IMS Workshop: Technologies for THZ Integrated Systems (WMD) Monday, June 3, 2013, Seattle, Washington (8AM-5PM) Transistors for THz Systems Mark Rodwell, UCSB rodwell@ece.ucsb.edu Co-Authors and Collaborators: Teledyne HBT Team: M. Urteaga, R. Pierson, P. Rowell, B. Brar, Teledyne Scientific Company Teledyne IC Design Team: M. Seo, J. Hacker, Z. Griffith, A. Young, M. J. Choe, Teledyne Scientific Company UCSB HBT Team: J. Rode, H.W. Chiang, A. C. Gossard , B. J. Thibeault, W. Mitchell Recent Graduates: V. Jain, E. Lobisser, A. Baraskar, UCSB IC Design Team: S. Danesgar, T. Reed, H-C Park, Eli Bloch WMD: Technologies for THZ Integrated Systems RFIC2013, Seattle, June 2-4, 2013 1 DC to Daylight. Far-Infrared Electronics *ITU band designations How high in frequency can we push electronics ? 1982: ~20 GHz 9 10 10 10 11 sub-mm-wave THF* 0.3-3THz 1-0.1 mm far-IR: 0.3-6 THz 12 10 Frequency (Hz) mid-IR 6-100 THz 50-3 m 13 10 14 10 optical 385-790 THz 10 mm-wave EHF* 30-300 GHz 10-1 mm ~2030: 3THz near-IR 100-385 THz 3-0.78 m microwave SHF* 3-30 GHz 10-1 cm 2012: 820 GHz ** IR bands as per ISO 20473 15 10 ...and what we would be do with it ? 100+ Gb/s wireless networks Video-resolution radar → fly & drive through fog & rain near-Terabit optical fiber links 2 THz Transistors: Not Just For THz Circuits 500 GHz digital logic → fiber optics precision analog design at microwave frequencies → high-performance receivers Higher-Resolution Microwave ADCs, DACs, DDSs THz amplifiers→ THz radios → imaging, communications 3 THz Communications Needs High Power, Low Noise Real systems with real-world weather & design margins, 500-1000m range: Will require: 3-7 dB Noise figure, 50mW- 1W output/element, 64-256 element arrays → InP or GaN PAs and LNAs, Silicon beamformer ICs 4 THz Communications Needs High Power, Low Noise Real systems→ LNAs with low Fmin, PAs with high Psat & high PAE Comparing technologies InP HEMTs give the best noise. InP HBT & GaN HEMT compete for the PA. CMOS is great for signal processing, but noise, power, PAE are poor. Harmonic generation is low power, inefficient. Harmonic mixing is noisy. 5 III-V PAs and LNAs in today's wireless systems... http://www.chipworks.com/blog/recentteardowns/2012/10/02/apple-iphone-5-the-rf/ THz Device Scaling 7 nm Transistors, Far-Infrared Integrated Circuits IR today→ lasers & bolometers → generate & detect Far-infrared ICs: classic device physics, classic circuit design It's all about the interfaces: ...wire resistance,... ...& charge density. contact and gate dielectrics... ...heat,... band structure and density of states ! 8 Transistor scaling laws: ( V,I,R,C,t ) vs. geometry Fringing Capacitances Depletion Layers C A T C finging / L ~ T 2v TIC Bulk and Contact Resistances R contact / A contact te rms dominate 2) IC interconne ct capacitanc es C finging / L ~ Thermal Resistance I max 4vsat (Vappl ) A T2 1) FET fringing capacitanc es L PIC K th L Ttransistor ~ P L ln K th L W Available quantum states to carry current → capacitance, transconductance contact resistance 9 THz & nm Transistors: State Density Limits 2-D: FET capacitance current C DOS 3-D: BJT q 2 m* 2 2 23 / 2 q 5 / 2 m * V 3 / 2 3 2 2 1/ 2 J sheet 2 conductivity q 2 c 3 1/ 2 n1/ 2 q 3 m *V 2 J 4 2 3 q2 3 c 8 2/3 n2/ 3 # of available quantum states / energy determines FET channel capacitance FET and bipolar transistor current access resistance of Ohmic contact 10 Bipolar Transistor Design We Tb b T 2 Dn 2 b Wbc Tc c Tc 2v sat Ccb Ac /Tc I c ,max vsat Ae (Vce,operating Vce,punch-through) / T emitter length LE 2 c P T LE Le 1 ln We Rex contact /Ae We Wbc contact Rbb sheet 12 Le 6 Le Acontacts 11 Bipolar Transistor Design: Scaling We Tb b T 2 Dn 2 b Wbc Tc c Tc 2v sat Ccb Ac /Tc I c ,max vsat Ae (Vce,operating Vce,punch-through) / T emitter length LE 2 c P T LE Le 1 ln We Rex contact /Ae We Wbc contact Rbb sheet 12 Le 6 Le Acontacts 12 Breakdown: Never Less than the Bandgap band-band tunneling: base bandgap impact ionization: collector bandgap 13 FET Design C gd C gs, f Wg gate width W g m C g ch (v / Lg ) C g ch g LgWg Tox / ox Twell / 2 well (q 2 /well state density ) voltage division ratio between v the above three capacitors RDS Lg /(Wg v ) RS RD 1 / 2 1 transport mass contact LS/DWg 14 FET Design: Scaling C gd C gs, f Wg gate width W g m C g ch (v / Lg ) C g ch g LgWg Tox / ox Twell / 2 well (q 2 /well state density ) voltage division ratio between v the above three capacitors RDS Lg /(Wg v ) RS RD 1 / 2 1 transport mass contact LS/DWg 15 FET Design: Scaling C gd C gs, f Wg 2:1 2:1 constant g m C g ch (v / Lg ) gate width W g 2:1 2:1 2:1 C g ch 2:1 LgWg 2:1 Tox / ox Twell / 2 well (q 2 /well state density ) 2:1 2:1 2:1 voltage division ratio between v three capacitors constant the above constant constant RDS Lg /(Wg v ) 2:1 2:1 RS RD constant 2:1 1 / 2 1 transport mass constant contact 4:1 LS/DWg 2:1 16 Changes required to double transistor bandwidth LG gate width WG FET parameter gate length current density (mA/m), gm (mS/m) transport effective mass channel 2DEG electron density gate-channel capacitance density dielectric equivalent thickness channel thickness channel density of states source & drain contact resistivities change decrease 2:1 increase 2:1 constant increase 2:1 increase 2:1 decrease 2:1 decrease 2:1 increase 2:1 decrease 4:1 fringing capacitance does not scale → linewidths scale as (1 / bandwidth ) We emitter length LE constant voltage, constant velocity scaling HBT parameter emitter & collector junction widths current density (mA/m2) current density (mA/m) collector depletion thickness base thickness emitter & base contact resistivities change decrease 4:1 increase 4:1 constant decrease 2:1 decrease 1.4:1 decrease 4:1 nearly constant junction temperature → linewidths vary as (1 / bandwidth) 2 17 THz & nm Transistors: what needs to be done Metal-semiconductor interfaces (Ohmic contacts): very low resistivity Dielectric-semiconductor interfaces (Gate dielectrics---FETs only): thin ! Ultra-low-resistivity (~0.25 W-m2 ), ultra shallow (1 nm), ultra-robust (0.2 A/m2 ) contacts Mo Ru InGaAs InGaAs Heat L TIC Available quantum states to carry current PIC K th L P L Ttransistor ~ ln K th L W → capacitance, transconductance contact resistance 18 THz InP HBTs 19 Scaling Laws, Scaling Roadmap Tb scaling laws: to double bandwidth HBT parameter emitter & collector junction widths current density (mA/m2) current density (mA/m) collector depletion thickness base thickness emitter & base contact resistivities We change decrease 4:1 increase 4:1 constant decrease 2:1 decrease 1.4:1 decrease 4:1 emitter Wbc Tc length LE 150 nm device 20 HBT Fabrication Process Must Change... Greatly 32 nm width base & emitter contacts...self-aligned 32 nm width emitter semiconductor junctions Contacts: 1 W-m2 resistivities 70 mA/m2 current density ~1 nm penetration depths → refractory contacts nm III-V FET, Si FET processes have similar requirements 21 Needed: Greatly