Abstract:
A method for modeling a transistor includes providing a transistor model having at least a source node, a drain node, and a gate node, simulating operation of a device using the transistor model in a computing apparatus, and generating an offset voltage at the gate node depending on a magnitude of a current passing through the device.

Description:
CROSS-REFERENCE TO RELATED APPLICATIONS 
       [0001]    Not applicable. 
       BACKGROUND 
       [0002]    The disclosed subject matter relates generally to semiconductor devices and, more particularly, to the modeling of gate transconductance of a transistor device using a sub-circuit transistor model. 
         [0003]    Compact models of metal-oxide-semiconductor field-effect transistors (MOSFETs) are widely used in simulations of integrated circuits. Conventional compact models, such as a Berkeley Short-Channel IGFET Model (BSIM) or a Berkeley Short-Channel IGFET Model for Silicon-on-insulator devices (BSIMSOI), have been primarily employed to model (or capture) transistor properties, such as drive current, I DEFF , for digital circuits. To implement the transistor model, a reference transistor model is defined. The modeling system uses selected data (e.g., current-voltage (IV) operational characteristics) taken from an actual transistor and loads that data into a software modeling program. Parameters of the reference transistor model are then varied to attempt to match the modeled operational characteristics with the corresponding operational characteristics of the actual transistor. 
         [0004]    Compact transistor models do not typically incorporate the breadth of parameters sufficient to accurately model transistor properties for analog circuits. One such analog parameter that is not accurately incorporated into the compact models is gate transconductance (g m ) in a low voltage regime (i.e., gate voltage close to the threshold voltage of the transistor). Furthermore, fabricated transistors are subject to process induced variations that cannot be controlled. For example, a series of actual transistors may have slightly different channel lengths, layer thicknesses, threshold voltages, etc., causing differences in actual operating characteristics from transistor to transistor. Consequently, it is useful to build these variations into the transistor model to allow the prediction of how the fabricated transistor will perform with these random variations. Simulations of advanced circuits require that the systemic and random variations in transistor properties be correctly modeled. Given the lack of parameters to accurately model g m , it is very difficult to create a model that can simultaneously capture both variations in g m  and variations in the digital properties (such as I DEFF ) simultaneously. 
         [0005]    One approach to modeling g m  involves using the parameters included in the compact models, such as carrier mobility, gate oxide thickness, and gate length, to model g m  and variations in g m . However, the digital properties (such as I DEFF ) of the transistor are usually sensitive to these parameters. Therefore, it is difficult to employ these parameters to model g m  and variations in g m  without sacrificing the accuracy of the modeling of the digital properties. 
         [0006]    This section of this document is intended to introduce various aspects of art that may be related to various aspects of the disclosed subject matter described and/or claimed below. This section provides background information to facilitate a better understanding of the various aspects of the disclosed subject matter. It should be understood that the statements in this section of this document are to be read in this light, and not as admissions of prior art. The disclosed subject matter is directed to overcoming, or at least reducing the effects of, one or more of the problems set forth above. 
       BRIEF SUMMARY 
       [0007]    The following presents a simplified summary of the disclosed subject matter in order to provide a basic understanding of some aspects of the disclosed subject matter. This summary is not an exhaustive overview of the disclosed subject matter. It is not intended to identify key or critical elements of the disclosed subject matter or to delineate the scope of the disclosed subject matter. Its sole purpose is to present some concepts in a simplified form as a prelude to the more detailed description that is discussed later. 
         [0008]    One aspect of the disclosed subject matter is seen in a method for modeling a transistor. The method includes providing a transistor model having at least a source node, a drain node, and a gate node, simulating operation of a device using the transistor model in a computing apparatus, and generating an offset voltage at the gate node depending on a magnitude of a current passing through the device. 
         [0009]    Another aspect of the disclosed subject matter is seen in a system including a storage device operable to store a transistor model having at least a source node, a drain node, and a gate node, and a computing apparatus operable to execute a simulation application to simulate operation of a device using the transistor model and generate an offset voltage at the gate node depending on a magnitude of a current passing through the device. 
     
    
     
       BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWINGS 
         [0010]    The disclosed subject matter will hereafter be described with reference to the accompanying drawings, wherein like reference numerals denote like elements, and: 
           [0011]      FIG. 1  is a diagram of a transistor model in accordance with one illustrative embodiment of the present subject matter, where gate transconductance is modeled as a function of drain current; 
           [0012]      FIG. 2  is a diagram illustrating gate transconductance offset voltage as a function of normalized drain current; 
           [0013]      FIG. 3  is a diagram of a transistor model, where gate transconductance is modeled as a function of drain current using a dummy voltage source; 
           [0014]      FIG. 4  is a diagram of a transistor model in accordance with an alternative embodiment of the present subject matter, where gate transconductance is modeled as a function of source current; 
           [0015]      FIG. 5  is a diagram of a transistor model, where gate transconductance is modeled as a function of source current using a dummy voltage source; 
           [0016]      FIG. 6  is a diagram of a transistor model in accordance with yet another alternative embodiment of the present subject matter, where gate transconductance is modeled as a function of drain current and drain-induced barrier lowering is modeled as a function of drain voltage; 
       
