Modeling and Simulation of Metal-Semiconductor-Metal Photodetector using VHDL-AMS

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1 Modelig ad Simulatio of Metal-Semicoductor-Metal Photodetector usig VHDL-AMS Shu Wu ad Sug-Mo Kag Deartmet of Electrical Egieerig, Uiversity of Califoria, Sata Cruz, Sata Cruz, CA 9564, USA ABSTRACT A circuit-level model of Metal-Semicoductor-Metal Photodetector (MSM-PD) was develoed ad imlemeted ito VHDL-AMS simulator hamster TM. The model was derived for a oe dimesioal (-D) structure from cotiuity equatios. Both trasiet ad steady-state simulatios results match well with exerimetal data.. INTRODUCTION Metal-semicoductor-metal hotodetector has become oular i moder otical commuicatio systems. It has several advatages over traditioal i hotodiodes [] [4]. Firstly, it has a laar structure, which is comatible with most semicoductor devices, makig it ideal for otoelectroic itegrated circuit (OEIC) alicatios. Secodly, because of its geometry, it has a lower caacitace for the same active area resultig i a lower (RC) time delay. Thirdly, the rocess for fabricatig this device is very simle ad is comatible with regular IC rocesses. With roer semicoductor material MSM-PD ca work well with differet trasmissio systems. For examle, GaAs-based receivers [5] is suitable for shortwavelegth short-distace commuicatio liks such as chi-to-chi otical itercoects, IGaAs-based receivers [6] ca be used i log-distace otical commuicatios i both.55 ad.3 µm bads because of their small badgas, GaN-based hotodetectors [7] i the wavelegth rage from to 365 m rage are imortat comoets i a variety of military as well as commercial alicatios for their solar blided, ultraviolet (UV) characteristic. Thus VHDL-AMS model for MSM-PD has become critical for system desig ad aalysis.. MODELING AND SIMUALATION The tyical MSM-PD cosists of iterdigitaled metal figers o to of the semicoductor layers, as show i Figure. To reduce the dark curret the Schottky barrier height ca be adjusted by choosig roer material of the layer udereath the metal figers. A buffer layer betwee the absortio layer ad the substrate is eeded to reduce the roagatio of the defects i the substrate. The bias voltage is added to the metal figers to create sufficiet electrical field withi the semicoductor layer. Light icidet o the to surface of the hotodector is absorbed to geerate electro-hole airs. The electrical field swees out the hotogeerated carriers out of the device. The -D cross sectio is show i Figure. The -D assumtio is valid if the hoto absortio deth is much smaller tha the distace betwee the adjacet metal figers L, as show i Figure. I fact, this coditio is ofte satisfied i most ractical situatios, sice absortio of hotos dee i the substrate is tyically avoided as it reduces the detector s resosivity ad badwidth [8]. The behavior of hoto-geerated carriers i MSM hotodetector ca be described by Poisso s equatio ad carrier cotiuity equatios give below. +V Schottky ehacemet layer Eergy bad smooth layer Absortio layer Buffer layer Substrate Fig.. Tyical structure of a MSM-PD Fig.. Cross sectio of iterdigital area i MSM-PD L x

2 ε ε ψ q( + N N ) () s D A G+ R + q t G+ R + q t (a) (b) where R / ad G are the electro/hole recombiatio ad geeratio rate, ψ is the electrostatic otetial. ad are electro ad hole curret desity give by qµ E + qd (3a) qµ E qd (3b) Where µ / ad D / are the electro/hole mobility ad diffusio costat, E is electric field. I order to get aalytical solutios a uiform electric field is assumed ad recombiatio rates are chose to be /τ ad / τ for electros ad holes resectively. τ / is carrier lifetime.. Steady-state behavior I steady-state, as the bias voltage raisig the behavior of MSM hotodetector ca be treated for two cases. Whe the bias voltage is lower tha the flat-bad voltage, the otetial barrier of the holes is lowered by the icreased bias voltage, which results i raid icrease of the curret. Whe the bias voltage reaches the flat-bad voltage, the hole barrier aroaches its limitig magitude, the Schottky barrier height. Further icrease i voltage will cause the curret to icrease slowly. The hotocurret ca be derived from above equatios () to (3) ad has the followig form. Ih I e qv KT We also add tuelig curret to the total curret flowig out of the MSM-PD. The followig equatios show the total curret i steady-state. I I e I Ae V V qv B KT V dc + h, < FB B V I I + Ae, V V dc h FB where I dc is the total curret, V is the bias voltage, V FB is the flat-bad voltage, T is the temerature, K is the (4) (5) (6) Boltzma costat, ad, A, B, I are fittig arameters. I h is give below. αd η q Ih w( R)( e ) (7) hν where w is area the ratio (area trasaret to light/ area exosed to light), α is the absortio coefficiet, d is the thickess of the absortio layer, η is the quatum efficiecy, hν is the hoto eergy, is the icidet light ower. We imlemet the model ito hamster TM usig VHDL- AMS. The VHDL-AMS codes are show i listig. Listig. VHDL-AMS CODES OF MSM-PD DC MODEL LIBRARY DISCIPLINES; LIBRARY IEEE; USE DISCIPLINES.ELECTROMAGNETIC_SYSTEM.ALL; USE IEEE.MATH_REAL.ALL; ENTITY MSMDC IS GENERIC ( T : REAL:3.;--k d : REAL:.e-4;--cm ); PORT(TERMINAL,m: ELECTRICAL; quatity h :real); --Iterface orts. END; ARCHITECTURE behav OF MSMDC IS --quatity declaratios. costat q :real:.6e-9;--c costat hc :real:6.66e-34;--s costat k :real:.387e-3;--/k QUANTITY Ih : REAL; QUANTITY I : REAL; QUANTITY v_i ACROSS i_out THROUGH TO m; BEGIN h.96e-6;--w Ihw*(.-R)*(.-ex(-.*alfa*d))*eta*q*h/hc/miu; IIh/(ex(q*Vfb**//k/T)-.); if v_i<vfb use i_outi*(ex(q*v_i*(.*vfb-v_i)/(*k*t))-.)+ih*a*ex(-.*b/v_i); else i_outih*(.+a*ex(-.*b/v_i)); ed use; END;

