LETTER pubs.acs.org/NanoLett
Electrical Breakdown of Nanowires Jiong Zhao, Hongyu Sun, Sheng Dai, Yan Wang, and Jing Zhu* Beijing National Center for Electron Microscopy, The State Key Laboratory of New Ceramics and Fine Processing, Laboratory of Advanced Materials, Department of Materials Science and Engineering, Tsinghua University, Beijing, 100084, China ABSTRACT: Instantaneous electrical breakdown measurements of GaN and Ag nanowires are performed by an in situ transmission electron microscopy method. Our results directly reveal the mechanism that typical thermally heated semiconductor nanowires break at the midpoint, while metallic nanowires breakdown near the two ends due to the stress induced by electromigration. The different breakdown mechanisms for the nanowires are caused by the different thermal and electrical properties of the materials. KEYWORDS: Nanowires, electrical breakdown, Joule heating, electromigration
T
he trend of miniaturization of electronic and electromechanical devices prevails these years, and nanowires (NWs), especially single crystalline NWs must be the most important components. The robustness of NWs that can withstand electrical load is one of the main concerns during design. Because of their small diameters, NWs usually have little intrinsic defects, including interfaces and dislocations. This greatly reduces the complexity of the electrical breakdown mechanism. There are already some reports about the breakdown of NWs, e.g., BN nanotubes,1 GaN NWs,2 ZnO NWs,3 carbon nanotubes,4 and metallic NWs like Ag,5 Au,6,7 etc. Nevertheless, the explanations are sometimes ambiguous, with the thermal and electrical factors not separated. Here we use an in situ transmission electron microscopy (TEM) approach, and successfully measure the breakdown voltage of the same nanowire in various lengths. The results reveal the thermal heating breakdown mechanism of semiconductor wires, while the metallic NWs are broken by electromigration induced stress. First of all, the NWs we discussed are single crystals or nearly single crystalline, as interfaces may introduce more heat dissipation barriers, atom diffusion paths, and electron scatterers. Second, we focus on the equilibrium state without considering kinetics. As for the large surface-to-volume ratio of NWs and the highly mobile atoms on the surface, the continuous electromigration of metallic surface atoms has been controllably demonstrated when forming nanogaps.8,9 What we are interested in is the avalanche-like instantaneous breakdown. To avoid the continuous atomic surface migration, we apply dc bias to two ends of NWs less than 100 ms every time. Third, both the width and length of the NWs we discussed are much larger than the room temperature mean free path (MFP) of the electrons; therefore only the diffusive electrical transportation is considered. Fourthly, the thermal effects include melting (the material undergoes solidliquid phase transition), decomposition (the material undergoes chemical reaction), thermomigration (the material undergoes unrepairable directional or nondirectional r 2011 American Chemical Society
migration, e.g., thermal stochastic motion or thermal gradient force induced motion), etc. All these phenomena happen due to the increase of temperature. The thermal effect we focused is thermal heating effects, like melting or decomposition, but not the thermomigration. The JEOL-2010F TEM and nanofactory (NF) in situ TEMscanning tunneling microscopy (STM) holder10 are used for applying dc bias on the NWs. The whole setup is schematically drawn in Figure 1a. Two kinds of homemade NWs are employed, GaN NWs and Ag NWs, representing semiconductors and metals, respectively. GaN NWs are made with a conventional catalyzed chemical vapor deposition (CVD) method,11 the HRTEM image of GaN NWs is presented in Figure 1b, showing a surface faceted, straight, and single crystalline structure. Then a suspended GaN NW is put between a Au substrate and a W tip by the NF nanomanipulator (Figure 1c). The metal (Au)semiconductor (GaN)metal (W) contact behavior can be quite well understood using the classical thermionic field emission (TFE) theory,12 which shows a rectified IV curve (Figure 1d). As indicated by Zhang et al.,13 the voltage applied on the GaN NW should be divided into three parts: V1 corresponds to the reverse biased Schottky barrier, V2 corresponds to the NW itself, and V3 corresponds to the forward biased Schottky barrier (here AuGaN and WGaN all form Schottky contact). V1 is the main contribution to the small and intermediate bias range and saturate in the large bias range, while V2 is becoming apparent in the large bias range and V3 is negligible. Therefore, the semiconductor contact can be simplified into a constant contact resistance in the large bias range in our discussion. If Ohmic contact (not in our case) is formed, the contact resistance assumption is also applicable. Received: June 27, 2011 Revised: September 19, 2011 Published: October 03, 2011 4647
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LETTER
modified to be15 Tmax ¼ T0 expðασU 2 =8Þ
Figure 1. (a) Schematic graph of the in situ TEM-STM. (b) HRTEM of single crystalline GaN NW. Scale bar is 2 nm. (c) Image of the electrical measurement. Scale bar is 500 nm. (d) IV curve of the GaN NW.
