stepping toward standard methods of small-signal …menrob10/00842955.pdf · the theoretical...

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 47, NO. 6, JUNE 2000 1139

Stepping Toward Standard Methods of Small-SignalParameter Extraction for HBT’s

Mohammad Sotoodeh, Lucia Sozzi, Alessandro Vinay, A. H. Khalid, Zhirun Hu, Ali A. Rezazadeh, Member, IEEE,and Roberto Menozzi

Abstract—An improved HBT small-signal parameter extractionprocedure is presented in which all the equivalent circuit elementsare extracted analytically without reference to numerical optimiza-tion. Approximations required for simplified formulae used in theextraction routine are revised, and it is shown that the presentmethod has a wide range of applicability, which makes it appro-priate for GaAs- and InP-based single and double HBT’s. Addi-tionally, a new method is developed to extract the total delay time ofHBT’s at low frequencies, without the need to measure 21 at veryhigh frequencies and/or extrapolate it with 20 dB/dec roll-off.The existing methods of finding the forward transit time are alsomodified to improve the accuracy of this parameter and its com-ponents. The present technique of parameter extraction and delaytime analysis is applied to an InGaP/GaAs DHBT and it is shownthat: 1) variations of all the extracted parameters are physicallyjustifiable; 2) the agreement between the measured and simulated

- and -parameters in the entire range of frequency is excellent;and 3) an optimization step following the analytical extraction pro-cedure is not necessary. Therefore, we believe that the present tech-nique can be used as a standard extraction routine applicable tovarious types of HBT’s.

Index Terms—Delay times, equivalent circuits, forward transittime, heterojunction bipolar transistors, parameter extraction,small-signal, III–V compound semiconductors.

I. INTRODUCTION

H ETEROJUNCTION bipolar transistors (HBT’s) based onIII–V material systems are very attractive candidates for

digital, analog, and power applications due to their excellentswitching speed combined with high current driving capability[1], [2]. In that respect, there has long been a strong competitionbetween III–V HBT’s and their FET counterparts (MESFETand HEMT).

As the range of HBT’s applicability constantly widens, theneed for accurate small- and large-signal models is a key factorfor successful employment of these devices in systems. Themost commonly used small-signal parameter extraction tech-nique is numerical optimization of the model generated-pa-rameters to fit the measured data. It is well known, however,that optimization techniques may result in nonphysical and/or

Manuscript received August 3, 1999; revised February 9, 2000. This workwas supported by the U.K. Engineering and Physical Sciences Research Council(EPSRC). The review of this paper was arranged by Editor A. S. Brown.

M. Sotoodeh, L. Sozzi, A. H. Khalid, Z. Hu, and A. A. Rezazadeh are with theDepartment of Electronic Engineering, King’s College London, London WC2R2LS, UK (e-mail: [email protected]).

A. Vinay and R. Menozzi are with the Department of Information Engi-neering, University of Parma, Parma, Italy.

Publisher Item Identifier S 0018-9383(00)04245-3.

nonunique values of the components. Also the optimized pa-rameters are largely dependent on the initial values of the opti-mization process. Alternative extraction methods which ensureunique determination of as many equivalent circuit elements aspossible are therefore of considerable importance. Several ap-proaches for a more accurate and more physical parameter ex-traction are suggested in the literature. Costaet al. [3] haveused several test structures to systematically de-embed the in-trinsic HBT from its surrounding extrinsic and parasitic ele-ments. However, this method requires three test structures foreach device size on the wafer, ignores the nonuniformity acrossthe wafer, and may involve an additional processing mask insome self-aligned technologies. Pehlke and Pavlidis [4] devel-oped an analytic approach to extract the-shaped equivalentcircuit elements of HBT’s. But this method, though attractive inmany aspects, had two major disadvantages. First, the methodwas still relying on optimization to find the parameters of theemitter branch and elements of the delay time, a problem whichwas later resolved in [5]. Second, the distributed nature of thebase resistance and base-collector capacitance was not takeninto account. This last assumption, which was later addressedby many other authors, may result in a negative collector seriesresistance [6] or a nonphysical frequency behavior of the calcu-lated emitter block [7].

Since 1992, other approaches were proposed, which tookthe distributed nature of and into account. Theapproach in [8] involves some unjustifiable assumptions (e.g.,

; see Fig. 1 for interpretation of theparameters), and some of the parameters are left to be obtainedusing numerical optimization and/or physical estimation. Thesame is almost true for the approach used by Schaper andHolzapfl [9], where it is assumed that and

. Rioset al. [10] proposed an attractive methodin which maximum amount of information, parameter values,and constraints are extracted in order to minimize the numberof unknown parameters to be evaluated by a final numericaloptimization process. Kameyamaet al. [11] used a similar ap-proach to extract the equivalent circuit elements of a pnp HBT,but they claimed that their method can be applied to npn HBT’swith a little modification. Measurement of-parameters underopen-collector condition is used in [6] to assist in finding theextrinsic series elements of the-equivalent circuit, althoughnonlinear extrapolation has to be used in order to find the serieselements (see [6, Fig. 2]). Additionally, all of the extrinsicseries elements are assumed bias-independent. Finally, Samelisand Pavlidis [7] applied a novel impedance block conditionedoptimization. This method seems rather involved in terms of

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1140 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 47, NO. 6, JUNE 2000

Fig. 1. Schematic cross-section of a small-geometry HBT together with its lumped element small-signal equivalent circuit. The impedance blocks defined in(A3)–(A7) are placed inside dashed boxes.

implementation and computation time, but otherwise has theadvantage of preserving the physical structure of the impedanceblocks.

