapes Gaussian convolved with Lorentzian by using the parameter ADDSTATE on MATERIALS statement of the corresponding region The lineshape center is speci fied using EX ECEN or GS ECEN depending on whether the state is added to the 1 exciton or 0 exciton states re spectively The parameters EX HOMOBROADENING and EX INHOMOBROADENING must be used to specify the corresponding values of broadening in electron volts The extra lineshapes in the present calculation are cen tered at 3 2 and 2 4 eV with both the homogeneous and inhomogeneous broadening both set to 10 meV We now consider room temperature spectrum at 300 K
5. molecule in a vibrational state with one or more phonons These transitions give peaks in emission spectra progressing below the zero phonon line Finally the two yellow lines indicate excitations that occur due to thermal excitations of phonons in the ground state and the excited state at quasi equilibrium These transi tions are suppressed exponentially by the corresponding Boltzmann factors January February March 2014 As explained in the next section the zero phonon tran sition is almost invisible in most systems because the overlap of nuclear wavefunctions in the 0 and 1 exciton manifolds is much higher at intermediate phonon oc cupations This results in a difference in the location of peaks in the absorption and emission spectra known as the Stokes shift The Stokes shift in organics is driven both by the above mentioned overlap and by the reorganiza tion energy of the environment when an exciton is intro duced into it 7 21 23 The former is calculated in our model from the exciton phonon coupling and the latter is used as a parameter since it is impossible to calculate reorganization energy of an arbitrary environment In Section II we provide the theoretical background and discuss the salient aspects of computation of spec tra in our approach In Section II we discuss results of our computations for Alq and compare them with ex perimental data We then discuss simulation of a 3 layer OLED device based on Alq DC
6. molecule in volume Q Take the ratio to radia tive while substituting absorption cross section and fluo rescence spectrum kyr 3R f dwo4 w FP w w4 8rr J dwFP w Krad If we normalize F such that f dw Flow 1 or F w E w fik_ We now get the traditional formula 10 25 o LB E asen Ro ENR Krad 5 do 30 w F Krad January February March 2014 Atlas Simulation of GaN Based Super Heterojunction Field Effect Transistors Using the Polarization Junction Concept Introduction Wide bandgap semiconductors such as SiC and GaN have attracted much attention because they are expected to break through the material limits of silicon In particu lar AIGaN GaN HEMTs are generally promising candi dates for switching power transistors due to their high electric field strength and the high current density in the transistor channel giving a low on state resistance Field plate FP technologies are generally used in or der to manage surface electric field distribution of GaN HEMTtTs Recently GaN Super Heterojunction Field Ef fect Transistors Super HFETs based on the polarization junction PJ concept have been demonstrated 1 2 This concept is based on the compensation of positive and negative polarization charges at heterointerfaces such as AlGaN GaN to achieve similar effect to RESURF or Su per Junction SJ in silicon devices In this article we will demonstrate the Atlas device simu
7. the emission spectrum of a thin Alq film exhibits no vi bronic structure and is left as a smooth profile shown in Figure 3 In this calculation we used larger inhomo geneous broadening of 150 meV and did not use extra January February March 2014 Voigt lineshapes to account for the background dielectric Thus a combination of 2 parameter Holstein model and a broad extra energy level can be used to successfully reproduce experimental spectra for this material We remark that the size and the occupancy of the phonon clouds are not free parameters as both these should be increased until the results converge B Light emission from Alq3 DCJTB based OLED We now demonstrate the ability to apply this model in simulating a typical 3 layer OLED The left panel in Figure 4 shows the structure of the device simulated The device is composed of a 30 nm wide emission layer EML with the host Alq3 doped to 1 with DCJTB At the top of EML is a 30 nm thick electron transport layer ETL of pure Alq3 and at the bottom is a hole transport layer HTL with material properties corresponding the a NPD The main energy level requirements to make this device emit are as follows The LUMO levels of the ETL and EML are aligned to facilitate electron injection into the EML while that of the HTL is about 300 meV higher Thus HTL essentially acts as an electron blocking layer and maximizes recombination of electrons with holes in the EML Similarly
8. the host to dopant emission wavelength The Simulation Standard Page 6 Figure 6 shows the average number of radiative transitions F rster transfers and Langevin recombinations per unit vol ume per time The Forster rate exceeds radiative rates for each species and thus we expect the dopant to make signifi cant contribution to the output spectrum of light The large F rster rate is due to a good overlap between the absorption spectrum of the dopant and emission spectrum of the host as displayed in the left panel of Figure 7 At the final bias point of 7 V we performed a reverse ray trace analysis to compute the light output by the device The resulting spectrum is shown in the right panel of Figure 7 The output spectrum is clearly dominated by emission from the dopant while the emission from the host contributes the smaller peak on the higher energy side Thus the effect of Forster transfer on the emission spectrum is captured quite well by the simulation rad Alq3 EML rad DCJTB EML Forster EML 4 amp langevin EML 3 4 Anode Voltage V Figure 6 The radiative emission rates Forster transfer rates and Langevin recombination rates per unit volume as a function of bias voltage Vertical scale 1 cm amp January February March 2014 DCTB Absorption DCJTB Emission Alq3 Emission 3 2 Energy eV 1 2 1 6 2 8 3 2 2 2 Energy eV Figure 7 Emission and abs
