KR20030093010A - Method and system for improving a bipolar transistor model - Google Patents

Abstract

PURPOSE: A bipolar transistor simulation method and system is provided to offer a model for definitely describing an internal current of a bipolar transistor, and to speedily extract parameters of an offered current source model. CONSTITUTION: A voltage and a temperature of an internal contact portion are calculated on a basis of measured data and a physical feature of a wafer, and a pseudo algebraic equation is built on a basis of the calculated voltage and temperature(8, 9). The built equation is solved and a thermal resistance is calculated(10). The voltage and the temperature of the internal contact portion are divided into m sections on a basis of the calculated thermal resistance(11). The value of a section is increased one by one for selecting one among the m sections(12). It is checked whether the section to be calculated is the first section(13). In a case that the section to be calculated is the first section, a current source function satisfying a zero bias boundary condition is generated(15). In a case that the section to be calculated is not the first section, a polynomial for a current source is built(16). It is checked whether the section to be calculated is the last section(18). In a case that the section to be calculated is the last section, the function of the current source to be calculated in each section is interlinked(19).

Description

Method and system for improving a bipolar transistor model

Reducing the production cost of semiconductor integrated circuits and reducing the design time for manufacturing various devices with desired performance in a short time are directly related to the competitiveness of integrated circuit devices. In terms of reducing design time, a more general method for evaluating and testing a circuit design is to simulate the entire circuit in a computer using a mathematical model that can describe the characteristics of the various elements in the circuit. will be.

The most commonly used mathematical model for the internal current source of bipolar transistors is the standard gummel-punch model (hereinafter referred to as SGP). This current model basically uses relational equations based on the physical phenomena of P-type and N-type semiconductor junctions, and is a function of temperature: reverse saturation current (Iss), abnormal coefficient (n), junction voltage (Vj), and Boltzmann It is expressed as a function of the constant (k), the charge amount of the electron (q), the absolute temperature (T), and the reference temperature (To).

I = Iss (exp ((q Vj) / (n k T))-1) (1)

The reverse saturation current Iss in Equation (1) is a function of the constant Isso, the adjustment constant w and the energy bend difference Eg of the semiconductor and is expressed as follows.

Iss = Isso (Tj / To) ^w exp (-q Eg (1 / To-1 / Tj) / k)) (2)

The current sources Ibc, Iee, Icc, and Ibe on the SGP DC equivalent circuit shown in FIG. 1 use a current source model based on Equations (1) and (2) above.

The SGP current source model was developed in 1972 for silicon transistors. Now, heterojunction bipolar transistors (HBTs) using compound semiconductors have been developed and are widely used in high-speed devices. The current of these HBTs is more complicated by junction voltage and temperature. Several improved models have been developed to more accurately represent these characteristics. One such example is the model "VBIC95" published by McAndrew et al. In the 1996 IEEE Journal of Solid-State Circuits, Vol 31, page 1476. Another model, HC De Graaf and WJ Kloostrerman, published in 1985 IEEE Transaction on Electronic Devices, Vol 32, page 2415, called "The New Current-Charge Relation of Bipolar Transistors for CAD," also known as the Mextram model. .

These SGP, VBIC95, and Mextram current source models are limited in accurately indicating the voltage and temperature effects of the current source. Newly developed devices need more accurate calculations.

The present invention relates to a new voltage, temperature-current relationship, and a method and system for calculating a device using the same, which can display complex characteristics according to such voltage and temperature.

The problem with the SGP current source model or the VBIC current source model in computer simulation of the bipolar transistor's function is that these models do not fully describe the behavior of the new high-performance devices in terms of junction voltage and temperature.

The present invention relates to the problem of accurately simulating bipolar transistors with complex characteristics over junction voltage and temperature. An object of the present invention is to create a model that can describe the internal current of a bipolar transistor well, and another object of the present invention is to make a process for accurately and quickly extracting and calculating the parameters of the current source model proposed in the present invention.

1 shows a simplified direct current equivalent circuit and contact resistance in a standard gummel-punch model.