    
    
       [0017]    While the disclosed subject matter is susceptible to various modifications and alternative forms, specific embodiments thereof have been shown by way of example in the drawings and are herein described in detail. It should be understood, however, that the description herein of specific embodiments is not intended to limit the disclosed subject matter to the particular farms disclosed, but on the contrary, the intention is to cover all modifications, equivalents, and alternatives falling within the spirit and scope of the disclosed subject matter as defined by the appended claims. 
       DETAILED DESCRIPTION 
       [0018]    One or more specific embodiments of the disclosed subject matter will be described below. It is specifically intended that the disclosed subject matter not be limited to the embodiments and illustrations contained herein, but include modified forms of those embodiments including portions of the embodiments and combinations of elements of different embodiments as come within the scope of the following claims. It should be appreciated that in the development of any such actual implementation, as in any engineering or design project, numerous implementation-specific decisions must be made to achieve the developers&#39; specific goals, such as compliance with system-related and business related constraints, which may vary from one implementation to another. Moreover, it should be appreciated that such a development effort might be complex and time consuming, but would nevertheless be a routine undertaking of design, fabrication, and manufacture for those of ordinary skill having the benefit of this disclosure. Nothing in this application is considered critical or essential to the disclosed subject matter unless explicitly indicated as being “critical” or “essential.” 
         [0019]    The disclosed subject matter will now be described with reference to the attached figures. Various structures, systems and devices are schematically depicted in the drawings for purposes of explanation only and so as to not obscure the disclosed subject matter with details that are well known to those skilled in the art. Nevertheless, the attached drawings are included to describe and explain illustrative examples of the disclosed subject matter. The words and phrases used herein should be understood and interpreted to have a meaning consistent with the understanding of those words and phrases by those skilled in the relevant art. No special definition of a term or phrase, i.e., a definition that is different from the ordinary and customary meaning as understood by those skilled in the art, is intended to be implied by consistent usage of the term or phrase herein. To the extent that a term or phrase is intended to have a special meaning, i.e., a meaning other than that understood by skilled artisans, such a special definition will be expressly set forth in the specification in a definitional manner that directly and unequivocally provides the special definition for the term or phrase. 
         [0020]    Referring now to the drawings wherein like reference numbers correspond to similar components throughout the several views and, specifically, referring to  FIG. 1 , the disclosed subject matter shall be described in the context of a sub-circuit transistor model  10 . The transistor model  10  defines a source node  20 , a drain node  30 , a body node  40 , and a gate node  50 . In some embodiments, the transistor may also define a substrate node (not shown). In the case of silicon-on-insulator (SOI) devices, the transistor model  10  may omit the body node  40 . The modeling of gate transconductance is facilitated by a gate transconductance node  60  represented by a current controlled voltage source (CCVS) connecting the gate node  50  to an input voltage node  70  provided to the model  10 . The various nodes  20 ,  30 ,  40 ,  60  connect to input/output ports  25 ,  35 ,  45 ,  65  of the transistor model  10 . 
         [0021]    The gate transconductance node  60  generates a gate voltage offset, dV G , in addition to that provided by the input voltage node  70 , V GS . The gate transconductance offset voltage is modeled as a function of the drain current, I D , in the form of a function dV G =f(I D ). The effective gate voltage provided to the gate node  50  is thus V GS +dV G . The gate transconductance seen external to the transistor model  10  is modeled by defining the function for the CCVS of the gate transconductance node  60 . The specific function employed to generate the transconductance offset may be determined by measuring the gate transconductance of actual devices or by employing speculative gate transconductance targets. 
         [0022]    In the illustrative embodiment, the gate transconductance function  100  is a bell-shaped function of drain current, as illustrated in  FIG. 2 . The drain current, I D , is normalized by the threshold current, I TH , seen when the threshold voltage, V TH , is applied to the gate. In an analog operation region  110 , the gate transconductance offset rises to a non-zero value. The gate transconductance offset decays to zero in a sub-threshold region  120  (i.e., where the gate voltage is below V TH  and the drain current, I D , is low). The gate transconductance offset also decays to zero in a digital operation region  130  (i.e., where the gate voltage is close to the nominal supply voltage and the drain current, I D , is high). By modeling both the analog and digital operating regions  110 ,  120 , the transistor model  10  models gate transconductance and variations thereof without sacrificing the accuracy of the digital property modeling. 
         [0023]    An exemplary equation for modeling the gate transconductance offset generated by the gate transconductance node  60  is: 
         [0000]    
       
