UDK621.3:(53 + 54+621 +66), ISSN0352-9045 Informacije MIDEM 26(1996)3, Ljubljana BASE TRANSPORT PROPERTIES OF npn SiGe HETEROJUNCTION BIPOLAR TRANSISTORS: PHYSICS AND MODELLING Saša Sokolič and Slavko Amon Faculty of Electrical Engineering, University of Ljubljana, Slovenia Keywords: semiconductors, bipolar transistors, HBT, lieterojunction bipolar transistors, BJT, bipolar junction transistors, physical properties, comparison of properties, SiGe HBT, SiGe heterojunotion bipolar transistors, base transport properties, base transit times, bandgap narrowing, effective mass, collector current, base transit time, Fermi-Dirac statistics,analitical modelling. Abstract: The base transport properties of npn SiGe heterojunction bipolar transistors (HBTs) are analyzed. Physical effects influencing the electron current in the base and the base transit time are discussed, and the modelling of these effects is described. The results of modelling demonstrate that the improvement of SiGe HBTs compared to Si BJTs increases with cooling and decreases with increasing doping concentration in the base, and that Fermi-Dirac statistics influence significantly the electron current in the base. The analytical approach to the modelling of base transport properties is presented, rendering simple and accurate evaluation of the electron current in the base and the base transit time in the wide range of doping concentrations at 77K and 300K. Transportne lastnosti baze v npn SiGe heterospojnih bipolarnih tranzistorjih: fizikalna slika in modeliranje Ključne besede: polprevodniki, transistorji bipolarni, HBT transistorji bipolarni heterospojni, BJT transistorji s spojem bipolarnim, lastnosti fizikalne, primerjava lastnosti, SiGe HBT transistorji bipolarni heterospojni, lastnosti transportne baze transistorja, časi tranzitni baze transistorjev, oženje pasu prepovedanega, masa efektivna, tok kolektorski, čas tranzitni baze, Fermi-Dirac statistika, modeliranje analitično Povzetek: V delu so analizirane transportne lastnosti baze v npn SiGe heterospojnih bipolarnih tranzistorjih (HBT). Razloženi so fizikalni efekti, ki vplivajo na tok elektronov v bazi in na tranzitni čas baze. Opisano je modeliranje teh efektov. Rezultati modeliranja kažejo, da se izboljšanje lastnosti SiGe HBT-jev v primerjavi s silicijevimi bipolarnimi tranzistorji povečuje z nižanjem temperature in znižuje z višanjem koncentracije primesi v bazi, ter da Fermi-Diracova statistika bistveno vpliva na tok elektronov v bazi. Predstavljen je pristop k analitičnemu modeliranju transportnih lastnosti baze, ki pripelje do enostavnega in natančnega izračuna toka elektronov v bazi in tranzitnega časa baze v širokem območju koncentracij primesi pri 77K in 300K. 1. Introduction Heterojunction bipolar transistors (HBTs) with strained SiGe layers in the base have been the subject of intensive research in the last few years /1 -7/. Compared to Si BJTs, SiGe HBTs with better current gain and greatly improved cutoff frequencies have been reported /1-3/. Moreover, SiGe BiCMOS technology has been presented, combining unique capabilities of SiGe HBTs with the advantages of CMOS devices /4/. It has been also demonstrated that SiGe HBTs are well suited for low temperature operation and that their performances improve naturally with cooling /5,6/. SiGe HBTs optimized for 77K operation have been recently reported /7/, exhibiting better performances than those of the same technology operating at 30QK. In addition to the superior performances of SiGe HBTs, their compatibility with existing silicon technology represent an important advantage for these devices to find wide use in the semiconductor market. The improvement of SiGe HBTs compared to Si BJTs is closely related to the transport properties of the SiGe base /1/. As a consequence of germanium and compressive strain, several effects influencing carrier transport appear in the base. The most important effect - bandgap reduction due to strain and alloying in the base - results in increased electron injection from the emitter to the base and, consequently, increased electron current in the base /1/. Further, graded germanium profile in the base introduces graded energy gap in the base and, consequently, a beneficial effective electrical field in the base, improving the high frequency characteristics of SiGe HBTs /1/. Beside the bandgap reduction, several other effects in the