Improved Ohmic Contacts Pt/Ti/Pd/Au ~5 nm Pt contact penetration (into 25 nm base) 22 Ultra Low-Resistivity Refractory Contacts -6 Barasakar et al IEEE IPRM 2012 P-InGaAs 2 Contact Resistivity (Wcm ) 10 N-InGaAs N-InAs Mo Mo -7 10 Ir W Mo -8 32 nm node requirements 10 -9 10 18 19 20 21 10 10 10 10 -3 concentration (cm ) 17 18 19 20 10 10 10 10 -3 concentration (cm ) 18 19 20 21 10 10 10 10 -3 concentration (cm ) In-situ: avoids surface contaminants Refractory: robust under high-current operation Low penetration depth, ~ 1 nm Contact performance sufficient for 32 nm /2.8 THz node. 23 Ultra Low-Resistivity Refractory Contacts -6 Barasakar et al IEEE IPRM 2012 P-InGaAs 2 Contact Resistivity (Wcm ) 10 N-InGaAs N-InAs Mo Mo -7 10 Ir W Mo -8 32 nm node requirements 10 -9 10 18 19 20 21 10 10 10 10 -3 concentration (cm ) 17 18 19 20 10 10 10 10 -3 concentration (cm ) 18 19 20 21 10 10 10 10 -3 concentration (cm ) Schottky Barrier is about one lattice constant what is setting contact resistivity ? what resistivity should we expect ? 24 Ultra Low-Resistivity Refractory Contacts -6 Barasakar et al IEEE IPRM 2012 P-InGaAs 2 Contact Resistivity (Wcm ) 10 N-InGaAs N-InAs Mo Mo -7 10 Ir W Mo -8 32 nm node requirements 10 -9 10 18 19 20 21 10 10 10 10 -3 concentration (cm ) 17 18 19 20 10 10 10 10 -3 concentration (cm ) 18 19 20 21 10 10 10 10 -3 concentration (cm ) 2/3 Zero - barrier contact resistivit y : 8 1 1 2/3 c 2 q2 3 (state density and T n quantum - reflectivi ty limit) n carrier concentrat ion T transmissi on coefficien t c 0.1 W m 2 at n 7 1019 / cm 3 . 25 Refractory EmitterImproved ContactsOhmic Contacts Needed: Greatly negligible penetration 26 HBT Fabrication Process Must Change... Greatly tall, narrow contacts: liftoff fails ! control undercut → thinner emitter thinner emitter → thinner base metal thinner base metal → excess base metal resistance Undercutting of emitter ends {101}A planes: fast {111}A planes: slow 27 Sub-200-nm Emitter Contact & Post Refractory contact, refractory post→ high-J operation Sputter+dry etch→ 50-200nm contacts Liftoff aided by TiW/W interface undercut Dielectric sidewalls TiW SiNx 100 nm W Mo HBT: V. Jain. Process: Jain & Lobisser 28 RF Data: 25 nm thick base, 75 nm Thick Collector 25 U Gains (dB) 20 H 15 10 5 21 f = 530 GHz f max 0 10 10 Required dimensions obtained but poor base contacts on this run = 750 GHz 11 10 Frequency (Hz) 12 10 E. Lobisser, ISCS 2012, August, Santa Barbara 29 DC, RF Data: 100 nm Thick Collector f 32 f = 480 GHz U H P = 20 mW/m 2 P = 30 mW/m 30 2 A = 0.22 x 2.7 m 2 25 21 je 20 15 I b,step = 200 A 10 20 5 0 16 A = 0.22 x 2.7 m 2 BV 0 1 2 V je 12 0 9 10 e 10 10 -3 10 -5 b P = 33.5 mW/m2 Vcb = 0.7 V -1 11 10 10 Frequency (Hz) ce Solid line: V Dashed: V cb cb 4 5 = 0.7V 20 = 0V 15 n = 1.19 c 10 n = 1.87 10 -7 10 -9 12 10 3 (V) b I b 5 I c 0 0.2 0.4 0.6 0.8 Vbe (V) 0 1 30 4 J = 20.4 mA/m2 10 c 8 Ic = 12.1 mA I , I (A) Gain (dB) e 24 = 1.0 THz J (mA/m ) 28 max Jain et al IEEE DRC 2011 2 THz InP HBTs From Teledyne Chart 31 Urteaga et al, DRC 2011, June 31 Towards & Beyond the 32 nm /2.8 THz Node Base contact process: Present contacts too resistive (4Wm2) Present contacts sink too deep (5 nm) for target 15 nm base → refractory base contacts Emitter Degeneracy: Target current density is almost 0.1 Amp/m2 (!) Injected electron density becomes degenerate. transconductance is reduced. → Increased electron mass in emitter 32 Base Ohmic Contact Penetration ~5 nm Pt contact penetration (into 