[IEEE 2014 International Conference on Electronics and Communication Systems (ICECS) - Coimbatore...

2014 International Conference on Electronics and Communication Systems (lCECS -2014), Feb.13 -14, 2014, Coimbatore, INDIA

Determining Base Transit Time of anAlyGal_yAs HBT using the Analytical Model Developed for

SiGe Device withExponentiallyDopedBase

Yeasir Arafat Department of Electrical and Electronic Engineering

Bangladesh University of Engineering and Tech. (BUET) Dhaka, Bangladesh

[email protected]

Abstract�Base transit time (BTT) of a graded base AIGaAs

Heterojunction Bipolar Transistor (HBT)has been determined by

using the analytical model previously developed for a SiGe HBT

(arafatetal. ).While thinking about the expansion of the SiGe BTT

model for any other ternary compound semiconductor material

like AIGaAs, the previous model could not be used directly

because most of the parameters used in the model depend on the

materials used. The novel part of the present work is that the

authors investigated published literature for those parameters

associated with AIGaAs and fed them into the SiGe model,

determined the BTT and verified the results.

Keywords-Base transit time of AIGaAs;ternary compound semiconductor HBT; graded base; exponential doping.

I. INTRODUCTION

Ternary compound semiconductors HBTs have greatpotential for high speed and optoelectronic applications. Direct band gap HBT devicesoffer a number of advantages over their indirect band gap counterparts. In this work, AlGaAs has been chosen for its higher speed compared to SiGe HBT under normal operating condition. As the base region of the HBT is graded and the base doping concentration follows an exponential function, the quasi-electric fields resulting from the gradients in doping and slopes in mole fraction increase the minority carrier velocity. However the advantage of this increase in velocity can't be fully utilized because of velocity saturation at a higher electrical field [1]. But the electron velocity versus electric field curve of GaAs has an overshoot in velocity before reaching its saturation value [2]. At low electric field, GaAs HBT can provide faster response, i.e. smaller base transit time. Base transit time of GaAs device also can be traded off with its base sheet resistance [3]. By focusing doping changes adjacent to the collector, the amount of low-doped base material and the resulting increase in base sheet resistance can be minimized. For both a step change in doping and graded change in doping, 10% decrease in base transit time is achieved while only causing a 4% increase in the base sheet resistance. The effectiveness of Algrading in the GaAsbase HBT has been demonstrated by the RF performance of the fabricated device long before [4] which shows a unity gain cut-off frequency (fJ of 37 GHz and a maximum power frequency ([max) of 30

[IEEE copyright notice]

Rowshon Ara Mannan, Priyanka Biswas, Nusrat lahan Department of Electrical, Electronic and Electronic

Engineering Military Institute of Science and Technology (MIST)

Mirpur, Dhaka, Bangladesh

GHz.Further analysis of j; associated with collector current densities indicates the intrinsic time of the device, which is the sum of the base transit time and the collector depletion region transition time [4].lt is found that the surface-recombination l/t noise can significantly be reduced by the heterojunction launcher of the abrupt junction with 30% aluminum mole fraction emitter. The depleted AiGaAs edge surface passivation further suppresses the surface-recombination current resulting a comparatively lower l/t noise comer frequency [5].

Total transit time ( TEe ) of a transistor of any genre detennines the unity gain cut-off frequency (td and maximum power frequency (tmax) of the device. Base transit time is more than70% of a junction transistor's (BJT, HBT) total transit time [6]. So, it plays a very crucial role in detennining a transistor's high frequency perfonnance. Therefore, it is of great importance to obtain an accurate yet relatively simple analytical model of base transit time and collector current density for high frequency HBT for efficient device design. A number of studies have been done on the base profiles of SiGe HBTs applying both analytical and numerical techniques [7][11]. Our groups have been working on the base region of SiGe HBT and developed novel analytic forms of base transit time for various base doping profiles, level of injections [12]-[13]. In this work, the authors have tried to verify the expandability of those previous SiGe (binary HBT) analytical BTT models for a ternary HBT like AIGaAs Heterojunction Bipolar Transistor. Theprevious models could not be used directly because most of the parameters used in those models depend on the materials used. Attempt has been taken to accommodate these dependency of parameters associated with AIGaAs.

Other assumptions related to the present AiyGa1_yAs HBT models are: the base doping profile is exponential with three different (triangular, trapezoidal and box) Ai profiles, band gap narrowing (BGN) effect, doping dependent minority carrier mobility, change in density of states (DOS) and modification in velocity saturation at the base-collector junction. For different Ai dose we compared base transit time of SiGe with base transit time of GaAs for uniform and exponential doping.