base additionally influence the device characteristics. The insight into the physics of the base transport mechanisms and related effects is inevitable for an understanding of the possibilities for further improvement of SiGe HBTs. Besides, the modelling of these effects is important for accurate analysis and optimization of SiGe HBTs. Since the current gain and the base transit time are controlled by the Ge profile in the base rather than by the doping profile, doping profile in the base can be optimized, resulting in additional freedom for device designers. Bearing in mind also the possibilities for low-temperature operation of SiGe HBTs, it is obvious that the germanium, doping and temperature dependence of mechanisms related to the base transport properties should be known for adequate modelling of SiGe HBTs. The purpose of this paper is to discuss the physical effects in the base related to the transport of carriers, and to suggest the models which are required for evaluation of the electron current in the base and the base transit time. In the following, the physics of SiGe base is examined and corresponding models are reviewed. The device performance issues such as SiGe HBT vs. Si BJT improvement, 77K vs. 300K operation, and the importance of Fermi-Dirac statistics for the carrier transport in the base are analyzed. Finally, an approach to the accurate analytical modelling of the electron current in the base and the base transit time is presented. 2. Physics of the SiGe base Due to the presence of germanium, the physics of carrier transport in the SiGe base differs from that in the conventional Si base. In this section we analyze the electron current in the base, which is the main contributor to the collector current in SiGe HBT. We examine the base transit time which is a parameter influencing significantly the high frequency performance of SiGe HBTs. Finally, we address the evaluation of pn product in the base which is an important base transport parameter. 2.1 Electron current in the base The electron current in the SiGe base can be described by the generalized Moll-Ross relation /8/, which takes into account the influence of nonuniform doping and energy gap grading in the base: qn i,Si exp BE kJ 1 exp 0 AD SiGe (X) kT N^{x)dx (1) where Na is the acceptor concentration in the base, n/.s/ is intrinsic carrier concentration in silicon, Dn,siGe is electron diffusion constant in the SiGe base, AGs/Ge is an apparent bandgap narrowing in the base which accounts for the deviation of pn product in SiGe from that in intrinsic silicon; the other symbols have their usual meaning. In contrast to most GaAs based heterojunction devices -where the carrier transport is controlled by the heterojunction barriers - the electron current in SiGe HBTs is determined by drift and diffusion and depends almost entirely on the bulk base properties. This is a consequence of the small conduction band discontinuity (approximately 10 meV /9/) which appears on the Si/SiGe heterojunction. It has been shown recently that even if thermionic emission of electrons over the conduction band discontinuity is taken into account, the small barrier does not influence the electron transport unless the temperature is extremely low (7 < 50 K) /10/. The minority electron diffusion constant and the apparent bandgap narrowing are thus the most important parameters determining the stationary electron transport in the base. Beside the effects related to the apparent bandgap narrowing, which will be addressed in more detail in the following, it is necessary to stress the Ge-dependence of electron diffusion constant in the base. It has been obsen/ed experimentally that the minority carrier mobility in SiGe is higher than that in silicon as a consequence of germanium and strain /11 /. A simple empirical model for diffusion constant enhancement due to strain and germanium has been recently presented /12/, where it has been assumed that the temperature and doping dependence of electron mobility in SiGe is the same as that in silicon. 2.2 Base transit time Taking into account the influence of nonuniform energy gap in the base, the base transit time {xb) can be described as proposed in /8/: = 1 exp kT wg exp kT N,{x)dx D„ .