From the brief review of the above works, it is clear that thereis still a lack of a standard direct technique for small-signalparameter extraction of HBT’s, although several positive stepshave been taken. This is in contrast to FET parameter extrac-tion that has for long benefited from a standard method [12],[13]. Therefore, it is necessary to review the existing methodsand develop a straightforward and reliable small-signal param-eter extraction technique with very reasonable assumptions thatmake it applicable to various types of HBT’s.

Recently, Li and Prasad discussed the basic expressions andapproximations used in small-signal parameter extraction ofHBT’s [14]. Based on this, they developed a procedure whichwas successfully applied to extract the parameters of an Al-GaAs/GaAs HBT with emitter area of 30m [15]. We believethat the Li and Prasad’s work with some modifications, to bediscussed in the present article, can be the basis for a standardmethod applicable to a wide range of HBT’s. The modificationsto [14] and [15] include different plotting and/or interpretationof the measured data, less restrictive assumptions, removingthe necessity of a final optimization process, more generalformulation of the common-base current gain, a different useof “cold-HBT” data, and physical explanation of some of theobserved variations (which could not be explained in [15]).These modifications are clearly addressed in the forthcomingsections.

In addition, new methods are introduced to obtain the totaldelay time and the forward transit timefrom the measured-parameters at low frequencies, without therequirement of extrapolating at higher frequency region.

The structure of this paper is as follows. Section II describesthe theoretical approximations of-parameters, assumptions

made, and the range of their applicability. Then in Section III, aparameter extraction technique based on the results of Section IIwill be developed. Section IV is devoted to the new methods offinding total delay time and forward transit time from the mea-sured -parameters at low frequencies. Discussion of the resultsin Section V will be finally followed by main conclusions of thiswork in Section VI.

II. -PARAMETERSFORMULATION AND APPROXIMATIONS

Fig. 1 shows the schematic diagram of an npn HBT togetherwith its associated small-signal lumped-element equivalent cir-cuit. This is a T-shaped equivalent circuit with three added par-allel capacitances due to the contact pads. Since the T-shapedequivalent circuit is more closely related to the original deriva-tion of the common-base -parameters of bipolar transistors[16], [17] and involves less simplifying assumptions than the

-equivalent circuit, it is usually employed in the literature (andin the present work) for the purpose of small-signal parameterextraction of HBT’s. The distributed nature of the base resis-tance and the base-collector capacitance is modeled in this dia-gram by dividing them into only two sub-elements; namely in-trinsic and extrinsic parts. Division of these elements into moresub-regions is discussed in, e.g., [18], [19], but one has to mainlyrely on optimization techniques to evaluate the extra elements.

One feature in common among different methods of param-eter extraction in the literature is that first the parasitic pad ca-pacitances are determined. Measurement of an open test struc-ture [3], and variation of the measured total capacitances atlow frequencies with reverse bias [18] or with junction area[20] are proposed to distinguish between the junction and par-asitic capacitances. Once the parasitic pad capacitances are de-termined, the internal device will be de-embedded from theseusing standard network parameter transformation. Usually, the

SOTOODEHet al.: SMALL-SIGNAL PARAMETER EXTRACTION FOR HBT’S 1141

subcollector of HBT’s is at least three to five times thicker thantheir base region. Therefore, is a very small resistance, es-pecially in npn III–V HBT’s where the much higher mobilityfor electrons is also responsible for a negligible . Conse-quently, one can merge the effects of and into a singleresistance connected in series with the collector inductance

. The resultant equivalent circuit, after de-embedding the padcapacitances, can be explained by a set of-parameters. Theformulation of -parameters in the present work is similar tothat in [14], and is repeated for readers’ convenience in the Ap-pendix. It is important to note that more physically completeequations for and , as compared to those in [14], areused here. Also reverse-biased junction resistances areconsidered for both the intrinsic and extrinsic parts. We furtherdefine:

(1)

(2)

(3)

If one assumes

(4)

(5)

(6)

then after some algebraic manipulation one can arrive at thefollowing simplified equations:

(7)

(8)

It is worth pointing out that assumptions (5) and (6) aresecond-order approximations, as opposed to first-order ap-proximations suggested in [14] for the intermediate frequencyrange (e.g., and ). This makes therange for applicability of (4)–(8) wider. If, for instance, “”means “at least ten times smaller”, then with some rather con-servative values of k , , , and

fF, the above approximations would be validfor GHz GHz. Therefore, even in InP/InGaAsHBT’s where is two to three times larger than GaAs-basedHBT’s, there would be a wide enough frequency range overwhich (4)–(8) are valid and small-signal parameters can beextracted using the technique discussed in this work. Anotherresult of the above discussion is that extremely low frequencyrange (characterized by ) and extremely highfrequency range (characterized by ) as definedin [14] require measurement frequencies as low as 50 MHz oras high as 500 GHz, which can not be achieved using presentlyavailable network analyzers.

Other useful relations that can be directly (without any as-sumption) derived from (A1) and (A2) are

(9)

(10)

Therefore, if , and are known, can beaccurately determined. However as will be shown in the nextsection, elements of can be determined at low frequencieswithout accurate knowledge of the above impedance blocks.

Under forward active mode of operation, and especially athigh current regime, the assumption:

(11)

would be valid in a wide frequency range and (A5) can be ap-proximated as

(12)

“Cold” condition for HBT’s is defined as the condition whenboth junctions are zero-biased (or reverse-biased). Under suchcondition, dc current is zero, hencewould be extremely smalland the device behaves like a passive component .Expressions (4)–(8) would still be valid. Also (A9) simplifiesto . Additionally, is very large and (11)–(12)are no longer valid. Instead, assuming and(4)–(6), one can write

cold cold

(13)

As will be shown in the next section ,and therefore, the last terms on the right-hand-side of (7) and(13) are extremely small and can be ignored.