2 is a view for explaining the basic function used in the present invention

3 is a view for explaining a polynomial expressed as a function of junction voltage and junction temperature used in the present invention.

4 is a flow chart showing the characteristics of a transistor model, the method of simulating a circuit by extracting model parameters of the transistor as a general function;

The voltage difference between node Bj and node Ej in FIG. 1 is referred to as the base-emitter junction voltage difference Vbej and the voltage difference between node B and node E is referred to as base-emitter terminal voltage difference Vbet. The voltage difference between node Bj and node Cj in FIG. 1 is referred to as the base-collector junction voltage difference Vbcj, and the voltage difference between node B and node C is referred to as base-collector terminal voltage difference Vbct.

The state in which the base-collector voltage of the bipolar transistor is biased in the reverse direction and the base-emitter voltage is biased in the forward direction is called a normal active bias state, and the base-collector voltage is biased in the forward direction and the base-emitter The state in which the voltage is biased in the reverse direction is called a reverse active bias state.

In the normal activation bias, the Ibc component and the Iee component can be ignored, and the collector current Ict flowing through the collector resistor Rc and the base current Ibt flowing through the base resistor Rb can be approximated to Icc and Ibe, respectively. The measured natural logarithms of Icc and Ibe are shown on the vertical axis. Curve 1 in FIG. 2 is a collector current and curve 2 is a base current. The horizontal axis of FIG. 2 is the base-emitter junction voltage Vbej, which is represented by the following equation with respect to the terminal voltage Vbet.

Vbej = Vbet- (Ict + Ibt) Re-Ibt Rb (3)

In the SGP model, Ibe vs Vbej and Icc vs Vbej are expressed using Equation (1). However, the SGP model has a disadvantage in that it does not represent a device that exhibits complex characteristics according to voltage and temperature, such as HBT, and has a disadvantage of undergoing a complex parameter extraction process including an optimization process.

In the present invention, in order to more accurately display the current of the device exhibiting the characteristics as shown in FIG. 2, the internal current source models Icc and Ibe in the region of the junction voltage as shown in the region-a of FIG. 2 are used as the Taylor series of dVbej and dTj as follows. It is expressed as functions (Fcc, Fbe) that take as arguments.

Icc = Fcc (dVbej, dTj) (4)

Ibe = Fbe (dVbej, dTj) (5)

Where dVbej and dTj become

dVbej = Vbej-Vbejo (6)

dTj = Tj-Tjo (7)

Here, Vbejo is a reference voltage with respect to the Vbej voltage and may be an arbitrary value near the region to be displayed, and may be set to 0, for example. Tj is the junction temperature, Tjo is the ambient temperature when the device is measured, and is the reference temperature for Tj.

In a similar manner, in the reverse activation bias state, the Ibe component and the Icc component can be ignored, and only the Ibc component and the Iee component become dominant currents. In the present invention, Iee and Ibc are represented by the following method.

Iee = Fee (dVbcj, dTj) (8)

Ibc = Fbc (dVbcj, dTj) (9)

Where dVbcj becomes

dVbcj = Vbcj-Vbcjo (10)

Here, Vbcjo is a reference voltage with respect to the Vbcj voltage and may be an arbitrary value near the region to be displayed, and may be set to 0, for example.

In the present invention, Fcc, Fbe, Fee and Fbc are calculated as follows in the Taylor series of dVbej, dVbcj and dTj.

Fcc (dVbej, dTj) = exp (A00 + A10 dVbej + A01 dTj + A20 dVbej 2 + A11 dVbej dTj + A02 dTj 2 + A30 dVbej 3 + A21 dVbej 2 dTj + A12 dVbej dTj 2 + A03 dTj 3 + A40 dVbej 4 ...) (11)

Fbe (dVbej, dTj) = exp (B00 + B10 dVbej + B01 dTj + B20 dVbej 2 + B11 dVbej dTj + B02 dTj 2 + B30 dVbej 3 + B21 dVbej 2 dTj + B12 dVbej dTj 2 + B03 dTj 3 + B40 dVbej 4 ...) (12)