(X) dz (2) The base transit time is controlled by the same physical effects as the electron current. However, in contrast to the electron current, which is influenced mostly by bandgap narrowing at the base side of the emitter-base depletion region, the base transit time is affected mainly by the grade of the apparent bandgap narrowing in the base. 2.3 pn product in the base The pn product in the SiGe base is an important parameter which influences significantly the electron current in the base and the base transit time. It is affected by the structure of conduction and the valence band in SiGe, which is modified as a result of compressive strain and alloying /9,13/. The conduction band of strained SiGe splits into fourfold degenerate and twofold degenerate states, influencing the effective density of states in the conduction band {Nc.SiGe) /13/. In the valence band of SiGe the heavy hole and the light hole bands split, with the heavy hole band moving up and the light hole band moving down in the energy diagram /9,13/. Both bands, together with the split-off band, are highly distorted and non-parabolic. As a result, the energy gap in SiGe is reduced compared to the energy gap in silicon /9,13,14/. Furthermore, the effective density of states in the valence band (Nv.SiGe) is changed owing to the lower hole effective mass (mp*) in SiGe /15-17/. Besides, the high doping concentration causes additional bandgap reduction {AEg,hci), which appears to be of the same origin as a corresponding bandgap reduction in silicon /18,19/. An apparent bandgap narrowing (AGs/Ge) can be defined to account for the difference between pn product in the SiGe base and the intrinsic carrier concentration in silicon; iP")siGe = nlsi exp AG,,, kT (3) Under the assumption of space charge neutrality, quasi-equilibrium and reparabolization of nonparabolic energy bands in the p-type SiGe base, a relation between Fermi level and the doping concentration in the base can be defined by the Fermi integral: P SiGe =N^=N. 'v.SiGe F, 1/2 -V.SiGe kT (4) where Ep is equilibrium Fermi level and Ev,siGe is the edge of reparabolized and shifted valence band. Ep can be expressed by minority electron concentration: EF =Ec,siGe + lL V, 3-10^W^ -- \ 2 : litt J 1 < 1 1 1 1 —■— : 0.0 0,1 Ge fraction 0.2 D Flg. 1: The hole effective mass calculated with the (/') model proposed In H 71. A model for mp*(NA,T,XGe) for 77 K< 7< 300 K, A//\ < 10^° cm'^ and XQe ^ 0.2 - taking into consideration both the available experimental data and the theoretical studies of the valence band structure /15,16/ -has been recently proposed /17/. Fig. 1 indicates the most important features of mp* in SiGe: strong doping dependence at low temperatures, low temperature dependence at high doping concentrations and strong Ge dependence. The ratio of densities of states between SiGe and intrinsic silicon is presented in Fig. 2, indicating that NcNv in SiGe is considerably lower than that in silicon. 1 - 0.05 0.10 0.15 Ge fraction 0.20 Fig. 2: The ratio of the product of effective densities of states in doped SiGe (including doped Si) and intrinsic Si. B. Bandgap narrowing due to doping For doping concentrations higher than 10''the interactions of carriers and dopant atoms cause reduction of the energy gap {AEg,hd)- Based on the assumption that the doping induced bandgap narrowing in SiGe is of the same origin as, and of the comparable magnitude to the doping induced bandgap reduction in silicon /18,19/, AEg,hd in p-type silicon can be regarded as a measure of' doping induced bandgap narrowing in SiGe. A model for AEg,hd in p-type silicon has been recently determined /22/from measured characteristics of Si BJTs, where it has been assumed that the contribution of Fermi-Dirac statistics can be accounted for by means of the model for mp*(NA,T,XGe=0) from /17/ (see Fig. 3): +[3.58 ■10-''N -7 A/0.281 [e\/]. (8) Bearing in mind that the doping concentration in the base of an optimized SiGe H BT exceeds 10^ ^ cm'^ /1,2/, and in some cases approaches 10'^" cm'"' /3/, the doping induced bandgap narrowing is an important effect that should be taken into account for analysis and optimization of the base transport properties of SiGe HBTs. Ge fraction > ci> UJ CD LU <3 0.00 10^® Doping concentration [cm Fig. 3: AEg,hd and AEg,Geas a function of doping and Ge-fraction, respectiveiy. C. Bandgap narrowing due to strain and alloying Compressive strain and alloying cause the energy gap reduction in SiGe base (AEg,Ge). Based on a comprehensive analysis of experimental data of SiGe HBTs, and on the