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-2 FIG. 1: (a) Sketch of the experimental setup: downward ar- V, V rows represent the primary electron beam; upward arrows show the current of electrons from the tin film. The layers represent: 1 - glass substrate, 2 - conductive oxide layer, 3 - tin film, 4 - insulating spacer between two electrodes filled FIG. 2: Current-voltage characteristics of the structure de- with plastic transparency (slide) films, 5 - second (copper or picted in Fig. 1 for three different insulating spacers between aluminum foil) electrode. A and V represent the ammeter the tin and second electrode. Note that the machine was re- and power source, z is the axis perpendicular to the tin elec- peatedly turned on and off, leading to the gaps in the plots. trode. (b) Band diagram with tin layer showing the Fermi level (dash-dotted line), the states filled with electrons (gray), and the work function W . The electron tunneling current is shown by the z-axis arrow. only weak dependence (the case of 13 layers in Fig. 2). (iv) Changing the electron fluence rate by an order of magnitude results in an insignificant (factor of 2) current ian Medical Systems, Palo Alto, California) medical lin- change. (v) No delays between voltage and currents were ear accelerator, operated in service mode (the machine observed, and the system behavior was not altered by in- diagnostic and research mode), was used to irradiate the termittent grounding, i. e. the structure did not retain sample. The electron fluence rate and their transmit- any significant charge upon beam removal. ted energy are estimated to be respectively G ≈ 109 electrons/(cm2-s) and w ≈ 2 MeV/electron. The irradi- To interpret these observations, we note that the sign ation was conducted in two 10-hour rounds, each spread of the charge acquired by a dielectric (particularly, glass) sample under electron irradiation depends on the sample out over five daily sessions two hours long each. The 21,23 sample structure is represented by layers 1,2,3 in Fig. 1 composition, electron stopping range and grounding. showing also the direction of irradiation. The 6 MeV electron stopping range of about 2 cm in a glass is considerably greater than the sample and pedestal To evaluate the field strength, a second electrode was integral thickness of ∼< 1 cm; hence the majority of pri- added, as illustrated in Fig. 1 (a); it was sufficiently thin < mary (originating from the beam itself) electrons pass (∼ 0.1 mm) that the beam characteristics were practi- completely through the experimental setup. This creates cally unchanged. To avoid shunting, the inter-electrode gap was filled (and its thickness defined) with several layers of plastic sheets of thickness < 0.1 mm each. The current voltage characteristics corresponding to different numbers of such sheets were measured with a Keithley dual channel source meter (Keithley Instruments, Inc., Cleveland, Ohio) as shown in Fig. 2. During each measurement, the beam was turned on and off several times. Note that neither the second electrode nor plas- tic sheets were present during the exposure leading to whisker growth. The following observations are important for evaluat- ing the electric filed distribution. (i) The measured cur- rent sense corresponds to the electron flow depicted in Fig. 1 (a), i. e. negative charge is acquired by the structure. (ii) The short circuit (V = 0) current does not depend on the gap thickness and the number of lay- ers inserted between the electrodes. (iii) The slope of current voltage characteristics does not depend on the FIG. 3: An example photograph of a single whisker grown number of layers until it is very large and then shows after 10 hours of electron beam exposure. 3

We found that the irradiation procedure was successful in growing whiskers. Moreover, control samples not ex- posed to the radiation grew no detectable whiskers what- soever over the same time period. Fig. 3 shows an example of single whisker, illustrating the high aspect ratio of this feature in comparison to the prevailing grain structure. Fig. 4 shows a larger region of the sample, illustrating the density of whiskers on the sample. Previous work by other groups has suggested that tin whisker length is described by a log-normal distribution25–27. Figure 5 shows a satisfactory fit of measured whisker lengths with the cumulative probabil- ity of a log-normal distribution. The fitting parameters correspond well to the directly determined values of av- erage length of 5.0µm with standard deviation of 2.5µm. FIG. 4: A representative wide overview showing many The average whisker density (whiskers per area) was de- whiskers (better seen under higher magnification). 10 termined to be (335±32) mm−2. whiskers were counted in this region corresponding to the den- 2 The sample was given then another 10 hours of radi- sity of 500 whiskers/mm ation before the second measurement of whisker length. Assuming that whisker growth was due entirely to the 20 hours of irradiation time, the whisker growth rate large numbers of electron-hole pairs as well as radiation- was 0.7±0.3 A/s,˚ which is in line with whisker growth induced conductivity in the glass.21 Some of these elec- induced by mechanical stress in some studies, and is at trons and holes can escape through the sample surface least an order of magnitude greater than what is reported leaving unbalanced positive or negative charges depend- for spontaneous whisker growth (∼ 0.0002 − 0.1 A/s)˚ 1,25. ing on the material composition23 and interfacial condi- It should be emphasized again that the tin film thickness tions; our data show that the sample is charged nega- used in this study is generally considered not to be prone tively. to whisker formation; hence, the field effect can provide In our setup without dedicated grounding, electric even more significant acceleration of whisker growth rate. charge exchange is achieved through the air ionization22 providing sufficient ionic conduction between the sample and the accelerator. Furthermore, the presence of sig- nificant ion concentration screens the electric field of the 1.0

