Statistical circuit simulations - from ‘atomistic’ compact models to statistical standard cell characterisation

This thesis describes the development and application of statistical circuit simulation methodologies to analyse digital circuits subject to intrinsic parameter fluctuations. The specific nature of intrinsic parameter fluctuations are discussed, and we explain the crucial importance to the semiconductor industry of developing design tools which accurately account for their effects. Current work in the area is reviewed, and three important factors are made clear: any statistical circuit simulation methodology must be based on physically correct, predictive models of device variability; the statistical compact models describing device operation must be characterised for accurate transient analysis of circuits; analysis must be carried out on realistic circuit components. Improving on previous efforts in the field, we posit a statistical circuit simulation methodology which accounts for all three of these factors. The established 3-D Glasgow atomistic simulator is employed to predict electrical characteristics for devices aimed at digital circuit applications, with gate lengths from 35 nm to 13 nm. Using these electrical characteristics, extraction of BSIM4 compact models is carried out and their accuracy in performing transient analysis using SPICE is validated against well characterised mixed-mode TCAD simulation results for 35 nm devices. Static d.c. simulations are performed to test the methodology, and a useful analytic model to predict hard logic fault limitations on CMOS supply voltage scaling is derived as part of this work. Using our toolset, the effect of statistical variability introduced by random discrete dopants on the dynamic behaviour of inverters is studied in detail. As devices scaled, dynamic noise margin variation of an inverter is increased and higher output load or input slew rate improves the noise margins and its variation. Intrinsic delay variation based on CV/I delay metric is also compared using ION and IEFF definitions where the best estimate is obtained when considering ION and input transition time variations. Critical delay distribution of a path is also investigated where it is shown non-Gaussian. Finally, the impact of the cell input slew rate definition on the accuracy of the inverter cell timing characterisation in NLDM format is investigated

Silicon carbide junction field effect transistor integrated circuits for hostile environments

