SNAA391 june   2023 LMK6C , LMK6D , LMK6H , LMK6P

 

  1.   1
  2.   Abstract
  3.   Trademarks
  4. 1Introduction
  5. 2MTBF and FIT Calculations for BAW Oscillators
  6. 3Using the Online Estimator to Calculate MTBF and FIT
  7. 4Importance of Mission Profiles for FIT Rate Calculations
  8. 5Summary
  9. 6References

2 MTBF and FIT Calculations for BAW Oscillators

Having a FIT rate of 1 indicates one failure over 1 billion hours of operation. A preferable method for calculating FIT is to use HTOL reliability data and use the Arrhenius equation for acceleration, assuming a χ2 distribution as a reasonable approximation of the failure distribution over time. The JESD85 standard document, referenced in Section 1 is used for the calculations. While JESD85 shows methodologies for assessing FIT due to different fail mechanisms, for most modern-day semiconductor technologies, the qualification acceptance is 0 failures.

Sample sizes for running HTOL vary from different qualification standards. For the LMK6x BAW oscillators from Texas Instruments, see www.ti.com for the HTOL test data under the quality, reliability, and packaging information for the LMK6x device. Select the part number in the web site for view or download the reliability data for that particular device. Based on the LMK6C, LMK6D, LMK6P, LMK6H data, sample size for HTOL is 7859, test duration is 1000 hours, the number of failures is zero, and the test temperature is 125 °C. This data is valid at the time this application note is written. For latest data, refer to the above product page links.

The step-by-step procedure for FIT calculation for LMK6x BAW oscillators is as follows:

Step 1: Calculate Acceleration Factor (AF)

Calculate the Acceleration Factor (AF) using the data in Table 2-1. A common practice to gauge FIT is to de-rate to 55 °C (operating or use temperature) based on the activation energy of 0.7 eV. The equation for calculating AF is shown in Equation 1.

Equation 1. A c c e l e r a t i o n   F a c t o r   =   exp E a k × 1 T u s e - 1 T s t r e s s

Substituting the values from Table 2-1 into the AF equation results in an factor of 78.6.

Equation 2. exp 0.7   e V 8.6 × 10 - 5   e V / K × 1 55   ° C - 1 125   ° C = 78.6
Table 2-1 Data for Acceleration Factor Calculation
Variable Value
Accelerated Test Temperature (Tstress) 125 °C
Operating or Use Temperature (Tuse) 55 °C
Activation Energy (Ea) 0.7 eV
Boltzmann's Constant (k) 8.6×10-5 eV/K

Step 2: Calculate the Failure Rate

After calculating the acceleration factor, the next step is to calculate the failure rate (FIT). For this calculation, the confidence level is 60% (which is typical for industrial calculations) and the data in Table 2-2 is used.

Table 2-2 Data for Failure Rate Calculation
Variable Value
Number of Samples (ss) 7859
Test Duration (t) 1000 hours
Confidence Level (CL) 60%

The equation for calculating FIT rate is shown in the following equation. Where χ2 is the chi-square value and f is the number of failures.

Equation 3. Failure Rate FIT= Χ2%CL, 2×f+2×1092×t×ss×AF

Table 2-3 provides a quick reference for χ2 (chi-squared) values for different failures and different confidence levels (60% and 90%).

Table 2-3 Chi-squared Values for Failure Number and Confidence level
Number of Failures (f) Confidence Level (60%) Confidence Level (90%)
0 1.833 4.605
1 4.045 7.779
2 6.211 10.645
3 8.351 13.362

With a confidence level of 60% and the number of failures equal to zero, (f) = 0, a χ2 value of 1.833 is obtained from Table 2-3. HTOL data for BAW oscillators is 0 failures in 7859 samples for 1000 hours of HTOL operation at 125 °C, which when substituted into Equation 3, the FIT value is calculated to be 1.5 for 55 °C operation.

Equation 4. Failure Rate FIT= 1.833×1092×1000×7859×78.6≅1.5

As described in Section 1, the MTBF value is the inverse of the FIT value, as demonstrated in Equation 5.

Equation 5. M T B F =   1 F I T = 6.66666667 × 10 8 = 6.7 × 10 8

This result indicates that the BAW oscillator mean time between failure is approximately 0.67 billion hours under the conditions used in this section. Figure 2-1 shows a snapshot from TI online data for LMK6x BAW oscillators, which supports these results.

GUID-20230612-SS0I-7KQK-BBJB-NVJBKCXGJRQL-low.jpg Figure 2-1 Snapshot of Online MTBF and FIT Estimates for the LMK6x

To find the MTBF or FIT data information shown in Figure 2-1, refer to the LMK6x data sheet folder Ordering & quality tab and click on the View or Download link under Quality reliability & packaging information column.

As a final example of how to use the information available on www.ti.com, for 35 °C operation, the FIT rate is calculated to be 0.3 with the exact same conditions used throughout this section. The MTBF is 3.32×109. This result indicates that the BAW oscillator can operate for 3.32 billion hours without a fail at 35 °C usage temperature.