assumption that the model for mp*(NA, T,XGe) from /22/ determines the Fermi level shift and Nv.SiGe reduction in SiGe, a model for AEg,Ge has been recently proposed /17/ (see Fig.3): AE, g,Ge = 0.937x^^-0.5x1 [el/]. As can be seen from Fig. 4, even a few percents of germanium result in influential bandgap reduction in the base, consequently influencing the base transport properties of SiGe H BTs. It is worth mentioning that this effect is the most important consequence of germanium in the base, which is basically responsible for the improved properties of SiGe HBTs compared to Si BJTs. D. Apparent bandgap narrowing Apparent bandgap narrowing, calculated according to (7) with the models described above, is presented in Fig.4. As expected, AGs/Oe increases with increasing doping concentration and Ge content. However, eq. (7) indicates that it is generally difficult to isolate the doping effects from those caused by germanium and alloying in AGs/Ge due to doping and Ge dependence oiNv.siGe-An important qualitative difference between apparent bandgap narrowing in SiGe and Si is temperature dependence /25/. While apparent bandgap narrowing in silicon is temperature independent in the most conditions of interest, AGs/Ge decreases with increasing temperature even at moderate doping concentrations. This temperature dependence is a result of lower densities of states in SiGe than in silicon, and at very low temperatures or at very high doping concentrations a consequence of Fermi-Dirac statistics. However, as discussed in /23/, the influence of this temperature dependence on transistor characteristics is significant, consequently affecting the interpretation of corresponding experimental data. 1020 Doping concentration [cm"' Fig. 4: Apparent bandgap narrowing as a function of doping caicuiated according to (7). The model for apparent bandgap narrowing in silicon proposed by Klaassen et al. /24/, which is frequently used to account for AEg^hd or even for the complete doping effects {AEg,hd + Fermi-Dirac statistics) in the SiGe base, generally does not correspond to AEg^hd- For the doping concentrations higher than cm~^ it accounts also for the influence of Fermi-Dirac statistics, which is different in silicon than in SiGe due to lower hole effective mass in SiGe. This difference should be carefully taken into account when Si data are used for modelling doping effects in SiGe devices. 3. Modelling results It is well known that one of the main advantages of SiGe HBTs compared to Si BJTs - in cases where both devices differ only by the presence of germanium in the base - is increased collector current due to reduced energy gap in the base, resulting in increased current gain (base current of SiGe HBT is comparable to the base current of Si BJT) /1 /. Further, the base transit time in SiGe HBTs is decreased due to increased minority carrier mobility and due to energy gap grading which induces an effective electrical field in the base /1 /. In this section we analyze several issues related to the base transport properties of SiGe HBTs. In addition to the model for apparent bandgap narrowing in the base and the model for Ge-induced mobility enhancement described above, we also use the model for minority electron mobility in silicon proposed by Klaassen /26/, and the model for intrinsic carrier concentration in silicon suggested by Green /21/. 3.1 SiGe HBT vs. Si BJT performance The ratio of the current gain between SiGe HBT and Si BJT is presented in Fig. 5. As can be seen, the box Ge profile in the base with 6% of germanium generates almost 3 times higher current gain at 300 K than that in Si BJT. The current gain improvement is slightly lower for trapezoidal Ge profile with the same Ge dose, because the electron current in the base is influenced significantly by the bandgap narrowing at the base side of the emitter-base depletion region. As can be seen from Fig. 5, the current gain ratio decreases with increasing doping concentration. This is a consequence of the lower hole effective mass in SiGe, which induces a higher Fermi level shift due to Fermi-Dirac statistics in the SiGe base at high doping concentrations and, consequently, a decrease of electron concentration in SiGe compared to that in Si. in ca AG(EM iTTER), the current gain naturally improves with cooling. Thermal activation of the apparent bandgap narrowing in the base is also responsible for the improvement of the base transit time at low temperatures. The improvement of SiGe HBTs at 77 K is evident from a comparison of 300 K and 77 K characteristics presented in Fig. 5 and Fig. 6. 