KR102596748B1 - Method of predicting life time of transistor - Google Patents

Abstract

A method for predicting transistor lifespan is disclosed. A method for predicting the lifespan of a transistor according to an embodiment includes collecting data on a transistor at a plurality of times using a combination of a plurality of temperatures and a plurality of currents that are different from normal use conditions; Processing the collected data to match a gamma process, which is a set of random variables following a gamma distribution; Estimating a parametric function expressing the characteristics of a gamma distribution based on the processed data; Obtaining the parameters of the parametric function for normal use conditions; and predicting the lifespan of the transistor under normal use conditions using a parametric function whose parameters are estimated.

Description

{Method of predicting life time of transistor}

This specification relates to a method for predicting the lifespan of a transistor, and more specifically, a method for predicting the lifespan of a bidirectional junction transistor based on a gamma process.

A bipolar junction transistor or Bipolar Junction Transistor (BJT) is a type of transistor that consists of two p-n junctions in which both electrons and holes are used as charge carriers. A small current flowing in one stage flows through the other two stages. to control the flow of much larger currents flowing between them. Bipolar junction transistors, or BJTs, are of n-type and p-type, as shown in FIG. 1.

Because bipolar junction transistors are still used as key components for switches or amplification, it is important to accurately predict the lifespan of BJTs.

This specification takes this situation into account, and the purpose of this specification is to provide a method for accurately predicting the life of a bipolar junction transistor.

A method for predicting the lifespan of a transistor according to an embodiment of this specification for realizing the above-described problem includes collecting data on the transistor at a plurality of times at a plurality of times by combining a plurality of temperatures and a plurality of currents that are different from normal use conditions; Processing the collected data to match a gamma process, which is a set of random variables following a gamma distribution; Estimating a parametric function expressing the characteristics of a gamma distribution based on the processed data; Obtaining the parameters of the parametric function for normal usage conditions; and predicting the lifespan of the transistor under normal use conditions using a parameter function whose parameters are estimated.

Therefore, it is possible to accurately predict the lifespan of the bipolar junction transistor.

1 is a diagram showing a bipolar junction transistor (BJT) with symbols,
Figure 2 is a graphical representation of the probability density function of the gamma distribution,
Figure 3 is a table listing the average and variance of BJT cumulative deterioration measured at multiple times in an accelerated deterioration test under temperature and current conditions;
Figure 4 is a table listing the parameters obtained under each condition of temperature and current for the shape parameter function selected while modeling the BJT cumulative degradation measured in the accelerated degradation test with a gamma distribution;
Figure 5 shows an operational flowchart for a method for predicting transistor lifespan according to an embodiment of this specification.

Hereinafter, an embodiment of a transistor life prediction method will be described in detail based on the accompanying drawings.

First, let's briefly look at the gamma process.

A gamma process or gamma process is a set of random variables { . The gamma distribution represents a continuous probability distribution for the time it takes for the αth event to occur, where α is called the shape parameter and β is called the scale parameter.

The random variable X(t) of the gamma process has the following characteristics.

P{X(0)=0} = 1 (1)

X(s)-X(t)~Ga(λ(s)-λ(t),η), where s>t>=0 (2)

X(t2)-X(t1) and X(t4)-X(t3) are independent, where t4>=t3>=t2>=t1>0 (3)

The first equation means that the probability that the random variable X(t) is 0 at t=0 is 1, that is, the initial value of the random variable X(t) is 0. The second equation means that X(t) follows the gamma distribution. The third equation means that the random variables have independent increments.

The probability density function of the random variable

(4)

Here, λ(t) is the shape parameter function and is greater than 0, and η is the scale parameter.

The mean and variance of the random variable X(t) at time t are given in the following equation (5).

(5)

In the embodiment of this specification, an accelerated deterioration test is performed on a plurality of bipolar junction transistors at two or more temperatures and two or more currents at a plurality of time intervals to obtain data on deterioration characteristic values, and based on this, We propose a method to predict lifespan.

The accelerated deterioration test is conducted using multiple temperatures and multiple currents as stresses. Among the applied stresses, the temperature can be two conditions of 90°C and 140°C, which are much higher than the room temperature of 25°C, and the currents are 212mA, 260mA, and 335mA. It can be 3 conditions, so it can be 6 conditions. Ten samples are used for each condition of temperature and current combination, and data can be obtained at multiple times.