In our experiment, each ramp (bias applied on GaN NW) is from 0 V to the maximum voltage (i.e., 35 V), and the ramp time is 100 ms. The maximum voltage applied is increased in steps of 1 V. When the peak of the ramp reaches a critical value, the GaN NW breaks near the middle (shown in Figure 2b, and Figure 2a shows the original NW). Then we use the nanomanipulator to make the W tip contact to one part of the broken GaN NW (Figure 2c) and again measure the critical breakage bias of the shortened GaN NW, and the broken NW is presented in Figure 2d. Similar to the first and second attempts, we repeat another three times to electrically breakdown the same GaN NW, the original NWs are shown in panels e, g, and i of Figure 2 while the broken NWs are in panels f and h of Figure 2 (the NW bounces off after the last breakage), respectively. The breakage bias versus length of the NWs is plotted in Figure 2j. All the breakage biases are around about 35 V and all the breakdown points on the NWs are near the middle. That means the breakdown electric field increases significantly with the shortened length of the GaN NW. The maximum temperature point of a suspended longitudinal dc biased NW is at the middle point due to Joule heating. Assuming constant electrical and thermal conductivity over the NW, the temperature difference between ends and the middle point is14 Tmax T0 ¼ ΔT ¼ σU 2 =8k
ð1Þ
T0 is the temperature at the boundary of the NW, σ is electrical conductivity, k is thermal conductivity, and U is the bias. If we include the Umklapp phononphonon scattering process, that is, k is inversely proportional to the temperature, assuming k = 1/αT, α is a constant, the maximum temperature is
ð2Þ
Here U equals to V2 which is the voltage drop on the NW, except for the contact area. Following this analysis, the GaN NWs break in a thermally manner. The middle point reaches the melting or decomposition temperature, actually we have seen some liquid Ga balls remaining on the NWs, similar to that seen in ref 2. According to eq 1 or 2, the maximum temperature is independent of the length (L) of the NW but only depends on the bias. Therefore in the experiments the breakdown biases for all the lengths of the GaN NW are the same. Another implication of the constant breakage bias is that only the middle points of the NWs are irreversibly destroyed every time, other parts of the NW are not affected, confirming the local thermal effect is the key factor for such semiconductor NWs’ breakage. Use typical parameters for GaN, we estimate the breakdown temperature as around 1050 K. As seen in panels b, d, and f of Figure 2, the breakage point is not exactly at the middle of the NWs, but a little bit toward the W tips, which is because of the poorer thermal conductive ability of W than that of Au. To investigate the breakdown behavior of metal NWs, the single crystalline Ag NW is prepared in a hydrothermal method.16,17 Using in situ TEMSTM method, the near-linear IV curve of the Ag NW can be obtained (Figure 3a). Following the same procedure as GaN NW, we complete two cycles of the breakdown measurement, shown in panels be of Figure 3. The same Ag NW in different lengths break near the end of the NW, in contrast to the GaN NW breakage. We perform the electrical measurement on some other Ag NWs and also find most of the breakage points are in the neighborhood of the ends. Some groups have observed this phenomenon before,5,7,18 but the breakdown mechanism is not clearly elucidated, especially for a fast ramp measurement which rules out the atom migration at the surface. The breakdown biases of the Ag NWs for the two cycles in panels be of Figure 3 are 550 and 1180 mV, respectively. The metal (Ag) NW resistance is relatively small compared to the whole in situ TEM electrical circuit. Although the breakdown current of the metal NWs is above the measuring range of our instrument, the breakdown bias can be directly converted to the current (U = RI, R is resistance of the whole circuit) and is enough for us to analyze the mechanism. The Joule heating effect at the contact point (AgW or AgAu) can be first excluded. If so, the breakdown