3.3 Influence of Fermi-Dirac statistics The importance of Fermi-Dirac statistics has been traditionally related to the operation of heavily doped emitters of Si BJTs. However, due to the lower hole effective mass in SiGe than in Si, lower possible temperature of operation, and higher doping concentrations in the base, it is expected that the Fermi-Dirac statistics will influence the base transport properties of SiGe HBTs. The influence of Fermi-Dirac statistics on the collector current of SiGe HBTs at low temperatures has been recently analyzed /27/. It has been shown that Fermi-Di-rac statistics is responsible for two effects: the Fermi 1020 Doping concentration [cm -3n Fig. 7: The ratio of the eiectron current in the base caicuiated with Boitzmann and Fermi-Dirac statistics. q CÖ CO H 1.0 0.9 0.8 0.7 10'® ---—_L '''I'M ' 300K ; : trapezoid ; (Xq^: 0.03-0,09) 1 1 1 ) i 1 1 1 ! 1 77K : 1020 Doping concentration [cm -3i Fig. 8: The ratio of the base transit time caicuiated with Boitzmann and Fermi-Dirac statistics. should be taken into account for optimization of these devices. If doping concentration in the base exceeds 4-10 cm-'^, the Fermi^Dirac statistics are important for the collector current also at 300 K. The base transit time IS affected by Fermi-Dirac statistics only if the base doping concentration is very high and operating temperature approaches 77 K. 4. Analytical modelling of base transport properties The analytical model describing carrier transport in the base with uniform impurity profile doped up to 1 and trapezoidal Ge profile with arbitrary grade is important for efficient analysis of the current gain and the base transit time of SiGe HBTs at both 77K and 300K. Present approaches to the analytical modelling of base transport properties are restricted to the exact consideration of AEg^Ge IV. Although fundamental insight into the influence of Ge profile on collector current or base transit time can be obtained in this way, accurate modelling and optimization also requires the consideration of Fermi-Dirac statistics as well as the Ge dependence of effective densities of states and diffusion constant. An approach to the analytical modelling of collector current at 77K has been recently presented in /27/. This idea has been further extended for 300K analysis and for the modelling of base transit time in /28/. The analytical approach here presented is based on effective Ge induced bandgap narrowing {AEg,Ge.eff) /27,28/, which takes into account all Ge dependerit effects responsible for minority electron current in the base: ^C.SiGe^V.SiGe V ^c.suN.^sij J (10) +kTln A/. Nv,s:Ge ~kTG, /V. {/^V.SiGe ) -kTln{j]), where r| is Dn,siGe/Dn,Si. Since AEg,Ge,eff is nearly a linear function of Ge fraction at both 300 K and 77 K (see Fig. 9), an effective trapezoidal Ge profile can be found for every grown trapezoidal Ge profile. By means of an effective trapezoidal Ge profile, analytical expressions for lc,SiGe and xB,SiGe can be derived: kT ,Ge,eff iO))exp\ (11) kT kT 1 -exp Xß =■ kT (12) kT 1-- 1-exp ^Eg^^offiOyAE^^ kf JJ where t] represents a position-averaged quantity of Dn,siGe/Dn,si. Since ii does not significantly depend on XGe, its averaging appears not to be serious limitation of the model. To complete the model, accurate analytical expressions for AEg,Ge,eff for both 300/ CD IIJ <1 0.00 0.05 0.10 0.15 0.20 Ge fraction (b) Fig. 9: Effective Ge-induced bandgap narrowing as a function of Ge fraction. Cun/es 1-6 correspond to different doping concentrations: W^^cm'^, 3.2-70^ W^^cm'^ and W^^cm'^. (b) 77 K. band are the most innportant effects induced by Ge in the base. A set of required models is suggested, and an analytical approach to the modelling of electron current in the base and the base transit time is presented. It has been demonstrated that the improvement of SiGe HBTs compared to Si BJTs decreases slightly with increased doping concentration, and increases significantly with cooling. It has been shown that Fermi-Dirac statistics significantly influence the electron current in the base and should be taken into account for accurate analysis and optimization of SiGe HBTs. 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