RU2796812C1 - Method for determining parameters of a two-link thermal equivalent circuit of a semiconductor product - Google Patents

Abstract

FIELD: semiconductors.

SUBSTANCE: method for measuring thermal characteristics of semiconductor products (SCP) in form of semiconductor devices (SCD) and integrated circuits (IC) and can be used to control the thermal parameters of SCP both at the stages of their development and production, and at the input control of SCP consumer enterprises. A method is claimed for determining parameters of a two-link thermal equivalent circuit of a semiconductor product, in which the semiconductor product is heated by a constant electric heating power of a given level P ₀. At given times t _i during the heating process, the temperature increments Δθ _ni (t _i ) of the active region of the semiconductor product are measured. In order to reduce time and reduce the error in determining the desired parameters of the temperature increment Δθ _ni (t _i ) measured at times t _1≈τ_Tp-k/2, t ₂ =2t ₁, t ₃₌3t ₁, t ₄≈τ_Tk-s and t ₅₌2t ₄, and the values of the parameters of the two-link thermal equivalent circuit are determined using formulas

τ _Tn-k = 2t ₁ / ln(1 / a) ; R _Tn-k = (2Δθ _n1 (t ₁ )- Δθ _n2 (t ₂ ))/P ₀(1-a)²; (1)

τ _Tk-c = t4 / ln (1 / b) ; R _Tk-c = (Δθ _n4 (t ₄ ) – P ₀R _Tn-k )/1 – b; (2)

where: a = exp(-t ₁/2τ _Tn-k ) = (3Δθ _n1 (t ₁ )- Δθ _n3 (t ₃ ))/(2Δθ _n1 (t ₁ )- Δθ _n2 (t ₂ )) – 2; b = exp(-t ₄/τ _Tk-c ) = (3Δθ _n5 (t ₅ )- P ₀R _Tn-k )/(Δθ _n4 (t ₄ )- P ₀R _Tn-k ) – 1; R _Tn-k , τ _Tn-k = R _Tn-k C _Tn-k , C _Tn-k are the junction-to-case thermal resistance, thermal time constant and heat capacity, and R _Tk-c , τ _Tk-c = R _Tk-c C _Tk-c , C _Tk-c - case-to-environment thermal resistance, thermal time constant and heat capacity of the semiconductor product, respectively.

EFFECT: reduction in time and error in determining the parameters of a two-link thermal equivalent circuit of semiconductor products.

1 cl, 2 dwg

Description

The invention relates to a technique for measuring the thermal characteristics of semiconductor products (SPS) in the form of semiconductor devices (SDS) and integrated circuits (ICs) and can be used to control the thermal parameters of SPS both at the stages of their development and production, and at the input control of consumer enterprises PPI.

.The key task of controlling the thermal properties of SPSs is to determine the parameters of their thermal equivalent circuit (see Fig. 1b), which can be used to calculate the temperature of the active region ( pn junction) of SPSs in any given (including dynamic) mode of operation. In the approximation of a one-dimensional thermal equivalent circuit of the SPS, the problem is reduced to determining a set of values of thermal resistances ( R _Ti ) and heat capacities ( C _Ti ) or thermal time constants ( τ _Ti = R _Ti · C _Ti ) of individual elements and layers of materials that make up the SPS structure (Fig. .1a). These parameters can be determined by the transient thermal characteristic (TTH) H ( t ) TRP, that is, by the change in temperature Δ θ _n ( t ) of the active region of the device during its self-heating by the dissipated electric power of a given level P _0, switched on at the time t = 0 :

.

и теплоемкость

переход-корпус, которые представляют собой тепловое сопротивление и теплоемкость слоев конструкции между активной областью (p-n переходом) и основанием корпуса; тепловое сопротивление

корпус-среда и теплоемкость

корпуса ППИ [см., например, Сергеев В.А., Ходаков А.М. Нелинейные тепловые модели полупроводниковых приборов. - Ульяновск : УлГТУ, 2012. - 159 с.].It should be noted that for most practical applications, including for quality control of the SPS assembly, it is sufficient to determine the parameters of the two-link thermal equivalent SPS circuit (see Fig. 2): thermal resistance

and heat capacity

junction-case, which represent the thermal resistance and heat capacity of the structural layers between the active region (pn transition) and the base of the body; thermal resistance

case-environment and heat capacity

PPI corps [see, for example, Sergeev V.A., Khodakov A.M. Nonlinear thermal models of semiconductor devices. - Ulyanovsk: UlGTU, 2012. - 159 p.].