In the embodiment of this specification, the deterioration characteristic value of the BJT measured through a deterioration test is analyzed using a gamma process, and the lifespan of the BJT can be predicted based on this.

The deterioration characteristic value of a BJT measured by performing a deterioration test is the current gain or beta (β), which indicates the ratio of the current flowing in the collector and the current flowing in the base.

The current gain of a BJT gradually decreases over time from its initial value. However, the random variable used in the gamma distribution must be in the form of a monotonically increasing function that continues to increase over time.

Therefore, it is necessary to process the current gain measured at multiple times as a deterioration characteristic value for the BJT to fit the gamma process. For this purpose, the current gain is normalized to the initial value, that is, the current gain measured at multiple times or points in time is divided by the initial value, and then the initial value is changed to 0, that is, the current gain is P{X(0)=0} = 1 To meet the condition, the normalized current gain at each point is subtracted from 1.

In this way, the current gain value of the BJT obtained by normalizing to the initial value and then subtracting the normalized value from 1 has an initial value of 0 and increases over time, resulting in the accumulated deterioration of the BJT (can also be simply referred to as the amount of deterioration). It can be expressed. The cumulative deterioration amount of the BJT obtained in this way becomes independent of the increase in the previous time as time passes, satisfying the random variable properties of the gamma distribution.

Therefore, in this specification, the cumulative current gain degradation of the BJT is analyzed using a degradation model using the gamma process, but it can be assumed that the shape parameter of the gamma distribution changes with time and the scale parameter is a constant that does not change.

Because shape parameters change over time, it is necessary to model the shape parameter function using measured data. Once the shape parameter function model is derived, a deterioration model under normal conditions can be obtained using this model, and the lifespan of the BJT can be predicted based on this.

To estimate the shape parameter and scale parameter of the gamma distribution, the average and variance data of the accumulated degradation amount described above can be used.

First, normalize the current gain of the BJT measured at each point to its initial value, set the initial value to 0, and subtract the normalized value from 1 to increase monotonically. For the accumulated deterioration amount obtained through processing, the angle of temperature and current The average and variance are calculated for each condition and time, and the average and variance for the cumulative amount of deterioration are listed in a table in Figure 3.

Based on the average and variance data of the accumulated deterioration of the BJT, the shape parameter and scale parameter are obtained at each time for each condition, that is, each combination of temperature and current, using Equation (5) described above. In addition, the scale parameter is treated as a constant regardless of conditions and time, and the pooled value, that is, the average value, is used.

The shape parameter function, which indicates how the shape parameter obtained for each combination of temperature and current changes over time, is estimated using the least squares method through regression analysis. The shape parameter for all combinations is calculated as one shape parameter function. It can be estimated as

To find the simplest function that best fits the shape parameter function λ(t), we consider several candidate functions of the curve: When the value is 0, it increases with time.

(6)

(7)

(8)

Using the data shown in Figure 3, the function with the highest coefficient of determination is selected as a model suitable for the shape parameter function. The model in equation (6) was selected because the coefficient of determination was the largest.

The two parameters of the shape parameter function λ(t) selected through this process can be obtained under each condition of temperature and current. In Figure 4, the shape parameter function selected while modeling the BJT cumulative degradation measured in the accelerated degradation test with a gamma distribution is shown. The parameters obtained under each condition of temperature and current are described.

Since the parameters of the shape parameter function shown in FIG. 4 are values estimated under the conditions of an accelerated deterioration test, the parameters of the shape parameter function to be used under normal conditions must be obtained.

To determine the relationship between cumulative deterioration and stress, the following stress-life equation can be applied.

(9)

In equation (9) above, θ is the parameter of the shape parameter function, T is the absolute temperature, i is the applied current, Ei is the activation energy, k is the Boltzmann constant, and n is a constant. Equation (9) is an equation proposed by multiplying the Arrhenius equation, which represents the temperature dependence of the reaction rate, by a component that takes into account the influence of current.

If regression analysis is performed using Equation (9) above based on the parameter a and b values in the table of Figure 4 obtained under each temperature and current condition for the previously selected shape parameter function, the temperature and current of 25°C, which are normal use conditions, are obtained. Parameters a and b at 176mA can be estimated.

Since the parameters a and b of the previously selected shape parameter function were estimated under normal use conditions, the probability density function of the gamma distribution for the cumulative deterioration of the BJT under normal use conditions can be determined.