9. 9 2003 Y Zhao G Li J Sun and W Wang J Chem Phys 129 124114 2008 R Boyd Nonlinear Optics Academic Press 2003 M Muccini M Brinkmann G Gadret C Taliani N Mas ciocchi and A Sironi Synth Met 122 31 2001 M Brinkmann G Gadret M Muccini and C Taliani J Am Chem Soc 122 5147 2000 C C Lee M Y Chang P T Huang Y C Chen Y Chang and S W Liu Journal of Applied Physics 101 114501 2007 V G Kozlov V Bulovic P E Burrows M Baldo V B Khalfin G Parthasarathy S R Forrest Y You and M E Thompson J Appl Phys 84 4096 1998 The Simulation Standard 26 From experimental data linearity is implied by the pres ence of uniformly spaced peaks in both photolumines cence PL and photoluminescence excitation PLE spec tra The insensitivity to excitation follows from the spacing being the same in both PL and PLE spectra 27 This creates a feedback mechanism whereby one can create a strongly non linear dependence of the emission spectrum on bias However this is not generally seen in common materials and thus within the most common parameter regime of the model explored here 28 The technique requires too many Green function evalua tions to be useful when broadening is negligible The Simulation Standard Page 8 Appendix A Derivation of conventional formula for Forster radius Absorption cross section o aV N QY pghO O i Gas there is 1
10. D block Opti cal intensity at the surface illustrates that the beam window is 2 um by 1 um Displaying Multiple Rays As previously shown displaying rays via Ray Trace in TonyPlot 3D is a useful illustrative tool to show the beam It can also be helpful to increase the number of rays il lustrated in a structure This is set via the NX and NZ options in the BEAM statement Setting NX and NZ both equal to 3 results in a 3x3 array of beams displayed as shown in Figure 4 Theta 85 deg Optical Intensity W cm2 oe VICTORY Data from beam_on str Optical Intensity W cm2 Aa 70 5 Figure 5 Examples of THETA 95 top and 85 bottom to set Figure 4 Setting nx 3 and ny 3 in the BEAM statement results the angle relative to the xy plane Angle realative to the x axis in 9 rays to be illustrated in TonyPlot 3D can also be set via BEAM parameter PHI The Simulation Standard Page 12 January February March 2014 Important Notes Regarding Angle and Origin To get correct simulation results itis required thatthe BEAM origin be defined as a point outside your 3D structure De fining an origin within the structure is likely to produce in correct results Additionally careful thought must be taken when defining BEAM parameters for origin X ORIGIN Y ORIGIN and Z ORIGIN and angles phi and theta If BEAM parameters are incorrectly defined it can result in rays that are do not illuminate the 3D stru
11. INTTRAP statements in this Super HFET simulation Threshold voltage and substrate leak age current are controlled by a concentration of acceptor and donor traps in the GaN buffer layer respectively Moreover we put the interface traps to represent Fermi level pinning at the bottom of the GaN buffer This as sumption is properly valid because an actual GaN epi taxial layer has quite many defects around the interface with the substrate It should be noticed that these traps play an important role in the convergence of the device simulation including a floating undoped GaN buffer re gion The Simulation Standard Section 1 from Super_0 str Section 1 from Super_0 str 5 000 0 040 to 5 000 0 200 5 000 0 040 to 5 000 0 200 374 25 a N a alien nl lee Depth um Figure 2 Band diagram left and vertical carrier profile right under the base electrode Simulation Results and Discussions Figure 2 shows the band diagram and the vertical carrier profile under base electrode calculated at zero bias condi tion As reported in 2 the accumulation of 2DEG and 2DHG has been verified at the lower and upper heteroin terfaces respectively The simulation results of the Id Vg and Id Vd characteris tics are shown in Figure 3 and Figure 4 respectively Very good agreement between simulations and experiments were obtained by setting some parameters properly For example
12. JTB Finally we conclude in Section IV Il Methodology A Structure and Setup At the top level of the simulation in Atlas we solve the coupled rate equations for densities of electrons holes intrinsic excitons and dopant excitons see Section 15 3 of Atlas manual Ignoring the Stark effect 21 the energy levels of the molecules do not shift with bias and there fore we compute the optical response for unit density of both the intrinsic and dopant molecules separately at the beginning of the simulation At subsequent bias steps this spectrum is used to compute radiative loss of exci tons and coupling between the intrinsic and dopant sin glets fully self consistently with the quantum mechanical model of fluorescence The total fluorescence from each mesh node is computed by combining the spectra the exciton density on each node When used in conjunction with ray tracing transfer matrix or finite difference time domain algorithms the total fluorescence spectrum gives the angular and spectral characteristics of the light out put by the device 27 The simulation is setup by dividing a device into re gions and associating a material with each region We have extended the MATERIAL statement in Atlas to fa cilitate the addition of up to 10 different exciton spe cies per region An exciton polaron species is added by specifying the parameter ADDPOLARON and specifying a name for the species as MIX NAME name At present the rate equ