charged sample forming a barrier shown in Fig. 1 (b); its 0.8 height is equal the tin work function W = 4.7 eV. The barrier shape is determined by the distribution of ions 0.6

data

in the air (the plastic layers do not have enough mobile fit

0.4 charges to contribute). The barrier thickness L is con- siderably smaller than the inter-electrode gap: using the 0.2 Cumulative Fraction Cumulative standard value of the air dielectric strength, E ≈ 30, 000 V/cm, one can estimate L = W/E ≈ 2 µm. The barrier- 0.0 dominant resistance then determines the value of short 4 8 12 circuit current accommodating practically the entire ex- Length (µm) ternal voltage applied and making the current voltage slope insensitive to the gap structure, which explains the FIG. 5: The log-normal fit of the whisker length statistical above observations (ii) - (iii). The observation (iv) con- distribution. firms that most of the created electron hole pairs recom- bine in the structure. Finally, (v) can be explained by We consider these results to be promising first steps 24 the radiation-induced conductivity making the corre- towards clarifying the role of electric field and trapped sponding RC times shorter than the characteristic times charges in tin whisker growth. More work is called upon of our experiments. including solder representative (micron thickness electro- After first 10 hours of electron beam exposure, the plated) tin samples, variations in radiation dose and flu- sample was examined, for whisker formation by a Hi- ence, etc. to investigate whisker growth as a function tachi S-4800 SEM. Measured whisker length was taken of time, field strength, film thickness, and alloy composi- as the entire whisker, including kinks if necessary (as op- tion/morphology under electric field; other groups efforts posed to merely the straight-line distance between the could strongly facilitate this ambitious effort. beginning and end). As a practically important result, this work shows that 4 radiation can have a significant effect on tin whisker reliability problems. growth that needs to be taken into account in medical device, space, and some other industries. Because ioniz- Acknowledgement. Microscopy for this study was done ing radiation is a well-controllable tool, it can be devel- with equipment at the Center for Materials and Sensor oped to become an accelerated life test in whisker-related Characterization of the University of Toledo.