PhD ThesisSilicon carbide (SiC), in particular its 4H polytype, has long been recognised as an appropriate semiconductor for producing hostile environment electronics due to its wide energy band gap, large chemical bond strength and high mechanical hardness. A strong research foundation has facilitated the development of numerous sensor structures capable of operating at high temperatures and in corrosive atmospheres. Front-end electronics suitable for in situ signal conditioning are however lacking. Junction field effect transistors (JFETs) circumvent the pitfalls of contemporary alternative SiC transistor variants and have been found to operate predictably and consistently under such extreme conditions. This thesis demonstrates for the first time the capability of producing the necessary stable and high-performance interface circuits from n-channel lateral depletion-mode (NLDM) JFETs. The temperature dependence of pertinent bulk 4H–SiC material parameters relevant for describing the operation of macroscopic JFETs were initially studied. An accurate phenomenological model was developed to account for the variation of the thermal equilibrium free carrier concentrations. The position of the electrochemical potential and the distribution of free electron energies were found to change markedly when conduction band nonparabolicity, higher energy intrinsic bands and extrinsic effects were accounted for. These in turn were found to influence the determination of p-n junction contact potentials. The worst case error introduced through use of the Boltzmann approximation when applied to the channel and gate regions of the JFETs under study, having nominal doping concentrations of 1 1017 cm3 and 2 1019 cm3, respectively, were approximately 0:1% and 2%, respectively. A set of efficient and well behaved closed form expressions were subsequently developed for the free carrier concentrations in the framework of the Joyce- Dixon approximation (JDA) which are ideally suited for use in circuit simulations. Expressions for the electron conductively effective mass and an appropriate weighting function for the momentum relaxation time were subsequently identified. While the conductivity effective mass along the basal plane remained almost independent of temperature the non-parabolic band dispersion in the direction of principle axis introduced a temperature variation of 19% and 21% between 25 C and 400 C in the first and second conduction bands, respectively. Monolithically integrated 4H–SiC signal-level homo-epitaxial NLDM JFETs, p-n junction diodes and resistors were electrically characterised between room temperature and 400 C and their static and dynamic properties studied. Their behaviours were found to be well represented by macroscopic drift-diffusion models and were in agreement with predictions based on the bulk material properties. The intrinsic voltage gain of the fabricated JFET structures with nominal 9 μm gate length, 300nm channel depth and 250 μm gate width, under typical bias conditions, was roughly 100. As a consequence of the finite doping concentration in the buffer layer beneath the active device channel, with an experimentally determined value of approximately 3 1015 cm3, the devices under study were found to exhibit a strong body-effect. The thermal performance of the utilised tungsten capped annealed nickel-titanium and aluminium-titanium contacts, on highly doped n- and p-type regions, respectively, were investigated and appropriate methods for their characterisation described. The lowest recorded value of specific contact resistance was 1:90(50) 105 cm2 with a corresponding sheet resistance of 7:89(9) 102 = . Lateral current flow through the contact side wall and the difference in sheet resistance under the contact were found to increase the value of the specific contact resistance determined from transfer length method (TLM) test structures by as much as 10% for n-type contacts. While exhibiting much larger contact resistance, the p-type contacts were found to have negligible impact on device performance due to the high impedance of the gate-channel and body-channel p-n junctions under typical operation. Physics based, Simulation Program with Integrated Circuit Emphasis (SPICE) compatible, integrated circuit (IC) consistent compact models were developed that are congruent with experimental measurements over the aforementioned range of temperature and across all essential bias levels. Most notably, a self-contained, asymmetric double-gated, non-selfaligned JFET model was developed that accurately accounts for the body-effect, voltage dependent mobility and temperature. An accurate yet efficient solver of the charge neutrality equation within each region of the device is utilised to account for incomplete ionisation of dopants and the temperature dependence of the p-n junction contact potentials. Meticulous agreement with experimental measurements was attained from a minimal number of input parameters. The modelled devices were used to simulate pertinent IC building blocks, including single stage and differential amplifiers, level-shifters and voltage buffers. The finite bodytransconductance of active load transistors were identified as a major degrading factor for the voltage gain. Practical methods to circumvent this are discussed with the aid of appropriate small-signal equivalent models. Finally, a design was presented for a two-stage 4H–SiC operational amplifier (op-amp) with direct current (DC) stability over the entire temperature range of study. Low-frequency small-signal voltage gains of 80 dB and 70 dB were achieved at 25 C and 400 C, respectively when utilising a 30V supply. A closed-loop non-inverting op-amp configuration with an ideal gain of 11 was then simulated and found to vary by just 1% between 25 C and 400 C. Such amplifiers are of great utility and form the cornerstone of numerous useful and important electronic systems.Engineering and Physical Sciences Research Council (EPSRC) and BAE Systems Maritime for financially supporting this research project

Realistic gate model for efficient timing analysis of very deep submicron CMOS circuits

The continuously shrinking technology has made it possible for designers to incorporate more functionality with better performance at a much higher density in Integrated Circuits (ICs). Fast and accurate timing simulation of such large circuit designs using ever more complex transistor models has become a challenging problem. In modern circuits, the gate delay is severely affected by process variations, environmental variations and cross talk. Moreover, technology scaling has also resulted in significant increase in interconnect parasitics (including resistors and capacitors) which can dramatically reduce the performance of a circuit. For the circuit design validation and delay test evaluation, the industry has long relied on fast gate-level timing simulators like ModelSim to validate the designs. However, with continued scaling and steadily increasing circuit performance requirements, gate level simulators can no longer provide acceptable simulation accuracy. On the other hand, circuit level SPICE simulation provides acceptable accuracy but at a very large computational cost. To provide a suitable trade-off between the accuracy of the SPICE simulation and the speed of the gate level simulation, this thesis proposes a realistic gate model which can be used for the fast and accurate timing simulation of circuits to analyze their timing behaviour. In this thesis, a heterogeneous gate model that combines a simple gate model like Non-Linear Delay Model (NLDMs) and an advanced current source model (CSM) using a classifier is proposed. The simple gate model allows fast timing simulation and gives acceptable accuracy in many cases while the advanced gate model always provides more accurate and reliable results, but at a much higher computational cost. The classifier is designed to choose the advanced gate model depending on special cases (eg, multiple input switching) where the simple gate model gives inappropriate results. This heterogeneous gate model is further applied to develop a circuit simulator that enables fast and accurate post-layout and delay fault simulation