III. PARAMETER EXTRACTION TECHNIQUE

In this section, an improved version of the techniqueexplained in [15] will be applied to extract the small-signal pa-rameters of an InGaP/GaAs double HBT with m

area (accounting for the estimated mesa undercut) andm area. The intrinsic part of the layer structure

of this DHBT consists of 1000 Å cm InGaPemitter, 1000 Å p cm GaAs base, 200 Å

cm GaAs spacer, and 4800 Åcm InGaP collector, all grown on semi-insulating GaAssubstrate. Device fabrication is discussed elsewhere [21]. DC


Fig. 2. Real parts of theZ-parameters as a function of frequency obtainedunder cold-HBT condition.

characterization of the device is carried out using HP4145BSemiconductor Parameter Analyzer. Then the- parametersare measured on-wafer using HP8510 Network Analyzer andCascade Microtech RF probes in the frequency range 100 MHzto 40 GHz.

Small-signal parameter extraction starts from de-embeddingthe internal device from parasitic pad capacitances surroundingit. Then, a series of -parameter measurements is carried outunder constant and variable collector current (including

, i.e., the cold-HBT). The cold-HBT measurement is toassist in finding , which is assumed bias-independent, aswell as . Measured data under variablewill be used toseparate current-dependent elements from those insensitive tocurrent.

As to the measurement of the parasitic pad capacitances, weemployed a combination of two methods. First method is mea-surement of an open test structure. Second is the variation ofreverse bias across and junctions of a cold-HBT todistinguish between the junction and parasitic capacitances [18].Both methods resulted in similar values of and , but

obtained from the second method was significantly largerthan that from the first. We believe that this is due to the fulldepletion of the emitter n-region under reverse bias conditionwhich results in a misinterpretation of the variation of the totalmeasured capacitance with bias. Therefore, we suggest to use

and measured from an open test structure, and onlyfrom the second method. This way, one avoids the extra

measurements of the cold-HBT at variable reverse biases; onlyone cold-HBT measurement is required to find , which hasto be carried out for the purpose of extracting anyway.

Once the pad capacitances are determined, the internaldevice can be de-embedded from them. Next, one shouldobtain maximum amount of information from measuredcold-HBT results. In this analysis, we will have the followingadditional assumptions which all seem physically justifiable:1) is assumed bias independent, 2) is constant at

Fig. 3. Plot of! � Im(Z ) versus! under cold-HBT condition.

low current levels, but it may change at higher currents, and 3)area area only under low current injection

condition; it may change at higher levels of current. It is quiteclear that the above assumptions are much less restrictivethan those in [15]. In [15] it is assumed that all the extrinsicseries elements ( and ) and areabsolutely bias-independent, while this is not required in thepresent work.

As seen from (7), (8), and (13), at high frequencies undercold condition the real parts of , and

saturate at , and, respectively (see Fig. 2). In case any of the

real parts is not completely saturating at high frequencies, onecan plot it versus then fit a straight line through the datapoints and extrapolate to the-intercept. Since at low currentsis equal to the area ratio between the and junctions,one has a system of three equations and four unknowns, namely

, and . Our approach to find these elementsis to assume a reasonable value for, which, for instance, canbe obtained from dc open collector measurement [22]. It is im-portant to mention that the above value of only serves as aninitial guess and it will be corrected in one of the early stages ofparameter extraction for hot-HBT, after which only one or max-imum two iterations will result in converging values of all theseries resistive elements. Once is known, the other three re-sistances can be found, but only will be assumed constantand fed into the parameter extraction procedure for hot-HBT.

Although the information obtained from imaginary parts ofthe -parameters measured under cold condition is not requiredfor the parameter extraction of hot-HBT, it is constructive toshow the variation of to confirm the validity of (7), (8),and (13). Fig. 3 shows a plot of

, and versus . Linear variation of these plotsconfirms, once again, the validity of the approximations usedto derive (7), (8), and (13). The-intercept of the plots are

, and , respectively. A zero-intercept for theplot of versus supports the earlier statementthat the last terms in (7) and (13) are indeed very small.


Next the -parameters of the device under forward activemode with variable and constant ( V in this case)will be measured. The reason for having a constantratherthan a constant will be clarified later. Bearing in mind that(7) and (8) are still valid under hot-HBT condition, one canobtain the values of

, and by plotting real parts ofand versus , and and

versus . Since is known from coldresults, can be determined and consequently andare evaluated. In [15], after is obtained, is determinedfrom and it is stated thatthis parameter is very much sensitive to the value of. Butin the present method and are obtained independentlyfrom -intercept and gradient of the plot ofversus , respectively.

If is plotted against , the gradient of thefitted line will be equal to . Since is known,

can be determined. If is extremely large, then the termwould be negligibly small and almost compa-

rable to the terms already neglected in the derivation of (8).Therefore, the plot of versus may resultin a nonlinear variation or even a negative slope. In such cir-cumstances, one can use a large value forbearing in mindthat this element does not affect the small-signal parameters sig-nificantly. As to the determination of and , one canconsider the inverse dependence of resistance on area:

area areaarea

(14a)

(14b)

At this stage, all of the terms on the RHS of (9) and (10) areknown, and therefore, and can be evaluated. Variationof with frequency will be discussed in the next section. Asto the determination of , magnitude of will be-come large at high frequencies. Consequently, any small errorin the determination of , or may resultin a significant deviation of at higher frequencies. But theeffect of the above impedance blocks on is just minimalat lower range of frequency where . Therefore,

can be evaluated from the real part of RHS of (10)at low frequencies. Fig. 4 shows the variation of withfrequency for different values of dc collector current. All of theplots in Fig. 4 saturate at low frequencies at , andat higher frequencies asymptotically approach, as expectedfrom the formulation of in (A5) [7]. Determined values of

can be plotted against to differentiate be-tween and (Fig. 5). The -intercept of this plot gives acorrected , which has to be used in order to obtain a cor-rected value of through the cold-HBT measured resis-tances. can also be found from the gradientof the plot in Fig. 5, which gives an ideality factor,, of 1.03.The sudden increase of at the highest current pointis due to device self-heating which is known to increase both

and [23].

