Optical Ring Modulator with MIT Virtual Source ModSpec Compact Model

Transcription

1 Optical Ring Modulator with MIT Virtual Source ModSpec Compact Model Lily Weng 1 Tianshi Wang 2 Jaijeet Roychowdhury 2 Luca Daniel 1 Massachusetts Institute of Technology 1 University of California, Berkeley 2 March 31 st, 2017

2 ACKNOWLEDGEMENTS The developers would like to thank Cheryl Sorace-Agaskar and Zhan Su at MIT for discussion and supports on developing the Optical Ring Modulator model. i

3 CONTENTS Contents ii 1 Optical Ring Modulator Introduction Device Physics Models User defined parameters and Terminals Integration with MIT Virtual Source Model (MVS) Introduction User defined parameters An Example of model usage Testbench Simulation Flow Simulation result Bibliography 25 ii

4 C H A P T E R 1 OPTICAL RING MODULATOR 1.1 Introduction An optical modulator is a device that modulates a beam of light. A Siliconbased modulator is the key element to develop high speed optical links in both optical telecommunications and optical interconnects. It has the benefit of easy integration with CMOS technology and low cost, although it is less mature and more limited than III-V material modulator. There are three mechanisms for group IV materials (Silicon and Germanium) to achieve optical modulations: Electro-absorption, Electro-refraction, and Free carrier concentration variations effect [1]. In Electro-absorption, the material can be tuned to be absorbant or transparent by applying an electrical bias. However, Silicon is transparent when the wavelength is beyond 1.1 µm, and therefore this mechanism is not possible at telecommunication wavelengths such as 1.3 µm or 1.55 µm. The idea of Electro-refraction is modifying the optical properties of semiconductors with electrical field. The refractive index varies when an electrical field (E) is applied, and it is called the 1

5 CHAPTER 1. OPTICAL RING MODULATOR 2 Figure 1.1: The carrier-depletion-based silicon optical ring modulator. Pockels (Kerr) effect if the refractive index is linear (quadratic) in E. However, there is no Pockels effect in silicon and the Kerr effect has low refractive index changes (around for E = V/cm) at telecommunication wavelengths. On the other hand, the free carrier concentration variations effect [2] is widely used in silicon photonics because it is efficient to achieve optical modulation in silicon. There are numerous ways to achieve free carrier concentration variations, for example, carrier injection in PN diodes with forward bias, carrier accumulation in MOS capacitor, carrier plasma shift in bipolar mode field-effect transistor, carrier depletion in PN diodes with reverse bias, etc. The optical ring modulator presented here is a vertical junction resonant microring/disk modulator which can achieve high modulation speed, lower power consumption, and compact size [3], as shown in Figure 1.1. The modulation mechanism is based on carrier depletion in PN junctions with reverse bias, and the idea of why this works is described in the next section.

6 CHAPTER 1. OPTICAL RING MODULATOR Device Physics Carrier-depletion based Si modulator When we apply a reverse bias across a p-n junction, the depletion width changes. When the depletion width changes, the width of the p-doped, n-doped and intrinsic Silicon layers also changes. The p-n junction is used as a ring/disk waveguide to propagate light, and has its effective phase index. The effective phase index is related to the proportion of the p-doped, n-doped, pure Si sections and all of them have different refractive indices due to charge-carrier effect [2]. When the effective phase index changes, the optical resonance of the ring/disk shifts, and the shifted resonances affect light transmission. P-N junction Depletion Width The depletion width (W dep ) could be estimated using 2ɛ N A + N D W dep = (φ B +V ), (1.1) q N A N D where ɛ is the permittivity of silicon, ɛ = n 2 Si ɛ 0, (1.2) q is electron elementary charge (unit:c), N A is the carrier concentration of acceptor (unit: cm 3 ), N D is the carrier concentration of donor (unit: cm 3 ), V is reverse bias ( 0, unit: V), φ B is built-in potential (unit: V), whose equation is φ B = kt q ln(n AN D n 2 ), (1.3) i and k is Boltzmann constant (unit: JK 1 ), T is temperature (unit: K). Denote 2ɛ N A + N D W φb = φ B, (1.4) q N A N D