25 nm base) 33 Refractory Base Process (1) Blanket liftoff; refractory base metal low contact resistivity low penetration depth Patterned liftoff; Thick Ti/Au low bulk access resistivity base surface not exposed to photoresist chemistry: no contamination low contact resistivity, shallow contacts low penetration depth allows thin base, pulsed-doped base contacts34 Refractory Base Process (2) -5 10 P-InGaAs Contact Resistivity, Wcm 2 -6 10 -7 10 32 nm node requirement -8 10 B=0.8 eV -9 10 0.6 eV 0.4 eV 0.2 eV step-barrier Landauer -10 10 18 2.5 1020 doping, 1/cm3 19 20 21 10 10 10 10 -3 Hole Concentration, cm Increased surface doping: reduced contact resistivity, but increased Auger recombination. 20 2 10 2 nm doping pulse 1.5 1020 1 1020 → Surface doping spike at most 2-5 thick. 19 5 10 0 100 0 5 10 15 depth, nm 20 25 Refractory contacts do not penetrate; compatible with pulse doping. 35 Refractory Base Ohmic Contacts Ru / Ti / Au <2 nm Ru contact penetration (surface removal during cleaning) 36 Degenerate Injection→ Reduced Transconductance 10 2 10 1 Boltzmann (-V )>>kT/q 2 J(mA/m ) be 10 10 -1 10 -2 10 -3 Current varies exponentially with Vbe J J s exp( qVbe / kT ). Transconductance is high g m / AE J 0 -0.3 J J s exp( qVbe / kT ). -0.2 -0.1 0 V - 0.1 0.2 be 37 Degenerate Injection→ Reduced Transconductance 10 2 10 1 Fermi-Dirac Boltzmann (-V )>>kT/q 2 J(mA/m ) be 10 10 -1 10 -2 10 -3 Current varies exponentially with Vbe J J s exp( qVbe / kT ). Transconductance is reduced 0 -0.3 -0.2 -0.1 0 V - 0.1 0.2 be 38 Degenerate Injection→ Reduced Transconductance 10 2 10 1 Fermi-Dirac Boltzmann (-V )>>kT/q 2 J(mA/m ) be Highly degenerate limit: 10 0 Highly degenerate (V ->>kT/q be 10 -1 10 -2 10 -3 current varies as the square of bias J m (Vbe ) * E 2 -0.3 q 3m * J 2 3 (Vbe ) 2 8 -0.2 -0.1 0 V - 0.1 0.2 be 39 Degenerate Injection→ Reduced Transconductance 10 2 10 1 Fermi-Dirac Boltzmann (-V )<<kT/q 2 J(mA/m ) be Highly degenerate limit: 10 0 Highly degenerate (V ->>kT/q be 10 -1 10 -2 10 -3 current varies as the square of bias J m (Vbe ) * E 2 Transconductance varies as J1/2 g m / AE mE* J ...and as (m*)1/2 -0.3 q 3m * J 2 3 (Vbe ) 2 8 -0.2 -0.1 0 V - 0.1 0.2 be At & beyond 32 nm, we must increase the emitter effective mass. 40 Degenerate Injection→Solutions At & beyond 32 nm, we must increase the emitter (transverse) effective mass. Other emitter semiconductors: no obvious good choices (band offsets, etc.). Emitter-base superlattice: increases transverse mass in junction evidence that InAlAs/InGaAs grades are beneficial Extreme solution (10 years from now): partition the emitter into small sub-junctions, ~ 5 nm x 5 nm. parasitic resistivity is reduced progressively as sub-junction areas are reduced. 41 3-4 THz Bipolar Transistors are Feasible. 4 THz HBTs realized by: Extremely low resistivity contacts Extreme current densities Processes scaled to 16 nm junctions Impact: efficient power amplifiers and complex signal processing from 100-1000 GHz. 42 InP HBT: Key Features 512 nm node: high-yield "pilot-line" process, ~4000 HBTs/IC 256 nm node: Power Amplifiers: >0.5 W/mm @ 220 GHz highly competitive mm-wave / THz power technology 128 nm node: >500 GHz f , >1.1 THz fmax , ~3.5 V breakdown breakdown* f = 1.75 THz*Volts highly competitive mm-wave / THz power technology 64 nm (2 THz) & 32 nm (2.8 THz) nodes: Development needs major effort, but no serious scaling barriers 1.5 THz monolithic ICs are feasible. 