II. ANALYSIS

A. Carrier Transport and Relevant Equations

For an npnAlyGa1_yAs base HBT in case of a trapezoidal profile, the Aluminum mole fraction (y) can be expressed as a function of distance (x) along the neutral base widthWB, as

(1)

where, mAL = 1JAzlWB ; 1JAI = Ye - YE ; Ye and YE are Almole fraction at the collector and emitter end respectively. ForYE = 0, (1) represents triangular profile; for YE = Ye, (1) represents box shape profile [14]. Total Al content within the base is called Al dose and is calculated as [IS]

Yo = YavWB

where, Yav = (Ye + YE)/2

(2)

(3)

Base transit time of a bipolar transistor can be expressed as [16]

f.WB n(x) d

r -q --x B - a In(x) (4)

where, n(x) is the minority carrier concentration and In(x)is the electron current density within the base, q is the charge of an electron. The minority carrier concentration for the base regioncan be found using the transport equations and electric field equation respectively [17].

and

dn(x) -In = qDn(x) - + q/ln(x)E(x)n(x) dx

E(x) = kT (_1_ dP(X) __ l_dnre(X)) q p(x) dx nre(x) dx

(Sa)

(Sb)

(6)

where, Dn(x) and Dp(x) are the electron and hole diffusivity,/ln(x) and /lp(x) are electron and hole mobility respectively. E(x) is the electric field, p(x) is the hole concentration and nie(X) is the effective intrinsic carrier concentration. Jnin (Sa) is defined such that it has a positive value. The base in AIGaAs/GaAs RBT is about 100 nm, even at doping concentration as high as 1 x 101gem-3 [18]. As the base width oftoday's high-speed RBT is less than 100nm [IS], so the carrier recombination in the base region can safely be neglected, resulting in Jp approximately zero and a constant Jnequals to collector current Jc• Using (Sa), (6) andEinstein's relation Dn(x) = /In(X)VT , the total current densitybecomes

-J = D (x) nre(x) d (n(x)(n(X)+NB(X))) n q n n(x)+NB(X) dx nre(x)

(7)

where, NB(x) is the base doping concentration. Doping profile used in this analysis is exponential and given by [19]

(8)

where, NB(O) is the peak doping concentration; m = 1J/WB and1J = In(NB(O)/NB(WB)) is the slope of base doping. The low field doping density dependent electron diffusivity in Si, given by [19] can be modified for GaAs as

(9a)

where, Dn = Dna (NB(O)/Nr)-Y1 ; Dna = 207 emz/s[20] ; m1 = my!; Y1 = 0.42 ; Nr = 1017 em-3.

and the electron diffusivity in Si in presence of Ge is given in [21]. For AIGaAs electron diffusivity can be expressed as-

DnAIGaAS(X) = bDnGaAs(X)

where, b = 1 + 3Yav.

(9b)

The saturation velocity inside the AIGaAs alloy also differs fromthat in GaAs. It can be expressedas-

where, e = 0.342/[0.342 + Yav (1 + Yav) ];

and Vs = 7 X 106 em/ s[2].

(10)

The effective intrinsic concentration in Si is given in [21]. For AIGaAs effective intrinsic concentration can be expressed as-

tJEgett(X) nteAIGaAs(X) = ntOGaAsYre kT (Ila)

where, nioGaAs = 2.1 x 106em-3 is theintrinsic carrier concentration in undoped GaAs [2]; Yr is the ratio of the effective DOS in AIGaAs base to theeffective DOS in GaAs and can be written in light of [7], [22]

Yr = exp( -.J5Yav) (11b)

k is the Boltzmann constant; T is the temperature in degrees Kelvin; llE

gett(x) is the effective bandgap reduction in the GaAs base that can be expressed as

(NB(X)) llEgeff (x) = qV

gHO In ---;;- + qV

gAy(x) (llc)

where, 1 st part of ( 11 c) is the BGN due to the presence of a different material (other than dopant) inside the alloy and the 2nd part is the BGN due to heavy doping effects. An approximation of the Siotboom-de Graff BGN model [16], [23]-[24], modified accordingly for AIGaAs gives the effective intrinsic concentration that can be expressed as-

nteAIGaAS(X) = nteAIGaAs(O) em3Zx (lId)

where, nteAIGaAs(O) = ntoAIGaAs(NB(O)/Nr)yz , Yz = V

gHO/VT ; ntoAIGaAS = YAntoAI ; YA = YrexP(Y

3YE) ; Y

3 =


VgAdVT; VT = kT /q; m2 = mY2 ; m3 = mAIY3; m32 = m3 -

m2; VgHD = 18 mV; V

gA = 688 mY.