Fee (dVbcj, dTj) = exp (D00 + D10 dVbcj + D01 dTj + D20 dVbcj 2 + D11 dVbcj dTj + D02 dTj 2 + D30 dVbcj 3 + D21 dVbcj 2 dTj + D12 dVbcj dTj 2 + D03 dTj 3 + D40 dVbcj 4 ...) (13)

Fbc (dVbcj, dTj) = exp (C00 + C10 dVbcj + C01 dTj + C20 dVbcj 2 + C11 dVbcj dTj + C02 dTj 2 + C30 dVbcj 3 + C21 dVbcj 2 dTj + C12 dVbcj dTj 2 + C03 dTj 3 + C40 dVbcj 4 ...) (14)

Where A00, A10 ..., B00 ..., C00 ..., D00 ... are constants for calculating the current source.

The advantage of this invention is that the user can select the number of coefficients of the polynomial properly when the internal current source is used in equations (11) to (14) above, and the more terms in the polynomial, the more accurate and detailed the voltage-current characteristic is displayed. It is possible. The user can control the degree of accuracy they need with the number of terms in the polynomial above.

Another advantage of this invention is that if the internal current source is represented by Eqs. (11) to (14) above, it is easier to find the coefficient of the polynomial used in the current source model from the measured voltage-current characteristic data.

Taking the logarithms of equations (11) to (14) above, all of the right terms are shown as polynomials without exponential functions. Thus, given the data, the above equation becomes a linear algebraic equation.

Thus, the coefficients of a polynomial can be accurately calculated using linear algebraic equations. This eliminates the need for optimization or scaling required to determine the parameters of existing SGP models.

Another advantage of this invention is that the thermal resistance (Rth) of the device can be determined easily and accurately using only a few terms at the beginning of the equation above. Considering only the first three terms among the multiple terms of Equations (11) to (14) above,

Icc = Fcc = exp (A00 + A10 dVbej + A01 dTj) (15)

Ibe = Fbe = exp (B00 + B10 dVbej + B01 dTj) (16)

Iee = Fee = exp (D00 + D10 dVbcj + D01 dTj) (17)

Ibc = Fbc = exp (C00 + C10 dVbcj + C01 dTj) (18)

The present invention devised a method for obtaining coefficients of equations (15) to (18) to minimize the squared error of the measured data and the model.

Taking the logarithm of equation (15) and equation (16) above gives:

ln (Icc) = A00 + A10 dVbej + A01 dTj (19)

ln (Ibe) = B00 + B10 dVbej + B01 dTj (20)

The temperature difference dTj between the temperature of the junction and the external temperature both occurs due to the power consumption of the device. The power dissipation (Pd) that occurs in a device under a normally active bias state is calculated as follows.

Pd = Ibe Vbet + Icc (Vbet-Vbct) (21)

When the thermal resistance of the device is Rth, the internal temperature rise dTj due to internal power consumption is expressed as follows.

dTj = Rth Pd (22)

Substituting Eq. (21) into Eq. (22) and substituting Eq. (22) into Eq. (19) is as follows.

ln (Icc) = A00 + A10 dVbej + Az (Ibe Vbet + Icc (Vbet-Vbct)) (23)

In the above formula, Az is A01 Rth. Substituting the measured values Icc, Ibe, Vbet, Vbej, Vbct and Vbcj into Equation (23) above, the above equation becomes a linear algebraic equation with A00, A10 and Az as unknowns. Using at least three measured information can solve the above equation.

Using three or more pieces of data from the normal activation region, equation (23) becomes an over-determined linear algebraic equation. As a result, transplantation results in a solution that minimizes the second-order square error of the data measured through the pseudo-inverse process. This solution determines the values A00, A10 and Az.

Differentiating and arranging Eq. (19) above for dTj yields the following equation.

Acc = -A01 / A10 (24)

Where Acc is the ratio of the differential increase d (dVbej) of dVbej to the differential increase d (dTj) of dTj, and the physical meaning is that when increasing the junction temperature with the collector current fixed. It means the voltage change of junction. This value depends on the physical properties of the device and its size can be around a few mV / oC. If the user of the model knows the Acc value, A01 can be easily calculated using equation (24).