7 CHAPTER 1. OPTICAL RING MODULATOR 4 Figure 1.2: The cross section of the ring modulator. then we have W dep = W φb 1 + V φ B, (1.5) and the depletion width that is on p-doped side (W p ) and n-doped side (W n ) are N D N A W p = W dep,w n = W dep. (1.6) N D + N A N D + N A Assume the height of the vertical p-n junction waveguide is H, and the p- doped and n-doped section is the same size, we can calculate that the height of p-doped Si section is H 2 W p, depletion section is W dep, and n-doped Si section is H 2 W n, shown in Figure 1.2. Charge-Carrier effects The refractive index of silicon is affected by charge carriers injection ( N ) into an undoped Silicon sample, or removal of free carriers ( N ) from a doped

8 CHAPTER 1. OPTICAL RING MODULATOR 5 sample. This effect is called Charge-carrier effect. The experiment results show that n e,h = A e,h N B e,h e,h + jc e,hn D e,h e,h, (1.7) where N e is the change of free electron concentration and N h is the change of free holes concentration, both in the unit of cm 3, A e = , B e = 1.08, C e = , D e = 1.2, A h = , B e = 0.772, C e = , D e = 1.1. Ring Resonator A ring resonator can be designed as an optical filter with bus waveguides. The most basic optical ring filter consists of one bus waveguide and one ring resonator. The wave "resonates" in the ring when the perimeter of the ring is equal to a multiple integer of the wavelength 2πr = mλ 0,m, (1.8) where r is the average ring radius, m is mode number, and λ 0,m is resonant wavelength. The resonant wavelength is related to the effective phase index of the ring waveguide. Operation principle The key of the optical ring modulator is to use a reverse bias across p-n junction waveguide to change its effective phase index and result in a resonance shift of the ring resonator. Light modulation is achieved based on the resonance shifting. The idea is to operate at the ring s resonance frequency (with vbias = 0). When vbias = 0, we get an optical 0; while vbias = 1, we get an optical 1 because the resonance is shifted.

9 CHAPTER 1. OPTICAL RING MODULATOR Models From the above sections, we know that the carrier-depletion based ring modulator is essentially based on the two optical ring filters with two different resonance. The resonances are tuned by applying bias voltages. So, the optical ring modulator models are similar to the optical ring filter, but with voltage control on the ring resonator waveguide. In the following, we will present the modspec compact model and simulation results of an optical ring modulator. An optical ring modulator consists of two modules: Coupler module and Voltage-Controlled Phase shifter module, shown in Figure 1.3. Coupler Module A coupler is a four port device shown in Fig 1.4, which correspond to input light field E in1,e in2 and output light field E out1,e out2. The relations between input and output are E out1 = r E in1 j te in2 E out2 = r E in2 j te in1, (1.9a) (1.9b) where t is cross coupling coefficient, and r and t satisfies for an ideal coupler without coupling loss. r 2 + t 2 = 1 (1.10)

10 CHAPTER 1. OPTICAL RING MODULATOR 7 Figure 1.3: The modules of an optical ring modulator.

11 CHAPTER 1. OPTICAL RING MODULATOR 8 Figure 1.4: A coupler Voltage-Controlled Phase Shifter Module A phase shifter shifts the phase of input light field to output light field, as shown in Figure 1.5. The amount of phase shift is determined by the length of the ring L, propagation loss α, and effective phase index n e f f. The relation between output light field E out3 and input light field E in3 is E out3 = E in3 e αl e j 2πf Ln e f f c, (1.11) where c is the light speed in free space and n e f f is effective phase index. Note that now n e f f is related to external the voltage bias (V ), and therefore it is a function of voltage bias, i.e. n e f f (V ). Meanwhile, the effective phase index is also associated to the waveguide structure (W, H) and material properties (refractive index of the core and cladding). In general, it is hard to get a closed-form analytical solution for an arbitrary rectangular waveguide in terms of its geometry and material refractive indices. For a 3-layered rectangular dielectric waveguide, the effective index method is useful to compute an approximate solution of n e f f by decomposing the problem into three one-dimensional slab waveguides problem [4]. However, our p-n junction ring waveguide is a 5-layered structure, whose core is composed of a p-n function (3 layers) and cladding is silicon dioxide (2 layers). Therefore, an optical waveguide mode solver is needed to calculate n e f f.

