Electron counting at room temperature in an avalanche bipolar Marc Lany, Giovanni Boero, and Radivoje Popovic

Citation: Appl. Phys. Lett. 92, 022111 (2008); doi: 10.1063/1.2830015 View online: https://doi.org/10.1063/1.2830015 View Table of Contents: http://aip.scitation.org/toc/apl/92/2 Published by the American Institute of Physics

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Electron counting at room temperature in an avalanche bipolar transistor ͒ Marc Lany,a Giovanni Boero, and Radivoje Popovic Ecole Polytechnique Fédérale de Lausanne (EPFL), CH-1015 Lausanne, Switzerland ͑Received 18 October 2007; accepted 9 December 2007; published online 18 January 2008͒ We report on real-time detection of single electrons inside a n-p-n bipolar junction transistor at room temperature. Single electrons injected through the base-emitter junction trigger with a high probability the avalanche breakdown of the strongly reverse-biased collector-base junction. The breakdown, rapidly stopped by an avalanche quenching circuit, produces a voltage pulse at the collector which corresponds to the detection of a single electron. Pulse rates corresponding to currents down to the attoampere range are measured with an integration time of about 10 s. © 2008 American Institute of Physics. ͓DOI: 10.1063/1.2830015͔

In bipolar junction ,1 charge quantization can current consists of emitter electrons that overcome the poten- usually be observed only indirectly as the microscopic tial barrier between the emitter and the base and reach the source of shot noise. By contrast, charge quantization can be collector-base junction.1,6,7 Once at the collector-base junc- directly observed in the operation mode of the bipolar tran- tion, any free electron will be accelerated by the strong elec- sistor demonstrated in this paper, which is similar to the op- tric field. Because the voltage applied on the collector-base eration of a in the Geiger mode.2 Both devices junction is higher than its , the electron is rely on the avalanche multiplication effect in a reverse- very likely to generate secondary electron-hole pairs by im- biased p-n junction: In a photodiode, the carriers to be mul- pact ionization.8,9 The other components of the emitter cur- tiplied are generated by photons, whereas in the present de- rent, namely, the hole current and the recombination current, vice, these carriers are injected by the emitter of the are carried through the base by holes and, therefore, cannot transistor. A photodiode operating in the Geiger mode is usu- initiate an avalanche. 2 ally called single photon avalanche , or SPAD. By Since both electrons and holes can cause impact ioniza- analogy, we can call a transistor operated in the electron- tion and create new electron-hole pairs, the avalanche is self- counting mode a single-electron bipolar avalanche transistor, sustaining above the breakdown voltage. Therefore, in order or SEBAT. to avoid the destruction of the device and to allow for the A SEBAT can be used to measure small currents by counting single electrons. This has already been achieved with single electron transistors ͑SETs͒.3,4 The SEBAT dem- onstrated in this work exhibits a larger leakage current than SETs as well as a lower electron detection efficiency. It may nonetheless be very useful because it operates at room tem- perature and can be realized using a conventional comple- mentary metal oxide ͑CMOS͒ integrated cir- cuit process. Compared to conventional current measurement techniques, the straightforward analog-to-digital conversion of the output signal as well as the small size and low current consumption of the device have significant advantages. Be- cause the injection of electrons into the device is a pure Poisson process, the timing of the electron detection could also be used for fast random number generation.5 The circuit permitting the operation of a bipolar transis- tor as a SEBAT ͑Fig. 1͒ is similar to a conventional common- base amplifier circuit.1,6 Contrary to all usual circuits, how- ever, the collector-base voltage VCB of a bipolar transistor in the Geiger mode exceeds the collector-base breakdown volt- FIG. 1. Operation of a SEBAT. ͑a͒ Circuit schematic of a n-p-n-type SE- age VBD. The device operates as follows: Initially, let the BAT associated with a passive quenching circuit. The symbol of the SEBAT emitter current of the transistor IE be zero. If we neglect the is similar to that of a conventional n-p-n bipolar transistor. The notations are leakage current of the collector-base junction, no current E, emitter; B, base; C, collector; CC, inherent capacitance of the collector- flows through the R . Therefore, V =V , and the base p-n junction, RQ, quenching resistor; VCC, supply voltage; IE, emitter Q CB CC ͑ ͒ collector-base junction of the SEBAT is reverse biased by the input current; IA, avalanche current; IR recharging current; and VCB, collector-base voltage. ͑b͒ Collector-base voltage V as a function of time. supply voltage V ϾV . If now a negative voltage is ap- CB CC BD Whenever an electron triggers the avalanche current IA, VCB drops from VCC plied to the emitter, the base-emitter junction is forward bi- to the breakdown voltage VBD. The width of the voltage pulses is determined ␶ ͗ ͘ ͗ / ͘ ased and an emitter current IE appears. Part of the emitter by the recharging time constant . The average pulse rate, f = 1 P ,is ͑ ͒ proportional to the ideal input current IEI. c The output voltage VOUT of the inverter as a function of time. VDD and VSS are the supply voltages of the a͒ Electronic mail: marc.lany@epfl.ch. inverter, and VT is its threshold voltage.