A01 = -Acc A10 (25)

Using A01 of Equation (25) calculated above, the thermal resistance Rth of the device can be calculated as follows.

Rth = Az / A01 (26)

In order to calculate the thermal resistance (Rth) by conventional methods, thermal measurement of the device was necessary. However, the newly designed method of Equation (26) can accurately calculate the thermal resistance value of the device without any thermal measurement if only the Acc value, which is the characteristic of the device, is known.

The above algebra can also be applied to the above equation (20) to produce the following algebraic equation.

ln (Ibe) = B00 + B10 dVbej + B01 Rth (Ibe Vbet + Icc (Vbet-Vbct)) (27)

In Rth of transplantation, Rth obtained from Equation (26) above is substituted. Similar to the method described above, using three or more data of the normal activation region, equation (27) becomes an over-determined linear algebraic equation with B00, B10, and B01 unknown. As a result, transplantation results in a solution that minimizes the second-order square error of the data measured through the pseudo-inverse process. Therefore, the values of B00, B10 and B01 are correctly determined.

Similarly, using the Rth values obtained above and the data measured in the reverse activation bias state, C00, C10, C01, D00, D10 and D01 values can be obtained.

Abe, Abc, and Aee can be calculated in the following way, similar to the equation (24) for Acc.

Abe = -B01 / B10 (28)

Abc = -C01 / C10 (29)

Aee = -D01 / D10 (30)

The coefficient Acc represents the change of the base emitter voltage according to the unit increase of junction temperature when the collector current is kept constant in the normal activation bias state, and Abe is the junction when the base current is kept constant in the normal active bias state. Base emitter voltage change with unit of temperature increase, Aee means base collector voltage change with unit increase of junction temperature when emitter current is kept constant in reverse active bias state, Abc Means the base-collector voltage change according to the unit increase of junction temperature when the base current is kept constant in the reverse active bias state. These coefficients (Acc, Abe, Aee, Abc) are constants that are independent of temperature, bias and device size and depend on the physical properties of the wafer.

Using these coefficients, the following values dZccj, dZbej, dZbcj and dZeej can be calculated.

dZccj = dVbej + Acc dTj (31)

dZbej = dVbej + Abe dTj (32)

dZbcj = dVbcj + Abc dTj (33)

dZeej = dVbcj + Aee dTj (34)

The new independent variable calculated above can be used to model the internal current source more accurately. As an example, FIG. 3 illustrates the relationship between the internal current source Icc and dZccj.

The accuracy can be further improved by dividing the Icc indicated by the new independent variable into several sections and applying Fcc differently in each section. In addition, the above new variables (31) to (34) represent a constant junction voltage drop rate according to the junction temperature rise regardless of the bias change, so that more stable calculation is possible and the characteristics of the actual device can be well reflected.

Iccs, which is an Icc value in the s-th region ＃s of Fig. 3, is calculated as follows.

Iccs = Fccs = exp (E0s + E1s dZccj + E2s dZccj ² ...) (35)

In the same way, Ibes, Iees, and Ibcs can be calculated.

Ibes = Fbes = exp (G0s + G1s dZbej + G2s dZbej ² ...) (36)

Iees = Fees = exp (J0s + J1s dZeej + J2s dZeej ² ...) (37)

Ibcs = Fbcs = exp (H0s + H1s dZbcj + H2s dZbcj ² ...) (38)

Where E0s, E1s ..., G0s ..., J0s ..., H0s ... are constants for the current source model. The above method can be applied to all areas except the first area (# 1).

The value in area 1 (# 1) includes when Vbej is zero, so the current should be zero when bias is zero. Therefore, Icc1 must be calculated as follows to satisfy the boundary condition of zero voltage bias state.

Icc1 = Fcc1 (Vbej-Vbejo, dTj)-Fcc1 (0-Vbejo, dTj) (39)

In the same way, Ibe1, Iee1, and Ibc1 can be calculated.

