IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 49, NO. 5, MAY 2002
863
The Correlation Resistance for Low-Frequency Noise Compact Modeling of Si/SiGe HBTs Mattia Borgarino, Member, IEEE, Laurent Bary, Davide Vescovi, Member, IEEE, Roberto Menozzi, A. Monroy, M. Laurens, Robert Plana, Member, IEEE, Fausto Fantini, Member, IEEE, and Jacques Graffeuil, Senior Member, IEEE
Abstract—The measurement of the correlation between the noise generators is a mandatory issue for the low-frequency noise modeling of bipolar transistors, and it is recognized as a very hard experimental task. In the present work, we introduce the concept of correlation resistance and we demonstrate that it can be usefully employed as a guideline for the low-frequency noise modeling in terms of intrinsic noise sources. As a proof of concept, the investigation technique is applied to submicron, BiCMOS-compatible Si/SiGe heterojunction bipolar transistors. It is pointed out that a satisfactory description of the transistor low-frequency noise behavior can be obtained by taking into account noise sources associated with surface recombination/fluctuation in the extrinsic base region. Index Terms—Heterojunction bipolar transistor (HBT), low-frequency noise, semiconductor device modeling, SiGe.
I. INTRODUCTION
T
HE NEW information society will lead to an ever-increasing demand for RF and microwave circuits. More precisely, for most of these applications, it will be very important to fabricate high spectral purity microwave sources, in order to maintain high sensitivity and bit rate. In this field, one key point gaining more and more relevance is the assessment of the phase noise behavior of RF and microwave oscillators. It is well known that the phase noise of any nonlinear circuit largely depends on the low-frequency noise (LFN) sources of the active devices through more or less complicated up-conversion processes. The ability of modeling the LFN behavior of active devices is thus pivotal for predicting the phase noise with good accuracy. Although many works have dealt with the LFN behavior of active devices, there is a lack of data concerning the modeling and the physical location of the noise sources. It is known that bipolar transistors perform better than fieldeffect ones in terms of LFN. In particular, during the last years the SiGe heterojunction bipolar transistor (HBT) has emerged as Manuscript received January 23, 2002. This work was supported in part by the Training and Mobility of Researcher (TMR) European Program “SiGe heterodevices for millimeter-wave applications,” by the ERASMUS European Program, and by the Italian Space Agency (ASI) under Contract I/R/056/01. The review of this paper was arranged by Editor J. N. Burghartz. M. Borgarino and F. Fantini are with the Dipartimento di Ingegneria dell’Informazione, Università di Modena e Reggio Emilia, and INFM, Modena, Italy (
[email protected]). L. Bary is with LAAS-CNRS, 31077, Toulouse, France. D. Vescovi and R. Menozzi are with the Dipartimento di Ingegneria dell’Informazione and INFM, Università di Parma, 43100 Parma, Italy. A. Monroy and M. Laurens are with the ST-Microelectronics, 38926, Crolles, France. R. Plana and J. Graffeuil are with LAAS-CNRS, 31077, Toulouse, France. They are also with the Université Paul Sabatier, Toulouse, France. Publisher Item Identifier S 0018-9383(02)04333-2.
a very promising device for mass-market wireless applications. It indeed fulfills the requirements of compatibility with silicon technology, low LFN magnitude, and high operating speed. Nevertheless, the LFN behavior of modern submicron devices is hard to model, because it is very difficult to discriminate the different noise sources present in the transistor: noise sources related to the ohmic contacts, access regions, device surface and so on. In particular, it is worth pointing out here that the recombination mechanisms taking place at the extrinsic base surface are involved in both the performance and the reliability of III–V HBTs [1]–[3] and modern submicrometer Si BJTs and SiGe HBTs [4]–[6]. The ability of addressing the surface noise source is therefore of particular relevance. Several efforts based on - and -topologies of the transistor small-signal model and on various methods and noise representations have been reported [7]–[19]. Among the various possible noise representations, the one describing the transistor noise behavior in terms of input equivalent noise generators [see Fig. 1(a)] allows to introduce the concept of correlation resistance. Another possible representation describes the transistor noise behavior in terms of short-circuited current noise generators connected at the input and at the output of the transistor [see Fig. 1(b)]. The aim of the present work is to briefly demonstrate that the correlation resistance can be employed as a guide for the intrinsic LFN source modeling of a bipolar transistor. As an example, the technique is applied to a submicrometer, double polysilicon Si/SiGe HBT. It is worth noticing that in the previously cited works [7]–[19], with the exception of [10], [13], [14], the implications of the proposed LFN model on the correlated quantities (e.g., the correlation coefficient) was not discussed. In particular, none of those introduces and debates the concept of correlation resistance. To the best of our knowledge, this is the first work reporting on an extensive discussion of the correlation resistance and its application to Si/SiGe HBTs. The paper is organized as follows. Section II introduces the LFN intrinsic noise source model, and defines the correlation resistance. Section III discusses the properties of the correlation resistance and shows how it can be exploited for LFN modeling. Section IV gives an application to the real case of a Si/SiGe HBT. Finally, the paper is briefly summarized and some conclusions are drawn in Section V. II. LOW-FREQUENCY NOISE MODEL The model employed for the present investigation is shown in Fig. 2. It is based on the model proposed by Kirtania et al. [20] and it also takes into account the contributions of the base and emitter series resistance, as already done by Kleinpenning
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IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 49, NO. 5, MAY 2002
From electrical network theory and the theoretical recommendations reported in [23], we obtain the following expressions for the equivalent input noise generators and and : their cross-spectrum
(1) (2)
(3) Fig. 1. Low-frequency noise representation describing the transistor noise behavior through (a) equivalent input noise generators or (b) short-circuit current noise generators connected at the input and at the output of the transistor. S and S are the equivalent input voltage and current, respectively, noise sources. S and S are the short-circuit base and collector current noise sources, respectively.
