Hot-Carrier Device Degradation Modeling and Extraction Methodologies

Abstract

The present invention is directed to a number of improvements in methods for hot-carrier device degradation modeling and extraction. Several improvements are presented for the improvement of building device degradation models, including allowing the user to select a device parameter used to build the device degradation model independent of the device parameter selected. The user can also select the functional relation between stress time and degradation level. To further improve accuracy, multiple acceleration parameters can be used to account for different regions of the degradation process. Analytical functions may be used to represent aged device model parameters, either directly or by fitting measured device parameters versus device age values, allowing devices with different age values to share the same device model. The concept of binning is extended to include device degradation. In addition to a binning based on device width and length, age is added. In an exemplary embodiment, only devices with minimum channel length have degraded models constructed. The present invention also allows the degradation of one device parameter to be determined based on an age value derived from another parameter. In yet another aspect, a degraded device is modeled as a fresh device with a voltage source connected to a terminal.

1 . A method of obtaining a device degradation model, comprising:
 stressing the device for a time period;   measuring values for a plurality of device parameters of the stressed device during the time period;   selecting one of the device parameters;   extracting a relation between stress time and the degradation of the selected parameter from the measured values for the selected parameter during the time period;   extracting a degradation rate for the device from the relation between stress time and the degradation of the selected parameter;   deriving from the degradation rate a device degradation model for a device parameter other than the selected device parameter.   
   
   
       2 . The method of  claim 1 , wherein the selected device parameter is source drain current. 
   
   
       3 . The method of  claim 1 , wherein the selected device parameter is threshold voltage. 
   
   
       4 . The method of  claim 1 , wherein the selected device parameter is transconductance. 
   
   
       5 . The method of  claim 1 , wherein the deriving from the degradation rate a device degradation model comprises:
 determining the dependence of the device parameter other than the selected device parameter upon the degradation rate.   
   
   
       6 . The method of  claim 5 , wherein the extracting a relation between stress time and the degradation of the selected parameter comprises:
 determining a first time acceleration parameter; and   wherein the determining the dependence of the device parameter other than the selected device parameter upon the degradation rate comprises determining one or more second time acceleration parameters.   
   
   
       7 . The method of  claim 6 , wherein the number of second time acceleration parameters is two. 
   
   
       8 . The method of  claim 1 , further comprising:
 prior to extracting a relation between stress time and the degradation of the selected parameter, selecting a functional form for the relation.   
   
   
       9 . The method of  claim 8 , wherein said functional form is that the degradation is proportional to the stress time to a power. 
   
   
       10 . The method of  claim 8 , wherein said functional form is that the logarithm of the degradation is proportional to the stress time to a power. 
   
   
       11 . A computer readable storage device embodying a program of instructions executable by a computer to perform the method of  claim 1 . 
   
   
       12 . (canceled) 
   
   
       13 . A method of obtaining a device degradation model, comprising:
 stressing the device for a time period;   measuring values for a plurality of device parameters of the stressed device during the time period;   selecting from a plurality of functional forms a functional form for the time dependence of degradation of one of the device parameters;   extracting a relation between stress time and the degradation of said one of the device parameters from the measured values for the selected parameter during the time period using the selected functional form; and   deriving a device degradation model from the relation between stress time and the degradation of said one of the device parameters.   
   
   
       14 . The method of  claim 13 , wherein said functional form is that the degradation is proportional to the time to a power. 
   
   
       15 . The method of  claim 13 , wherein said functional form is that the logarithm of the degradation is proportional to the time to a power. 
   
   
       16 . The method of  claim 13 , wherein said extracting a relation between stress time and the degradation comprises determining a degradation rate, and wherein the device degradation model is a function of the degradation rate. 
   
   
       17 . The method of  claim 16 , wherein said determining a degradation rate includes specifying the power of the ratio of the substrate current and the source to drain current upon which the degradation rate depends. 
   
   
       18 . The method of  claim 16 , wherein the degradation rate is only specified up to a proportionality constant. 
   
   
       19 . The method of  claim 16 , wherein the deriving a device degradation model comprises:
 determining the dependence said one of the device parameters upon the degradation rate.   
   
   
       20 . The method of  claim 19 , wherein the extracting a relation between stress time and the degradation of the selected comprises:
 determining a first time acceleration parameter; and   wherein the determining the dependence said one of the device parameters upon the degradation rate comprises determining one or more second time acceleration parameters.   
   
   
       21 . The method of  claim 20 , wherein the number of second time acceleration parameters is two. 
   
   
       22 . A computer readable storage device embodying a program of instructions executable by a computer to perform the method of  claim 13 . 
   
   
       23 . A method for transmitting a program of instructions executable by a computer to perform a process of simulating the degradation of a circuit, said method comprising:
 causing the transmission of a program of instructions to a client device, thereby enabling the client device to perform, by means of such program, the process of the method of  claim 13 .   
   
