ÖZET Elektronikte, özellikle tümdevre tasarımında, devrelerin bilgisayarla simülasyonu çok önemlidir. Simülasyonlann yapılabilmesi için elemanların, uç büyüklüklerine bağlı olarak, gösterdiği davranışların bilinmesi gereklidir. Bunun için, gerekli data dosyalan oluşturularak bilgisayar belleklerine yüklenebilir fakat bu yöntem bilgisayarların bellek kapasiteleri ve hızlan gözönüne alındığında, tercih edilebilir değildir. Bu noktada, kullanışlı bir çözüm olarak, elemanların matematiksel modelleri karşımıza çıkmaktadır. Elemanların modelleri, belirli şartlar altında kurulmalarına rağmen, hem elemanın her davranışını yansıtmaz hem de modellediği davranışlan tam doğru biçimde veremez. Pratikte, elemanın gerekli, önemli, davranışlan modellenir ve yapılan modellemde hatalar, eksikler, vardır. Yani herhangi bir fiziksel davranış tam olarak fiziksel modele yansıtilamaz, yansıtılmak istendiğinde ise yakınsama problemleri doğar. Modellemede tek sıkıntı bu değildir, model parametrelerinin doğru tesbiti aynı derecede önemli bir problemdir. Bir elemanın matematiksel modeli kurultuktan sonra modelin zaaflanm azaltmanın tek çaresi parametrelerin optimum, hatayı enaz yapacak biçimde, teshilidir. Bu aynı zamanda önemli bir problemdir. Bu çalışmada, sözü edilen problemin, MOS tranzistorun SPICE L, 2. ve 3. düzey statik modellerinde, çözümü için araştırmalar yapılıp, algoritmalar geliştirilmişrtir. Bu algoritmalar, C dilinde yazılan, bilgisayar programlarıyla pratiğe geçirilmiştir. y SUMMARY COMPUTER-AIDED EXTRACTION OF SPICE STATIC MODEL PARAMETERS OF MOSFET After founding the mathematical model of a device, the only öne remedy of reducing deficiencies of a model is the optimum extraction of its parameters. There are several researchs made and methods developed about this subject [1,2,3,4,5,6,7,8]. The extraction of parameters, as to the basic points, can be made in two different ways. The first of them is the classical methods and the other is the mathematical methods. The fîrst is to extract each parameter by means of examining the region ör regions, equation ör equations on which the parameter is effective [1]. This method can be used in both hand-made analysis and computer-aided analysis. in these methods, parameters are extracted sequentially, öne at a time ör in small groups and assumed fixed and accurate for use in extracting further parameters (for example, in extracting the SPICE level 2 model parameters of MOSFET; VTO, LAMBDA, KP and GAMMA are extracted sequentially. Then, UEXP, UCRIT and UTRA as a group, NFS which is the parameter of weak inversion as a single parameter are extracted. Similarly, ali the parameters are extracted.). But in these methods, the interaction of parameters is not taken into account. For example in level 2 model of MOSFET, without extracting RS and RD which are the resistances coming in series to drain and source, the other parameters are extracted. in the thesis, the methods used to extract level l and 2 model parameters of MOSFET are the classical methods. But in addition to that, the algorithm has been developed to remove the interaction of parameters which is an important disadvantage for these methods. The algorithms which are used in extracting the parameters of level l and 2 have been developed generally by using the methods put fonvard in [1]. First of ali, the parameters of level l are extracted. The extraction of LAMBDA and GAMMA are made by means of the classical methods, but the mathematical optimization technique also can be used. Here, the point that is worth çare appears in extracting the value of VTO; there is some difference betvveen the values which vi11.600E-006 1.200E-006 -Ids(A) 8.000E-007 - 4.000E-007 O.OOOE+000 tu» = -0.05V MEASURED OOOOO LEVEL 2 < LEVEL 3 In LEVEL 2. 3.5356 RMS Error In LEVEL 3, 2.296S8 RMS Error -Vos(V) Figure 4 The simulation and measured characteristics of the P type transistor, in the linear region. VK = -2.5V MEASURED ) LEVEL 2 i LEVEL 3 In LEVEL 2. 22.76* RMS Error In LEVEL 3. 2.975» RMS Error 2.0O0E-005 1.600E-005 - -Ids(A) : 1.200E-005 : 8.Q00E-006 -_ 4.000E-006 : O.OOOE+000 0 1 2 -VDS(V) Figure 5 The simulation and measured drain characteristics of the P type transistor. XI1.000E-004 S.0O0E-005 -Ids(A) 6.000E-005 4.QO0E-005 2.000E-005 O.OOOE+000 MEASURED OCOOG LEVEL 2 LEVEL 3 In LEVEL 2. 31.7» RMS Error In LEVEL 3, 5.08S8 RMS Error -VGS(V) Figure 6 The simulation and measured characteristics of the P transistor, in the saturation region. type It can be seen from the figures that, the results obtained for level 2 model are not good as opposed to the results obtained for level 3 model. The reason of this is that, the interaction of parameters was able to be removed for most parts, but the parameters have been usually extracted from the linear region and the saturation region has not been taken into account. So, the method, used for extracting level 2 model parameters, gives good results for the linear region, but in the saturation region, the results are not pleasing. For level 3 model, pleasing results have been obtained. This can be seen from the figures. Therefore, we can generalize the method used for extracting level 3 model parameters to extract parameters of another model. But this method is in need of the initial values to converge the result like the other mathematical optimization methods. At this point, it can be said that, the method used for extracting level 2 model parameters, can be used as a solution for this problem and has already carried out a similar task in extracting level 3 model parameters; the values of KP, Vto and Rs(=Rd) extracted for level 2 model are taken as the initial values for the algorithm used for extracting level 3 model. Finally, to obtain pleasing results, we must use the mathematical methods which take important characteristics of the model into account and we must not forget that, we need the initial values for these methods and these values can be extracted with the help of the classical methods. Xll1.600E-006 1.200E-006 -Ids(A) 8.000E-007 - 4.000E-007 O.OOOE+000 tu» = -0.05V MEASURED OOOOO LEVEL 2 < LEVEL 3 In LEVEL 2. 