0003-6951/2008/92͑2͒/022111/3/$23.0092, 022111-1 © 2008 American Institute of Physics 022111-2 Lany, Boero, and Popovic Appl. Phys. Lett. 92, 022111 ͑2008͒ detection of a subsequently injected electron, the avalanche current IA needs to be stopped. This function is identical to the quenching of the avalanche current in a SPAD.2 In the configuration we use ͑Fig. 1͒, the bipolar transistor is biased through a resistor on the collector side, forming what is known as a passive quenching circuit. The value of the re- Ӷ sistance RQ is chosen so that during an avalanche, IR IA, where IR is the current flowing through the resistor. Therefore, the avalanche current IA will start discharging the collector-base capacitance C . The collector-base voltage FIG. 2. ͑Color online͒͑a͒ Photomicrograph of the circuit, comprising the C ͑ ͒ V V I bipolar transistor BT , the quenching resistor RQ, and the integrated inverter CB drops down to a level slightly above BD, at which A ͑INV͒. ͑b͒ Schematic cross section of the bipolar transistor optimized for becomes lower than the self-sustaining level. At this point, Geiger-mode operation. Notations: E, emitter; B base; C, collector; S, sub- + + the avalanche stops. The current IR starts recharging CC, strate; P , base contact; N , collector contact; and GR, guard ring. bringing VCB back to its initial value VCC. When the next electron injected by the emitter reaches the collector-base of about 85 fF. The quenching resistor is realized in highly junction, the same cycle may start again. Each of these resistive polysilicon and has a resistance of about 250 k⍀. cycles results in a negative pulse in VCB. The average fre- ͗ ͘ This leads to a theoretical characteristic recharge time con- quency f of these voltage pulses can be tentatively modeled stant ␶ of about 20 ns. The photomicrograph of the transistor by associated with its quenching resistor and buffer circuit is ͗ ͘ ␣ / ͗ ͘ ͑ ͒ ͑ ͒ f = qIEI e + f p , 1 shown in Fig. 2 b . The collector-base breakdown voltage VBD of the fabri- where cated test devices is about 45 V at room temperature ͑ / ͒ ͑ ͒ ͑ϳ297 K͒. When V ϾV , square pulses appear in V IEI = IEI0 exp eVBE kT . 2 CC BD OUT ͓Fig. 3͑c͔͒. Each pulse corresponds to an avalanche IEI is the “ideal” part of the emitter current carried by charges breakdown–avalanche quenching cycle. During all Geiger- that overcome the base-emitter potential barrier, i.e., the mode experiments, we maintained V approximately 3 V emitter current without carrier recombination within the CC base-emitter depletion region and without minority carrier ␣ generation. q is the detection efficiency, which can be inter- preted as the product of the common-base current gain of the transistor ͑without recombination͒1,6,7 and the probability for an electron reaching the collector-base junction to trigger an ͑ ͒ ͗ ͘ avalanche breakdown i.e., the avalanche probability . f p is the average rate at which the collector-base junction breaks down without electron injection from the emitter ͑i.e., for ͒ IEI=0 . It is the equivalent of the dark count rate in a SPAD. e is the elementary charge, k is the Boltzmann constant, and T is the absolute temperature. ␣ The detection efficiency q and the parasitic count rate ͗ ͘ f p depend on VCB and on the temperature, mainly because 2 of changes in the avalanche triggering probability. IEI0 de- pends only on temperature and, consequently, IEI is a purely exponential function of VBE at constant temperature. In principle, the structure of a SEBAT may be the same as that of a conventional bipolar junction transistor: a semi- conductor n-p-n or p-n-p structure, with a highly doped first ͑emitter͒ layer and a moderately doped and very thin me- dium ͑base͒ layer. However, in order to function properly as SEBAT, other specific characteristics of the bipolar transistor detailed in the Supplemental Online Material need to be optimized.10 We realized our first generation of SEBATs us- ing a modern CMOS technology with 0.35 ␮m minimum feature size. We cointegrated an inverter as output buffer to minimize the parasitic capacitance added C to C. ͑ ͒͑͒ FIG. 3. Color online a Output voltage VOUT as a function of time at a The schematic cross section of the realized transistor is ͗ ͘ mean avalanche firing rate f of about 100 kHz, corresponding to VBE shown in Fig. 2͑a͒. To avoid the premature edge breakdown Х ͑ ͒ ͗ ͘Х Х ͑ ͒ 0.25 V. b VOUT for f 1 MHz, which corresponds to VBE 0.3 V. c ͑ ͒ ͑ ͒͗ ͘ ͉ ͉ of the collector-base junction, we designed a floating guard Detail of b showing typical pulses in VOUT. d f and IE recorded simul- ͑ ͒ ring similar to the one described in Ref. 11. taneously as functions of VBE at ambient temperature 297 K . The count From the process parameters, we estimate the collector- rate scale is linked to the current scale through the relationship f =I/e. base diode capacitance to be 25 fF and the collector- Therefore, it is possible to compare visually IE expressed as an electron count rate to the measured output pulse rate. Also shown are IE for VCC substrate diode capacitance to be 45 fF. The integrated out- Ͻ ͑ ͒ ␣ VBD VCC =38.5 V and, as a black line, the theoretical value of qIEI for ␣ put buffer permits us to achieve a total collector capacitance T=297 K, with the coefficient qIEI0 as the only fitting parameter. 022111-3 Lany, Boero, and Popovic Appl. Phys. Lett. 92, 022111 ͑2008͒

