JP5147105B2 - IGBT simulation apparatus and IGBT simulation program - Google Patents

Description

  The present invention relates to a simulation of the operation of an insulated gate bipolar transistor (IGBT), which is a three-terminal semiconductor element configured by combining a field effect transistor and a bipolar transistor.

  Conventionally, an insulated gate bipolar transistor (IGBT) is known as one of semiconductor elements. This IGBT is a three-terminal semiconductor element, and is used for switching of high power (for example, 500 V / 200 A for automobiles).

  In a circuit using such an IGBT, it is necessary to confirm the operation under various conditions. For this purpose, a simulation using a circuit simulator is performed.

  In the circuit simulator, the operation of the IGBT is reproduced using an IGBT element model. As this element model, a behavior model and a physical model (Hefner Model) (see Non-Patent Document 1) are known.

Kuang Sheng, Barry W. Williams, and Stephen J. Finney "A Review of IGBT Models" IEEE TRANSACTIONS ON POWER ELECTRONICS, VOL. 15, NO. 6, NOVEMBER 2000

  Here, when the time change of the carrier distribution inside the element during the turn-off period of the specific IGBT is examined by the circuit simulation using the Hefner Model, the time change of the carrier distribution is a device simulation in which the IGBT is modeled. It turned out to be quite different from the result of.

  This is considered to be because when the time-dependent diffusion equation for the excess carriers in the transient state is approximately solved, the excess carriers are expressed as a function of a finite term (third order) with respect to the position. Therefore, a method of developing the excess carrier distribution in an infinite series is conceivable, but it is not practical to perform a circuit simulation because the calculation time is enormous.

The present invention includes a field effect transistor having a source region, a channel region, and a drain region, the drain current of which is controlled by an input signal to the gate electrode, an emitter region, a base region, and a collector region, It includes a bipolar transistor in which a drain current is input to a base region and a collector current is controlled, a cathode is connected to the source region and the collector region, an anode is connected to the emitter region, and an anode-cathode is connected by the input signal current is controlled, the IGBT simulation apparatus which simulates the operation of the insulation federated gate bipolar transistor is a semiconductor device of three-terminal (IGBT), a hole current I _E to be discharged to the cathode of the IGBT, flows from the anode Between the Lumpur current I _C, the three current of the drain current I _Drain, flowing through the channel region connected to the gate electrode through the gate oxide film from the cathode toward the base region, and said emitter region and said base region in is regarded as being determined by the potential difference _{V EB} with expressed by a function of _{V EB,} while changing the potential difference _{V EB,} the Kirchhoff's law of _{I E = I C + I Drain} , calculated iteratively, calculated results seeking a potential difference V _EB where error is less than a predetermined value, by using a potential difference V _EB obtained, and obtains the respective currents in quasi-static state in which no time-dependent.

In addition, the transient current flowing in the element during the switching of the IGBT is divided into a stored charge Q _DC (t) in a steady state and a transient stored charge q (t) assuming a time delay τ and a quasi-static state. Is calculated as a time change dq (t) / dt of the charge amount q (t) accumulated in the element determined using f (τ, Q _DC (t), q (t)), which is a function of The obtained transient current is preferably added to the current in the quasi-static state to obtain each current, and the time delay τ is preferably expressed using the potential difference V _EB .

The time delay τ is preferably expressed by τ = W ² / D. Here, W is the width of the neutral base region of the IGBT, and D is the excess carrier diffusion coefficient in the neutral base region.

Further, the present invention includes a field effect transistor having a source region, a channel region, and a drain region, the drain current of which is controlled by an input signal to the gate electrode, and an emitter region, a base region, and a collector region. The field effect transistor includes a bipolar transistor in which a drain current is input to a base region and a collector current is controlled, a cathode is connected to the source region and the collector region, an anode is connected to the emitter region, and the input signal In the IGBT simulation program for simulating the operation of an insulated gate bipolar transistor (IGBT), which is a three-terminal semiconductor element, the current between the anode and cathode is controlled by the hole current discharged to the cathode of the IGBT And I _E, the hole current I _C flowing from the anode, the three current of the drain current I _Drain, flowing through the channel region connected to the gate electrode through the gate oxide film from the cathode toward the base region, said emitter region together represent a function of _{V EB} is regarded as being determined by the potential difference _{V EB} between the said base region, while changing the potential difference _{V EB,} the Kirchhoff's law of _{I E = I C + I Drain} , iteratively A potential difference V _{EB in} which an error in the calculation result is equal to or less than a predetermined value is calculated, and each current in a quasi-static state that does not depend on time is calculated using the obtained potential difference V _EB .