3.5356 RMS Error In LEVEL 3, 2.296S8 RMS Error -Vos(V) Figure 4 The simulation and measured characteristics of the P type transistor, in the linear region. VK = -2.5V MEASURED ) LEVEL 2 i LEVEL 3 In LEVEL 2. 22.76* RMS Error In LEVEL 3. 2.975» RMS Error 2.0O0E-005 1.600E-005 - -Ids(A) : 1.200E-005 : 8.Q00E-006 -_ 4.000E-006 : O.OOOE+000 0 1 2 -VDS(V) Figure 5 The simulation and measured drain characteristics of the P type transistor. XI1.000E-004 S.0O0E-005 -Ids(A) 6.000E-005 4.QO0E-005 2.000E-005 O.OOOE+000 MEASURED OCOOG LEVEL 2 LEVEL 3 In LEVEL 2. 31.7» RMS Error In LEVEL 3, 5.08S8 RMS Error -VGS(V) Figure 6 The simulation and measured characteristics of the P transistor, in the saturation region. type It can be seen from the figures that, the results obtained for level 2 model are not good as opposed to the results obtained for level 3 model. The reason of this is that, the interaction of parameters was able to be removed for most parts, but the parameters have been usually extracted from the linear region and the saturation region has not been taken into account. So, the method, used for extracting level 2 model parameters, gives good results for the linear region, but in the saturation region, the results are not pleasing. For level 3 model, pleasing results have been obtained. This can be seen from the figures. Therefore, we can generalize the method used for extracting level 3 model parameters to extract parameters of another model. But this method is in need of the initial values to converge the result like the other mathematical optimization methods. At this point, it can be said that, the method used for extracting level 2 model parameters, can be used as a solution for this problem and has already carried out a similar task in extracting level 3 model parameters; the values of KP, Vto and Rs(=Rd) extracted for level 2 model are taken as the initial values for the algorithm used for extracting level 3 model. Finally, to obtain pleasing results, we must use the mathematical methods which take important characteristics of the model into account and we must not forget that, we need the initial values for these methods and these values can be extracted with the help of the classical methods. Xll1.600E-006 1.200E-006 -Ids(A) 8.000E-007 - 4.000E-007 O.OOOE+000 tu» = -0.05V MEASURED OOOOO LEVEL 2 < LEVEL 3 In LEVEL 2. 3.5356 RMS Error In LEVEL 3, 2.296S8 RMS Error -Vos(V) Figure 4 The simulation and measured characteristics of the P type transistor, in the linear region. VK = -2.5V MEASURED ) LEVEL 2 i LEVEL 3 In LEVEL 2. 22.76* RMS Error In LEVEL 3. 2.975» RMS Error 2.0O0E-005 1.600E-005 - -Ids(A) : 1.200E-005 : 8.Q00E-006 -_ 4.000E-006 : O.OOOE+000 0 1 2 -VDS(V) Figure 5 The simulation and measured drain characteristics of the P type transistor. XI1.000E-004 S.0O0E-005 -Ids(A) 6.000E-005 4.QO0E-005 2.000E-005 O.OOOE+000 MEASURED OCOOG LEVEL 2 LEVEL 3 In LEVEL 2. 31.7» RMS Error In LEVEL 3, 5.08S8 RMS Error -VGS(V) Figure 6 The simulation and measured characteristics of the P transistor, in the saturation region. type It can be seen from the figures that, the results obtained for level 2 model are not good as opposed to the results obtained for level 3 model. The reason of this is that, the interaction of parameters was able to be removed for most parts, but the parameters have been usually extracted from the linear region and the saturation region has not been taken into account. So, the method, used for extracting level 2 model parameters, gives good results for the linear region, but in the saturation region, the results are not pleasing. For level 3 model, pleasing results have been obtained. This can be seen from the figures. Therefore, we can generalize the method used for extracting level 3 model parameters to extract parameters of another model. But this method is in need of the initial values to converge the result like the other mathematical optimization methods. At this point, it can be said that, the method used for extracting level 2 model parameters, can be used as a solution for this problem and has already carried out a similar task in extracting level 3 model parameters; the values of KP, Vto and Rs(=Rd) extracted for level 2 model are taken as the initial values for the algorithm used for extracting level 3 model. Finally, to obtain pleasing results, we must use the mathematical methods which take important characteristics of the model into account and we must not forget that, we need the initial values for these methods and these values can be extracted with the help of the classical methods. Xll 71