12 CHAPTER 1. OPTICAL RING MODULATOR 9 Figure 1.5: A voltage-controlled phase shifter From the above sections, we know that we can calculate the height of each layer: the height of p-doped Si section is for the depletion section is H 2 W p, W dep, and n-doped Si section is H 2 W n, and that W p,w dep and W n are all functions of reverse voltage bias V. Therefore, we can use regression methods to obtain the relations of n e f f and V with the optical waveguide mode solver. The code to calculate the regression coefficient is provided, and the polynomial order is set to 3. We also provide codes to obtain the samples from mode solver, and the users only have to wrap around their mode solvers which can output the effective phase index given geometry and materials. If the users do not have access to any mode solvers, the following free online mode-solver could for instance be considered: Codes that help to

13 CHAPTER 1. OPTICAL RING MODULATOR 10 compute the structure and refractive indices with different bias voltage are also provided. Finally, the Coupler and Voltage-Controlled Phase Shifter module are cascaded together, and we have E in2 = E out3 E in3 = E out2, (1.12a) (1.12b) since the light propagates continuously at the intersection.

14 CHAPTER 1. OPTICAL RING MODULATOR User defined parameters and Terminals User-defined parameters Table 1.1: User-defined parameters Parameter Default Value Definition t 0.1 Coupling Coefficient α (1/m) attenuation constant L 4π 10 6 (m) Length of ring resonator W 0.40 (µm) Waveguide width H 0.24 (µm) Waveguide height T 300 (K) Temperature N A (cm[-3]) Doping level (Acceptor) N D (cm[-3]) Doping level (Donor) a zeroth order term in neff a first order term a second order term a third order term V 7 (V) Voltage Bias Terminals As shown in Figure 1.4 and 1.5, there are four terminals for a coupler (port c1 c4), and three terminals for a phase shifter (port p1, p2, e). The overall (explicit) terminals of an optical ring modulator will be three terminals, and they are port c1, c3, e because port c2,c4 will be connected to p1 and p2 respectively. The external voltage can be defined in the transient simulation (e.g. a periodic pulse signal) and send to port e. As will be introduced in the next section, we

15 CHAPTER 1. OPTICAL RING MODULATOR 12 will use an inverter circuit to drive the phase shifter, which will not be an ideal pulse signal anymore.

16 C H A P T E R 2 INTEGRATION WITH MIT VIRTUAL SOURCE MODEL (MVS) 2.1 Introduction MIT virtual source model is a semi-empirical model describing the current and voltage characteristics of a short-channel metal-oxide-semiconductor field-effecttransistor (MOSFET), where the current and charges are functions of its terminal voltage. The symbol of MVS and its current and charges representation are shown in Figure 2.1. In 2014 and 2015, Dr. Shaloo Rakheja and Dr. Dimitri Antoniadis has published compact models for MVS in Verilog-A format [5]. The readers are referred to [5] for more details about MVS model. After the Verilog-A MVS model was published, a MVS model in ModSpec was developed based on hand-translation from the Verilog-A model by Berkeley team shortly. For more details about the ModSpec MVS model, readers are encouraged to use the help command in MAPP to look up the examples. The inverter circuit with MVS MOSFETS is shown in Figure 2.2. The inverter 13

17 CHAPTER 2. INTEGRATION WITH MIT VIRTUAL SOURCE MODEL (MVS) 14 Figure 2.1: The MIT VS model [5] Figure 2.2: An inverter circuit with MVS MOSFETs.

