The simulation results of current mirror circuit and differential pair circuit are
shown in Fig. 3-8(a), Fig. 3-8(b), Fig. 3-9(a) and Fig. 3-9(b), respectively. The results of Monte Carlo method with Gaussian distribution and our proposed model which is also real data distribution are represented by red line and black line individually. From Fig. 3-9(a) and Fig 3-9(b), it can be observed that the simulation results of current mirror circuit and differential pair circuit of P-type using Monte Carlo analysis with Gaussian distribution are almost the same as the results using our proposed model. On the other hand, the simulation results of N-type current mirror and differential pair circuit using Monte Carlo method with Gaussian distribution are different to the results using our proposed model. Namely, Monte Carlo analysis with Gaussian distribution can be used as the distributions of parameter difference for P-type TFT, but it cannot be used as the parameter difference distributions for N-type TFT. It can also be observed that simulation using Gaussian distribution will underestimate the N-type circuit performance.
Generally, Monte Carlo analysis used in most simulation tools doesn’t support Lorentzian and Gaussian Lorentzian profiles for circuit simulation. Moreover, the major reason making the simulation results of N-type circuits difference between Gaussian distribution and our proposed model distribution is the distribution of Mu difference. From the Fig. 2-15, it can be found that the Mu difference distribution of N-type TFT is a little wider than that of P-type TFT. So the standard deviation value of Mu differences of N-type TFT is bigger than that of P-type TFT. Therefore, the Gaussian distribution defined by the average value and standard deviation of the Mu differences of N-type TFT is much wider than the real Mu difference distribution of N-type TFT. However, the concentration degree of the Mu difference distributions of N-type TFT and P-type TFT are almost the same. Accordingly, the Gaussian distribution might be defined by the inter-quartile range of the Mu difference data of N-type TFT instead of the standard deviation. From Fig.3-10(a) the Gaussian
distribution which is defined by inter-quartile range of the Mu difference data of N-type TFT has a better fitness for the Mu difference distribution of N-type TFT. In the same way, let other distributions be described as the Gaussian profile defined by inter-quartile region of parameter differences again. They are shown in Fig. 3-10(a) ~ (d), respectively. From these graphs, the Gaussian distributions defined by inter-quartile region are all similar to real distribution which is our proposed distribution. And the circuit simulation results using the Gaussian distribution defined by the inter-quartile range can be obtained in Fig. 3-11(a) ~ (d). It can also be found that the simulation results are almost the same with those using our proposed model.
In conclusion, if the inter-quartile range of the parameter differences data is used for the definition of Gaussian distribution, the parameter difference distribution described as Gaussian profile or Lorentzian profile is almost the same. Therefore, Monte Carlo analysis with Gaussian distribution still can be used to simulate LTPS TFT circuits in simulation tool and the more accurate circuit simulation results can be obtained than before.
Chapter 4
Conclusion
In this thesis, the variation characteristics of LTPS TFTs are statistically investigated. In order to study the respective effects of micro and macro variation, a special layout of TFTs called “crosstie” is adopted in this work. By introducing this special layout of TFTs, the dependence of distance for device variations can be found.
In chapter two, we classify two kinds of variation behaviors by grouping the difference of parameters in TFTs under different device distances. It can be observed that the variation in the range will be piecewise linear and the micro variation will be invariant in device position. The following is the proposed models for the difference of parameters. In this model, it can be observed that the shape of these distributions seems to be no changes with different device distances. This result tells us the micro variation will be invariant in device position indeed.
The following is the application for these models we proposed. The simulations of the mismatch due to the device variation in differential pair circuit and current mirror circuit are demonstrated. The simulation results of N-type circuits using Gaussian distribution defined by the average value and standard deviation of parameters difference are different to results by using our proposed models. It was also found that Gaussian model commonly assumed might underestimate the circuit performance. On the contrary, the simulation results of P-type circuits are almost similar to the results using our proposed models. However, the concentration degree of the Mu difference distributions of N-type and P-type is almost the same. Another way to describe Gaussian distribution is proposed. The Gaussian distributions defined by the inter-quartile range of parameters difference data have a good fitness for the
real data distribution compared with Gaussian distribution defined by the standard deviation. Therefore, the inter-quartile region of parameters difference is a major factor to decide the profile of these distributions and Monte Carlo analysis with Gaussian distribution still can be used to simulate LTPS TFT circuits in simulation tools. Furthermore, the circuit simulation results will be more accurate than before.
References
[1] Cheng-Ho Yu, “Study of Reliability Variation for Low Temperature Polysilicon Thin Film Transistors”, Diss. National Chiao Tung University, p. 69, 2005.
[2] Kitahara, Yoshiyuki; Toriyama, Shuichi; Sano, Nobuyuki, “A new grain boundary model for drift-diffusion device simulations in polycrystalline silicon thin-film transistors”, Japanese Journal of Applied Physics, Part 2: Letters, v 42, n 6 B, p.
L634-L636, 2003.
[3] Wang, Albert W., Saraswat, Krishna C., “Modeling of grain size variation effects in polycrystalline thin film transistors”, Technical Digest - International Electron Devices Meeting, p. 277-280, 1998.