If the time when the current gain of the BJT becomes 1/3 of the initial value is set as the criterion for failure of the BJT or the lifespan of the BJT, the random variable value of the accumulated deterioration at the time of failure is (1-1/3)=2/ It becomes 3. In other words, it can be assumed that the lifespan of the BJT is when the expected value of the accumulated deterioration becomes 2/3.

In equation (5), the expected value of cumulative deterioration amount, 2/3, is expressed as the product of the shape parameter function, which is a time function, and the scale parameter, which is a constant. Therefore, the shape parameter function is the expected value of cumulative deterioration amount, 2/3, as a constant scale. It becomes a value divided by the parameter, and t that satisfies that value can be said to be the point at which it fails or its lifespan.

In addition, if the current gain of the BJT is calculated with the initial value of the BJT known, the time corresponding to the current state is calculated using the accumulated deterioration amount of the current BJT as the expected value, similar to the method described previously, and the current gain is equal to the initial value. If you calculate the lifespan at 1/3 of the time using the method described above, you can also calculate the remaining lifespan of the BJT.

Figure 5 shows an operational flowchart for a method for predicting transistor lifespan according to an embodiment of this specification.

First, perform a deterioration test to collect data on the BJT (S510).

Data can be obtained by performing a deterioration test with the same number of BJTs for each combination of a plurality of temperature conditions and a plurality of current conditions, and measuring the deterioration characteristic value of the BJT at multiple times. At this time, the deterioration characteristic value may be the current gain of the BJT.

In order to apply it to the gamma process, the BJT's deterioration characteristic data is processed (S520). Since the random variable used in the gamma process has an initial value of 0 and an increasing value, the current gain of the BJT measured as the deterioration characteristic value at multiple times is normalized to the initial value and then the normalized value is subtracted from 1. This processed value corresponds to the cumulative deterioration amount of the BJT.

Shape parameter and scale parameter that express the characteristics of the gamma distribution using the formula for calculating the mean and variance from the probability density function of the gamma distribution based on the accumulated deterioration data of the BJT for each condition of temperature and current and each time. Estimate (S530).

First, the average and variance of the accumulated deterioration amount are obtained under temperature, current, and visual conditions, and this is applied to equation (5) to obtain the shape parameter and scale parameter. At this time, the scale parameter can be treated as a constant and the average value can be used. there is.

In order to express the shape parameters obtained at multiple times as a function of time for each combination of temperature and current, regression analysis is performed on multiple candidates to select the most appropriate function. The multiple candidates are It is a function whose value is 0 and whose value increases as time progresses. It can be simply defined with only two parameters.

Among the plurality of candidates, the candidate with the largest coefficient of determination is selected as the shape parameter function, and two parameters expressing the selected shape parameter function are obtained from each combination of temperature and current.

Since the parameters of the shape parameter function are values estimated for accelerated deterioration test conditions, their values are estimated for normal conditions (S540). By applying the Arrhenius equation, the parameters of the shape parameter function under normal conditions are estimated using an equation that multiplies the Arrhenius equation related to temperature by an item related to current.

Apply the estimated parameters to determine the probability density function of the gamma distribution for the cumulative deterioration of the BJT under normal use conditions, and use this to predict the life of the BJT or the remaining life of the BJT (S550).

The lifespan can be the point at which the current gain of the BJT becomes 1/3 of the initial value, which corresponds to the point at which the accumulated deterioration amount becomes 2/3, and the expected value of the random variable of the accumulated deterioration amount becomes 2/3. The value of the shape parameter function can be obtained, and the time t required to reach the value can be determined as the lifespan of the BJT.

The transistor life prediction method described in this specification can be described as follows.

A method for predicting the lifespan of a transistor according to an embodiment includes collecting data on a transistor at a plurality of times using a combination of a plurality of temperatures and a plurality of currents that are different from normal use conditions; Processing the collected data to match a gamma process, which is a set of random variables following a gamma distribution; Estimating a parametric function expressing the characteristics of a gamma distribution based on the processed data; Obtaining the parameters of the parametric function for normal use conditions; and predicting the lifespan of the transistor under normal use conditions using a parametric function whose parameters are estimated.

In one embodiment, the transistor may be a bipolar junction transistor (BJT).

In one embodiment, the data for the transistor may be the current gain of the BJT.

In one embodiment, the processing step may change the current gain to a deterioration amount that has an initial value of 0 and increases in value over time.