18 CHAPTER 2. INTEGRATION WITH MIT VIRTUAL SOURCE MODEL (MVS) 15 Figure 2.3: ORM with MVS interver circuit. circuit is used to drive the optical ring modulator. In our previous release of Optical Ring Modulator Modspec model, we use the ideal pulse functions to drive the modulator. For now, we consider a more realistic situation and use the inverter circuit as external voltage driver for the optical ring modulator, as shown in Figure 2.3.

19 CHAPTER 2. INTEGRATION WITH MIT VIRTUAL SOURCE MODEL (MVS) User defined parameters Table 2.1: User-defined parameters, MVS v1.0.1 Parameter Default Value Definition Type 1 nfet Type = 1, pfet Type = -1 W 1e-4 (cm) Transistor width Lgdr 80e-7(cm) Physical gate length dlg 10.5e-7(cm) Overlap length including both source and drain sides Cg 2.2e-6(F/cm 2 ) Gate-to-channel areal capacitance at the virtual source etov 1.3e-3 (cm) Equivalent thickness of dielectric at S/D-G overlap delta 0.10(V/V) Drain-induced-barrier-lowering (DIBL) n0 1.5 Subthreshold swing factor Rs0 100 [Ω-um] Access resistance on s-terminal Rd0 100 [Ω-um] Access resistance on d-terminal Cif 1e-12 [F/cm] Inner fringing S or D capacitance Cof 2e-13 [F/cm] Outer fringing S or D capacitance vxo 0.765e7 [cm/s] Virtual source injection velocity Mu 200 [cm 2 /V.s] Low-field mobility Beta 1.7 Saturation factor. Typ. nfet=1.8, pfet=1.6 Tjun 298 [K] Junction temperature phib 1.2 [V] Body factor Gamma 0.0 [sqrt(v)] Access resistance on d-terminal Vt [V] Strong inversion threshold voltage Alpha 3.5 Empirical parameter for threshold voltage shift mc 0.2 Choose an appropriate value between 0.01 to 10 CTM_select 1 If CTM_select = 1, then classic DD-NVSAT model is used CC 0 [V] Fitting parameter to adjust Vg-dependent inner fringe cap nd 0 [1/V] Punch-through factor gmin 1e-12 [V] minimum conductance between drain and source

20 C H A P T E R 3 AN EXAMPLE OF MODEL USAGE All the simulations are performed in Matlab R2016b with optical Network Interface Layer and optical Equation Engine in MAPP-opto. MAPP-opto is currently a private release, so please send to mapp-queries@draco.eecs.berkeley.edu for access. The mode solver used in the simulations is developed by the MIT photonics group. Available commercial solvers include MODE Solutions by lumerical, and available on-line free solver includes the 2-D variational effective index mode solver [6]. 3.1 Testbench The testbench of the optical ring filter model connects light source to port c1 and light sink to port c3. The light source model and light sink model are provided as LightSource.m and LightSink.m. The coupler module is in Coupler.m and the phase shifter module is in VoltageControlledPhaseShifter.m. The port e is connected to scaled output of the MVS inverter circuit in MVSinverterOutput.m, 17

21 CHAPTER 3. AN EXAMPLE OF MODEL USAGE 18 which is defined by the parameter vbias_max. The netlist file is provided as OpticalRingModulator_netlist.m and the run file is ORM_MVS_1_0_0.m. 3.2 Simulation Flow All the simulation files are summarized in Table 3.1. The simulation flow is listed as follows: 1. If the user has access to a mode solver, then please revise the file "compute_neff_with_wrapper.m" and provide a wrapper on the available mode solver. The details are commented in the codes. 2. If the user does not have access to a mode solver, then please run "generate_wg_height.m" to generate refractive indices and waveguide structures. Use the listed values with the free online mode solver to obtain effective phase index values and store it in neff-vbias.mat. 3. Run "get_neff_vbias_relation.m" to obtain coefficients (a 0, a 1, a 2, a 3 ), and set it in "OpticalRingModulator_netlist.m". Also other parameters of coupler and voltage controlled phase shifter can be set in the netlist file. 4. Run "ORM_MVS_1_0_0.m" to perform DC and transient analysis.