13. Simulation Standard Engineered Excellence A Journal for Process and Device Engineers Modeling the Optical Response of Phonon dressed Excitons in OLED Simulations Abstract We demonstrate the modeling of optical response of exciton polarons based on the well established Holstein Hamiltonian to model coupled exciton phonon systems in organic molecular chains Our approach uses Green s functions to compute the density of states and the linear optical susceptibility and thus eliminates the conventional and computationally expensive step of diagonalizing a large Hamiltonian matrix We exploit this technique fur ther to focus exclusively on the optically active states when computing the linear optical response and significantly reduce the computational effort to construct the optical susceptibility In this article we demonstrate the compu tation of absorption and emission spectra of Alq at 4 2 K and at room temperature using our model Using the two parameters of the Holstein model the inhomogeneous broadening energies and a phenomenological reorga nization energy of the solute we obtain excellent fits to established experimental results We then use this model inside the larger simulation of a 3 layer organic light emit ting OLED structure composed of Alq Alg DCJTB and a NPD which are the electron transport emissive and hole transport layers respectively In our methodology we also couple the optical response into t
14. ach with regards to performance Simulation time can decrease by orders of magnitude e More resources are available to the simulation the user is not limited by the number of CPUs or the total amount of memory on a specific computer e This approach provides a way of using the resources within the network efficiently e For certain very large problems it might be the only feasible approach especially in cases when the amount of memory required exceeds the limits of any one available computer As problem size increases this becomes more and more relevant Figure 2 January February March 2014 Page 15 The Simulation Standard To set up the distributed computing feature for the You will be asked for a password or a passphrase if Silvaco TCAD applications on Linux you specified one above If you have an ssh agent ing th i h to th 1 List the names of the computers that will be used a ne ee oo E ADOS same computer the authentication will be done au thomatically You probably have ssh agent running already in a file You can use the Linux command hostname to get the name The name of the computer from which the simulation will be started should be placed first in the file Refer to ssh agent documentation for further infor mation how to launch ssh agent in case you don t Example have one running The hostfile is named my hosts and looks like this You will also need to have a
15. ann factors Computation of x w x wm by 2 and 3 is done by solving a series of linear systems By organizing the basis states according to whether they are dipole allowed or not we minimize the number of systems that must be solved The spectra are subjected to energy dependent inhomogeneous broadening in the end The power radiated per unit volume in energy interval E E AE by spontaneous emission is given by the imaginary component of x T ent E AE 14 W _ Jorien dE on E 4 il h J Ag E where f_ accounts for averaging over the random ori entations of the exciton dipoles in amorphous materials Thus the radiative rate normalized to 1 exciton per unit cell volume is 1 0 EE dE EX irem E 5 h3m hoy Jo em E In the case of doped materials the F rster transfer rate of rad a singlet from donor site D to acceptor A is 2 J AGN E OX Lem E y da 6 Sr Roh 6 Kaa From this formula we also compute the F orster radius which is inter molecular distance at which the non ra diative transfer equals the radiative decay of excitons Note that conventional formulas for Forster transfer use slightly different definitions for the spectra used in the overlap integral 6 See Appendix A for equivalence of k to conventional formula We now turn to results of our simulations with this model lll Results and Discussion A Spectrum of Alq Alq is one of the most important host mat
16. ap of the phonon clouds at the initial and final site in a hopping event The Simulation Standard The main benefit of using harmonic oscillator to model the vibrational modes is that Frank Condon factors can be computed analytically from the inner product of shifted oscillator wavefunctions Thus the two parameters J and g fully determine the effective mass of the polaron The same Frank Condon factors also determine the amplitudes and selection rules of optical transitions A fully cohrent exciton polaron in a lattice carries a defi nite momentum and the energymomentum relationship yields a set of exciton bands as a function of the momen tum k Since the photon momentum is negligible com pared to that of an exciton optically driven transitions occur only at k 0 We therefore compute only k 0 states and exploit the fact that large inhomogeneous broaden ing rather than band dispersion dominates density of states at k 0 This formulation of the DOS is also consis tent with assumptions underlying the hopping model of exciton dynamics simulated in Atlas C Radiative Emission and Energy transfer Following the standard treatment of dipole coupling be tween light and matter the Hamiltonian for the interaction of an exciton polaron with a plane wave electric field is Holt e Y E e d where the sum includes both positive and negative fre quencies and is the position operator A standard approach to compute absor