43 Can we make a 1 THz SiGe Bipolar Transistor ? InP emitter 64 2 SiGe 18 0.6 nm width Wm2 access 18 0.7 nm contact width, Wm2 contact Key challenge: Breakdown 15 nm collector → very low breakdown collector 53 36 2.75 15 125 1.3? nm thick mA/m2 V, breakdown Also required: low resistivity Ohmic contacts to Si very high current densities: heat f fmax 1000 2000 GHz GHz Simple physics clearly drives scaling transit times, Ccb/Ic → thinner layers, higher current density high power density → narrow junctions base small junctions→ low resistance contacts 64 2.5 1000 2000 PAs 1000 1000 GHz digital 480 480 GHz (2:1 static divider metric) Assumes collector junction 3:1 wider than emitter. Assumes SiGe contacts no wider than junctions 44 THz InP Bipolar Transistor Technology Goal: extend the operation of electronics to the highest feasible frequencies THz InP Heterojunction Bipolar Transistors 1 THz device 60-600 GHz IC examples; demonstrated & in fab Scaling roadmap through 3 THz 220 GHz power amplifiers ultra-efficient 85 GHz power amplifiers 188 mW, 33% PAE 182 mW 50 GHz sample/hold 40 GHz op-amp 100 GHz ICs for *electronic* demultiplexing of WDM optical communications 40 Gb/s phase-locked coherent optical receivers Enabling Technologies : ~30 nm fabrication processes, extremely low resistivity (epitaxial, refractory) contacts, extreme current densities, doping at solubility limits, few-nm-thick junctions Teledyne Scientific: moving THz IC Technology towards aerospace applications 1.1 THz pilot IC process 204 GHz digital logic (M/S latch) 670 GHz amplifier 614 GHz fundamental oscillator (VCO) 300 GHz fundamental phase-lock-loop Vtune VBB VEE Vout THz InP HEMTs and III-V MOSFETs 46 Changes required to double transistor bandwidth LG gate width WG FET parameter gate length current density (mA/m), gm (mS/m) transport effective mass channel 2DEG electron density gate-channel capacitance density dielectric equivalent thickness channel thickness channel density of states source & drain contact resistivities change decrease 2:1 increase 2:1 constant increase 2:1 increase 2:1 decrease 2:1 decrease 2:1 increase 2:1 decrease 4:1 fringing capacitance does not scale → linewidths scale as (1 / bandwidth ) We emitter length LE constant voltage, constant velocity scaling HBT parameter emitter & collector junction widths current density (mA/m2) current density (mA/m) collector depletion thickness base thickness emitter & base contact resistivities change decrease 4:1 increase 4:1 constant decrease 2:1 decrease 1.4:1 decrease 4:1 nearly constant junction temperature → linewidths vary as (1 / bandwidth) 2 47 FET scaling challenges...and solutions Gate barrier under S/D contacts → high S/D access resistance addressed by S/D regrowth High gate leakage from thin barrier, high channel charge density (almost) eliminated by ALD high-K gate dielectric Other scaling considerations: low InAs electron mass→ low state density capacitance → gm fails to scale increased m* , hence reduced velocity in thin channels minimum feasible thickness of gate dielectric (tunneling) and channel 48 III-V MOS Peak transconductance; VLSI-style FET: 2.5 mS/micron ~85% of best THz InAs HEMTs VDS=0.05 V 2.4 2.0 VDS=0.5 V 2.0 1.6 1.2 1.6 Lg = 40 nm (SEM) 1.2 0.8 0.8 0.4 0.4 0.0 -0.2 0.0 0.2 0.4 Gate Bias (V) Sanghoon Lee 0.6 0.0 Peak Transconductance (mS/m) 2.4 Gm (mS/m) Current Density (mA/m) III-V MOS will soon surpass HEMTs in RF performance 2.8 90 [011] 0 [01-1] 2.4 2.0 1.6 1.2 0.8 0.4 0.0 at Vds=0.5V 0.1 1 Gate