B. For Low Level of Injection

For low injection, n(x) « NB(x) and the quasi-neutral condition p(x) = n(x) + NB(x)becomes [25]

p(x) = NB(x) (12)

Putting (12) in (6) and replacing the GaAs terms by AiGaAs terms,E(x) can be written as

(13)

where, m023 = m + m32'

Similarly, replacing the GaAs terms by AiGaAs terms in (7), Inl can be written as

-I = D (x) n[eAIGaAs(X) d ( nl(x)NB(X) ) nl q nAIGaAs N (x) dx n2 (x) B ,eAIGaAs

(14)

Using (8), (9b), (1ld) and (14), differential equation for minority carrier concentration inside the AIGaAs base region of the HBT can be solved for nl(x) as

where, nl(O) is the value of minority carrier concentration at E-B junction; m012 = 7](1 + Y1 + Y2)/WB ; m0123 =

m012 + m3; DnA = bDn; and Inl is the low injection electron current density.

The boundary value of nl(O) with necessary correction forAiGaAs, theelectron concentration at x = 0 can be written following[26]-[27]considering Webster effect.

(16)

Assuming that the velocity of electron in the base collectordepletion region of the AIGaAs base HBT saturates at vsA, the electron current density Unl = qVsAnl(WB) gives the electron concentration at x = W B i.e. nl (WB )can be expressed as

(17)

where, WI) = (exp(7]023) - exp( -7]1))/m0123 ; 7]023 =

m023WBand7]1 = m1WB·

The low injection base transit time (TBI) of a graded base AIGaAs HBT cab be determined from (4) as

wJ (1-e-111 1-eI)023 ) nl(O)WB (1-eI)023 ) TBI = -- + -- - -- (18)

1)0123DnA 1)1 1)023 nl(W B)VsA 1)023

C. For All Level of Injections

The analyses for low level of injection can be extended to incorporate moderate level of injection with slightrnodification using perturbation theory. For moderate injection,the modified injected minority carrierconcentration is nm(x) = twnl(x)and the current densityis Inm = twInl' Assuming thatthe injected electron concentration is perturbed by themodulated electric field from nm(x) only a little (on(x) ) and also usingquasineutrality of charge equation, we find p(x) for moderate injection as below-

p(x) = nm(x) + on(x) + NB(x) (19)

Assuming that the magnitude of on(x)is much smaller than nm(x) + NB(x) and using equations (7), (9), (1ld)&(19),we can solve the differential equationfor minoritycarrier concentration n(x)of a AiGaAsHBTas

where, Pm(x) = nm(x) + NB(x);

NI)(x) = nmol) (em01X _ 1) _

NB(O) (e-m0123X - 1)

7]01 7]0123 -

nm1) (e-m322x - 1); (21) 1)322

(20)

and, nmol) = nm(O) - nml); nml) = nm(WB)VsA/(DnAm0123); m321 = m32 + m1 ; m322 = m321 + m1 ; mOl = 7]01/WB ; 7]01 = 7](1 - Y1)

As the base-collector junction is under reverse bias condition, applying velocity saturation at this depletion region, collector current In can be found as

(22)

Substituting x=WB in (20)-(21) and using (22), n(WB) can be expressed as

(23)

Integrating (20), the per unit area stored charge (QbAIGaAs)

within the AIGaAsbase of the HBT can be found. Then, using (22)-(23) and QbAIGaAs. the base transit time of a AlyGal_yAs HBT with exponentially doped base and trapezoidal (also boxor triangular)Ai profile can be obtained for all levels of injection as

(24)

III. RESULT

The minority carrier current density Un) of an RBT is a function of its base-emitter voltage. This relation is plotted for different shape of Ai profiles and shown in Fig.l. For triangular Ai profile, In increases with Vbe maintaining almost constant logarithmic slope but for the trapezoidal & boxshape profiles, the slopes of the curves decrease after Vbe = 1.1 V.


Comparing the linearity of logarithmic slopes of AIGaAs to those of SiGe [13], it is found that AIGaAs remains linear over a large range of Vb" predicting an extended flat region of base transit time (supported by Fig. 2). Current density Un) is also effected by the slopes of the Al profiles. For a box shape Al profile (zero gradient),fn is higher than that of a triangular profile (maximum gradient) and for a trapezoidal profile (moderate gradient),lnis also moderate.

