IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 56, NO. 6, JUNE 2009 1309 Analysis of the Bipolar Current Mirror Including Electrothermal and Avalanche Effects Niccolò Rinaldi, Member, IEEE, Vincenzo d’Alessandro, and Lis K. Nanver, Member, IEEE Abstract—An experimental and numerical study of the bipolar current mirror characteristics under strong self-heating and avalanche conditions is presented, and a theoretical model to describe the observed behavior is proposed. It is shown that both electrothermal effects and impact ionization may lead to a marked degradation of the mirroring action, eventually resulting in an instability phenomenon which limits the usable operating range of the circuit. Both the separate and combined actions of these positive-feedback mechanisms are investigated. The model com- pares favorably with experimental data measured on silicon-on- glass and GaAs current mirrors and allows deriving a theoretical relation for the critical condition corresponding to the onset of the instability. The impact of the most significant technology and design parameters is discussed, and design criteria are given in order to ensure an unconditionally stable behavior. Index Terms—Bipolar junction transistor (BJT), breakdown voltage, current mirror, electrothermal simulation, heterojunction bipolar transistor (HBT), impact ionization, thermal instability, thermal resistance. I. INTRODUCTION D EVICE scaling is leading the heterojunction bipolar tech- nology in its restless march toward the terahertz band- width operation range [1], [2]. However, it is known that scaling rules have some adverse implications for reliability, as they tend to enhance thermal effects as well as impact ionization. While III–V heterojunction bipolar transistor (HBT) technologies are already thermally limited [3], [4], self-heating is expected to become more severe also in silicon bipolar junction transistors (BJTs) and SiGe HBTs due to the following different evo- lutionary trends: 1) the increase in collector current density needed to support higher operating frequencies [5]; 2) the use of advanced isolation schemes [e.g., oxide- [6] or even air-filled trenches [7], and silicon-on-insulator (SOI) [8] and silicon-on- glass (SOG) [9] processes]; 3) the decrease in parasitic resis- tances, as needed to improve the intrinsic device speed, which results in a diminished ballasting action with respect to the electrothermal feedback [10]. Thermal effects not only degrade device performance in terms of both functional operation and long-term reliability [11] but can also cause instability effects if certain critical conditions are reached, and this poses a limi- Manuscript received November 6, 2008; revised February 27, 2009. First published April 28, 2009; current version published May 20, 2009. The review of this paper was arranged by Editor J. Cressler. N. Rinaldi and V. d’Alessandro are with the Department of Electronics and Telecommunications Engineering, University of Naples Federico II, 80125 Naples, Italy (e-mail: vindales@unina.it). L. K. Nanver is with the Laboratory of Electronic Components, Technology, and Materials, Delft Institute of Microsystems and Nanoelectronics, Delft University of Technology, 2628 Delft, The Netherlands. Digital Object Identifier 10.1109/TED.2009.2018171 tation in the usable operating range of the device [12], [13]. The avalanche-related reliability issues imposed by scaling trends in collector engineering are well known [14], [15], and they result in an inherent tradeoff between operation speed and breakdown voltage that is usually referred to as the “Johnson Limit” [16]. The limitations imposed on device operation by self-heating and impact ionization are critically dependent on the conditions under which the device is driven [12], [17]. It is well known that the situation during avalanching under open-base conditions is particularly precarious, since the holes generated by impact ionization in the base-collector space-charge region cannot flow out of the base node and are injected into the emitter, thereby creating a positive-feedback mechanism. Under these condi- tions, the device is limited by the open-base breakdown voltage BV CEO . In practical circuit applications, the base is never driven with an infinite impedance, and the maximum usable dc output voltage is typically limited by the onset of impact- ionization-induced instabilities to values ranging from BV CEO to the open-emitter breakdown voltage BV CBO , depending on the driving conditions [17]–[19]. Because of the reduction of the usable operating range imposed by scaling trends, it is of primary importance for the designer to have a clear picture of the actual limits on circuit operation, particularly in appli- cations such as output stages or bias circuits where operation above BV CEO is required [20]–[22]. Only then, it is possible to fully exploit the performance potentials of a given technology. In past work, the influences of thermal effects and impact ionization on the usable operating range of the current mirror were studied separately. A few papers have been published, which investigate thermal issues in current mirrors fabricated in bipolar technology [23]–[27]. These works showed that the electrothermal feedback acting on the output transistor may lead to significant mirror ratio (MR) degradation. In [28], the current mirror scheme is adopted as a test structure for estimating the impact of electrothermal issues in SOI BJTs and for characterizing the thermally limited safe operating area (SOA). The influence of avalanching on the characteristics of current mirrors was investigated by Veenstra et al. [20]. In this work, it is demonstrated that current mirrors can safely operate at voltages above BV CEO , up to a breakdown voltage BV CED , the value of which depends only on the emitter area ratio of the devices. Furthermore, new topologies for bias current circuits are proposed in [20] to extend the operation range to higher voltage values. In a more recent paper [29], a semiempirical approach is used to estimate the overall SOA including thermal and avalanche effects, as well as hot carrier-induced degrada- tion. However, none of these works offer a complete theoretical treatment elucidating all relevant complex mechanisms such as 0018-9383/$25.00 © 2009 IEEE Authorized licensed use limited to: Universita degli Studi di Napoli. Downloaded on May 22, 2009 at 12:14 from IEEE Xplore. Restrictions apply.