17. ations are limited to two species per node only Specifying the HOLSTEIN parameter for a particu lar region initiates the quantum calculation of optical re sponse for each species defined in the region Since the model described below does not depend explicitly on the spatial distribution of excitons a single model per January February March 2014 species is solved for each region rather than each mesh node This simplification is correct as long as spatial dis tribution of energy levels can be captured by inhomo geneous broadening When this cannot be justified it is best to divide up a region into smaller pieces over which we expect energy levels and their couplings to lie within inhomogeneous broadening Below we describe the Hamiltonian for quantum me chanical description of exciton polaron dynamics in an organic materials We then describe our computation of optical response and the main physical quantities calcu lated in the simulation B Exciton polaron states The fundamental description we use here for the exciton phonon system is given by the Holstein Hamiltonian H J gt abans al 41 2 al an g b bn g Eo Evib gt b bn n n 1 where a a annihilate and create an exciton at molecular site n respectively while b and bi perform the same func tion for phonons The parameter J is the hopping energy g is the exciton phonon coupling E is the band gap or the difference between the HOMO a
18. ctory Device how do I illuminate my 3D device in an opto electronic simulation A The 2 basic commands needed to illuminate a struc ture in Victory Device are BEAM and SOLVE A single or multiple BEAM statement s are specified containing the light source properties The SOLVE statement is used to execute a BEAM at a user defined optical intensity Top Down Blanket Illumination To perform a top down blanket illumination an example BEAM statement would be BEAM NUM 1 X ORIGIN 2 Y ORIGIN 2 Z ORIGIN 5 PHI 0 THETA 90 WAVELENGTH 0 5 SAVE RAYS Which specifies that beam 1 is a illumination of wave length 0 5 um that originates at xyz 2 2 5 and ap proaches the structure from the top at an angle of 90 to the xy plane The SAVE RAYS option will save the rays to any subsequent saved structure A SOLVE statement is then specified SOLVE Bl 1 Solves the structure with beam 1 applied at an optical intensity equal to 1 W cm The resulting structure is shown in Figure 1 Blanket Illumination Optical Intensity W cm2 at Figure 1 Top down blanket illumination of a 3D block The ray trace illustrates a beam origin of 2 2 5 The contour plot illus trates an optical intensity of 1 W cm at the top surface January February March 2014 Blanket Illumination From Bottom substrate Optical Intensity W cm2 Fak Figure 2 Bottom up blanket illumination of a 3D block The ray illustrates a beam ori
19. cture By review ing ray traces in the structure file via TonyPlot 3D users can correctly define their BEAM statement Ray Splitting If a user defined BEAM is going to intersect more than one material regions the ray will automatically be split This allows efficient calculation of ray interaction in materials with differing refractive indices Figure 6 illustrates how a single ray is split into two rays the first intersecting silicon and the second intersecting the aluminum Ray Splitting Materials H Silicon Figure 6 A single ray is split in two when intersecting different material regions such as Silicon and Aluminum Reflections at Material Interfaces By default no reflected rays are traced However users may want to account for ray reflection of the front sides or bottom of the 3D structure For example BEAM NUM 1 X ORIGIN 4 Y ORIGIN 2 Z ORIGIN 5 PHI 0 THETA 100 WAVELENGTH 0 5 SAVE RAYS XMIN 0 5 XMAX 0 5 ZMIN 0 5 ZMAX 0 5 REFLECTS 2 BACK REFLECT January February March 2014 BEAM with Reflections Optical Intensity W cm2 1 eri ee UDS Figure 7 Illustration of ray reflection at the back of structure The 3D silicon block is made transparent in TonyPlot 3D for visibility of rays will consider 2 reflections In this case only reflections with the back of the structure will be considered as the back reflect flag is active Front reflections and sidewall ref
20. eo Absorption Spectra 1 M Hoffmann Z G Soos and K Leo 237 2006 2 V Agranovich Excitations in Organic Solids Oxford 2009 3 M Hoffmann and Z Soos Phys Rev B 66 024305 2002 4 S Reineke M Thomschke B L ssem and K Leo Rev Mod Phys 85 1245 2013 5 L Hung and C Chen Mater Sci Eng R Reports 39 143 2002 6 M D Halls and H B Schlegel Chem Mater 13 2632 2001 7 O Gardens ed Trends in Optical Materials Nova 2007 January February March 2014 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 H Kanno N C Giebink Y Sun and S R Forrest Appl Phys Lett 89 023503 2006 Y Sun N C Giebink H Kanno B Ma M E Thompson and S R Forrest Nature 440 908 2006 T Forster Discuss Faraday Soc 27 7 1959 D Beljonne C Curutchet G D Scholes and R J Sil bey 113 2009 G D Scholes Annu Rev Phys Chem 54 57 2003 G Scholes and D Andrews Phys Rev B 72 125331 2005 A Khler and H B ssler Mater Sci Eng R Reports 66 71 2009 A Olaya Castro and G D Scholes Int Rev Phys Chem 30 49 2011 l Vragovi R Scholz and M Schreiber Europhys Lett 57 288 2002 Vragovi and R Scholz Phys Rev B 68 155202 2003 J T Devreese and A S Alexandrov Reports Prog Phys 72 066501 2009 N Karl Synth Met 133 134 64
21. ept This device has many factors of convergence difficulty such as large polarization charges and abrupt heterojunctions as well as the existence of a p GaN base region and a floating undoped GaN buffer region Owing to its sophisticated physical models At las has proved to be capable of ensuring well converged solutions with the device characteristics consistent with reference 1 It allows users to speed up the product de sign process and shorten the development period References 1 A Nakajima Y Sumida M H Dhyani H Kawai and E M S Narayanan GaN based super heterojunction field effect transistors using the polarization junction concept IEEE Electron Device Lett vol 32 no 4 p p 542 544 Apr 2011 2 A Nakajima Y Sumida M H Dhyani H Kawai and E M S Narayanan High density 2 D hole gas induced by negative polarization at GaN AlGaN heterointerface Appl Phys Express vol 3 no 12 p 121004 Dec 2010 3 State of the art 2D and 3D process and device simula tion of GaN based devices Simulation Standard July August September 2013 4 Atlas User s Manual Super HFET breakdown Vg 15V Wg 1mm Figure 5 Breakdown characteristics left and impact generation rate distribution in the GaN Super HFET right January February March 2014 Hints Tips and Solutions Q In Vi