[4] Wang, Albert W. (Agilent Technologies); Saraswat, Krishna C., “Strategy for modeling of variations due to grain size in polycrystalline thin-film transistors”, IEEE Transactions on Electron Devices, v 47, n 5 , p. 1035-1043, 2000.
[5] Shi-Zhe Huang, “Statistical Study on the Uniformity Issue of Low Temperature Polycrystalline Silicon Thin Film Transistor”, Diss. National Chiao Tung University, p. 14, 2005.
[6] Razavi, “Design of analog integrated circuit”, p. 121, 2001.
Fig. 1-1 The block diagram of an active matrix display
Fig. 1-2 The integration of peripheral circuits in a display achieved by poly-Si TFTs
Fig. 1-3 The initial characteristics of LTPS TFTs are different from one another due to various distributions of grain boundaries
Fig. 2-1 The layout of the crosstie TFTs
n + n - Poly-Si n - n +
Fig. 2-2 The schematic cross-section structure of the N-type poly-Si TFT with lightly doped drain
Fig. 2-3 The schematic cross-section structure of the P-type poly-Si TFT
Fig. 2-4 (a) The distributions of threshold voltage for N-type TFTs
Fig. 2-4 (b)The distributions of mobility for N-type TFTs
Fig. 2-4 (c)The distributions of subthreshold for N-type TFTs
Fig. 2-5 (a)The distributions of threshold voltage for P-type TFTs
Fig. 2-5 (b)The distributions of mobility for P-type TFTs
Fig. 2-5 (c)The distributions of subthreshold for P-type TFTs
Fig. 2-6 The threshold voltage distribution along the device position
Vth
position
Fig. 2-7 Simulation of the threshold voltage distribution along the device position for a long range
Fig. 2-8 (a) The average and the standard deviation of the threshold voltage differences of N-type TFTs
Fig. 2-8 (b) The average and the standard deviation of the mobility differences of N-type TFTs
Fig. 2-8 (c) The average and the standard deviation of the subthreshold swing differences of N-type TFTs
Fig. 2-9 (a) The average and the standard deviation of the threshold voltage differences of P-type TFTs
Fig. 2-9 (b) The average and the standard deviation of the mobility differences of P-type TFTs
Fig. 2-9 (c) The average and the standard deviation of the subthreshold swing differences of N-type TFTs
Fig. 2-10 (a) The distribution of Vth difference of N-type TFT and its fitting curve under the device distance of 40 µm
Fig. 2-10 (b) The distribution of Vth difference of N-type TFT and its fitting curve under the device distance of 200 µm
Fig. 2-10 (c) The distribution of Vth difference of N-type TFT and its fitting curve under the device distance of 2000 µm
Fig. 2-10 (d) The distribution of Vth difference of P-type TFT and its fitting curve under the device distance of 40 µm
Fig. 2-10 (e) The distribution of Vth difference of P-type TFT and its fitting curve under the device distance of 200 µm
Fig. 2-10 (f) The distribution of Vth difference of P-type TFT and its fitting curve under the device distance of 2000 µm
Fig. 2-11 (a) The distribution of mobility difference of N-type TFT and its fitting curve under the device distance of 40 µm
Fig. 2-11 (b) The distribution of mobility difference of N-type TFT and its fitting curve under the device distance of 200 µm
Fig. 2-11 (c) The distribution of mobility difference of N-type TFT and its fitting curve under the device distance of 2000 µm
Fig. 2-11 (d) The distribution of mobility difference of P-type TFT and its fitting curve under the device distance of 40 µm
Fig. 2-11 (e) The distribution of mobility difference of P-type TFT and its fitting curve under the device distance of 200 µm
Fig. 2-11 (f) The distribution of mobility difference of P-type TFT and its fitting curve under the device distance of 2000 µm
Fig. 2-12 (a) The distribution of S.S difference of N-type TFT and its fitting curve under the device distance of 40 µm
Fig. 2-12 (b) The distribution of S.S difference of N-type TFT and its fitting curve under the device distance of 200 µm
Fig. 2-12 (c) The distribution of S.S difference of N-type TFT and its fitting curve under the device distance of 2000 µm
Fig. 2-12 (d) The distribution of S.S difference of P-type TFT and its fitting curve under the device distance of 40 µm
Fig. 2-12 (e) The distribution of S.S difference of P-type TFT and its fitting curve under the device distance of 200 µm
Fig. 2-12 (f) The distribution of S.S difference of P-type TFT and its fitting curve under the device distance of 2000 µm
Fig. 2-13 The distributions of Vth difference of N-type and P-type TFTs
Fig. 2-14 The distributions of SS difference of N-type and P-type TFTs
Fig. 2-15 The distributions of Mu difference of N-type and P-type TFTs
Fig. 3-1 (a) The coupling effects of the clock signal
I
REFI
oM1 M2
I
REFI
oM1 M2
Fig. 3-1 (b) The signal transmission is done by differential signal
Fig. 3-2 A basic N-type current mirror circuit structure
M1 M2
Fig. 3-3 The N-type differential pair circuit with an active load biasing by a current mirror
Fig. 3-4 Simple distribution with four variables