Organization of Thesis

Chapter 1. Introduction and Motivation for Research 1-1. Why LTPS TFTs

1-2. LTPS TFTs Device Variation 1-3. Simulation Method Review

1-3-1 Worst Case Method 1-3-2 Monte Carlo Method 1-4. Why Ring Oscillator 1-5. Organization of Thesis Chapter 2. Device Variation

2-1. Introduction to Crosstie TFTs

2-2. LTPS TFTs Initial Parameter Distribution

2-3. The Distribution of Initial Parameter Difference with Different Device Distance

Chapter 3. Implementation of Ring Oscillator with LTPS TFTs 3-1. Device Fabrication

3-2. Testkey Design and Layout

3-3. Measurement and Device Parameter Extraction Method 3-3-1 Measurement Method

3-3-2 Parameter Extraction 3-4. Results

Chapter 4. Device Variation Effects on Ring Oscillator

4-1. Microscopic Device Variation Effect on Ring Oscillator 4-2. Macroscopic Device Variation Effect on Ring Oscillator 4-3. Summary

Chapter 5. Conclusions and Future Works

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Fig. 1-1 The variation of the transfer characteristics of Id-Vg curve for LTPS TFTs.

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Fig. 1-2The variation of the transfer characteristics of Id-Vd curve for LTPS TFTs.

Fig. 1-3 The diagram of different TFTs with various amount of grain boundaries existing in the channel.

Fig. 1-4 Probability density function for (a) a Gaussian and (b) a uniform random

Chapter 2 Device Variation

2-1. Introduction to Crosstie TFTs

In previous studies, it is known that LTPS TFTs are found to suffer serious device variation even under well-controlled process. Since device variation will directly affect the circuit performance and reliability prediction, it is essential to understand where the variation may come and how the behavior variation could be. Due to the low process temperature, LTPS TFTs have different processes from IC industry. Besides, LTPS TFTs have less controllable defect number and distribution in the channel film. These may be the sources of device variation. In MOSFETs (Metal Oxide Semiconductor Field Effect Transistors), device variation sources can be divided into micro variations characterized by short correlation distances and macro variations characterized by long correlation distances, where the correlation distance is defined as the distance in which a process disturbance affects the device performance. Generally, the behaviors of the macroscopic and microscopic variation are the common and random variation, respectively. On the other hand, from the varying phenomena we can understand what variation type was occurred in the devices. Usually, macro variations come from the issues of process control, including gate insulator thickness lightly doped drain (LDD) length fluctuation and ion implantation uniformity; micro variations come from the difference of the defect site, defect density in the active region and the activation efficiency. If this correlation distance is lower than the distance between devices, the disturbance constitutes micro variations and affects few devices (e.g. a charge trapped in the gate oxide layer). On the other hand if this distance is longer than mutual device distance, the disturbance composed of micro variations and macro variations affects all the devices within a defined region. Therefore, the devices placed at longer distance suffer

more serious variation than devices placed close to each other.

In order to study the relationship between uniformity issue and device distance, a special layout of the devices adopted in this work is shown in Fig 2-1. The structure of the poly-Si film and the gate metal are in the order that resembles the crosstie of the railroad and therefore this layout is called the crosstie type layout of LTPS TFTs. The distance of mutual device is equally-spaced 40µm. In this small distance, the macro variation may be ignored and the variation of device behavior can therefore be reduced to only micro variation. So we can find out the relationship between the variation behaviors and the distance of mutual device by adopting the crosstie layout TFTs.

2-2. LTPS TFTs Initial Parameter Distribution

Before the following analysis, we introduce the statistical expressions, average value and standard variation. The average value AVG , X , is defined as

The standard deviation value STD, σ, is usually used to investigate the distribution of the observed value. The standard deviation value is given as

( )

In order to obtain the more accurate parameter distributions of crosstie layout TFTs, large amount of TFT devices parameters are required. More than 1600 devices are measured and taken into statistical analysis in this work. The threshold voltage (Vth) and mobility (Mu) distributions of N-type TFT are shown respctively in Fig. 2-2 and Fig. 2-3 and those of P-type

are shown in Fig. 2-4 and Fig. 2-5. Table 2-1 is the average values and standard variation values of these initial parameter.

N-type Vth(V) Mu(cm²/Vs)

Table 2-1 The average values and standard deviation values of device parameters.