from these results ͓cf. Eq. ͑2͔͒. In all cases, the temperature determined using this procedure matches the measured chip temperature within 2 K. At low forward bias, the measured IE depends linearly on VBE. This parasitic current is likely to be caused by the presence of a base-emitter resistive leakage path ͑ϳ ⍀ ͒ ͑ Ͼ 2.5 T at 297 K . Under sufficient forward bias VBE ϳ0.4 V at 297 K͒, the parasitic current sources ͑leakage and carrier generation recombination͒ become negligible com- Х / pared to IEI and IE IEI. Therefore, comparing IE e at high ͗ ͘ ͗ ͘ ␣ forward bias and f − f p allows us to evaluate q.Inthe measurements shown here, obtained by maintaining VCC ap- ␣ Ϯ proximately 3 V above VBD, we have q =0.7 0.1. This is considerably lower than the maximum common-base current gain of the bipolar transistor itself, which is about 0.97 for ␣ the tested device. It indicates that in these conditions, q is essentially determined by the avalanche probability and, con- sequently, that the avalanche probability is about 0.7. The count rate shown in Fig. 3͑d͒ and 4 is the average FIG. 4. ͑Color online͒ Average output pulse rate after subtraction of the count rate over a period of about 10 s. Despite this relatively ͗ Ј͘ ͗ ͘ ͗ ͘ parasitic count rate f = f − f p and emitter current IE as a function of the short measurement time, ͗f ͘ is sufficiently low at 273 K to base-emitter voltage at three different temperatures. ͗f ͘ is evaluated by p p −18 ͗ ͘ Ͻ ͗ ͘ −1 ͑ ͒ measuring f for VBE −0.2 V. The values of f p are about 14 s at allow for the measurement of IEI in the attoampere 10 A 273 K, 147 s−1 at 298 K, and 1368 s−1 at 323 K. A least squares exponential range. fit of ͗f͘ is shown as a continuous line. 1W. Shockley, M. Sparks, and G. K. Teal, Phys. Rev. 83,151͑1951͒. 2S. Cova, M. Ghioni, A. Lacaita, C. Samori, and F. Zappa, Appl. Opt. 35, above VBD. In these conditions, the measured collector cur- ͑ ͒ 6 1956 1996 . rent corresponds to an average of about 10 charges crossing 3T. Fujisawa, T. Hayashi, Y. Hirayama, H. D. Cheong, and Y. H. Jeong, the collector-base junction during one avalanche pulse. As Appl. Phys. Lett. 84, 2343 ͑2004͒. ͑ ͒ ͗ ͘ 4 ͑ ͒ ͑ ͒ shown in Fig. 3 d , the measured f as a function of VBE J. Bylander, T. Duty, and P. Delsing, Nature London 434,361 2005 . ͑ ͒ 5M. Stipcevic and B. M. Rogina, Rev. Sci. Instrum. 78, 045104 ͑2007͒. corresponds well to the simple model expressed by Eqs. 1 6 ͑ ͒ ͗ ͘ S. M. Sze, Semiconductor Devices: Physics and Technology, 2nd ed. and 2 . The electron injection and, therefore, f depend ͑Wiley, New York, 2002͒, pp. 130–142. 7 exponentially on VBE. With a sufficiently large reverse base- D. A. Neamen, Semiconductor Physics and Devices, 3rd ed. ͑McGraw- emitter bias, electron injection becomes negligible and we Hill, New York, 2003͒, pp. 385–392. ͗ ͘ 8K. G. McKay, Phys. Rev. 94, 877 ͑1954͒. observe a constant parasitic count rate f p . Deep-level as- 9R. H. Haitz, A. Goetzberger, R. M. Scarlett, and W. Shockley, J. Appl. sisted generation is likely to be the dominant cause of these ͑ ͒ 12 Phys. 34,1581 1963 . parasitic counts. The results of the same measurements at 10See EPAPS Document No. E-APPLAB-92-095801 for more details about ͗ ͘ three different temperatures after subtraction of f p are design considerations, materials, and methods. This document can be shown in Fig. 4. The measurements clearly show that the reached through a direct link in the online article’s HTML reference sec- tion or via the EPAPS homepage ͑http://www.aip.org/pubservs/ device is specifically sensitive to IEI, which remains positive epaps.html͒. even for a reverse bias of the base-emitter junction. Least 11Y. C. Kao and E. D. Wolley, Proc. Inst. Electr. Eng. 55,1409͑1967͒. squares exponential fits allow us to extract the value of e/kT 12G. Vincent, A. Chantre, and D. Bois, J. Appl. Phys. 50, 5484 ͑1979͒.