Ibe1 = Fbe1 (Vbej-Vbejo, dTj)-Fbe1 (0-Vbejo, dTj) (40)

Iee1 = Fee1 (Vbcj-Vbcjo, dTj)-Fee1 (0-Vbcjo, dTj) (41)

Ibc1 = Fbc1 (Vbcj-Vbcjo, dTj)-Fbc1 (0-Vbcjo, dTj) (42)

To obtain the coefficients of the function defined in each area, determine the maximum order (r) of the function in each area, substitute the measured data into the equations represented by (35) to (42), and limit the continuity of each interval. Conditionally, for each current source, over-determined linear algebraic equations with unknowns such as E0s, E1s ... Ers, G0s ... Grs, J0s ... Jrs, H0s ... Hrs You get Thus, the grafts have a pseudo-inverse process to obtain solutions that minimize the quadratic square error of the measured data for each unknown, and accurately determine the unknown coefficients of all 4 (r + 1) m terms. have.

Equations calculated through this process are accurately calculated with the desired accuracy of the electrical and thermal properties of the device, and these calculations can be performed systematically without any optimization or adjustment. In addition, this method can accurately calculate the thermal resistance of the device without thermal characterization.

The mathematical calculations are performed in devices used to simulate electronic components and circuits. The figure below shows the method used in the apparatus.

4 shows the process that needs to be calculated to generate a transistor model and simulate the circuit. Box 8 is the starting point for creating such a transistor model. Data from the internal junction voltage and junction temperature are calculated from the measured data and the physical properties of the wafer, and a pseudo-algebraic equation is established based on the data. Information about these equations is passed to Box 10 and solved to calculate the thermal resistance. When box 11 is reached, the junction voltage and temperature are divided into m intervals based on the calculated thermal resistance information and each region s = 0 is selected. When box 12 is reached, the number of s is increased by one to select one of several regions. Box 13 determines whether the area to be calculated is the first part, and if it is the first area, box 15 generates a current source function that satisfies the zero bias boundary condition. If not, create a polynomial for the current source that displays the measured data in that area. When box 18 is reached, it is determined whether it is the final point of the area to be calculated. If it is not the last point, return to the process of box 12 and select the next area and repeat the same process. If the area calculated in the process of box 18 is the final point, we work to connect the calculated current source functions in each area and complete the calculation.

As described above, the present invention provides an improved simulation system to better represent the measurement data of the bipolar transistor and to easily and accurately calculate parameters of a model such as a thermal resistance.

Claims (11)

A method of improving the simulation of a bipolar transistor using the new equation of the current source model, wherein the current source function in the new internal current source function is represented by an exponential function having a polynomial according to junction voltage and temperature as a factor. The method of claim 1; Calculating the difference between the junction voltage and the reference junction voltage as one of the new independent variables. The method of claim 1; Calculating the difference between the junction temperature and the reference temperature as one of the new temperature independent variables. The method of claim 1; Calculating the linear combination of junction voltage and temperature as one of the independent variables for the new current source function. The method of claim 1; Adjusting the number of polynomials of the current source functions according to the desired accuracy. The process of claim 1, 2, 3, or 4; Dividing the independent variables into several sections and calculating a plurality of different current source functions described above in these sections. The method of claim 4; Using the voltage drop constants of the junction according to the temperature in calculating the linear combination of junction voltage and temperature as a new independent variable. The method of claim 1; The method for obtaining a thermal resistance coefficient from the data measured at a single ambient temperature and the voltage drop rate according to the temperature of the transistor without the separate thermal characteristics test for the process of obtaining the coefficient of thermal resistance. A method of improving the simulation of a bipolar transistor using the new equation of the current source model, the method comprising: converting the current sources into a linear algebraic equation to calculate the coefficient of the new internal current source function and calculating the coefficients from the equation. The method of claim 9; A method of constructing an overdetermined linear algebraic equation using the plurality of measured data, and using the pseudo inverse transformation described above to find a constant therefrom. The method of claim 10; Adjusting the current source functions to satisfy a boundary condition where the junction current is always zero when the junction voltage is zero.