   
       24 - 32 . (canceled) 
   
   
       33 . A method of obtaining a degraded device model, comprising:
 stressing the device for a time period;   measuring values for device parameters and device characteristics of the stressed device during the time period;   building a device degradation model of the device using the measured device parameter values;   building a fresh model for the device from the measured device characteristic values;   building from the measured device characteristic values a degraded model for the device corresponding to a value in the time period device;   obtaining an intermediate quantity from the device degradation model and the measured device characteristic values; and   obtaining a relation for a model parameter as a function of the intermediate quantity from the fresh and degraded models.   
   
   
       34 . The method of  claim 33 , wherein the device is a MOSFET and the device characteristics include the current-voltage behavior. 
   
   
       35 . The method of  claim 33 , wherein the obtaining a relation for a model parameter as a function of the intermediate quantity comprises fitting the degraded model parameter versus device age curves. 
   
   
       36 . The method of  claim 33 , further comprising:
 obtaining a model for the device incorporating the relation for the model parameter as a function of the intermediate quantity.   
   
   
       37 . A computer readable storage device embodying a program of instructions executable by a computer to perform the method of  claim 33 . 
   
   
       38 . A method for transmitting a program of instructions executable by a computer to perform a process of simulating the degradation of a circuit, said method comprising:
 causing the transmission of a program of instructions to a client device, thereby enabling the client device to perform, by means of such program, the process of the method of  claim 33 .   
   
   
       39 . A method of obtaining a degraded device model, comprising:
 stressing the device for a time period;   measuring values for device parameters and device characteristics of the stressed device during the time period;   building a device degradation model of the device using the measured device parameter values;   building a fresh model for the device from the measured device characteristic values;   obtaining an intermediate quantity from the device degradation model and the measured device characteristic values;   obtaining a relation for a device parameter as a function of the device age from the fresh model, the intermediate quantity, and measured parameter values; and   obtaining relation for a model parameter as a function of the intermediate quantity from the relation for a device parameter as a function of the intermediate quantity.   
   
   
       40 . The method of  claim 39 , wherein the device is a MOSFET and the device characteristics include the current-voltage behavior. 
   
   
       41 . The method of  claim 39 , wherein the device is a MOSFET and the device parameter is the source drain current. 
   
   
       42 . The method of  claim 39 , wherein the device is a MOSFET and the device parameter is the transconductance. 
   
   
       43 . The method of  claim 39 , wherein the device is a MOSFET and the device parameter is the threshold voltage. 
   
   
       44 . The method of  claim 39 , wherein the obtaining a relation for a device model parameter as a function of the intermediate quantity comprises fitting the measured device parameters versus device age. 
   
   
       45 . The method of  claim 39 , further comprising:
 obtaining a model for the device incorporating the relation for the model parameter as a function of the intermediate quantity.   
   
   
       46 . A computer readable storage device embodying a program of instructions executable by a computer to perform the method of  claim 39 . 
   
   
       47 . A method for transmitting a program of instructions executable by a computer to perform a process of simulating the degradation of a circuit, said method comprising:
 causing the transmission of a program of instructions to a client device, thereby enabling the client device to perform, by means of such program, the process of the method of  claim 39 .   
   
   
       48 . A method of obtaining a degraded device model, comprising:
 providing non-degraded models for the device at a plurality of widths for a plurality of lengths;   determining a degraded device model for the device at the plurality of widths for the minimum length of the plurality of the lengths; and   for the device having a length between the minimum length and a second of the lengths and having a width between a first and a second of the widths, generating a degraded device model from the non-degraded device models at the minimum length and second of the lengths for the first and second widths and from the degraded device model models at the minimum length for the first and second widths.   
   
   
       49 . The method of  claim 48 , wherein the determining comprises:
 stressing the device for the plurality of widths for the minimum length for a period of time;   measuring values for parameters and characteristics of the stressed device during the time period;   building device degradation models for the stressed device using the measured parameter values; and   building the degraded device models for the devices from device degradation models for the device at the plurality of widths for the minimum length.   
   
   
       50 . The method of  claim 49 , wherein the building the degraded device models comprises:
 building degraded device models for the first width at the minimum length at a first set of degradation levels; and   building degraded device models for the second width at the minimum length at a second set of degradation levels, wherein the first set of degradation levels is different than the second set of degradation levels; and   determining degraded device models for the second width at the minimum length at the first set of degradation levels from the degraded device models for the second width at the minimum length at a second set of degradation levels.   
   
   
       51 . A computer readable storage device embodying a program of instructions executable by a computer to perform the method of  claim 48 . 
   
   
       52 . (canceled) 
   
   
       53 . A method of obtaining the degradation level of a first device parameter of a device, comprising:
 obtaining an age value for the device from a second device parameter, wherein the second device parameter is different than said first device parameter;   generating the degraded characteristics of the device using the device degradation value; and   extracting the degradation level of the first device parameter from the degraded characteristics of the device.   
   
   
       54 . The method of  claim 53 , wherein generating the degraded characteristics of the device comprises:
 producing a degraded device model card using the device degradation value; and   using the degraded device model card to simulate the degraded characteristics of the device.   
   
   
       55 . The method of  claim 53 , wherein extracting the degradation level of the first device parameter comprises:
 expressing the degradation level of the first device parameter as a function of the age value.   
   
   
       56 . The method of  claim 55 , wherein the function is of the form of the age value raised to a power. 
   
   
       57 - 69 . (canceled)