Fig. 4. Plots ofReal(Z ) versus frequency under variableI . All the curvessaturate at low frequencies to the value of(R + R ).

Fig. 5. Variation of(R +R ); (� +R �C ), and� as determinedfrom Figs. 4, 7, and 8, respectively, with(1=I ). Extrapolatedy-intercepts ofthe fitting lines giveR ; � , and� + (R +R )C , respectively.

Although any change in will be directly reflected to achange in , and with more or less similar mag-nitude, the resultant variation of the latter parameters only has aminor effect on and , which are determined in the lowfrequency region where . Therefore, the above pro-cedure will be a very fast converging iteration with only oneor two steps required. It is worth mentioning that in [15]

, and are determined by numerical optimization and/orusing assumptions related to extremely high frequencies, whilefully analytical methods in measurable range of frequency areemployed in the present work.

Once the iteration procedure is converged, one can plot theimaginary part of versus to find and thus

. Imaginary part of , obtained from the RHS of (10), isvery much sensitive to the value of. Therefore, an accurate


TABLE IDIRECTLY EXTRACTED AND OPTIMIZED PARAMETERS UNDERVARIABLE COLLECTOR CURRENT AND CONSTANT V OF 0.80 V. THE

RELATIVE ERRORS OFCALCULATION , AS DEFINED IN [15], ARE ALSO GIVEN

Fig. 6. Im(Z ) versus! under various collector current levels. The gradientof the fitting line is equal to(L � R C ).

value of considering the undercutting of and junc-tions is crucial in determining , otherwise one would observea nonphysical saturating behavior for .is an increasing function of (see Fig. 6), but once correctedfor the variation of , shows an almost constant value of

versus collector current. Values of all the extracted param-

eters for the device under study with variableand constantV are summarized in Table I.

IV. DELAY TIME ANALYSIS

In the previous section, direct extraction of the parameterwas explained using (9). The frequency dependence of this

parameter includes sufficient information to extract , and. This is to be discussed in this section. Using (A8) given in

the Appendix one can write

Then, expanding the Taylor series of and ignoring theterms (and higher powers of), the following equation can

be derived:

(15)

Therefore, and the term inside the square bracket in (15)can be extracted from the-intercept and gradient ofversus . This plot is shown in Fig. 7 for the device understudy at various collector current levels. A linear behavior canbe observed in this plot for the low to medium frequency range.

If one further assumes

(16a)

(16b)


Fig. 7. Variation of1=j�j with ! , andIm(�)=Re(�)with ! under variousI levels.

then

(17a)

(17b)

Therefore, can be obtained from a plotof versus (Fig. 7).The values of at various current levels areplotted against in Fig. 5. Since is already known asa function of can be determined from the gradientof the above plot. This method assumes that does not varysignificantly with slight changes of in the current range con-sidered. Linearity of this plot confirms that the latter assumptionis a reasonable one. The obtained value of is fF. Theforward transit time, , can also be accurately evaluated fromthe -intercept of the above plot. This method of characterizingthe forward transit time is only relying on an accurate value of

, which is to be used in (9) to find ; collector series in-ductance can be shown to have a negligible effect on. There-fore, the present method is expected to be much more reliablethan the conventional method of plotting total delay time,,versus , which additionally requires a prior knowledge of

and (see (19) and Fig. 5). Also it is shown by Lee [24]that this method of determining is much less sensitive to er-rors in de-embedding pad capacitances. However, the methodsuggested by Lee [24], [25] is slightly different from the oneused in the present work. Lee has suggested to use

(18)

while the last approximate equality in (18) clearly ignores theterm in (17). Therefore, the present methodis expected to give more accurate results.

After finding from the plot in Fig. 5, the plots in Fig. 7give us two equations for the two unknowns and . Themethod of extracting and in this work can be consideredas a modified version of our previous work [5]. Finally, canbe evaluated using (A9). At this stage it must be pointed out thatLi and Prasad [14], [15] used the invalid assumption of(which ignores ) and a plot of , obtainedfrom Fig. 6, versus to find . Therefore, they obtaineda nonlinear plot (Fig. 13 in [15]) and an inaccurate value ofwhich necessitated numerical optimization. But even optimiza-tion is relatively insensitive to , and hence, could notbe determined accurately in their work. This problem does notexist in the present work. Additionally, the formula for in[15] is incorrectly stated as and the term

is ignored in their expression. Based onthese formulae, Liet al.observed values of which were un-expectedly varying with both and (Tables II and III in[15]). In contrast, ’s obtained in the present work are almostconstant with bias ( ps), since a physically correctformula for [(A9)] is used here.

The total delay time in HBT’s can be written as [26]:

(19)

The conventional method of finding the total delay time is toplot versus frequency and extrapolate the graph with theslope 20 dB/dec (single-pole approximation for ) to locatethe frequency, , where reaches 0 dB gain. However,usually deviates from the20 dB/dec roll-off due to the impor-tance of higher order poles and zeros, the transit time effect [27],or frequency dispersion related to extrinsic base surface recom-bination [28]. This makes the task of finding a precise valuefor very difficult, especially in the case of state-of-the-artHBT’s with cutoff frequencies in excess of 200 GHz. There-fore, a method of characterizing the total delay time based onlow frequency measured data would be extremely valuable. Inthe following, it will be shown that

at low frequencies. (20)

Since is one of those elements which can be evaluated quiteprecisely at low frequency, the above equation serves as a lowfrequency rule to find an accurate value of total delay time. Inorder to prove (20), one needs to consider some “first-order”approximations:

(21)

(22)

Equations (21) and (22) are more restrictive than (4)–(6), butone expects them to be still valid for almost an order of magni-tude of frequency (typically GHz GHz). Usingassumptions (21) and (11), can be written as the ex-pression shown at the bottom of the next page, whereis theimaginary part of . Now if one uses the low frequency assump-


Fig. 8. Variation ofRe(Z ) with frequency under variousI levels. Thesaturated values of the plots at low frequencies are equal to� =C . Thesudden increase inRe(Z ) at I = 40 mA is due to the device self-heating(see the text).

tions of (i.e., (16)) and additionally assumes , thenand (20) follows.

