Method for testing and extracting thermal resistance and thermal capacity characteristics of MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor) by adopting alternating current small signal

Abstract

The invention discloses a method for extracting thermal resistance and thermal capacity characteristics of an MOSFET (Metal-Oxide-Semiconductor Field Effect Transistor) by adopting an alternating-current small signal test, which is a method for extracting thermal resistance and thermal capacity of a device based on the alternating-current small signal test without calibrating characteristic frequency. According to the invention, the thermal resistance and thermal capacity characteristics of the MOSFET are obtained according to the DC output characteristics of the device and the AC small signal Y parameter. Basic data used in the thermal impedance extraction process are drain current-drain voltage data at different environment temperatures and alternating current small signal conductance and capacitance data at different frequencies, and the test data are conventional test data in the transistor modeling process. Therefore, additional testing equipment such as an infrared thermal imaging instrument is not needed, and the thermal characteristic frequency does not need to be obtained. The thermal resistance and thermal capacitance characteristic parameters extracted by the method can be accurately used for thermal characteristic modeling of semiconductor devices, and then the self-heating effect and transistor junction temperature changes under different power levels are evaluated, so that the influence of the self-heating effect is stripped from the devices.

Description

Technical Field

[0001] The present invention belongs to the field of thermal reliability research of semiconductor devices, and particularly relates to a method for testing and extracting the thermal resistance and heat capacity characteristics of MOSFETs by using AC small-signal testing. Background Art

[0002] With the advancement of the process node, the self-heating effect (SHE) of MOSFET devices has been significantly enhanced, triggering electro-thermal coupling failure mechanisms such as carrier mobility thermal degradation and threshold voltage drift, which severely restricts the circuit performance and reliability. Therefore, establishing a cross-scale electro-thermal coupling model and realizing multi-physical field collaborative design have become the core path to break through the bottleneck of nano-scale integration technology, and this process highly depends on the support of a high-precision model parameter library that can accurately characterize the electro-thermal behavior of devices. Therefore, it is crucial to find an accurate characterization method, extract the SHE parameters and subtract their influence from the MOSFET characteristics to achieve accurate circuit modeling. Currently, several methods for extracting thermal parameters mainly include infrared imaging method, pulsed IV method, gate resistance method, correction method for DC measurement, and low-frequency conductance method, etc. Among them, the infrared imaging method requires complete contact between the device and the device under test; the pulsed IV method requires ultra-short pulses for scaling nodes, has high requirements for test conditions, and is easily affected by noise; the gate resistance method requires changing the device structure, thus unable to characterize the intrinsic thermal characteristics of the device; although the correction method for DC measurement has no problem in modifying the structure, it is only applicable to the case where the output conductance is negative when the device operates in the saturation region.

[0003] In the field of semiconductor device thermal parameter extraction technology, the low-frequency conductance method and the capacitance method have become widely used methods in the industry because they can extract thermal parameters only using electrical parameters and the operation is relatively simple. However, due to the above two methods being easily affected by other effects, it is not easy to distinguish the output conductance break point, and the selection method of the characteristic frequency is not unified, resulting in differences in the thermal resistance and heat capacity values extracted by the two methods. Therefore, a detailed analysis and optimization of this method based on AC small-signal analysis not only provide a theoretical support for the accurate thermal characterization of devices, but also lay a powerful technical means for the electro-thermal co-design of nano-scale integrated circuits. Summary of the Invention

[0004] The object of the present invention is to overcome the deficiencies of the prior art and propose a method for extracting the thermal resistance and heat capacity of semiconductor devices by using AC small-signal testing. This method is specifically optimized based on the conductance method and the capacitance method, and the thermal resistance R th and the heat capacity C th, since there is no need to extract the characteristic frequency, the final SPICE transient simulation fitting result shows that the device temperature error is less than 1%, solving the error problem caused by the inconsistent method of extracting the characteristic frequency. Moreover, this invention is applicable to the thermal characteristic parameter test and extraction of any kind of semiconductor process device. As long as the ambient temperature and electrical data are given, the thermal resistance and heat capacity of the device can be calculated.

[0005] The specific technical solution for achieving the purpose of the present invention is as follows:

[0006] A method for extracting the thermal resistance and heat capacity of a MOSFET by using an AC small signal test, the method comprising the following steps:

[0007] Step 1: Measure the transfer characteristic curves of the device at different ambient temperatures, that is, the drain current I d varying with the gate voltage V g , and extract the zero temperature coefficient point, that is, the gate voltage V g,ZTC corresponding to the ZTC point;

[0008] Step 2: When the gate voltage is greater than V g,ZTC , measure the drain current I d of the device at different ambient temperatures T0, and obtain the variation characteristic of I d with T0;

[0009] Step 3: Under the same DC bias as in Step 2, perform an AC small signal test to obtain the curve of the output conductance G ds varying with frequency, and extract the output conductance at low frequency and high frequency;

[0010] Step 4: Under the same DC bias as in Step 2, perform an AC small signal test to obtain the curve of the drain capacitance C dd varying with frequency, and extract the drain capacitance at low frequency and high frequency;