bias (breakdown current density) responsible for Joule heating should be the same for different length NWs, which is contradictory to our experimental results. Applying typical parameters for Ag NWs to eq 1, we can estimate the maximum temperature rise at midpoint to be less than 102 ∼ 10 K. Metal NWs can sustain a large current density which causes electromigration. According to Blech’s analysis on electromigration in metal films,19 the vacancies are swept in the metal NWs from anode to cathode (or cathode to anode, depending on the materials), establishing a vacancy concentration gradient. The vacancy gradient simultaneously causes a stress gradient, maximum tensile stress at one end and maximum compressive stress at the other end. Now that the vacancy flux in the NW obeys19 jv ¼
Dv C v ∂Cv Dv Cv ∂s eZ Fj Dv Ω ∂x kT ∂x kT
ð3Þ
the first term on the right is electromigration force induced flux, Dv is vacancy diffusion coefficient, Cv is vacancy concentration, 4648
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Figure 2. (ai) TEM image for the five breakdown measurements of the same GaN NW, inset of (b) presents a magnified broken area, scale bar in (a) is 1 μm. (j) The plot of breakage bias and GaN NW length, showing the near constant breakage voltage.
Z* is the effective charge, j is electrical current density, and F is the electrical resistivity; the second term is vacancy concentration gradient induced flux; the last term is stress induced vacancy flux. To differentiate from electrical conductivity, we use s for mechanical stress instead of σ here. By omitting the smaller second term, and assuming an equilibrium state (jv = 0), we can obtain19,20 jL ¼ ΩΔs=eZF
ð4Þ
This relationship was first used by Blech19 in 1976 in the case of thin films but here we extend it to the 1D wires. When the local tensile or compressive stress near the two ends of the NW reaches the yielding stress, the part undergoes an avalanche-like breakdown. That is why the metal NWs usually break at the two ends but not at the midpoint. Moreover, for the constant circuit resistance here, the product of the breakdown bias and the NW length should be the same for the same material, in accordance to the Ag NWs results (shown in Table 1). Due to the intrinsic electrical and thermal transport mechanism differences, the semiconductor and metal NWs are electrically broken in different manners. The thermal conductivity for semiconductors is much lower than that for the metals; therefore the temperature rise is much more obvious for
semiconductors which at last leads to a thermal breakdown. The thermal conductivity also influences the breakage volume of the NWs, larger thermal conductivity induces smaller temperature gradient, and when the avalanche occurs, the quickly increased Joule heat generated around the necking part can cause more volume of the metal NWs melted or destroyed, as seen by Liu et al.18 The substrate can give another heat dissipation path and lower the NW temperature gradient,2 but substrate cannot change the breakdown mechanism for suspended NWs. The radial size effect of the NWs is not covered here, in which larger diffusion ability of the surface atoms, the size effect of electrical and thermal conductivity, or even size effect of the tunneling, ballistic transportation and thermionic field emission property at the metalsemiconductor contact21 have to be considered. Just considering the influences of the thermal and electrical conductivities and also electromigration effective charge on the breakdown mechanism, if we combine eqs 1 and 4, the tendency of thermal heating breakdown or electrobreakdown of a certain nanowire can be estimated σ=Z2 8e2 ΔT ∼ 2 2 k Ω Δs 4649
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Figure 4. Schematic diagram for the electrical breakdown mechanism of NWs. The straight line is σ/kZ*2 = 2 104(K/ΩW), derived from eq 5, using general parameters of solids, shown for reference. The region in the upper left is electro-breakdown regime, while on the lower right is thermo-breakdown regime. The data are obtained from our experimental results as well as refs 13, 5, 6, 18, and 2224.
