As shown in Fig. 4.1, a flowchart of the simulation-based optimization methodology illus-trates the sequence of process and device simulations [22–24,40,41,50,61–63], fluctuation analysis [51, 53, 58, 59], and a optimization kernel [1, 6, 56, 57, 67–69]. For a given device specification, such as the on- and off-state currents and the threshold voltage, the simula-tor searches out a set of optimal settings to fit the prescribed target and then estimates the variation of the threshold voltage accordingly. Starting from an initial process recipe, a 2D process simulation is applied to generate the corresponding device structure and dop-ing profile. Together with device parameters and physical models, the results of process simulation are used in the 2D device simulation to obtain the preliminary results. If we include the random-dopant induced characteristics fluctuation, we pass the physical results to perform the fluctuation analysis by solving the quantum correction model with perturba-tion and monotone iterative methods. At the same time, we calculate the error between the simulated result and the target to get the fitness (or the cost function). When the stopping tolerance is met, the solution procedure is terminated and the final results are outputted.
Otherwise, the hybrid optimization is enabled to do the evolutionary searching process with respect to several specified constraints. The refined fabrication conditions as well as the physical model parameters are then used as inputs to the process simulation and device simulation is repeated. The iteration between the TCAD simulation and optimization is
terminated when the simulated device’s specification and the correspondingly computed tolerance of characteristic fluctuation meet the target. We note that to automatically search for the optimal recipes for device fabrication, the problem is now treated as a reverse mod-eling problem, which is a multidimensional minimization problem. It minimizes the er-rors between the specified (or measured) physical (and electrical) characteristics and the simulated results. The dimension of the optimization problem depends upon how many parameters are to be optimized; in general, it is about 30 process and device parameters.
For ultra-small devices, 3D simulation should be considered to account for geometry effect.
Figure 4.2 shows the target I-V curves to be optimized and several most concerned physical quantities empirically. Inset of Fig. 4.2 is a 2D cross-section view of the simulated 65nm MOSFET with LDD doping profile.
The developed evolutionary system for the semiconductor device fabrication contains two independent parts, the evolutionary core kernel and the external simulation programs, shown in Fig. 1. The former part mainly uses evolutionary algorithms, such as the genetic algorithm and the particle swarm method; and the external programs consist of the codes for device simulation and process simulation which can be replaced with any existing TCAD software. During the iterative procedure, the optimizer computes the fitness score for each setting (i.e., the process recipe) through a fitness function. The fitness function measures the error between simulated and target characteristics and the fluctuation of threshold voltage.
The fitness function used in this work is
f itness = weightID(log(ID) − log(IDtarget)
log(IDtarget) ) + weightσvth(σvth
VT ). (4.14)
where the ID means the simulated data, the IDtarget is the specified target to be achieved, and σvth is the fluctuation of the threshold voltage (VT). weightIDand weightσvth are the weighted value for the I-V curves and σvth, respectively. In our work, we set weightID = weightσvth= 1, which means that the device performance and the fluctuation of the thresh-old voltage have the same weight. However, it can be adjusted according to different de-sign purposes. To retrieve the simulated physical characteristics including I-V curves, the optimizer sends the setting to be evaluated to the external process and device simulation programs, and the external programs perform the simulations and generate the I-V curves.
Physical-based empirical knowledge embedded in the evolutionary core kernel defines the relationship of the parameters and the device characteristics, as shown in Fig. 4.2.
According to engineering observation, parameters to be optimized are grouped into two categories, one is process-related and the other is device-related. The former part plays the important role of determining a device’s preliminary characteristics. The I-V curves are physically divided into the linear, the off-state and the saturation regions. We first optimize process-related parameters by minimizing errors between simulation and target in the linear and off-state regions. To achieve error minimization, parameters relating to implantations
Gate Voltage (V)
Figure 4.2: An illustration of the target I-V curves to be extracted and empirical knowledge. The important sections are pointed out in circles. The inset plot is a cross-section view of the simulated MOSFET with LDD doping profile.
of VT, well, lightly doped drain (LDD), and source/drain are first computed simultane-ously; allowing an accurate threshold voltage to be obtained. In the evolutionary part of the procedure, parameters coupled to band-to-band tunneling and saturation velocity are taken into consideration [22, 64–66]. Otherwise, parameters may possess unreasonable physical meanings, and then the optimization becomes meaningless. By minimizing errors in the saturation and off-state regions, device-related parameters are optimized with respect to
the mobility model, band-to-band tunneling model, and saturation velocity [22, 64–66]. To reduce the fluctuation of the threshold voltage, we focus on VT and LDD implantations.
Finally, if necessary, the linear, off-state, and saturation regions are simultaneously opti-mized one more time. The optimization is terminated when errors are miniopti-mized for all I-V curves. We note that the device performance, in particular, for VT and the linear region of I-V curves is significantly dominated by process-related parameters. Therefore, we put emphasis on the linear region and then the saturation region of I-V curves in the optimiza-tion procedure. During the optimizaoptimiza-tion procedure, once a larger error within a certain region of I-V curves is observed, an empirical rule is employed to destroy the evolution, which may result in different mutation and is useful in the iteration loop of simulation and optimization.
Generally, the number of parameters to be optimized depends upon the device para-meters selected in the TCAD simulation, and the process-related parapara-meters that directly affect the device structure and doping profile. From empirical knowledge, we especially investigate the parameters for VT, LDD and well implantations due to their significance in the threshold voltage and the linear region of the I-V curves. Moreover, the VT and LDD implantations are crucial when considering the random-dopant-induced characteris-tics fluctuation. We also adjust the mobility and saturation velocity parameters in the device simulation for fine-tuning the I-V curves.