Fig. 2. Intrinsic noise source model. It is based on a 5-topology small-signal bipolar transistor model. Note that the sources S and S split the base access resistance into three terms.
[11]. The model in [20] neglects these contributions as well as and . The source is associated with the sources base surface recombination [16], [20], [21]. In addition, the dif[20], [21], which fusion or quantum noise is described by can also account for the carrier number fluctuations due to minority carrier trapping in the base bulk or at the base–emitter is related to recombination heterojunction interface [8]. effects in the base bulk and in the base–emitter space-charge region (SCR) as well as to quantum noise [20], [21], and diffusion is associated with base surface recombination noise [8]. effects [7], [15], [17], [18], [20], which include SCR recombination components when the base–emitter SCR gets close to the base surface [20]. This source may account also for recombination/fluctuation phenomena occurring at the mono-/polycrystal Si/SiGe interface close to the LOCOS bird’s beak (the deposited Si/SiGe layer is monocrystalline over the Si and polycrystaline over the LOCOS) and in the poly-Si/SiGe layer on the LOCOS and take into account the noise [22]. The sources associated with the base and emitter access regions and contacts.
where is the small-signal current gain (assumed to be equal to and are the emitter and base acthe dc current gain), is the transistor dynamic cess resistances, respectively, and , input impedance, given by the dynamic resistance of the base–emitter junction. being Note that the input intrinsic noise sources split the base access and . Obviously resistance into three terms . The expressions (1)–(3) derive from Van der Ziel’s theory [21] and assume that the intrinsic noise sources are independent. and However, it is worth noticing that the noise sources may be associated to similar physical mechanisms (surface recombination) and therefore one could expect that they may exhibit some degree of correlation, leading to the pres(the cross-spectrum between ence of the real part of and ) in the expressions of and and the sources to the presence of the whole complex cross-spectrum in the expression of , which therefore becomes a complex quantity. Under the hypothesis of independent noise sources, is a purely real quantity. which is adopted in this work, and are reThis hypothesis implies that the sources lated to different surface recombination or fluctuation mechanisms, following what reported in [21], [22]. The correlation resistance is defined as follows: (4) where is the real-part operator. From the model of Fig. 2, its expression is shown in (5) at the bottom of the next page, and can be rewritten as follows:
(6) where
(7)
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and (8) Equation (6) offers the advantage of concentrating the efand in only two terms, fects of the sources and . and represent, respectively, the input equivalent noise current generator and the cross-spectrum and only were that would be observed if the sources present. In this case, (4) becomes (9)
OF THE CORRELATION AND LFN MODELING
III. PROPERTIES
RESISTANCE
Equation (5), shown at the bottom of the page, shows that depends on the values of the access resistances and but it is independent of their noise contributions. What is represents the weighted average of the most important, , , , four resistances , with the intrinsic noise sources and , , , and , respectively, as weights. This a useful indicator of the relative importance of makes each source. In this way, it can provide helpful suggestions for LFN modeling, as will clearly appear from the following considerations. In the absence of surface recombination and/or of extrinsic fluctuation, we can observe from equation (5) that . If can be neglected, , . otherwise On the other hand, the presence of surface recombination . and/or of extrinsic fluctuation leads to a decrease of can be expected, because Values lower than and weight resistances . Fig. 3 shows an ex. In this ample of the simulated frequency dependence of . Note that example, we set at the lowest frequencies, where the contribution and is not negligible. The figure also of the sources in the whole frequency range. shows only is considered and is neglected, In particular, if is as in [21], the minimum possible value for , while if only is taken into account, the min. On the basis of the imum possible value reduces to is an previous discussion, it should clearly appear that indicator of base surface recombination in bipolar transistors. Finally, it should be noted that choosing does not imply a lack of generality: the same trends as observed . in Fig. 3 are found with different values of
Fig. 3. Simulation of the frequency dependence of the correlation resistance, as obtained from the model described in Fig. 2. Note that if only the sources S and S were present, the correlation resistance ( in this case) would be in the whole frequency range.