22. erials used in OLEDs It is known to emit green light at wavelengths of approximately 530 nm In addition it is also one of the simplest applications of the model described above Frenkel excitons in Alq couple to the bending modes of the molecule where the exciton resides However the inter molecular hopping is weak and thus the vibra tional modes of Alq are expected to create small phonon clouds only The large inhomogeneous broadening gen erally render the vibrational modes unobservable in the emission and absorption spectra of Alq However in their experiments Brinkman et al were able to obtain this for crystalline Alq at 4 2 K 23 From their observations the authors concluded that the Huang Rhys factor g E 2 6 0 4 and E 0 065 22 23 Using the value g 1 6E in our model and setting the January February March 2014 Calc Absorption Calc Emission Expt Absorption x Expt Emission 2 6 2 8 3 3 2 Energy eV Figure 2 Comparison of the calculated Alq3 spectra to those measured at for the crystalline phase at 4 2 K The dots and crosses are digitized experimental data from 23 Homogeneous broadening was set to 10 meV and inhomogeneous broadening to 22 meV A single Voigt lineshape is added for both the emis sion and absorption to take into account the background dielec tric due to higher energy states hopping parameter J 0 1E y single Alq region using our model inside Atlas
23. es tend to be insensitive to the presence of an exciton and their coupling to the excitons is linear 26 The magnitude of the linear coupling gives a timescale for intra molecular relaxation The localized vibrational mode follows the exciton if the intra molecular relaxation is faster than inter molecular charge transfer 3 This effectively dresses the exciton with a phonon cloud creating a new quasi particle called an exciton polaron which has different transport and optical properties than the bare electron hole pair comprising the Frenkel exciton In our methodology we compute the optical properties for this composite quasi particle thus taking into account the strong phonon dressing exactly within the model of linear coupling Figure 1 summarizes the radiative transitions between vibrational modes of typical organic molecules The vi brational energy of the molecule defines a potential en ergy surface which can be approximated as a parabola in nuclear coordinates near equilibrium If no coupling to phonons existed in the molecule the emission and The Simulation Standard Page 2 lt Ww un o O a Figure 1 Schematic illustration of the fundamental optically driven transitions in the presence of exciton phonon coupling The vertical scale is energy and the horizontal scale is a set of generalized nuclear coordinates The lower parabola repre sents the potential energy surface of the electronic ground
24. formation including e User defined photogeneration models e Setting material optical properties e Defining multi spectral beams as well as in depth information on the topics presented here please consult the Victory Device and TonyPlot 3D manuals or your contact local Silvaco support office Call for Questions If you have hints tips solutions or questions to contribute please contact our Applications and Support Department Phone 1 408 567 1000 Fax 1 408 496 6080 e mail support silvaco com Hints Tips and Solutions Archive Check out our Web Page to see more details of this example plus an archive of previous Hints Tips and Solutions www silvaco com January February March 2014 Hints Tips and Solutions Q How do I run a simulation on a cluster of computers using the distributed computing feature A new feature that is introduced in Silvaco s TCAD ap plications allows the user to run a parallel simulation on a cluster of computers within a network Currently this feature is supported in the solution of lin ear systems using the PAM solver The PAM solver is a domain decomposition type solver which is parallelized with MPI message passing interface There are many advantages to using distributed com puting especially for large computationally intensive simulations e Splitting a large problem into smaller ones and computing them in parallel is clearly a superior appro
25. gin of 2 2 9 The contour plot illustrates an optical intensity of 1 W cm2 at the bottom surface Bottom up Blanket Illumination Alternatively if a bottom up blanket illumination is needed the BEAM statement would be BEAM NUM 1 X ORIGIN 2 Y ORIGIN 2 Z ORIGIN 9 PHI 0 THETA 270 WAVELENGTH 0 5 SAVE RAYS The beam origin is now below the structure at xyz 2 2 9 and approaches the structure from the bottom at an angle of 270 to the xy plane as shown in Figure 2 Beam Collimation Through a Window Users may also want to collimate the light source through a defined window This can be accomplished by includ ing min max values to the BEAM statement Note if min max is not specified the entire structure will be il luminated A BEAM statement of BEAM NUM 1 X ORIGIN 2 Y ORIGIN 2 Z ORIGIN 5 PHI 0 THETA 90 WAVELENGTH 0 5 SAVE RAYS XMIN 1 XMAX 1 ZMIN 0 5 ZMAX 0 5 will crop collimate the beam centered at x 2 y 2 through a is 2 um by 1 um window as shown in Figure 3 The Simulation Standard Non Normal BEAM Angles Collimated Beam Optical Intensity W cm2 Victory Device also allows simulation of beams at angles other than normal 90 to the device surface Modifying O75 BEAM parameter THETA statement will change the angle of approach relative to the xy plane as seen in Figure 5 0 5 Theta 95 deg Optical Intensity W cm2 FL TO Figure 3 1 Top down collimated illumination of a 3