  In the present invention, the hole current flowing from the anode of the element, the hole current discharged to the cathode, and the drain current flowing into the base region (= base current) are expressed using the emitter-base voltage VEB, and Kirchhoff's law is applied to these currents. Thus, each current in a state independent of time is obtained. Accordingly, a steady solution (quasi-static solution) of these currents can be obtained as an analytically exact solution by simulation using the IGBT operation as one element model.

  In addition, the temporal change in the transient accumulated charge is obtained based on the time change dq (t) / dt of the charge amount accumulated in the element, and this is added to the quasi-static current for simulation. Therefore, calculation such as expansion in an infinite series is unnecessary, high-precision calculation can be performed without sacrificing calculation speed, and device structure can be optimized.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings.

  FIG. 1 shows an equivalent circuit diagram of the IGBT. The anode terminal is connected to the emitter of a bipolar PNP transistor BJT, and the collector of this transistor BJT is connected to the cathode terminal. The base of the transistor BJT is connected to the drain of an N-channel MOS transistor MOSFET, and the source of the transistor MOSFET is connected to the cathode. A gate terminal is connected to the gate of the transistor MOSFET. In an IGBT as a three-terminal element, a region to which an anode is connected is called a collector, and a region to which a cathode is connected is called an emitter. In this specification, the collector and emitter are basically transistors BJT (PNP). This means the collector and emitter.

The voltage application to the gate terminal controls the supply of the drain current I _Drain of the transistor MOSFET to the base of the transistor BJT, thereby controlling the collector current I _C and the emitter current I _{E of the} transistor BJT. That is, holes are injected from the emitter side of the transistor BJT and flow toward the collector side. In the collector portion of the transistor BJT, a MOS current (electron current) is injected and the collector current is discharged.

  FIG. 2 schematically shows the configuration of one IGBT. In this figure, the whole is shown as a rectangle. A cathode 10 is provided at the upper end. Under the cathode 10, two layers of a P + region 12 on the left side and an N + region 14 on the right side thereof are laminated. A P− (body) region 16 is disposed below the two regions of the P + region 12 and the N + region 14. Further, an N− (Base) region 18 is disposed below the P− region, and a P + (Collector) region 20 is disposed below the N− (Base) region 18. An anode 22 is provided under the P + region 20.

  A gate electrode 26 is provided on the right side of the N + region 14 and the P− region 16 and on the upper right corner of the N− region 18 via a gate insulating film 24.

  In such an IGBT, a predetermined voltage is applied between the cathode 10 and the anode 22. For example, the cathode 10 is connected to the ground, and the anode 22 is set to + 500V. Then, a predetermined positive voltage, for example, 15 V is applied to the gate electrode 26.

By applying a positive voltage to the gate electrode 26, a depletion layer is generated in the upper layer portion (right side) of the P− region 16 below (left side) of the gate electrode 26, and from the N + region 14 toward the N− region 18. A drain current (electron) I _Drain flows. This drain current I _Drain flows into the base region in the BJT portion and can be considered as a base current (I _Drain = I _Base ). In response to the drain current I _Drain , a hole current I _C flows from the anode 22 to the P + region 12, and an electron current I _E flows from the cathode 10 to the P + region 20. The electron current I _E disappears in the N− region 18 due to recombination.

"Quasi-static state"
First, in the quasi-static state, each terminal voltage is given, and I _E , I _C , and I _Drain corresponding thereto are derived. This derivation uses the fact that I _E -I _C = I _Drain holds from Kirchhoff's current law.