Fig. 8 shows the variation of with frequency for var-ious ’s. The plot at all different current levels saturate at lowfrequencies. The constant range of the plots gets narrower forlower current levels, primarily due to the narrower range of va-lidity for assumption (11). The values of thus calculatedare compared in Table I with those obtained from extrapolationof at higher frequencies. The slight difference between thetwo sets of ’s is mainly due to the fact that in all ofthe cases rolls off with gradient less than 20 dB/dec (18.5–19.5dB/dec in these cases). Therefore, using is expected togive more accurate delay times. Finally, it should be pointed outthat both the above sets of calculated ’s are for the devicede-embedded from pad capacitances, which do not belong to theactual device anyway.

V. DISCUSSION

Sections II and III presented a completely analytical HBT pa-rameter extraction technique, which was successfully applied toa m InGaP/GaAs DHBT. All the extracted param-eters under variable collector current and constantof 0.8 V

Fig. 9. Comparison between the measured (symbols) and calculated (solidlines)S-parameters atI = 25 mA andV = 0:80 V. Both measured andcalculatedS are scaled down by a factor of 40.

are summarized in Table I. Fig. 9 compares the measured-pa-rameters with those calculated using extracted elements at col-lector current of 25 mA. Excellent agreement between the mea-sured and calculated data can be observed in the entire range

(22)


of frequency. It is known that polar plots of-parameters donot perfectly reflect the quality of agreement between measuredand calculated data. Also the high frequency portion (GHz) of the -parameters in a polar plot is compressed in asmall area of the plot. Therefore, we have shown the real andimaginary parts of the measured and calculated-parametersfor mA in Fig. 10(a) and (b), respectively. The calculated

-parameters also show a very good fit to the measured ones.Excellent agreement between the measured and calculated pa-rameters eliminates the necessity for a final optimization step.Indeed, to prove the latter we have carried out an optimizationprocess using HP-ADS optimization facility with the extractedparameters as initial guess. The values of the elements after op-timization for mA are also shown in Table I, togetherwith the average relative errors, as defined in [15], for both cal-culated and optimized parameters. It is clear that optimizationdoes not improve the error significantly.

Fig. 11 shows the variation of the extracted total junc-tion capacitances in Table I versus collector current. Also shownare the measured capacitances under constantof 0.5 and 1.2V, and constant of 2.1 V. It can be observed that reduceswith increasing under constant condition, similar to thetrends observed in [29] and [30]. The reduction of with cur-rent is attributed to current-induced broadening of the de-pletion layer, and the variation of space charge with dueto electron velocity modulation [30]. However, all these currentdependent phenomena happen inside the intrinsic part of the de-vice where injection of electrons occurs. Therefore, one expects

to remain constant, and all the change in should bereflected to a similar change in . Consequently, we havechosen to keep constant in our recommended parameter ex-traction procedure. will be calculated using low current(or cold) measured and area area underthe same value as in the high current data; any change in

with current will be directly reflected into a similar changein and . However, one should notice that the variation of

at high current does not change anything in the determinationof from cold-HBT data.

Under a constant of 2.1 V, shows an initial increasewith . This is due to fact that higher requires higher , andhence, a lower under constant condition. Therefore, both

and will increase initially, and it would be difficult todifferentiate between them. Variation of with current underconstant was also observed in [15], but the authors did notexplain this behavior.

Other interesting features of the data in Table I include a re-duction of (and to a smaller extent) at higher currentsdue to the emitter current crowding. The values of inductances

, and seem to be more or less constant with bias; athighest bias point they all show some increase due to the deviceself-heating. shows a continuous increase with collector cur-rent and saturates at higher currents before starting to fall-off atthe highest bias point. This reflects to a similar trend for the vari-ation of common-emitter dc current gain,, with current. Thesudden change of many of the parameters at mA is mostprobably due to the device self-heating rather than Kirk effect.Kirk effect (or base push-out) is expected to happen at collectorcurrents around 100 mA for the dimension and collector doping

(a)

(b)

Fig. 10. Comparison between the calculated (solid lines) and measured(symbols): (a) real and (b) imaginary parts of theZ-parameters as a function offrequency underI = 9 mA andV = 0:80 V condition. A differentI level,as compared to Fig. 9, is used to demonstrate the applicability of the presentapproach for a wide range of bias.

level of the device under study. (See also the following discus-sion on delay times.) Since device temperature rise is expectedto increase both and [23], we have evenly divided thesudden increase of at mA between the twoelements.


Fig. 11. Extracted values of the totalB=C capacitance versus collector currentfor constant values ofV (0.50, 0.80, and 1.20 V) andV (2.10 V). Solid linesare used just to guide the eyes.