In one embodiment, the processing step normalizes the current gain measured at each time by the current gain obtained at the first time of the same combination, and then subtracts the normalized value from 1 to obtain the amount of degradation at that time.

In one embodiment, the estimating step involves estimating the shape parameter and scale parameter expressing the characteristics of the gamma distribution based on the amount of degradation, but the scale parameter is treated as a constant and the shape parameter is obtained as a shape parameter function that changes with time. You can.

In one embodiment, the estimating step may calculate the shape parameter and scale parameter based on the expected value and variance of the amount of degradation obtained for each condition and each time.

In one embodiment, the scale parameter may use a pooled value for all combinations and all times.

In one embodiment, the estimating step may express the shape parameter estimated at each time for each combination as a shape parameter function that includes two parameters, is expressed as a function of time, and is described as one for all combinations.

In one embodiment, the estimating step involves obtaining one shape parameter function through regression analysis among a plurality of candidate functions that include two parameters, the value of which is 0 when time is 0, and the value of which increases with time. You can.

In one embodiment, the obtaining step includes obtaining two parameters of the shape parameter function for each combination; and estimating two parameters for normal use conditions based on the two parameters obtained for each combination.

In one embodiment, the step of estimating two parameters may use the Arrhenius equation related to temperature multiplied by a term related to current.

In one embodiment, the predicting step includes obtaining the value of a shape parameter function such that the expected value of the amount of deterioration is a predetermined value; and calculating the time that becomes the value of the shape parameter function as the lifespan.

The present invention is not limited to the described embodiments, and it is obvious to those skilled in the art that various modifications and changes can be made without departing from the spirit and scope of the present invention. Accordingly, such modifications or variations should be considered to fall within the scope of the claims of the present invention.

Claims (13)

collecting data on the transistor at a plurality of times and at a plurality of temperature and current combinations that are different from normal use conditions;
Processing the collected data to match a gamma process, which is a set of random variables following a gamma distribution;
estimating a parametric function expressing characteristics of the gamma distribution based on the processed data;
obtaining parameters of the parametric function for the normal use conditions; and
A method for predicting the lifespan of a transistor, comprising predicting the lifespan of the transistor under normal use conditions using a parametric function for which the parameters are estimated. According to claim 1,
A method for predicting transistor lifespan, wherein the transistor is a bipolar junction transistor (BJT). According to clause 2,
A method for predicting transistor lifespan, wherein the data for the transistor is the current gain of the BJT. According to clause 3,
The processing step is characterized in that the current gain is changed to a deterioration amount that has an initial value of 0 and increases over time. According to clause 4,
In the processing step, the current gain measured at each time is normalized by the current gain obtained at the first time of the same combination, and then the normalized value is subtracted from 1 to obtain the amount of degradation at that time. Prediction method. According to clause 4,
The estimating step involves estimating a shape parameter and a scale parameter expressing the characteristics of the gamma distribution based on the amount of degradation, where the scale parameter is treated as a constant and the shape parameter is obtained as a shape parameter function that changes with time. A method for predicting transistor lifespan, characterized in that: According to clause 6,
In the estimating step, the shape parameter and scale parameter are calculated based on the expected value and variance of the amount of degradation obtained for each condition and each time. According to clause 6,
A method for predicting transistor lifespan, characterized in that the scale parameter uses a pooled value for all combinations and all times. According to clause 6,
In the estimating step, the shape parameter estimated at each time for each combination is expressed as a shape parameter function that includes two parameters, is expressed as a function of time, and is described as one for all combinations. Prediction method. According to clause 9,
The estimating step is characterized by obtaining the one shape parameter function through regression analysis among a plurality of candidate functions that include the two parameters, have a value of 0 when time is 0, and increase in value with time. Transistor life prediction method. According to clause 9,
The steps to obtain the above are,
Obtaining two parameters of the shape parameter function for each combination; and
A method for predicting transistor life, comprising the step of estimating the two parameters for the normal use conditions based on the two parameters obtained for each combination. According to claim 11,
The step of estimating the two parameters is a method for predicting transistor lifespan, wherein the Arrhenius equation related to temperature is multiplied by an item related to current. According to clause 6,
The prediction step is,
obtaining a value of the shape parameter function such that the expected value of the amount of deterioration becomes a predetermined value; and
A method for predicting the lifespan of a transistor, comprising calculating the time at which the value of the shape parameter function becomes the lifespan.

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