These figures show the variation behaviors in different parameters of LTPS TFTs. The Vth distrubtion of N-type TFT reveals the slight left-skewed property and the sharper peak compared with the Gaussian distribution. The Mu distribution of N-type TFT is apparently asymmetric and incisive in its peak. This phenomena indicates that field effect mobility exhibits severe non-uniformity behavior compared with threshold voltage. Then, the distribution S.S of N-type TFT follows the Gussian distribution. As for the Vth and Mu distributions of P-type TFT, both of them are similar to the Gussain distribution. The P-type TFT SS distribution shows two peak and asymmetric. In conclusions, some of these parameter distributions are diverse and cannot be explained. Although several studies have been made on the relationship between the grain boundaries in channel and threshold voltage and field effect mobility [3-6], there seems to be no well-established theory to explain.

Therefore, if we want to find the variation behaviors with respect to the distance, it can not just classify them via these distributions and another grouping method should be mentioned.

In the next section, it will get the more identical distributions, which will be more useful to

evaluate the variations in LTPS TFTs.

2-3. The Distribution of Initial Parameter Difference with Different Device Distance

Fig. 2-6 illustrates the threshold voltage distribution along the device position. We can take this graph as a part of Fig. 2-7, which is the same kind of graph but in longer distance.

Analogy to the small signal analysis in the circuit theory, the macro variation just likes the range near the bias point and appears in piecewise linear form, while the micro variation can be taken as the noise. In order to identify the effects of the macro and micro variation, the parameter differences of two devices under certain distance are divided with several groups according to the distance between two devices. In previous studies [7], the averages of parameters differences stand for macro variation of LTPS TFTs, while the standard deviation of parameter differences shows the micro variation in the devices. Fig. 2-8 and Fig. 2-9 show the average and the standard deviation of parameters differences of LTPS TFTs. As the mutual device distance increases, the deviations of these parameter differences almost do not change with the device distance. It can be explained that the micro variation will merely vary with distance as we expect. As for the macro variation, these figures show the diverse results.

In the difference Vth, the average is increasing with device distance. However, the average of the Mu difference is decreasing when the distance of mutual devices is increasing. Although the averages of the differences of these parameters show different behaviors, they still appear in linear form. On the other hand, the effects of variation in a range are still minor than those of the micro variation under short device distance.

Since we know the device variation behaviors by above statistical analysis, how to apply these results to evaluate the effects of variation on the circuit performance is a topic we are interested in. Because the distance between two devices will not be too long for the layout

of the circuit, the macro variation is not our concern. A better approach is to find the proper mathematical expression for the distribution of the differences of these parameters. Firstly, we introduce the coefficient of determination (R square) to evaluate the fitness of our work, which is defined as

Generally speaking, the values of R square above 0.7 represnent the good fitness for the chosen funcion.

For the distribution of the difference of Vth, Gaussian-Lorentzian cross product is apply to the fitting, which is

c is fitting parameter related to the width of the distribution

d is fitting parameter varying from 0 to 1; 0 represents the pure Gaussain function ,while 1 is a pure Lorentzian distribution

Fig. 2-10 and Fig. 2-11 are shown respcetively the Vth difference distributions of N-type and P-type TFT with different device distance.

As for the distribution of the difference of Mu, the Lorentzian distribution is apply to the

c is fitting parameter related to the width of the distribution

The Mu difference distributions of N-type and P-type TFT with different device distance are shown in Fig. 2-12 and Fig. 2-13. The values of R square of the above fittng curves are both higher than 0.85. It clearly shows the good fitness of our proposed mathemtical model and most of the fitting parameters slightly changing with distance, which supports the effects of macro variation are minor than those of micro variation we mentioned before.

Fig. 2-1 The layout of the crosstie TFTs

Fig. 2-2 The initial distribution of N-type TFT threshold voltage (Vth)

Fig. 2-4 The initial distribution of P-type TFT threshold voltage (Vth)

Fig. 2-5 The initial distribution of P-type TFT mobility (Mu)

Fig. 2-6 A chart demonstrates device parameter distribution along distance corresponding to the concept of noise

Fig. 2-7 A chart demonstrates device parameter distribution along distance corresponding to the concept of signal and noise

Fig. 2-8 The average and standard deviation of TFT threshold voltage (Vth) difference

Fig. 2-9 The average and standard deviation of TFT mobility (Mu) difference

Fig. 2-10 The distribution of N-type TFT threshold voltage (Vth) difference

Fig. 2-11 The distribution of P-type TFT threshold voltage (Vth) difference

Fig. 2-12 The distribution of N-type TFT mobility (Mu) difference

Fig. 2-13 The distribution of P-type TFT mobility (Mu) difference