26. he 2DHG through the top p GaN layer and is electrically connected to the gate by specifying COMMON parameter on the CONTACT statement January February March 2014 Section 1 from Super_0 str 5 000 0 040 to 5 000 0 200 g 3 2 E de Figure 1 Cross sectional diagram of a GaN Super HFET left and interface charge density under the base electrode right Atlas uses specific physical models and material param eters to take into account the mole fraction and doping of the AlGaN GaN system 3 We chose to model low field mobility using the ALBRCT model allowing the separate control of electrons and holes We selected a nitride specific high field mobility model by specify ing GANSAT N on the MODEL statement In order to take into account the relatively deep ionization levels for acceptors in p type GaN we set the INCOMPLETE parameter on the MODEL statement 4 In the simula tion of high current operation self heating effect may be important We set the LAT TEMP parameter on the MODEL statement to enable the heat flow simulation by the GIGA module As for the breakdown simulation an impact ionization model should be taken into account We can use the tabular Selberherr model with the build in parameters for GaN Performance of GaN device and convergence of its sim ulation can be significantly influenced by the presence of defects We introduced bulk and interface traps by setting DOPING and
27. he rate equa tions for exciton dynamics in addition to computing the spectrum of light output by the device Keywords Frenkel Exciton Phonon Organic OLED tris hydroxyquinoline Holstein model Optical emission Optical absorption Introduction Organic light emitting OLED and photovoltaic PV technologies are growing at a rapid pace Compared to the inorganic semiconductor based technology organics pro vide much simpler and cheaper fabrication methodolo gies With continuing research in this field a vast number of organic materials have become potential candidates for device applications and they generally exist in diverse Volume 24 Number 1 January February March 2014 forms ranging from crystalline phases to fully disordered solutions This provides a challenge for developing reliable and widely applicable models for understanding experi mental data and predicting device characteristics Yet the optical and transport properties of these materials can often be captured via models with one or more ex cited states excitons hopping on the underlying molecu lar lattice and linearly coupled to its internal vibrational modes 1 3 Each type of vibrational mode can in turn be modeled as a harmonic oscillator Here we describe a meth odology that exploits this fact to simulate exciton dynamics and light emission from OLEDs The primary purpose of this work is to provide a physically based model to compute the optical re
28. lation of GaN Super HFETs in comparison with the ex perimental data based on 1 2 Convergence difficulties in this simulation generally arise from the formation of large polarization charges and the use of abrupt hetero junctions with a Schottky gate as well as the existence of a p GaN base region and a floating undoped GaN region Atlas s sophisticated physical models properly account for all physical mechanisms inherent in a GaN Super HFET structure thereby ensuring well converged solutions with consistent simulation results Device Structure and Physical Models The Super HFET structure created by Atlas syntax is shown in Figure 1 The layer structure consists of an undoped dou ble hetero GaN AIGaN GaN structure with a p GaN cap layer The feature of the Super HFET structure is the pres ence of the 2 D hole gas 2DHG induced by negative po larization charge at the upper GaN AlGaN heterointerface as well as the 2 D electron gas 2DEG at the lower AlGaN GaN heterointerface The computation of 2DEG and 2DHG due to polarization effect was performed automatically dur ing the simulation with our built in model 3 The Super HFET has four electrodes source gate base and drain The source and drain electrodes form ohmic contacts to the 2DEG by setting their work function identical to the electron affinity of the AlGaN layer The gate forms a Schottky con tact to the AlGaN layer The base electrode makes an ohmic contact to t
29. lections can also be included as outlined in the Victory Device manual Figure 7 illustrates the reflections off of the back surface Multi Beam Illumination Simulation is not limited to a single beam as multiple beams can be defined Each beam is defined with a BEAM statement with unique properties BEAM NUM 1 X ORIGIN 4 Y ORIGIN 2 Z ORIGIN 5 PHI 0 THETA 100 WAVELENGTH 0 5 SAVE RAYS XMIN 0 5 XMAX 0 5 ZMIN 0 5 ZMAX 0 5 BEAM NUM 2 X ORIGIN 0 Y ORIGIN 2 Z ORIGIN 5 PHI 0 THETA 80 WAVELENGTH 0 5 SAVE RAYS XMIN 0 5 XMAX 0 5 ZMIN 0 5 ZMAX 0 5 Again a SOLVE statement is specified to solve both beam numbers 1 and 2 concurrently with intensities of 1 W cm and 2 W cm respectively SOLVE Bl 1 B2 2 Figure 8 illustrates both beams intersecting the structure surface The Simulation Standard Multiple Beams Optical Intensity W cm2 PZ ge Pal oS Figure 8 Two beams of different intensities 1 W cm and 2 W cm the structure surface Optoelectronic Simulation Modes A number of different optoelectronic simulation modes are available via the SOLVE statement 1 Discrete Solve SOLVE VGATE 1 2 B1 0 5 B2 1 The device structure will be solved at a static gate bias of 1 2 V with two beams illuminating the device of intensi ties of 0 5 W cm and 1 W cm 2 Intensity Sweep SOLVE B1 0 1 LIT STEP 0 1 NSTEP 4 The device structure will be solved with the beam inten sity stepped from 0 1 W cm to
