Solve MOSFET characteristic variation and reliability degradation issues
Characteristic variation can fall into several categories like global variation, local variation, systematic variation and random variation. Among them, random variation is a strong contributor to rapid yield loss by causing a significant drop in operating margin or a malfunction of the integrated circuit, which can occur even if each stand-alone device of a circuit works properly. Random dopant fluctuation (RDF) has been a dominant factor of random variation but studies now suggest that beyond the 20-nm process node, random telegraph noise (RTN) is the main contributor of random variation. Recent research indicates that RTN is related to the bias temperature instability (BTI), which causes reliability degradation.
In scaled MOSFETs, characteristic variations caused by RTN and BTI are recognized as significant factors to device-level and circuit-level functionality, and reliability degradation, but their measurement methods are not widely understood. This article introduces the phenomena of RTN and BTI, their measurement methods, and their challenges, along with tips for handling those challenges successfully.
Random telegraph noise
RTN on MOSFET occurs when a channel carrier, a hole or an electron, is captured in an oxide trap and the captured charge is emitted from the trap. As this charge capture and charge emission continue, the drain current (Id) fluctuates, which causes the threshold voltage (Vth) to shift. The ratio of the time constant to emit a captured charge (τe) and the time constant to capture a charge (τc) is expressed as
where A is the degeneracy factor, Et is the energy level of the trap, EF is the Fermi level, k is Bolzmann constant, and T is absolute temperature .
As shown in figure 1, the time-domain of an RTN signal shows binary fluctuation of Id (i.e. Vth) caused by continuous charge captures and charge emissions in a single trap. In the frequency domain, an RTN signal is inversely proportional to the square of the frequency (1/f2) after a plateau in low-frequency region.
Until now, the random dopant fluctuation (RDF) has been considered the dominant factor of random variation. According to a simple model of RTN, however, the amount of Vth shift is proportional to the reciprocal of gate area (i.e. 1/LW) for RTN , while it is proportional to the reciprocal square root of gate area for RDF. As a result, RTN is expected to be a main contributor of random variation at the 20-nm generation and beyond.
Bias temperature instability
Reliability degradation is also a difficult issue that has to be taken into account. On one hand, underestimating reliability degradation directly affects circuit functionality but on the other hand, overestimating reliability degradation makes circuit design very difficult or even impossible.
BTI is a phenomenon that introduces a significant reliability issue for the gate insulator by shifting the Vth of a MOSFET. The degradation of Vth due to BTI has been known since 1960s. It was recognized as a dominant reliability issue in scaled CMOS technologies in late 1990s.
Around the interface between the silicon (Si) substrate and the silicon dioxide (SiO2) gate oxide of a MOSFET, there are dangling-bond defects that build an interface state that in turn degrades the transistor characteristics. To avoid this, after the gate oxide is formed, hydrogen is annealed to bond Si-H to terminate the unattached hands of silicones.
When a negative bias is applied to the gate oxide of p-channel MOSFET, holes become majority carriers. At the Si-SiO2 interface, if a hole reacts with Si-H, it creates a dangling-bond of Si, which generates an interface state and a hydrogen ion (H+). The generated H+ is diffused into the oxide and captured. It interferes with carriers and as a result, decreases Id and shifts Vth (see figure 2).
This phenomenon is described by reaction-diffusion (RD) theory, which had gained broad acceptance. As process nodes shrink, though, researchers observed a fast recovery phenomenon in which the degradation abated with the release of the applied stress. This prompted broad study of an RTN-like capture-emission mechanism . Today, it is widely recognized that BTI consists of two components: a recoverable component, which starts recovering right after the stress is released, and a permanent component, which completely or almost completely fails to recover. It is also widely recognized that reliability degradation caused by negative BTI (NBTI) in scaled MOSFETs is more prominent than that caused by positive BTI (PBTI).
Grasser et al. indicate that RTN and the recoverable component of BTI are caused by the same defects , but the results reported by a different group indicate that RTN and BTI are uncorrelated threats for the device performance . Finding out the whole truth about RTN and BTI will require further research with precise measurements.
Impact to circuit design and process design
RTN is known to increase phase noise and jitter in analog circuits and decrease the noise margin of static random access memory (SRAM) in digital circuits. The Vth shift of a MOSFET significantly affects SRAM in large-scale integrated circuits (LSI), thus RTN is a serious issue that affects the yield and performance of LSIs.
Optimizing a design margin requires enough data for statistical analysis. If the sample size is small, changes in process conditions might be hard to observe. If underestimating variability is not acceptable, statistical errors associated with the circuit simulator input must be overestimated. As process nodes shrink, designing circuits by estimating variability is getting harder and harder, and soon it will become impossible; therefore, it is important to correctly measure the variability and reasonably estimate the effect to avoid the underestimating and overestimating.
If the Vth shift caused by RTN strictly followed a simple statistical distribution, it would be possible to make a certain level of prediction from a small amount of data. Because multiple defects are involved, however, the statistical distribution is not simple and the tail of actual distribution is longer than that of normal distribution; as a result, a large amount of data is required to accurately estimate the worst value. It is thus important to appropriately predict the worst value through the statistical estimation and feed that information back to the circuit design and process design. Actually, the Vth variation of RTN for the 25-nm generation reached 70 mV . The Vth variation of RTN may exceed the Vth variation of RDF as we move to future process nodes.
In case of BTI, it is necessary to assess the functionality degradations, including a fast recovery component. In terms of reliability, in order to avoid overestimating the BTI effect, it is necessary to separate a fast recovery component from other components, which is a dominant factor of reliability degradation.