[0011] Step 5: According to the results of Steps 1 - 4, extract the thermal resistance R th and heat capacity C th of the device; where:

[0012] When the device is working, V g > V g,ZTC, and is in the saturation state;

[0013] When the AC small signal is in the low frequency state, that is, when the frequency is lower than 10 kHz, the output conductance and capacitance remain unchanged. At this time, the device self-heating includes the influence of DC self-heating and AC self-heating; in the range of 10 kHz to 10 MHz, the AC self-heating is gradually stripped; when the device is in the high frequency state, that is, when the frequency is higher than 10 MHz, the AC self-heating is stripped, the temperature cannot follow the AC signal, and remains constant at the value determined by the static power consumption;

[0014] I described in step 2 d The variation characteristic with T0 is represented by a first-order function:

[0015] I d = -aT0 + b (1)

[0016] Where a and b are fitting constants;

[0017] The said step 3 specifically includes:

[0018] Step 3.1: Establish an AC small-signal equivalent circuit model of the device;

[0019] Step 3.2: Under the same DC bias as in step 2, obtain the intrinsic admittance parameter Y-parameter matrix Y = [Y11, Y22; Y21, Y22] of the device, and strip the external parasitic parameter network;

[0020] Step 3.3: According to the relationship between the intrinsic parameters and the matrix in the equivalent circuit model described in the following formulas (2) and (3), calculate the output conductance G ds and the drain capacitance C dd values:

[0021] G ds = Re(Y22) (2)

[0022]

[0023] Where ω represents the angular frequency, Re(Y22) represents the real part of the parameter Y22, and Im(Y22) represents the imaginary part of Y22;

[0024] The said step 5 specifically includes:

[0025] Step 5.1: Obtain the difference between the high and low frequency G ds and C dd caused by the stripping of the transient self-heating effect:

[0026] ΔG SHE = G ds_max - G ds_min (4)

[0027] ΔC SHE = C dd_max - C dd_min (5)

[0028] Where G ds_min and G ds_max are the low-frequency output conductance and the high-frequency output conductance obtained in step 3 respectively; C dd_max and C dd_min are the low-frequency drain capacitance and the high-frequency drain capacitance obtained in step 4 respectively;

[0029] Step 5.2: According to the device heat transfer theory and the definition of small-signal voltage and current at the device ports, we get:

[0030]

[0031]

[0032] In the formula, ω represents the angular frequency; It is replaced by the value of the constant -a in formula (1), that is This value is represented by d the slope of the I

[0033] Step 5.3: Let ω = 0 in the formula to obtain the expressions for the thermal resistance R th and the heat capacity C th of the device:

[0034]

[0035]

[0036] Step 5.4: After obtaining the thermal resistance R th and the heat capacity C th of the device, the thermal time constant τ is obtained through the following formula (10):

[0037] τ = R th *C th (10) Advantages of the present invention:

[0038] 1) The present invention only needs to obtain I d , G ds and C dd and other electrical parameters to simultaneously extract the thermal resistance and heat capacity of the device, eliminating the step of determining the characteristic frequency f th . The measurement steps are simpler and the results are more accurate.

[0039] 2) The present invention is not limited by the process and can be used for extracting the thermal parameters of the self-heating effect of MOS transistors with different processes. As long as the test data are provided, the values of R th and C th can be fitted. Description of the Drawings

[0040] Figure 1 is the equivalent thermal resistance and heat capacity network diagram of the device in the present invention;

[0041] Figure 2 is the flow chart of the present invention;

[0042] Figure 3 is the drain current I of the present inventiond Schematic diagram of variation with ambient temperature;

[0043] Figure 4 Schematic diagram of the variation of output conductance with frequency during the AC small-signal test of the present invention;

[0044] Figure 5 Schematic diagram of the variation of drain capacitance with frequency during the AC small-signal test of the present invention;

[0045] Figure 6 Schematic diagram of temperature variation during transient test by fitting the extracted thermal resistance and heat capacity according to the present invention. Detailed implementation manners

[0046] The present invention will be described in detail below with reference to the accompanying drawings and embodiments. The specific scheme of this embodiment is applicable to the rapid measurement of the thermal resistance and heat capacity of GAAFET and other types of transistors.

[0047] Embodiment

[0048] In this embodiment, a nanosheet-all-around gate field-effect transistor with a channel length of 12 nm, a channel width of 40 nm, and 3 nanosheets is taken as an example to establish its small-signal equivalent circuit model, and the output conductance and drain capacitance at low frequency and high frequency are extracted respectively. As Figure 1 shown, T1 represents the device temperature, the model is a first-order R th C th network, I ds_dc V ds_dc represents the DC bias, and ΔI ds V ds represents the AC small signal applied to the device. As Figure 2 shown, the working extraction process of this embodiment specifically includes the following steps:

[0049] Step 1: Conduct a DC output test on the device to measure the transfer characteristic curve I d V g at different ambient temperatures, and obtain the position of the zero temperature coefficient point V gs,ZTC = 0.58 V;