1 G. T. Galyon, Annotated Tin Whisker Bibliography And Trans. Elec. Packaging Manufacturing, 28, 75-81 (2005). Anthology, IEEE Transactions on electronics Packaging 16 M. A. Ashworth, G. D. Wilcox, R. L. Higginson, R. J. Manufacturing, 28, 94 (2005); Heath, and C. Liu, Effect of direct current and pulse plat- http://thor.inemi.org/webdownload/newsroom/TW_ ing parameters on tin whisker growth from tin electrode- biblio-July03.pdf posits on copper and brass substrates, Transactions of the 2 J. Brusse, G. Ewell, and J. Siplon, Tin Whiskers: At- Institute of Metal Finishing, 91, 260-268 (2013). tributes and Mitigation, Capacitor and Resistor Technol- 17 A. Melchinge and S. Hofmann, Dynamic double layer odel: ogy Symposium (CARTS), March 25-29, pp. 68-80, (200). Description of time dependent charging phenomena in in- 3 G. Davy, private communication, October 2014; quated in sulators under electron beam irradiation, J. Appl. Phys. Ref. 9. 78, 6224, (1995). 4 Y. Zhang, Tin Whisker Discovery and Research, in Solder- 18 Z. G. Song, C. K. Ong, and H. Gong, A time-resolved ing in Electronics, Edited by K. Suganuma, Marcel Dekker, current method for the investigation of charging ability of Inc. p. 121 (2004) insulators under electron beam irradiation, J. Appl. Phys. 5 K.N. Tu, J.O. Suh, and Albert T. Wu, Tin Whisker 79, (1996). Growth on Lead-Free Solder Finishes, in Lead-Free Solder 19 M. Touzin, D. Goeuriot, C. Guerret-Piecourt, D. Juve, D. Interconnect Reliability, Edited by D. Shangguan, ASM Treheux, Electron beam charging of insulators: A self- International, p. 851 (2005). consistent ight-drift model, J. Appl. Phys., 99, 114110 6 D. Bunyan, M. A. Ashworth, G. D. Wilcox, R. L. Higgin- (2006). son, R. J. Heath, C. Liu, Tin whisker growth from electro- 20 Y. Mizuhara, J. Kato, T. Nagatomi, and Y. Takai, Quan- plated finishes a review, Transactions of the institute of titative measurement of surface potential and amount of metal finishing, 91, 249-259 (2013). charging on insulator surface under electron beam irradia- 7 NASA Goddard Space Flight Center Tin Whisker Home- tion, J. Appl. Phys. 92, 6128 (2002). page, website http://nepp.nasa.gov/whisker. 21 G. Wilson, J. R Dennison, A. Evans, and J. Dekany, Elec- Bibliography for Tin Whiskers, Zinc Whiskers, Cad- tron Energy Dependent Charging Effects of Multilayered mium Whiskers, Indium Whiskers, and Other Conduc- Dielectric Materials, IEEE trans. on Plasama Science, 41, tive Metal and Semiconductor Whiskers, John R. Barnes; 3536 (2103). http://www.dbicorporation.com/whiskbib.htm 22 S. T. Lai, An overview of electron and ion beam effects in 8 V.G.Karpov, Electrostatic Theory of Metal Whiskers, charging and discharging spacecraft, IEEE Transactions on Phys. Rev. Applied, 1, 044001 (2014). nuclear science, 36, 2027, (1989). 9 V.G.Karpov, Electrostatic Mechanism of Nucleation and 23 H. Miyake, Y. Tanaka, T. Takada, Characteristic of charge Growth of Metal Whiskers, SMT Magazine, February accumulation in glass materials under electron beam irra- 2015, p. 28. diation, IEEE Trans. On Dielectrics And Electrical Insu- http://iconnect007.uberflip.com/i/455818/44 lation 14, 520 (2007). 10 M. Umalas, S. Vlassov, B. Polyakov, L. M. Dorogin, R. 24 J. R. Dennison, J. Gillespie, J. Hodges, R. C. Hoffmann, Saar, I. Kink, R. Lohmus, A. Lohmus, A. E.Romanov, J. Abbott, S. Hart, and A. W. Hunt, Temperature De- Electron beam induced growth of silver nanowhiskers, J. pendence of Radiation Induced Conductivity in Insulators, Cryst. Growth, 410, 63 (2015). Edited by: F. D. McDaniel, B. L. Doyle, Application of 11 E. Friedland, Radiation Damage in Metals, Critical Re- Accelerators in Research and Industry, Book Series: AIP views in Solid State and Materials Sciences, 26, 87 (2010). Conference Proceedings 1099, 203 (2009) 12 G. H. Vineyard, Theory and Mechanism of Radiation Ef- 25 T. Fang, M. Osterman, M. Pecht, Statistical Analysis of fects in Metals, Nuclear Metallurgy, IMD Special Report Tin Whisker Growth, Microelectronics Reliability 46, 846 Series No. 3, AIME, 1 (1956). (2006). 13 S. H. Liu, C. Chen, P. C. Liu, and T. Chou, Tin whisker 26 L. Panashchenko, Evaluation of environmental Tests for growth driven by electrical currents, J. Appl. Phys. 95, tin whisker assessment, MS Thesis, University of Maryland 7742 (2004). (2009). http://hdl.handle.net/1903/10021 14 E. R. Crandall, Factors governing thin whisker 27 D. Susan, J. Michael, R. P. Grant, B. McKenzie & W. G. growth, Ph. D. Thesis, Auburn, Alabama (2012); Yelton, Morphology and Growth Kinetics of Straight and http://ldfcoatings.com/articles/ErikaCrandall.pdf. Kinked Tin Whiskers, Metall and Mat Trans A, 44, 1485 15 R. D. Hilty, N. Corman, and H. Herrmann, Electrostatic (2013). fields and current-flow impact on whisker growth, IEEE