30. n from phenoxide to the the pyridyl ring of a single molecule 6 7 Radiative recombination of excitons gives rise to lumi nescence In the absence of spin orbit coupling SOC photons are emitted only by singlets due to the optical selection rules Heavy metal impurities are increasingly being used to enhance radiative annihilation of triplets with SOC 4 8 9 One of the main attractions of using organic materials is that the color of emitted light can be easily controlled by doping with molecules of different band gaps 4 the relative population of excitons on each species determines the overall shift in the main emission wavelengths The transfer of excitons between the host and the dopant controls the relative populations and this transfer is fundamentally driven by Forster energy transfer 2 10 13 for singlets and Dexter transfer 2 14 15 for triplets In our methodology the radiative and transfer rates are computed from the quantum mechani cal model for the optical response of each species One of the most important aspects of Frenkel excitons in organic materials is their strong modification by the inter nal vibrational modes of the molecular units 1 3 16 20 These modes may vary from bending stretching or rota tional modes and they can range from being localized at one molecule to being spread out over an entire polymer chain Providing great simplification in modeling is the unifying aspect of these modes their energi
31. nd the LUMO levels see Figure 1 and E is the energy of a single excitation phonon of the vibrational mode The term proportional to 2 1 aligns the LUMO level and the band gap to the user specified value The band gap E plays no essential role in determining the eigenvalues and eigenstates of the system except for shifting the resulting spectrum by the band gap energy Note that the above form of the Ham iltonian does not make reference to the detailed spatial structure of the exciton and nuclear wavefunction That information has been absorbed into the parameters de scribed above Following Hoffman et al 3 we compute the energy spectrum of this Hamiltonian in the basis represented as In v where n represents exciton at site n and v an Vag Vi capes represents a phonon cloud with vo specifying the phonon occupation in the oscillator at site l y m The oscillator at the exciton site is shifted by amount g Figure 1 as dictated by 1 and we represent its occupa tion number by a different symbol v Thus by virtue of the dependence of phonon occupa tion on the location of exciton the state of the molecular distortion is coupled fully to the exciton The resulting Hamiltonian can be diagonalized using the Lang Firsov transformation 3 in which the system is described by exciton polaron whose hopping energy is given by J x F where where F are called Frank Condon factors and they are equal to the overl
32. ole transport layer of a NPD Right Current Voltage characteristics of 3 layer device intrinsic and dopant exciton densities Langevin recombination rates and the Forster exchange per unit volume In Figure 5 we show the density of host and dopant ex citons in the ETL and EML layers Good injection of car riers into the active region EML is apparent from the much larger magnitude of the densities in the EML For a given Forster radius following from the device spectrum the relative fraction of dopant excitons to host excitons is highly sensitive to the ratio of this radius to host dopant distance We set the inter molecular distance equal to 3 7 nm in these simulations corresponding to host density of approximately 4x10 cm The simulation yields a F rst err radius to be approximately 3 6 nm for exciton transfer to the dopant The radius is approximately 1 nm for the reverse process Thus exciton migration to the dopant is very nearly one directional 1 2e 14 Alq3 exciton ETL o Alq3 exciton EML DCJTB exciton EML le 14 8e 13 6e 13 4e 13 2e 13 4 Anode Voltage V Figure 5 Densities of excitons cm on Alq and DCJTB in the electron transport and emissive layers left Spectrum of light emitted from the EML layer right and computed using reverse ray trace with source terms restricted to the respective layers The larger density of excitons on DCJTB explains the overall shift in the spectrum from
33. orption spectra for the host Alq and the dopant DCJTB The good overlap between host emission and dopant absorption yields high Forster transfer rates The vertical scale on the left panel indicates the response from a volume of 1 molecular unit The vertical scale on the right panel is the power spectral density IV Conclusion We have implemented the calculation of OLED optical response using the Holstein Hamiltonian The shape of spectra is determined by only 2 parameters while the ad ditional parameters account for the position and scaling The computation is fully integrated with the LED device simulation in Atlas This integration is performed both at the level of light output coupling as well as at the deeper level of determining the radiative and excitation trans fer rates in exciton dynamics With the addition of Voigt lineshapes to model the background dielectric contribu tions we have demonstrated the model to fully capture the important physical features of measured spectra for Alq We demonstrated the full methodology of using this model in Atlas by simulating a typical 3 layer OLED device with a doped emissive layer We extracted the dynamical rates computed using our model within each region and verified that the relative magnitudes of the dynamical rates are well correlated with the main quali tative aspects of the emission and absorption spectra of the host and dopant molecules References 1 M Hoffmann Z G Soos K L
