Background
Micro-nano sensors typically have internal structures on the micrometer or even nanometer scale. Its design and fabrication involve a variety of disciplines and engineering techniques such as physics, semiconductors, optics, electrical engineering, chemistry, materials engineering, mechanical engineering, medicine, information engineering, and biotechnology.
Packaging is a major factor affecting the overall production cost of the micro-nano sensor. Common industrial wafer level vacuum packaging processes include anodic bonding, silicon-silicon bonding, and eutectic solder bonding. For a common plastic sealed pressure sensor, the packaging represents 20% of the total production cost, whereas for a pressure sensor operating continuously in a severe environment (high pressure and rapid temperature change), the packaging represents 95% of the total production cost. Other micro-nano sensors have similar packaging costs.
The complicated geometry, high diversity and small size of the micro-nano sensor are the reasons for high packaging cost, so that the study on the air tightness and the prediction on the air tightness failure of the packaging are needed, but the size of the packaging cavity of the micro-nano sensor is small, and the packaging failure can be caused by undetectable leakage.
Therefore, how to predict the package air tightness failure time of the micro-nano sensor is a technical problem to be solved by the person skilled in the art.
Disclosure of Invention
The invention aims to predict the packaging air tightness failure time of a micro-nano sensor, and provides a method for predicting the packaging air tightness failure time of the micro-nano sensor.
The technical scheme of the invention is that the method for predicting the air tightness failure time of the micro-nano sensor package comprises the following steps:
s1, determining leak rates of the micro-nano sensor at different moments, and establishing a functional relation between the leak rates and time;
S2, establishing a prediction model based on the functional relation and the internal volume of the packaging cavity of the micro-nano sensor, and determining the change relation between the pressure in the packaging cavity and time according to the prediction model;
s3, predicting the package air tightness failure time based on the change relation and the failure threshold value of the pressure in the package cavity.
Further, the function relation between the leak rate and time is specifically shown as the following formula:
Wherein L (t) is a function of the leak rate and time, L0 is an initial leak rate value, t0 is 1 hour, and t is time.
Further, the prediction model is specifically shown as the following formula:
wherein P (t) is the pressure in the packaging cavity at the moment t, L (t) is the functional relation between the leak rate and time, and V is the internal volume of the packaging cavity.
Further, the change relation between the pressure in the packaging cavity and time is specifically shown as the following formula:
Wherein P (t) is the pressure in the packaging cavity at the moment t, L (t) is the functional relation between the leak rate and time, V is the internal volume of the packaging cavity, t0 is 1 hour, and t is time.
Further, the step S3 specifically includes the following sub-steps:
s31, determining a failure threshold value of the pressure in the packaging cavity;
S32, determining the failure time based on the prediction model and the failure threshold value.
Compared with the prior art, the invention has the following beneficial effects:
The method comprises the steps of determining leak rate of the micro-nano sensor at different moments, establishing a functional relation between the leak rate and time, establishing a prediction model based on the functional relation and the internal volume of a packaging cavity of the micro-nano sensor, determining a change relation between pressure in the packaging cavity and time according to the prediction model, and predicting packaging air tightness failure time based on the change relation and a failure threshold value of the pressure of the packaging cavity, so that the air tightness failure time of the micro-nano sensor is predicted.
Detailed Description
The following description of the embodiments of the present application will be made clearly and completely with reference to the accompanying drawings, in which it is apparent that the embodiments described are only some embodiments of the present application, but not all embodiments. All other embodiments, which can be made by those skilled in the art based on the embodiments of the application without making any inventive effort, are intended to be within the scope of the application.
The application provides a method for predicting the air tightness failure time of a micro-nano sensor package, as shown in fig. 1, which is a flow chart of the method for predicting the air tightness failure time of the micro-nano sensor package, and comprises the following steps:
s1, determining leak rates of the micro-nano sensor at different moments, and establishing a functional relation between the leak rates and time.
In the embodiment of the application, the leak rate of the micro-nano sensor at different moments can be obtained by a designated instrument, and the leak rates at different moments are shown in the following table 1:
TABLE 1
In the embodiment of the application, the functional relationship between the leak rate and time is specifically shown as the following formula:
Wherein L (t) is a function of the leak rate and time, L0 is an initial leak rate value, t0 is 1 hour, and t is time.
And S2, establishing a prediction model based on the functional relation and the internal volume of the packaging cavity of the micro-nano sensor, and determining the change relation between the pressure in the packaging cavity and time according to the prediction model.
In the embodiment of the application, the prediction model is specifically shown as the following formula:
wherein P (t) is the pressure in the packaging cavity at the moment t, L (t) is the functional relation between the leak rate and time, and V is the internal volume of the packaging cavity.
Specifically, for molecular flow, the relationship between conductance and leak rate is:
L=CPair;
wherein L is leak rate, C is conductance, and Pair is standard atmospheric pressure.
According to the gas flow equation, the difference in pressure in the packaging cavity is:
Wherein V is the internal volume of the packaging cavity, Q is the leakage amount of gas in unit time, C is the conductance, Pout is the external pressure of the packaging cavity, P is the internal pressure of the packaging cavity, dP (t) is the differential of the pressure, and dt is the differential of time
Because the pressure difference inside and outside the packaging cavity, outside air can enter the inside through the leak hole, and the inside pressure changes into:
Wherein P (t) is the pressure in the packaging cavity at the time t, C is the conductance, Pair is the standard atmospheric pressure, P0 is the initial pressure in the cavity, exp is an exponential function based on e, V is the internal volume of the packaging cavity, and L (t) is the function relation between the leak rate and time.
The internal pressure varies with time and the slope of the latter section gradually decreases in the front section, which is close to a straight line. For the micro-nano hermetic package reliability analysis, the failure occurs in the front section, so the model can be simplified, and the prediction model can be obtained by combining the above:
Wherein P (t) is the pressure in the packaging cavity at the moment t, L (t) is the functional relation between the leak rate and time, and V is the internal volume of the packaging cavity, so that the complexity of the simplified model is reduced under the condition of ensuring accuracy.
In the embodiment of the application, the change relation between the pressure in the packaging cavity and time is specifically shown as the following formula:
Wherein P (t) is the pressure in the packaging cavity at the moment t, L (t) is the functional relation between the leak rate and time, V is the internal volume of the packaging cavity, t0 is 1 hour, and t is time.
And verifying the model through experimental data of air pressure and time change in the micro-nano sensor packaging cavity. The data comes from MEMS devices which adopt a Surface Activated Bonding (SAB) method to bond Si/Si at room temperature, and as shown in a comparison of a prediction curve of a prediction model shown in FIG. 2 and experimental data, the prediction of the model on the pressure inside the packaging cavity is closer to the experimental data.
And S3, predicting the package air tightness failure time based on the change relation and the failure threshold value of the pressure in the package cavity.
In the embodiment of the present application, the step S3 specifically includes the following sub-steps:
s31, determining a failure threshold value of the pressure of the packaging cavity;
S32, determining the failure time based on the prediction model and the failure threshold value.
Specifically, according to a specific working condition, determining a failure threshold value of pressure in a micro-nano sensor packaging cavity, and under the condition that the initial leakage rate L0＝2×10-15Pa m3/s and the packaging cavity volume is 6.72mm3 and the failure threshold value is 500Pa, the failure time of the micro-nano sensor airtight packaging caused by leakage is about 35.5 years.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.