The base transit time remained almost constantps as the collector current was varied in the range (2–40) mA.This further supports the idea that Kirk effect is not happened at

mA. The base transit time can be written as [31]

(23)

where is the neutral base width, is the diffusion con-stant in the base, and is an average velocity of electronsat the base end of the depletion region. is higherthan the static saturation velocity of electrons due to the velocityovershoot effect. We adopt cm/s for the latter param-eter as in [23]. For the base doping density in the present device,minority electron mobility of cm /V s is expected [32]which results in cm /s. Therefore, usingÅ one obtains ps from (23). The larger measuredvalue of is due to the carrier trapping behind the triangularpotential barrier at the heterojunction, as discussed in [5].Also, since minority electron mobility inside the base varieswith temperature as [33], will be almost temperatureindependent. Consequently, does not change significantly asself-heating occurs, though it may change slightly through thereduction of .

The collector depletion layer delay time can also be expressedas , where is the depletionlayer width (Fig. 1). can be estimated usingfF as m. Therefore, average value of at low cur-rent levels ( ps) results incm/s inside InGaP collector, which is supposed to be somewhatsmaller than the average velocity of electrons inside GaAs [5].When self-heating occurs, this velocity is expected to be signifi-cantly reduced [23], hence causing a sharp increase ofunderhigh current condition. The increase of , and withtemperature are other contributors to the enlargement ofat

the highest current level in Fig. 5. The-intercept of the linearfit to the low current variation of with is 5.65 ps

. Using average values of ,and in Table I, the term can be calculatedas 3.35 ps, which results in ps. This is close, butnot exactly equal, to the-intercept of versus

, which is 2.41 ps. As discussed in Section IV, the lattermethod is expected to give more accurate values of.

VI. CONCLUSION

In this work, an improved HBT small-signal parameter ex-traction technique is developed and applied to extract the pa-rameters of an InGaP/GaAs DHBT. The method relies on mea-surement of -parameters under constant but variable , in-cluding cold-HBT measurement. The approximationsused to derive the simplified-parameter formulations were re-vised, and it was shown that the present method benefits from awide range of applicability, which makes it appropriate for var-ious types of HBT’s including InP-based and GaAs-based singleand double HBT’s. Furthermore, all equivalent circuit elementsare extracted directly without reference to numerical optimiza-tion, and it was shown that an optimization step following theanalytical extraction does not improve the error significantly.Therefore, we believe that this method can be used as a stan-dard technique to extract the equivalent circuit elements of var-ious types of HBT’s. We have also applied the above parameterextraction technique to InP-based HBT’s, results of which willbe presented in a forthcoming publication.

In addition, it was shown in Section IV that for thedevice de-embedded from parasitic pad capacitances

at low frequencies. Therefore, totaldelay time of an HBT can be extracted at low frequencies,without the need to measure at very high frequencies and/orextrapolate with dB/dec roll-off. Furthermore, themethods presented in [5] and [25] for extracting the forwardtransit time was modified to evaluate and its components( and ) more accurately.

Analysis of the extracted elements in Section V demonstratedthat all of them behave according to physical expectations.Among the physical phenomena observed and explained werethe reduction of junction capacitance at high collectorcurrents, the effect of self-heating on small-signal elementsand delay times, and reduction of and due to emittercurrent crowding.

APPENDIX

-PARAMETER RELATIONS

Consider the HBT small-signal equivalent circuit shown inFig. 1. After de-embedding the parasitic pad capacitances andmerging and into a single element , as discussedin Section II, one can arrive at the following-parameter rela-tions:

(A1a)

(A1b)


(A1c)

(A1d)

Therefore

(A2a)

(A2b)

(A2c)

The impedance blocks in equations (A1) and (A2) are defined(see also Fig. 1) as

(A3)

(A4)

(A5)

(A6)

(A7)

The common-base current gain and the input capacitancecan also be written as [16], [17]:

(A8)

(A9)

wherecommon-base dc current gain;base transit time;collector depletion region delay time;empirical factor that fits the single-pole expression ofbase transport factor to its more accurate secant hyper-bolic representation [16].

A value of is used in the majority of the previous pub-lications. includes the terms related to both depletioncapacitance and the so-called base diffusion (or storage) capac-itance.

ACKNOWLEDGMENT

The authors would like to thank K. Smith for technical assis-tance, and A. Lai for optimization of parameters. M. Sotoodehalso wishes to acknowledge the scholarship provided by theMinistry of Culture and Higher Education (MCHE) of Iran.

REFERENCES

[1] B. Bayraktaroglu, “GaAs HBT’s for microwave integrated circuits,”Proc. IEEE, vol. 81, pp. 1762–1785, Dec. 1993.

[2] P. M. Asbecket al., “GaAs-based heterojunction bipolar transistors forvery high performance electronic circuits,”Proc. IEEE, vol. 81, pp.1709–1726, Dec. 1993.

[3] D. Costa, W. U. Liu, and J. S. Harris Jr., “Direct extraction of theAlGaAs/GaAs heterojunction bipolar transistor small-signal equivalentcircuit,” IEEE Trans. Electron Devices, vol. 38, pp. 2018–2024, Sept.1991.

[4] D. R. Pehlke and D. Pavlidis, “Evaluation of the factors determiningHBT high-frequency performance by direct analysis ofS-parameterdata,” IEEE Trans. Microwave Theory Tech., vol. 40, pp. 2367–2373,Dec. 1992.

[5] M. Sotoodehet al., “Direct extraction and numerical simulationof the base and collector delay times in double heterojunctionbipolar transistors,”IEEE Trans. Electron Devices, vol. 46, pp.1081–1086, June 1999.

[6] C.-J. Wei and J. C. M. Hwang, “Direct extraction of equivalent circuit pa-rameters for heterojunction bipolar transistors,”IEEE Trans. MicrowaveTheory Tech., vol. 43, pp. 2035–2040, Sept. 1995.

[7] A. Samelis and D. Pavlidis, “DC to high-frequency HBT-model param-eter evaluation using impedance block conditioned optimization,”IEEETrans. Microwave Theory Tech., vol. 45, pp. 886–897, June 1997.