22 CHAPTER 3. AN EXAMPLE OF MODEL USAGE 19 Files Table 3.1: All the simulation files Description ORM_ MVS _1_0_0.m Run file, includes DC and TRAN analysis OpticalRingModulator_netlist.m Netlist file LightSource.m Light source module LightSink.m Light sink module Coupler.m Coupler module VoltageControlledPhaseShifter.m Voltage controlled phase shifter module MVSinverterOutput.m Output of MVS inverter circuit generate_neff_vbias_data.m Generate neff_vbias.mat compute_neff_with_wrapper.m Utility func. in generate_neff_vbias_data.m get_neff_vbias_relation.m Calculate the coefficients of neff on vbias. compute_neff_coeff.m Utility func. in get_neff_vbias_relation.m generate_wg_height.m Compute the pn junction waveguide structure 3.3 Simulation result Here we simulate an optical ring modulator in the frequency range of THz to THz with all user-defined parameters equal to default values. The output power is defined as P = E out 2, (3.1) and the normalized output power is defined as P n = P/P max. (3.2) With all the default parameters, the relations of effective phase index and bias voltage is plotted in Figure 3.1. It is shown that the approximation with a 3rd order polynomial is in good agreement with the samples. Figure 3.2 plots the normalized output power with respect to frequency of light field. It shows that the resonance is indeed shifted when the reverse bias is applied.

23 CHAPTER 3. AN EXAMPLE OF MODEL USAGE 20 The DC analysis of MVS inverter circuit is plotted in Figure 3.3, and the transient analysis result is shown in Figure 3.4. The resulted modulated optical signal (power) is shown in Figure 3.5. Figure 3.1: Simulation results: neff and vbias relations. The doping level is cm 3

24 CHAPTER 3. AN EXAMPLE OF MODEL USAGE 21 Figure 3.2: Simulation results: resonant frequencies of the ORM with and without bias. It shows that the resonance is shifted when the reverse bias is applied.

25 CHAPTER 3. AN EXAMPLE OF MODEL USAGE 22 Figure 3.3: Simulation results: the input and output curve of the MVS inverter circuit

26 CHAPTER 3. AN EXAMPLE OF MODEL USAGE 23 Figure 3.4: Simulation results: the transient analysis of the MVS inverter circuit

27 CHAPTER 3. AN EXAMPLE OF MODEL USAGE 24 Figure 3.5: Simulation results: the input of MVS inverter circuit, the modulation voltage signals and modulated optical power (output) when the operation frequency is set to be the resonance of zero bias.

28 BIBLIOGRAPHY [1] L. V. Delphine Marris-morini and G. Rasigade, Optical modulators in silicon photonics circuits. [Online]. Available: eu/download/silicon-photonics-course [2] R. Soref and B. Bennett, Electrooptical effects in silicon, IEEE journal of quantum electronics, vol. 23, no. 1, pp , [3] M. R. Watts, W. A. Zortman, D. C. Trotter, R. W. Young, and A. L. Lentine, Vertical junction silicon microdisk modulators and switches, Optics express, vol. 19, no. 22, pp , [4] C.G.Fonstad, Rectangular waveguides, photonic crystals and radiative recombination. [Online]. Available: http: //ocw.mit.edu/courses/electrical-engineering-and-computer-science/ compound-semiconductor-devices-spring-2003/lecture-notes/ Lecture17v2.pdf [5] D. A. Shaloo Rakheja, Mvs nanotransistor model (silicon)(version 1.1.1), [6] O. Ivanova, R. Stiffer, and M. Hammer, A variational mode solver for optical waveguides based on quasi-analytical vectorial slab mode expansion, University of Twente, technical report, 19 pages,