         
           
             
               
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         [0000]    where A, B, C, and N are model fitting parameters, and I TH  is a threshold grain current that varies depending on the transistor technology. To model random variations in gate transconductance, perturbations in the values of the model fitting parameters from baseline values may be introduced. The particular perturbations may vary depending on the type of variation being modeled. In one example, for systemic variation in gate transconductance, the baseline value of the A parameter may be changed. In one embodiment, a positive voltage parameter (e.g., 1.02 V) may be used for A for a fast process corner, while a negative voltage parameter (e.g., −1.02 V) may be used for a slow process corner. For random variation, random values for A may be used. 
         [0024]    A variation of the embodiment of  FIG. 2  is illustrated in  FIG. 3 , where a dummy voltage source  80  is connected between the drain node  30  and the input/output port  35  of the transistor model  10 . The value of the drain current, I D , may be read directly from the dummy voltage source  80  and provided to the gate transconductance node  60  for determination of the voltage offset. 
         [0025]    Another embodiment of the transistor model  10  is illustrated in  FIG. 4 . The gate transconductance node  60  is modeled as a function of source current, I S , rather than drain current, so dV G =f(I S ). The transistor model  10  of  FIG. 4  functions similar to that of  FIG. 2 , as the source and drain currents are approximately equal. 
         [0026]    A variation of the embodiment of  FIG. 4  is illustrated in  FIG. 5 , where a dummy voltage source  90  is connected between the source node  20  and the input/output port  25  of the transistor model  10 . The value of the source current, I S , may be read directly from the dummy voltage source  90  and provided to the gate transconductance node  60  for determination of the voltage offset. 
         [0027]      FIG. 6  illustrates an embodiment of the transistor model  10  incorporating the modeling of gate transconductance and drain-induced barrier lowering (DIBL), another parameter difficult to capture in a compact transistor model, DIBL is modeled using a voltage controlled voltage source  95  that provides an additional offset to the gate voltage as a function of the drain voltage, V D . The DIBL offset is directly proportional to the drain voltage, 
         [0000]      V DIBL =kV D , 
         [0000]    where the value of k may vary depending on the particular transistor being modeled. Random and systemic variation may be simulated by varying the magnitude and sign of k. The transistor model  10  of  FIG. 6  allows concurrent modeling of both gate transconductance and DIBL in a compact transistor model. Although the model  10  of  FIG. 6  is illustrated as being combined with the model of  FIG. 1 , any of the embodiments of the models  10  described herein may be used. 
         [0028]    Turning now to  FIG. 7 , a simplified diagram of selected portions of the hardware and software architecture of a computing apparatus  200  such as may be employed in some aspects of the present subject matter. The computing apparatus  200  includes a processor  205  communicating with storage  210  over a bus system  215 . The storage  210  may include a hard disk and/or random access memory (“RAM”) and/or removable storage, such as a magnetic disk  220  or an optical disk  225 . The storage  210  is also encoded with an operating system  230 , user interface software  235 , and a simulation application  265 . The user interface software  235 , in conjunction with a display  240 , implements a user interface  245 . The user interface  245  may include peripheral I/O devices such as a keypad or keyboard  250 , mouse  255 , etc. The processor  205  runs under the control of the operating system  230 , which may be practically any operating system known in the art. The simulation application  265  is invoked by the operating system  230  upon power up, reset, user interaction, etc., depending on the implementation of the operating system  230 . The simulation application  265 , when invoked, performs a method of the present subject matter. The user may invoke the simulation application  265  in conventional fashion through the user interface  245 . Note that although a stand-alone system is illustrated, there is no need for the data to reside on the same computing apparatus  200  as the simulation application  265  by which it is processed. Some embodiments of the present subject matter may therefore be implemented on a distributed computing system with distributed storage and/or processing capabilities. 
         [0029]    It is contemplated that, in some embodiments, the simulation application  265  may be executed by the computing apparatus  200  to implement any of the transistor models  10  described herein, such as those illustrated in FIGS.  1  and  2 - 6 , to model the performance of a transistor as well as any other devices encompassed by the simulation. Data for the simulation may be stored on a computer readable storage device (e.g., storage  210 , disks  220 ,  225 , solid state storage, and the like). 
         [0030]    The particular embodiments disclosed above are illustrative only, as the disclosed subject matter may be modified and practiced in different but equivalent manners apparent to those skilled in the art having the benefit of the teachings herein. Furthermore, no limitations are intended to the details of construction or design herein shown, other than as described in the claims below. It is therefore evident that the particular embodiments disclosed above may be altered or modified and all such variations are considered within the scope and spirit of the disclosed subject matter. Accordingly, the protection sought herein is as set forth in the claims below.