A known method of measuring PTH PPI with pn -junctions along the cooling curve (see Davidov P. D. Analysis and calculation of thermal conditions of semiconductor devices. M .: Energiya. - 1967. - p. 33), consisting in the fact that the studied PPI is heated electric power of a known level to a steady thermal regime, then the heating power is turned off, and at given times the change in the temperature of the pn -junction is measured by the change in the temperature-sensitive parameter (TCP), which is most often used as a direct voltage drop across the pn -junction PPI with a small direct current. The desired thermal parameters in this method are determined, in fact, graphically by the angle of inclination of the HST, built on a semi-logarithmic scale, in areas of fast and slow growth.

The disadvantages of this method are the long measurement time, determined by the preliminary heating of the PPI to a steady thermal regime and subsequent cooling to ambient temperature, as well as the large measurement error due to the asymmetry of the cooling and heating curves of the PPI due to the difference in the shape of heat flows during cooling and heating of the PPI: heating of the SPP is carried out by heat sources on the surface of the crystal, and heat is removed from all heated surfaces of the SPS structure.

Electronic component manufacturers (International Rectifier, Infineon, Fairchild, STMicroelectronics, etc.) use the MIL-STD-750-3 [Test Methods For Semiconductor Devices. MIL-STD-750-3. Department of Defense.] based on PTH conversion. In this method, a controlled PPI is heated by a sequence of pulses of heating electric power of a given levelP ₀ with logarithmic-changing duration. After each pulse durationt _i by changing the FST, the increment of the transition temperature Δ is determinedθ _ni (t _i ) And calculate PTHH(t _i ) as ratio of junction temperature increment to heating powerP ₀ . The parameters of the thermal equivalent circuit of the PPI in this method are determined by the minima and maxima of the first derivative of the PTH, obtained by numerical differentiation.

There is a method for determining the parameters of the thermal equivalent circuit CMOS digital integrated circuits (CIS) according to PTH [Sergeev V.A., Tetenkin Ya.G. Assessment of the adequacy of the thermal model of CMOS digital integrated circuits by transient thermal characteristics. Izv. universities. Electronics. - 2017. -№4. - S. 350-360.]. In this method, the CIS is continuously warmed up by electrical power by connecting the logic elements of the CIS according to the ring oscillator (CG) scheme, at specified times t _i after turning on the CG, the power P ( t _i ) consumed by the CIS, and the temperature increment Δ θ _ni ( t _i ) the active region of the CIS by changing the frequency of the CG used as the ST. The measured values of Δ θ _ni ( t _i ) and P ( t _i ) calculate the values of PTH at given times t _i . The parameters of the thermal equivalent circuit are determined by the values of the PTH corresponding to the zeros of its second derivative obtained by numerical differentiation. To determine the thermal parameters with sufficient accuracy, it is necessary to have at least 8-10 HTC values in each decade of the time scale, while the time values t _i are set with a logarithmic step.

The disadvantage of all the methods described above is the long measurement time, determined by a large number of temperature readings in the process of heating the controlled PPI, as well as a large error in determining the thermal parameters due to the error in numerical differentiation.

The technical problem is to reduce the time and reduce the error in determining the parameters of a two-link thermal equivalent circuit of semiconductor products.

измеряют в моменты времени t _1≈ τ _Тп-к/2, t ₂=2t ₁, t ₃₌3t ₁, t ₄≈τ _Тк-с и t ₅₌2t ₄, а значения теплового сопротивления переход-корпус полупроводникового изделия, тепловой постоянной времени переход-корпус полупроводникового изделия, теплового сопротивления корпус-среда полупроводникового изделия и тепловой постоянной времени корпус-среда полупроводникового изделия находят по формулам:The technical result is achieved by the fact that in the method for determining the thermal resistance of the junction-case of a semiconductor product, the thermal time constant of the junction-case of a semiconductor product, the thermal resistance of the body-environment of the semiconductor product and the thermal time constant of the body-environment of the semiconductor product, in which the semiconductor product is heated by a constant electrical heating power of a given levelP ₀, at given timest _i during the heating process, temperature increments Δθ _ni (t _i ) of the active region of the semiconductor product, and the temperature increments

measured at timest _1≈ τ _Tp-k/2,t ₂=2t ₁,t ₃₌3t ₁,t ₄≈τ _Tk-s Andt ₅₌2t ₄, and the values of the thermal resistance of the junction-case of the semiconductor product, the thermal time constant of the junction-case of the semiconductor product, the thermal resistance of the body-environment of the semiconductor product, and the thermal time constant of the body-environment of the semiconductor product are found by the formulas:

,

- тепловое сопротивление и тепловая постоянная времени переход-корпус полупроводникового изделия, а

- тепловое сопротивление и тепловая постоянная времени корпус-среда полупроводникового изделия. Where

,

- thermal resistance and thermal time constant of the junction-case of a semiconductor product, and

- thermal resistance and thermal time constant of the body-environment of the semiconductor product.

активной области (перехода) ППИ после подачи на него в момент времени t=0 импульса греющей мощности будет описываться следующим выражением: The essence of the invention is as follows. In the approximation of a two-link thermal equivalent circuit PPI, the change in temperature

the active region (transition) of the SPS after applying a heating power pulse to it at the time t = 0 will be described by the following expression:

- тепловая постоянная времени переход-корпус ППИ,

- температура перехода ППИ, θ ₀ - температура окружающей среды,

- тепловая постоянная времени корпус-среда ППИ. Where

- thermal time constant of the transition-body PPI,

- PPI transition temperature, θ ₀ - ambient temperature,

- thermal time constant of the case-environment PPI.

For given times t _1≈ τ _p-to /2, t ₂ \u003d 2 t ₁ , t ₃₌ 3 t ₁ , t ₄ ≈ τ _k-s , t ₅₌ 2 t ₄ taking into account the fact that for most designs modern PPI the condition τ _p-k << τ _k-s is fulfilled, we can write

и

.In expressions (4)-(8), to simplify cumbersome formulas, the notation

And

.

Multiplying both parts of expression (4) by 2 and 3, and subtracting expressions (5) and (6) from the obtained expressions, respectively, we obtain two equations for finding the values of the parameter a and thermal resistance

After dividing (10) by (9), it is not difficult to obtain an expression for a :

from where the value is easily calculated

легко находится, например, из (9):while the value

is easily found, for example, from (9):

If the first term on the right side of expressions (7) and (8) is transferred to the left side, and the transformed expression (8) is divided by the transformed expression (7), then we obtain the following expression for the parameter b :

The specified value of τ _k-s is determined by the formula

соответственно, можно легко выразить из (5) and the value

respectively, can be easily expressed from (5)

The technical result - reduction of the measurement time - is achieved due to the fact that in the proposed method it is necessary to carry out only 5 measurements of the PPI temperature increment during the heating process, while it is not required to achieve a stationary thermal regime of the PPI. And the decrease in the error in determining the parameters is achieved by the fact that the values of the desired thermal parameters are found from the measurement results from simple arithmetic formulas.

Note that the proposed method does not require the exact equalities t _1≈ τ _Tp-k /2 and t ₄ ≈ τ _Tk-s , an approximate equality is sufficient. At the same time, the values of thermal time constants for a particular type of PPI can be approximately estimated from preliminary measurements or from passport data of the PPI provided by the manufacturer. Of course, the method is not applicable to PPI, for which the condition τ _p-c << τ _c-c is not met.

Claims (4)

A method for determining the thermal resistance of the junction-case of a semiconductor product, the thermal time constant of the junction-case of a semiconductor product, the thermal resistance of the body-environment of a semiconductor product, and the thermal time constant of the body-environment of a semiconductor product, in which the semiconductor product is heated by a constant electric heating power of a given level P ₀ , at given times t _i during the heating process, the temperature increments Δ θ _ni ( t _i ) of the active region of the semiconductor product are measured, and the temperature increments

measured at times t _1≈ τ _Tp-k /2, t ₂ =2 t ₁ , t ₃₌ 3 t ₁ , t ₄ ≈τ _Tk-s and t ₅₌ 2 t ₄ , and the values of thermal resistance of the junction-housing semiconductor product, the thermal time constant of the transition-case of the semiconductor product, the thermal resistance of the body-environment of the semiconductor product and the thermal time constant of the body-environment of the semiconductor product are found by the formulas:

Where

- thermal resistance and thermal time constant of the junction-case of a semiconductor product, and

- thermal resistance and thermal time constant of the body-environment of the semiconductor product.

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