3 Table. Parameters i DC model for MSM-PD Parameters (uit) Value T (K) 3 C (m/s) 3e8 λ (m).3e-6 d (cm) e-4 w η.5683 R..3 A (A).534 B (V) 3.9 The simulatio results show i Fig. 3 have good agreemet with Fig. 3 i [6]. The arameters used i simulatio are listed i Table.. Temoral behavior We ca get temoral behavior for () to (3) by usig variable searatio ad Fourier series techique. The electro distributio as a fuctio of both ositio ad time is ( x, t) ex ( Ax) { T ex( t) si( kπx L) } k β, (8) k, k, / where arameters A, β ad T k, are µ E A D β T Dkπ + µ E L k, + 4D (9) () τ G A L k + [( ) ex( AL) ] k, A + ( k ) π / L A + ( k + ) π / L k {,,3...} () The hole distributio has the same form with electro excet usig µ, D ad τ istead of µ, D ad τ corresodig to hole quatities. The ulse resose show below ca be obtaied by uttig (8) back to () to (3). The arameters i () ad (3) have same meaigs as before. Photocurret (A) kπ () _ ulse ( t) qd Tk, ex( β k, t) k L kπ (3) k _ ulse ( t) qd ex( AL) Tk, ( ) ex( β k, t) k L To reduce the comlexity we ca use the followig equatio to model the ulse resose of MSM-PD. π ulse ulse si g ( tt ) π (4) λt g( t) λ e, λ (π τ ) Bias Voltage (V) Fig. 3. DC resose of MSM-PD. (light itesity atteuated at 3 db stes from.96 µw with a.3 µm laser) where ulse is fittig arameter, τ is trasit time. Simulatio was doe by usig (3) corresodig to the exerimet data i refereces [9] ad []. Fig. 4 is corresods to Fig 4 i [9] ad Fig. 5 is corresods to Fig i []. The arameters used for simulatio are show i the figures. Our simulatio results matched those i [9], []. Normalize curret τ.95 s, t 6 s τ.875 s, t 6 s τ.675 s, t 6 s Fig. 4 Simulatio results of ulse resose of MSM-PD i [9]

4 Normalized curret.6.4. τ.865 s, t 5. s τ.75 s, t 7 s τ.6375 s, t s ormalized curret Fig. 5 Simulatio results of ulse resose of MSM-PD i [] The frequecy resose of MSM-PD ca be obtaied by takig Fourier trasform of () ad (3), resultig i kπ ( ω ) qd T, (4) k k L β k, iω for electros ad holes, µ..µ 4.µ 6.µ 8.µ.µ.µ4.µ6.µ Other iut resose of the hotodetector ca be obtaied by takig the covolutio of the ulse resose show i (6) ad (7) with the iut fuctio as () t () t S() t ( tt ) S( t ) dt t Fig 7. Simulatio result of the MSM-PD resose uder sie fuctio iut, ulse. _ ulse (6) kπ k ( ω ) qd ex( AL) Tk, ( ) (5) k L βk, iω The 3-dB frequecy for the electros is f -3dB β k, /π ad for holes is f -3dB β k, /π. We did frequecy resose simulatio with.8 V bias voltage usig (4) ad (5). The lots are show i Fig 6. Simulatio results show that the hole is the mai limitatio of the whole hotodetector badwidth due to its slow mobility. Normalized curret electro total hole Frequecy (Hz) Fig. 6 Frequecy resose of electro, hole ad total curret i a MSM-PD where S(t) is the icidet light waveform fuctio ad ulse is the ulse resose show i (4). To demostrate this feature we simulate the MSM-PD resose uder siusoidal otical iut. The simulatio result is show i Fig. 7. The trasit time was chose to be 9.6 µs i simulatio. 3. SUMMARY A circuit-level model of MSM-PD was demostrated i this aer. The model has bee imlemeted ito VHDL- AMS simulator hamster TM icludig steady-state, temoral ad frequecy domai behavior of MSM-PD. The model was derived i a oe dimesioal (-D) structure from cotiuity equatios. Both time-deedet ad steady-state simulatios have good agreemets with ublished exerimetal data. 4. REFERENCES [] Berger P R, MSM hotodiode IEEE Potetials, 996, 55 9 [] Soole B D ad Schumacher H, IGaAs metal semicoductor metal hotodetectors for log wavelegth otical commuicatios, IEEE. Quatum Electro. Vol. 7, 99, [3] P. Fay, W. Wohlmuth, A. Mahaja, C. Caeau, S. Chadrasekhar ad I. Adesida, A comarative study of itegrated hotoreceivers usig MSM/HEMT ad PIN/HEMT techologies, IEEE Photo. Techol. Lett., vol., 998, 58 4

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