[0050] Step 2: Under the bias of gate voltage V g = 0.7 V and drain voltage V d = 0.7 V, obtain the output characteristic curve I d V d of the device at different ambient temperatures, and obtain the drain current I d at different temperatures. Refer to Figure 3 , and use the slope to represent with a value of 0.06157 μA / K;

[0051] Step 3: At the same DC bias point as in Step 2, perform AC small-signal tests on the device through TCAD, capture the variation of Y-parameters with frequency in real time, and extract the real part therefrom, i.e., the variation of the output conductance, refer to Figure 4 , and obtain the parameters G ds_min and G ds_max therefrom, and calculate the conductance difference ΔG SHE to be 2.78 μS;

[0052] Step 4: Similar to Step 3, extract the imaginary part from the Y-parameters, i.e., the variation of the drain capacitance, refer to Figure 5 , and obtain the parameters C dd_min and C dd_max therefrom, and calculate the conductance difference ΔC SHE to be 0.891 pF;

[0053] Step 5: According to the parameters obtained in Steps 1-4, and in combination with Formulas (8) and (9), calculate the values of the thermal resistance and heat capacity of the device, and finally the extracted R th is 0.2662 K / μW, and C th is 1.094 pJ / K, and the thermal time constant τ obtained by multiplying the two is 291 ns.

[0054] Step 6: Import the extracted values of the thermal resistance and heat capacity into the SPICE software for fitting transient simulation, and compare and analyze with the actual test results. The fitting of the device temperature change is good, and the error rate is within 1%, refer to Figure 6 .

Claims

1. A method for extracting the thermal resistance and heat capacity of a MOSFET by using AC small-signal testing, characterized in that, The method includes the following steps: Step 1: Measure the transfer characteristic curves of the device at different ambient temperatures, that is, the drain current I d as a function of the gate voltage V g , and extract the zero temperature coefficient point, that is, the gate voltage V g,ZTC corresponding to the ZTC point; Step 2: When the gate voltage is greater than V g,ZTC , measure the drain current I of the device at different ambient temperatures T0 d , and obtain the variation characteristics of I d with respect to T0; Step 3: Under the same DC bias as in Step 2, perform an AC small-signal test to obtain the output conductance G ds and extract the output conductance at low and high frequencies from the curve of the output conductance varying with frequency; Step 4: Under the same DC bias as in Step 2, perform an AC small-signal test to obtain the curve of the drain capacitance C dd varying with frequency, and extract the drain capacitance at low and high frequencies; Step 5: Extract the thermal resistance R th and heat capacity C th ; where: When the device is operating, V g > V g,ZTC, and it is in the saturation state; When the AC small signal is in the low-frequency state, that is, when the frequency is lower than 10 kHz, the output conductance and capacitance remain unchanged. At this time, the device self-heating includes the effects of DC self-heating and AC self-heating; in the range of 10 kHz to 10 MHz, the AC self-heating is gradually stripped; when the device is in the high-frequency state, that is, when the frequency is higher than 10 MHz, the AC self-heating is stripped, the temperature cannot follow the AC signal, but remains constant at the value determined by the static power consumption; I described in Step 2 d The variation characteristic with respect to T0 is represented by a first-order function: I d = -aT0 + b (1) where a and b are fitting constants; Step 3 specifically includes: Step 3.1: Establish an AC small-signal equivalent circuit model of the device; Step 3.2: Under the same DC bias as in Step 2, obtain the intrinsic admittance parameter Y-parameter matrix Y = [Y11, Y22; Y21, Y22] of the device, and strip the external parasitic parameter network; Step 3.3: Calculate the values of the output conductance \(G\) at high frequency and low frequency respectively, according to the relationship between the intrinsic parameters and matrices in the equivalent circuit model described by the following formulas (2) and (3). ds and the drain capacitance \(C\) dd as follows: G ds = Re(Y22) (2) where ω represents the angular frequency, Re(Y22) represents the real part of the parameter Y22, and Im(Y22) represents the imaginary part of Y22; Step 5 specifically includes: Step 5.1: Obtain the difference between the high and low frequency G ds and C dd resulting from the peeling due to the transient self-heating effect: ΔG SHE = G ds_max - G ds_min (4) ΔC SHE = C dd_max - C dd_min (5) Wherein, G ds_min and G ds_max are respectively the low-frequency output conductance and the high-frequency output conductance obtained in step 3; C dd_max and C dd_min are respectively the low-frequency drain capacitance and the high-frequency drain capacitance obtained in step 4; Step 5.2: According to the device heat transfer theory and the definition of small-signal voltage and current at the device ports, obtain: In the formula, ω represents the angular frequency; is replaced by the value of the constant -a in formula (1), that is This value is represented by d the slope of the I and T0 curves; Step 5.3: Let ω = 0 in the formula to obtain the thermal resistance R th and heat capacity C th of the device: Step 5.4: After obtaining the thermal resistance R th and heat capacity C th , the thermal time constant τ is obtained by the following formula (10): τ = R th *C th (10).

Images