34. ption and emis sion spectra is in terms of the matrix elements of d taken between the exact eigenstates of exciton polarons This is an extremely expensive calculation since a very large num ber of phonon cloud states exist for a given modest size and phonon occupancy In addition since most of the states are optically forbidden their inclusion in the spectrum serves only as an additional broadening mechanism In our methodology we use a much faster Green function based method to compute the absorptive and emissive contributions optical susceptibility x w x wm respec tively In this method only the optically accessible states are referenced explicitly by the calculation while the presence of the remaining states appears as an additional broadening mechanism as is expected physically The technique is mathematically equivalent to exact diago nalization and becomes useful in the presence of suffi cient broadening as is the case for organic materials 28 With homogeneous broadening specified by n the sus ceptibility can be written as ezo bs Heth e Evib kBT Xal E 0 v d E H in d 0 v Z 2 eo Pe e N 0 Evo kpT Xem E lla d E H ir d lla x_____ tem Y Lal l 7 ll a m The Simulation Standard Page 4 where 0 is the density of molecules and N a is the num ber of phonons in the exciton polaron state Y and Z is the partition function normalizing the Boltzm
35. r files in the HOME ssh directory Galittan uections with the following permissions If you have hints tips solutions or questions to contribute please contact our Applications and Support Department FWT authorized_keys Phone 1 408 567 1000 Fax 1 408 496 6080 e mail support silvaco com Hints Tips and Solutions Archive Check out our Web Page to see more details of this example rw r r known_hosts plus an archive of previous Hints Tips and Solutions rw r r id_rsa pub Next ssh to each of the computers in the hostfile www silvaco com The Simulation Standard Page 16 January February March 2014 USA Headquarters Silvaco Inc 4701 Patrick Henry Drive Bldg 2 Santa Clara CA 95054 USA Phone 408 567 1000 Fax 408 496 6080 salesOsilvaco com www silvaco com Worldwide Offices Silvaco Japan jpsales silvaco com Silvaco Korea krsales silvaco com Silvaco Taiwan twsales silvaco com Silvaco Singapore sgsales silvaco com Silvaco Europe eusales silvaco com SILVACO
36. sponse with a small set of parameters Materials for which a widely accepted measured spec trum over the desired energies does not exist are a clear target application The model is also relevant for well known materials since the optical response for most organic systems varies widely due to their sensitivity to their environments and their contact with charge in jection layers in devices With a small parameter set in which parameters are related to fundamental physical mechanisms the present model calibrated against exper imental data acquires predictive value for exploring an entire class of devices For instance emissive layers with similar vibrational modes excitonphonon coupling and inhomogeneous broadening can fall within the range of a single model fit once to reliable experimental data Continued on page 2 INSIDE Atlas Simulation of GaN Based Super Heterojunction Field Effect Transistors Using the Polarization Junction Concept Hints Tips and Solutions SILVACO Our methodology applies to electroluminescent organic materials such as Alq DCM DCJTB etc which are gen erally a mixture of short chains of molecules or inde pendent units with random orientations for the dipolar charge excitations 2 4 5 Electrons and holes injected into these materials form Frenkel excitons in which both the electron and the hole reside on the same molecular unit For example in Alq3 the exciton forms by electron transitio
37. state 0 exciton and the upper parabola represents the potential en ergy surface of the first excited state containing 1 exciton The dashed horizontal lines indicate the quantized energy levels of the vibrational potential phonons Both energy surfaces are modeled using the same parabolic potential and thus the modes in each are those of a harmonic oscillator The wavefunctions in the upper level are shifted by amount g that parameterizes the exciton phonon coupling The peaks on the right schematically depict the emission red absorption blue and zero phonon line green absorption spectra will both consist of a single peak represented by the green line in Figure 1 called the zero phonon transition which is between 0 and 1 exciton states containing no phonons In the presence of coupling to phonons optical excitation creates both the exciton and its phonon cloud The blue line indicates transitions from the lowest vibrational state the only state at 0 K to 1 exciton state containing one or more phonons These transitions give a progression of uniformly spaced peaks above the zero phonon transition which merge into a single broad spectrum after inhomogeneous broadening is taken into account In the emission spectrum the phonon occupation of the ground state is probed The red line indicates lumines cence transition in which the exciton having achieved quasi equilibrium to its lowest energy state recombines and leaves the
38. the HOMO level of the HTL is only slightly above the HOMO level of the EML which fa cilitates hole injection while the HOMO level of ETL is much lower to block holes at the EML HTL interface We used the organic defect model described in Atlas User s Manual to simulate exciton transport in each layer The Holstein model was applied to ETL and EML for com puting the emission spectra and the radiative as well as Forster rates We used the Poole Frenkel field dependent mobility model with parameters taken from 24 The right panel in Figure 4 shows the typical current voltage relationship of an LED o o D O 0 7 Calculation e Experiment o D o o O A 02 lt 5 O LL S 0 jo gt lt D 99 o o N OQ DORSO 2 5 3 3 5 Energy eV o Figure 3 Comparison of the calculated Alq3 absorption spec trum to the measured spectrum for a thin film at 300 K The dots and crosses are digitized experimental data from 23 A single Voigt lineshape is added to take into account the background dielectric due to higher energy states The Simulation Standard erials 0 01 02 03 04 05 06 07 08 0 9 1 Microns Anode Current A o un o o o o W zo D L U 5 O u se O lt q 3 4 Anode Voltage V Figure 4 Left Structure of the three layer device with 30 nm electron transport layer with Alq3 30 nm emission layer with Alq DCJTB and a 40 nm h
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