[8] S. J. Spiegel, D. Ritter, R. A. Hamm, A. Feygenson, and P. R. Smith,“Extraction of the InP/GaInAs heterojunction bipolar transistor small-signal equivalent circuit,”IEEE Trans. Electron Devices, vol. 42, pp.1059–1064, June 1995.

[9] U. Schaper and B. Holzapfl, “Analytical parameter extraction of theHBT equivalent circuit with T-like topology from measuredS-parame-ters,” IEEE Trans. Microwave Theory Tech., vol. 43, pp. 493–498, Mar.1995.

[10] J. M. M. Rios, L. M. Lunardi, S. Chandrasekhar, and Y. Miyamoto, “Aself-consistent method for complete small-signal parameter extractionof InP-based heterojunction bipolar transistors (HBT’s),”IEEE Trans.Microwave Theory Tech., vol. 45, pp. 39–45, Jan. 1997.

[11] A. Kameyama, A. Massengale, C. Dai, and J. S. Harris Jr., “Analysis ofdevice parameters for pnp-type AlGaAs/GaAs HBT’s including high-injection using new direct parameter extraction,”IEEE Trans. ElectronDevices, vol. 44, pp. 1–10, Jan. 1997.

[12] G. Dambrine, A. Cappy, F. Heliodore, and E. Playez, “A new methodfor determining the FET small-signal equivalent circuit,”IEEE Trans.Microwave Theory Tech., vol. 36, pp. 1151–1159, July 1988.

[13] M. Berroth and R. Bosch, “Broad-band determination of the FET small-signal equivalent circuit,”IEEE Trans. Microwave Theory Tech., vol. 38,pp. 891–895, July 1990.

[14] B. Li and S. Prasad, “Basic expressions and approximations in small-signal parameter extraction for HBT’s,”IEEE Trans. Microwave TheoryTech., vol. 47, pp. 534–539, May 1999.

[15] B. Li, S. Prasad, L.-W. Yang, and S. C. Wang, “A semianalytical pa-rameter-extraction procedure for HBT equivalent circuit,”IEEE Trans.Microwave Theory Tech., vol. 46, pp. 1427–1435, Oct. 1998.

[16] R. L. Pritchard,Electrical Characteristics of Transistors. New York:McGraw Hill, 1967.

[17] W. Liu, Handbook of III–V Heterojunction Bipolar Transistors. NewYork: Wiley, 1998.

[18] Y. Gobert, P. J. Tasker, and K. H. Bachem, “A physical, yet simple,small-signal equivalent circuit for the heterojunction bipolar transistor,”IEEE Trans. Microwave Theory Tech., vol. 45, pp. 149–153, Jan. 1997.

[19] M. Vaidyanathan and D. L. Pulfrey, “Extrapolatedf of heterojunc-tion bipolar transistors,”IEEE Trans. Electron Devices, vol. 46, pp.301–309, Feb. 1999.

[20] R. Anholt et al., “Measuring, modeling, and minimizing capacitancesin heterojunction bipolar transistors,”Solid-State Electron., vol. 39, pp.961–963, July 1996.

[21] A. H. Khalid, M. Sotoodeh, and A. A. Rezazadeh, “Planar self-alignedmicrowave InGaP/GaAs HBT’s using He/O implant isolation,” inProc. 5th Int. Workshop High Performance Electron Devices for Mi-crowave and Optoelectronic Applications, 1997, pp. 279–284.

[22] I. E. Getreu,Modeling the Bipolar Transistor. New York: Elsevier,1978.

[23] D. A. Ahmari et al., “Temperature dependence of InGaP/GaAs hetero-junction bipolar transistor DC and small-signal behavior,”IEEE Trans.Electron Devices, vol. 46, pp. 634–640, Apr. 1999.

[24] S. Lee, “Effects of pad and interconnection parasitics on forward transittime in HBT’s,” IEEE Trans. Electron Devices, vol. 46, pp. 275–280,Feb. 1999.

[25] , “Forward transit time measurement for heterojunction bipolartransistors using simpleZ parameter equation,”IEEE Trans. ElectronDevices, vol. 43, pp. 2027–2029, Nov. 1996.


[26] W. Liu, D. Costa, and J. S. Harris Jr., “Derivation of the emitter-collectortransit time of heterojunction bipolar transistors,”Solid-State Electron.,vol. 35, pp. 541–545, Apr. 1992.

[27] S. Prasad, W. Lee, and C. G. Fonstad, “Unilateral gain of heterojunctionbipolar transistors at microwave frequencies,”IEEE Trans. Electron De-vices, vol. 35, pp. 2288–2294, Dec. 1988.

[28] B. Ihn et al., “Surface recombination related frequency dispersionof current gain in AlGaAs/GaAs HBTs,”Electron. Lett., vol. 34, pp.1031–1033, 1998.

[29] L. H. Camnitz and N. Moll, “An analysis of the cutoff-frequencybehavior of microwave heterostructure bipolar transistors,” inCom-pound Semiconductor Transistors: Physics and Technology, S. Tiwari,Ed. Piscataway, NJ: IEEE Press, 1993, pp. 21–45.

[30] Y. Betser and D. Ritter, “Reduction of the base-collector capacitance inInP/GaInAs heterojunction bipolar transistors due to electron velocitymodulation,”IEEE Trans. Electron Devices, vol. 46, pp. 628–633, Apr.1999.

[31] M. B. Das, “High-frequency performance limitations of mil-limeter-wave heterojunction bipolar transistors,”IEEE Trans. ElectronDevices, vol. 35, pp. 604–614, May 1988.

[32] S. Adachi,GaAs and Related Materials: Bulk Semiconducting and Su-perlattice Properties, Singapore: World Scientific, 1994, p. 602.