length (m) 40 nm devices are nearly ballistic 49 FET Drain Current in the Ballistic Limit mA Vgs Vth J K1 84 m 1 V normalized drive current K 1 0.35 3/ 2 , where K1 InGaAs <--> InP 1 (c g m* mo 1/ 2 * dos,o / cequiv ) g ( m / mo ) Si 3/ 2 g=2 g=1 0.3 cequiv ( 1/cox 1/cdepth )1 0.25 εSiO2 /EET 0.2 0.3 nm 0.4 nm 0.15 0.1 0.05 g # band minima cdos,o q 2 m0 / 2 2 0.6 nm EET=Equivalent Electrostatic Thickness =ToxSiO2/ox+TinversionSiO2/semiconductor 0 0.01 0.1 m*/m EET=1.0 nm 1 o In ballistic limit, current and transconductance are set by: channel & dielectric thickness, transport mass, state density 50 Transit delay versus mass, # valleys, and EOT 1/ 2 Lg m* 1 Volt Qch ch K 2 where K 2 7 ID 2.52 10 cm/s Vgs Vth m0 EOT=1.0 nm 2 1.5 Normalized transit delay K 1/ 2 1/ 2 * cdos,o m 1 g ceq mo 0.6 nm 1 nm 0.4 nm 0.6 nm 0.4 nm Si, GaN 1 cequiv ( 1/cox 1/csemi )1 InGaAs 0.5 εSiO2 /EOT g=1, isotropic bands g=2, isotropic bands EOT includes wavefunction depth term (mean wavefunction depth*SiO2 /semiconductor ) 0 0 0.05 0.1 0.15 0.2 0.25 m*/m 0.3 0.35 0.4 o Low m* gives lowest transit time, lowest Cgs at any EOT. 51 3000 f 2000 4000 2500 max 1500 3500 3000 fmax 2000 f f , GHz 2500 canonical scaling stepped # of bands transport only , GHz FET Scaling: fixed vs. increasing state density 1500 1000 500 500 0 2.5 0 1000 SCFL static divider clock rate, GHz drain current density, mA/m 1000 mA/m→ VLSI metric 2 1.5 1 0.5 200 mV gate overdrive 0 0 10 20 30 40 gate length, nm 50 Need higher state density for ~10 nm node 60 SCFL divider speed 800 600 400 200 0 0 10 20 30 40 gate length, nm 50 60 52 2-3 THz Field-Effect Transistors are Feasible. 3 THz FETs realized by: Ultra low resistivity source/drain High operating current densities Very thin barriers & dielectrics or MOSFET high-barrier HEMT Gates scaled to 9 nm junctions Impact: Sensitive, low-noise receivers from 100-1000 GHz. 3 dB less noise → need 3 dB less transmit power. 53 4-nm / 5-THz FETs: Challenges 4 nm Gate dielectric 0.1 nm EOT: UTB 0.2 nm EOT: fin Estimated (WKB) tunneling current is just acceptable at 0.2 nm EOT. Channel thickness 0.8 nm: UTB 1.6 nm: fin atomically flat How can we make a 1.6 nm thick fin, or a 0.8 nm thick body ? 54 Thin wells have high scattering rate Scattering probabilit y 1 / m T Sakaki 2 6 q well . APL 51, 1934 (1987). Need single-atomic-layer control of thickness Need high quantization mass mq. 55 III-V vs. CMOS: A false comparison ? UTB Si MOS UTB III-V MOS III-V THz MOS/HEMT III-V THz HEMT III-V MOS has a reasonable chance of future use in VLSI The real THz / VLSI distinction: Device geometry optimized for high-frequency gain vs. optimized for small footprint and high DC on/off ratio. 56 Conclusion 57 THz and Far-Infrared Electronics IR today→ lasers & bolometers → generate & detect Far-infrared ICs: classic device physics, classic circuit design It's all about classic scaling: ...wire resistance,... contact and gate dielectrics... ...heat,... ...& charge density. Even 1-3 THz ICs will be feasible band structure and density of quantum states (new!). 58 (backup slides follow) 59 Electron Plasma Resonance: Not a Dominant Limit T 1 Lkinetic A q 2nm* T 1 Rbulk A q 2nm* m dielectric relaxation frequency scattering frequency 1 Rbulk 1 / 2 f scatter f dielecic 2 Lkinetic Cdisplacement Rbulk 1 1 2m 2 n - InGaAs 3.5 10 / cm 19 p - InGaAs 7 10 / cm 19 3 Cdisplacement A T plasma frequency 1 / 2 f plasma LkineticCdisplacement 800 THz 7 THz 74 THz 80 THz 12 THz 31 THz 3 60