EE650R: Reliability Physics of Nanoelectronic Devices Lecture 18: A Broad Introduction to Dielectric Breakdown Date: Nov 1, 2006 ClassNotes: Jing Li Review: Sayeef Salahuddin 18.1 Review As discussed before, there are three major reliability concerns for MOSFET-based logic transistors: NBTI, HCI and TDDB. In the previous lectures, we have focused on NBTI and discussed various features of this problem such as time, temperature and field dependence. Similar to BFRW problem, we start from Empirical and Statistical observations and interpret these phenomena by setting up Physical models. In today s lecture, we will begin to talk about Time Dependent Dielectric Breakdown, namely TDDB, following the same procedure. However, the device oxide thickness that we shall talk about in this lecture is much larger than those used in today s logic transistors. Let us start by comparing TDDB with three other phenomena which are otherwise quite well known: 1) Lightning 2) Discharge tubes 3) Avalanche Diode The common feature of these phenomena, including TDDB, is that they all involve dielectrics. Nevertheless, there is an important distinction. The three phenomena, as listed above, are reversible that is once the stress voltage is removed, the dielectric is restored to its pristine state. TDDB, on the other hand, is irreversible which means that when it takes place, there will be a permanent damage. It is also worth noting that molecular dielectric break-down (e.g. air during lightning or inert gas in discharge tubes) and solid state dielectric breakdown (e.g. avalanche diode) are fundamentally similar. In each case, the thermally-generated or electrode-injected electrons are accelerated by the field and when with sufficient energy gained from the field, they can knock electrons off other neutral atoms. The positively charged molecule (gas dielectric)/holes (semiconductor) are accelerated in the opposite direction and they can continue to participate in the impact ionization process. The only difference among the gas-phase and solid-state processes are in the relevant band gaps: In gas phase, the typical band gap is 10~14eV; while in solid state, the typical number is 5~10eV.
18.2 Phenomenological Description of Dielectric Breakdown Phenomena Let us now discuss the four stages of gate dielectric degradation and breakdown. 18.2.1 Stage I: Initiation of Impact Ionization in Lightning/Gas-Discharge Tube/Avalanche Diode Dielectric breakdown is initiated with some seed electrons. In case of lightning, first note that ionsphere, which is 50 kilometer above the earth, is an equi-potential and the earth surface itself is also an equal potential. The potential difference is about 400 kv. Air is a gas-phase dielectric in between. At some given temperature, statistically, an electron could be thermally ejected out. Because of the large electric field, it gets accelerated immediately and down the road, it may strike another atom and one more electron will be injected out and so on and so forth. The neutral molecules become positively charged and begin to drift under this electric field. Since the effective mass of molecule is much larger than electrons, the drift velocity is slow. The physics of impact ionization in gas discharge tube is similar, except the fact that the seed for impact ionization can come from the electrodes. Finally, in solid state devices, holes play the same role as the positive ions in gas dielectrics and participate in the multiplication process. e drift
18.2.2 Stage II: Spatial/Temporal Distribution Impact ionization is a spatially and temporally correlated stochastic process. For example, the impact ionization can be initiated at random location and the resulting electrons and holes can travel to random direction before either creating a new electron-hole pair by impact ionization (a new trace begins in the figure below) or recombining with a hole removing an electron-hole pair (a trace is terminated in the figure below). There are many measurements of spatial configurations of the ionization trees generally known as Litchenburg diagrams. They have a fractal dimension of approximate 1.7 that is they are neither 1D line nor fully 2D surface, rather they cover the surface with an intermediate dimension of 1.7. i In addition, the impact ionization process is also stochastic in time. In other words, if one were to collect the electrons arriving at the anode as a function of time, they will show noise associated with random multiplicative process (see Figure on the right). Indeed, this is one way to distinguish between Zener breakdown (low noise) and avalanche breakdown (high noise) in reversed biased p-n junction.. t 18.2.3 Stage III/IV: Defect Generation and Dielectric Breakdown In the third stage, permanent defects (red circles) are generated within the oxide by the energetic electrons and holes created in second stage. These defects allow hopping conduction through the oxides and increase leakage current. Eventually, when the defects finally form a bridge across the oxide, there will be a sudden energy discharge through the percolation path. The final stage can be represented by the equivalent
circuit viewed from the gate electrode to channel is shown below. Once the bridge is formed, the percolation resistance drops suddenly to its minimum value and a huge amount of current will flow through the oxide region which may destroy the oxide in the process. R perc C ox R perc t 18.2.3 Somewhat for Quantitative Description of Four Stages I 4 3 2 lnt 1 Stage 1: It is the region that impact ionization gets initiated. The current just begins to flow under certain voltage condition. It will keep going for an order of milliseconds (ms) depending on supply voltage. Stage 2: Impact Ionization Process begins. The frequency of the impact ionization current depends on the efficiency of impact ionization process. However, the impact ionization is strongly affected by the supply voltage. As a result, region 2 is also dependent on the supply voltage. t
Stage 3: There is a ln (t) dependence and will be discussed in more details in next lecture. Stage 4: Once there are enough traps in the oxide, the percolation resistance would go all the way down to its minimum value in a very short period of time. Because it happens so fast, it can be visualized as a switch (step function). At this point, there will be huge amount of current flowing through the oxide. If the accumulated heat reaches the melting point, it will result in a permanent damage and an eventual IC failure. Stages 1 & 2: It should be emphasized that impact ionization is a statistical process. One may do a simple mathematical treatment to study, under what conditions the impact ionization will turn on: In dynamic equilibrium, mν τ = qε ν = qετ m So that the energy gain from the field equals the energy lost through collision with phonons, i.e. de dt 2 2 q ετ = qεν = = ħ m ϖ τ 0 where de dt is kinetic energy gain and ħϖ 0 is the energy of optical phonon. ε ω 1 = ħ i q τ 2 0 2 2 ε ω0 1 = ħ i where 2 2 q τ 1 τ = m 2 3 E Then the minimum energy at which impact ionization turns on is the band-gap energy (E G ).
ε BD ω 2 0 3 = ħ im i q E G However, it should be noted that if supply voltage (V) is not high enough and energy is less than the band gap (E G ), impact ionization can still happen and it is called sub-band gap ionization. Another point of interest is the mechanism of initiation. Although, in gas, as we discussed before, it is started by thermal process, in solid state, impact ionization is more dominantly influenced by electrodes. Good electrodes lower the injection barrier and make it easy for electrons to be injected into the system. Stage 4: The current is a percolation current and not a tunneling current and it is a few orders of magnitude larger than the tunneling current (I P >>I T ). T 2 cρ = εj perc + Kox T t ε J perc 2 w T = a ln > Tmelt 2Kox a Where a is the width of percolation (2~3nm) Silicon dielectric generally has lower thermal conductivity than silicon. The heat will dissipate through window length T ox which has been illustrated in the figure below. T ox a 18.4 Conclusion: Dielectric breakdown in gate insulators is related to broad range of breakdown phenomena in nature and engineering. One can learn much regarding the mechanics and statistics of TDDB by studying the related phenomena elsewhere. Indeed, in many ways dielectric breakdown in thick oxides and fracture mechanics of solid material are so closely related that many concepts of one can easily be related to other. We will discuss this topic later if time permits.