[33] K. Beyzaviet al., “Temperature dependence of minority-carrier mobilityand recombination time inp-type GaAs,”Appl. Phys. Lett., vol. 58, no.12, pp. 1268–1270, 1991.

Mohammad Sotoodeh was born in 1968. Hereceived the B.Sc. and M.Sc. degrees (with highesthonors), both in electronic engineering, fromIsfahan University of Technology, Iran, and fromthe University of Tehran, Iran in 1991 and 1994, re-spectively. He is currently pursuing the Ph.D. degreeat King’s College London, U.K. His research thesisis on design, optimization, and characterization ofInGaP/GaAs double HBT’s for microwave powerapplications.

His research interests include heterojunctionbipolar transistors for high frequency, high power, and/or high temperatureapplications, numerical simulation of semiconductor devices, dc and highfrequency characterization of HBT’s, III–V semiconductor compounds andtheir material parametrization.

Mr. Sotoodeh is the winner of the first award in the third NationwideOlympiad of Mathematics held in Zahedan, Iran, in 1986.

Lucia Sozziwas born in Piacenza, Italy, in 1974. Sheis currently pursuing the Laurea degree in electronicengineering at the University of Parma, Parma, Italy.During her final year’s project she spent a researchleave with the Department of Electronic Engineering,King’s College London, U.K., where she worked onHBT, rf, and dc modeling and characterization.

Alessandro Vinay was born in Piacenza, Italy, in1973. He is currently pursuing the Laurea degree inelectronic engineering at the University of Parma,Parma, Italy. During his final year’s project he spenta research leave with the Department of ElectronicEngineering, King’s College London, U.K., workingon HBT modeling and characterization.

A. H. Khalid received the M.Sc. degree in physics from Government College,Lahore, Pakistan, and the M.Phil. degree in experimental semiconductor physicsin 1990 from Quaid-i-Azam University, Islamabad, Pakistan.

He joined the Department of Electronics, Quaid-i-Azam University, as a Re-search Associate, to characterize the conductive polymers. In 1992, he regis-tered for the Ph.D. at King’s College, London, U.K. His research work was onfabrication and design of transparent gate field effect transistors (TGFET’s). Hethen worked on EPSRC funded projects on fabrication of multilayer MMIC’son GaAs substrate. He also worked on fabrication of self-aligned double het-erostructure bipolar transistors (DHBT’s). His research interests are in mate-rial properties of indium-tin oxide (ITO) and ITO-based contact technology,and novel fabrication techniques for advanced semiconductor devices such asHEMT’s and HBT’s. He is currently with King’s College.

Zhirun Hu received the B.Eng. degree in telecom-munication engineering from Nanjing Institute ofPosts and Telecommunications, Nanjing, China,in 1982, and the M.B.A. degree and Ph.D. degreein electrical and electronic engineering from theQueen’s University of Belfast, Belfast, U.K., in 1988and 1991, respectively.

In 1991, he joined the Department of Electricaland Electronic Engineering, University Collegeof Swansea, U.K., as a Senior Research Assistantin semiconductor device simulation. In 1994, he

rejoined the Department of Electrical and Electronic Engineering, Queen’sUniversity of Belfast, as a Research Fellow in silicon MMIC design. In 1996,he joined GEC Marconi Instruments as a Microwave Technologist workingon the new generation of microwave power detector/sensors. He is presentlya Lecturer in the Department of Electronic Engineering, King’s College,University of London. His main research interests include computer-aideddesign and optimization of microwave and millimeter-wave integrated circuits,artificial neural network modeling for passive 3-D microwave components, andwide-band gap heterojunction device simulation and optimization.

Ali Rezazadeh (M’91) received the Ph.D. degreein applied solid state physics from the University ofSussex, Brighton, U.K., in 1983.

In September 1983, he joined GEC-MarconiHirst Research Centre as a Research Scientist andbecame the Group Leader responsible for researchand development into advanced HBT devices andcircuits for high-speed and digital applications. In1988, he became a Senior Research Associate-GroupLeader responsible for research and developmentinto advanced high electron mobility transistor

devices and circuits for analogue applications. In October 1990, he joined theacademic staff of the Department of Electronic Engineering at King’s College,London. He is currently a Reader in Microwave Photonics and ConsultingEngineer in the Department of Electronic Engineering, King’s College. He isalso the Head of Microwave Circuits and Devices Research Group, one of thefour research groups in the department. His present work involves the physicsand technology of III–V heterojunction devices and circuits for microwave andoptoelectronic applications. He has contributed three chapters of books andproduced 40 refereed journal papers and 50 conference papers.

Dr. Rezazadeh is the Chairman of IEEE UK&RI MTT/ED/AP/LEO JointChapter and the Chairman of IEE Professional Group E3 (Microelectronics andSemiconductor Devices). He also serves on the Technical Committees of severalinternational conferences. In 1993, he founded The IEEE International Sym-posium on Electron Devices for Microwave and Optoelectronic Applications(EDMO).


Roberto Menozziwas born in Genova, Italy, in 1963.He received the Laurea degree (cum laude) in elec-tronic engineering from the University of Bologna,Bologna, Italy, in 1987, and the Ph.D. degree in in-formation technology from the University of Parma,Parma, Italy, in 1994.

After serving in the army, he joined a researchgroup at the Department of Electronics, Universityof Bologna, Bologna, Italy. Since 1990, he has beenwith the Department of Information Technology,University of Parma, where he became Research

Associate in 1993 and Associate Professor in 1998. His research activitieshave covered the study of latch-up in CMOS circuits, IC testing, power diodephysics, modeling and characterization, and the dc, rf, and noise characteri-zation, modeling, and reliability evaluation of compound semiconductor andheterostructure electron devices such as MESFET’s, HEMT’s, HFET’s, andHBT’s.

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