1o'0'r---------------. _Box AI profile

--.-Triangular AI profile

10 ----6-Trapezoidal AI profile

10 N�

E u

�W-c

--,

10 WB=100nm,1l=3

NB(0)=5x10'B

cm-3

10-1"'-.......................................................................... ....-0,6 0,8 1,0 1,2 1.4 1,6

Vbe(volt)

Figure I.Current densities (In) vs, base-emitter voltage (Vbe) for different shape of Al profilesAI % at boundaries is : for triangular profile YE = 0%; Yc = 20%, for trapezoidal profile YE = 10%; Yc = 20% and for box profile 20%,

Fora graded base npnAlGaAs HBT,basetransittimehas been calculated using (24) assuming exponentialbase doping and trapezoidal, triangular or box shape Alprofiles under all level of injection. Different Al profile effects are incorporated by changing the value of YE and the results are shown in Fig.2.Base transit time TB is smallest for triangular Alprofile where it remains almost constant upto 1.4 volt but for the other two profi les (box and trapezoidal) T B starts to increase after 1.2 volt and 1.3 volt respectively.

g,O ,...-------------....."

7,5

'VJ c. 'Q;" 6,0 -E

:;:;

� 45 -c .

jg Q) � 3.0 co

• • • 0.0 �0:-'; ,6�� 0,�8.....L-:1� ,Oo:--L...::-1 �,2:-'-1::-' ,4�.&...::1""'; ,6� Vbe(volt)

Figure 2, Base transit time as a function ofbase-emitter voltage for different shape of Al profilesAI % at boundaries is : for triangular profile YE = 0%; Yc = 20%, for trapezoidal profile YE = 10%; Yc = 20% and for box profile 20%,

Box shape Al profile takes highest transit time among the three Al profiles and the trapezoidal Al profile takes inbetween time. Also comparingthis result to [13],it is evident that for AIGaAs HBT, transit time through the base is a minimum when the triangular Al profile is chosen (similar to

triangular Ge profile for SiGe HBT), only the base-emitter voltage range over which the base transit time remains constant is higher for AIGaAs.

In Fig. 3 below, the variation of T B with dose for uniformly doped base of SiGe HBT and AlGaAs HBT are compared. Here, gradually increasing YC(=YE)' the value of Al dose (YD)

is changed for box profile.In case of SiGeHBT, TB decreases with increase in YD while for AlGaAsHBT, TB increases with Yo but the value ofTB for AlGaAs is much lower than that of SiGe irrespective of Yo. This finding is in compliance with the AlGaAsHBT's being a faster device than SiGeHBT.

4 �----------------------�

3

-0- SiGe(uni dop)

-0- AIGaAS(uni dop)

NB(0)=5x1 0 1Bcm-3

WB=45nm,1l=O

o 2 4 6 Dose,yo

8 10 12

Figure 3,Comparison between the base transit times of a graded base AIGaAsHBTto that of a similar SiGeHBT for uniformly doped base as a function of dose,

The relationship between TB and dose for exponentially doped base SiGeHBT and AlGaAs HBT is also illustrated in Fig. 4. In both the cases, triangular dose profilesare used by keeping YE=O and gradually increasing Yc. The base transit time, TB decreases for both SiGeHBT and AlGaAs HBT with increase in YD but the value OfrB for AlGaAs still remains lower than that for SiGe, pleading for AlGaAs being a faster device than SiGe. Observing Fig. 3 and Fig. 4, it is clear that device becomes faster when base doping profile is exponential (compared to uniform); this phenomenon is well established [28].

1,4

'VJ1,2 c. Q) ,S :;; 1,0 <f) c

jg � 0,8 ro

co

0,6

o 2

_SiGe(expo dope)

--'-AIGaAs(expo dope)

NB(0)=5x1 0 1Bcm-3

WB=45nm,1l=3.5

3 4 5 Dose,yo

6

Figure 4,Comparison between the base transit times of a graded base AIGaAsHBTto that of a similar SiGeHBT for exponentially doped base as a function of dose.


IV. CONCLUSION

Base transit time is calculated for a AIGaAs HBT with Exponentially doped base employingall types (box, trapezoidal and triangular) of AI profile. It was found that the transit time decreases as the profiles change from box to triangular types. The transit time has also been seen to be doping dependent. Under similar parametric conditions, comparison between SiGe

HBT and AIGaAs HBT depicts lower base transit time for exponential base doping. It is also noticed that the base transit time for AIGaAs HBT is smaller than that of SiGe HBT for both exponential and uniform doping.

ACKNOWLEDGMENT

The authors of this work would like to express gratitude to the corresponding Department/Institute of their respective Universities for various supports during the preparation of this manuscript.

[I]

[2]

[3]

[4]

[5]

[6]

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