Figure 3. (a) The electrical property of Ag NW and the in situ measuring system. (be) The two breakdown measurements of the Ag NW. Scale bar in (b) is 200 nm. The dashed red circles mark the broken areas.
thermally heated, while metal NWs were broken down by the stress accumulated at the two ends induced by electromigration.
’ AUTHOR INFORMATION Corresponding Author
*E-mail:
[email protected].
Table 1. The Breakage Measurement of Ag NW Ag NW length
breakage
(L)/ μm
bias (U)/V
UL/μm V
1st measurement
0.87
0.55
0.47
2nd measurement
0.45
1.18
0.53
In Figure 4, the k ∼ σ/Z*2 of various kinds of NWs and nanotubes are presented. We substitute general parameters for materials into the right side of eq 5 and the linear relationship of k ∼ σ/Z*2 is shown as a straight line in the middle of Figure 4. When the slope is larger than this, electromigration induced stress will break the NW, otherwise thermal energy will dominate. Near the straight line, the thermal and electro-breakdown may compete with each other on the carbon nanotubes23 and graphene materials.24 Some approximations must be noted in using eq 5; constant electrical and thermal conductivity and temperature independent critical yield stress are assumed. Therefore, this is a qualitative estimation (Figure 4). At room temperature, the inelastic electron scattering (lin) and elastic electron scattering (le) MFPs for semiconductors are typically 100 and 10 nm.25 For metals or for higher temperatures, these values will be smaller. In most of the applications of NWs, we apply the electrical field (current) on the two ends of the wires, and the length of the NWs is normally larger than hundreds of nanometers. In this sense, the characteristic length of the device is usually much larger than the electron MFPs of the materials; the classical or semiclassical theory for electrical transportation is still workable. We conclude that the electrical breakdown mechanism of NWs depends mainly on the materials. Specifically, typical semiconductor NWs broke down when
’ ACKNOWLEDGMENT This work was financially supported by National 973 Project of China, Chinese National Natural Science Foundation. This work made use of the resources of the Beijing National Center for Electron Microscopy. ’ REFERENCES (1) Xu, Z.; Golberg, D.; Bando, Y. Nano Lett. 2009, 9, 2251. (2) Westover, T.; Jones, R.; Huang, J. Y.; Wang, G.; Lai, E.; Talin, A. A. Nano Lett. 2009, 9, 257. (3) Zhang, Q.; Qi, J.; Yang, Y.; Huang, Y.; Li, X.; Zhang, Y. Appl. Phys. Lett. 2010, 96, 253112. (4) Wei, Y.; Liu, P.; Jiang, K.; Liu, L.; Fan, S. Appl. Phys. Lett. 2008, 93, 023118. (5) Wiley, B. J.; Wang, Z.; Wei, J.; Yin, Y.; Cobden, D. H.; Xia, Y. Nano Lett. 2006, 6, 2273. (6) Wang, C.; Hu, Y.; Lieber, C. M.; Sun, S. J. Am. Chem. Soc. 2008, 130, 8902. (7) Hadeed, F. O.; Durkan, C. Appl. Phys. Lett. 2007, 91, 123120. (8) Strachan, D. R.; Johnston, D. E.; Guiton, B. S.; Datta, S. S; Davies, P. K.; Bonnell, D. A.; Johnson, A. T. C. Phys. Rev. Lett. 2008, 100, 056805. (9) Taychatanapat, T.; Bolotin, K. I.; Kuemmeth, F.; Ralph, D. C. Nano Lett. 2007, 7, 652. (10) www.nanofactory.com (11) Chen, C. C.; Yeh, C. C.; Chen, C. H.; Yu, M. Y.; Liu, H. L.; Wu, J. J.; Chen, K. H.; Chen, L. C.; Peng, J. Y.; Chen, Y. F. J. Am. Chem. Soc. 2001, 123, 2791. (12) Padovani, F. A.; Stratton, R. Solid-State Electron. 1966, 9, 695. (13) Zhang, Z. Y.; Jin, C. H.; Liang, X. L.; Chen, Q.; Peng, L. M. Appl. Phys. Lett. 2006, 88, 073102. 4650
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