Here, in the present embodiment, the emitter current I _E and the collector current I _C are expressed as a function of V _EB that is the element internal potential. Further, by using an approximation that assumes exp [qV _CB / kT] ≈0, the emitter current I _E and the collector current I _C are expressed as a function of the element internal potential V _EB (eq.1, eq.2). .

Here, each variable in the above equation is as follows, and is determined by setting conditions such as an element structure (a manufacturing factor for determining a carrier diffusion length such as diffusion concentration, element size, crystallinity).
A: active region area of element q: elementary charge (1.6 × 10 −19 C)
D _B: BJT portion (PNP) base region (IGBT N-Drift region) the minority carrier diffusion coefficient D _C: BJT portion (PNP) a collector region (IGBT P-Body regions) the minority carrier diffusion coefficient D _E: BJT portion (PNP) Emitter region (IGBT collector region) minority carrier diffusion coefficient L _B : BJT portion (PNP) base region (IGBT N-Dift region) minority carrier diffusion length L _C : BJT portion (PNP) collector region (IGBT P-Body region) minority Carrier diffusion length L _E : BJT part (PNP) emitter region (IGBT collector region) Minority carrier diffusion length k: Boltzmann constant (1.38 × 10 −23 J / K = 8.62 × 10 −5 eV / K)
P _B : base region impurity concentration n _C : BJT portion (PNP) collector region (IGBT P-Body region) impurity concentration n _E : BJT portion (PNP) emitter region (IGBT collector region) impurity concentration where W is a neutral base width, an emitter - is represented by the following relational expression obtained by subtracting the depletion layer width W _depletion from the base junction width W _B.

here,
W: Neutral base width W _B : IGBT BJT (PNP) transistor base width (emitter-collector junction width)
W _depletion : depletion layer width q: elementary charge (1.6 × 10 −19 C)
ε _Si : dielectric constant of silicon (11.9)
ε ₀ : dielectric constant of vacuum (8.854 × 10 −12 F / m)
N _A : P-Body impurity concentration N _D : IGBT BJT part (PNP) transistor part base impurity concentration P _{base-injection} : BJT part (PNP) transistor part base region concentration of IGBT n: IGBT Electron concentration n _i injected into BJT (PNP) transistor base region: intrinsic semiconductor carrier concentration V _bi : IGBT PNP transistor base-collector diffusion potential V _anode : anode voltage (IGBT collector voltage)
V _EB : IGBT's BJT (PNP) transistor part emitter-base potential difference.

The MOS current injected into the base region of the BJT (PNP) transistor portion of the IGBT is expressed as follows.

Here, V _Drain is expressed by the following equation.

here,
Z: gate width L: gate length μ: mobility C _ox : gate insulating film capacitance V _g : gate voltage V _th : threshold voltage δ: coefficient based on drift-diffusion approximation x _p : IGBT p-body (MOS substrate ) Indicates the side depletion layer width.

Thus, the collector current I _C , the emitter current I _E , and the drain current I _Drain in the IGBT are expressed using the base-emitter voltage V _EB of the BJT. Kirchhoff's law is applied to these currents. Therefore, iterative calculation (iterative calculation) is performed so that I _E = I _C + I _Drain is satisfied, V _EB is obtained, and the value of each current can be obtained based on the obtained VEB.

"Transient state"
It is assumed that the transient current I (t) is represented by the sum of the conduction current IDC that constantly flows between the main electrodes (between the collector and the emitter) and the time variation dq (t) / dt of the internal charge of the device.

I (t) = IDC + dq (t) / dt
Here, q (t) represents the accumulated charge in the device and the induced charge.

Further, it is assumed that the time change dq (t) / dt of the transient charge q (t) follows with the time delay τ, and the time change dq (t) / dt is quasi-static with the time delay τ. As a function of the steady state charge Q _DC and the transient charge q (t).

dq (t) / dt = f (τ, Q _DC (t), q (t))
Then, this dq (t) / dt = f (τ, Q _DC (t), q (t)) is calculated by a recurrence formula obtained by differentiating.

  For example, the time change dq (t) / dt is obtained using any of the following equations.

{Dq (t _i ) −dq (t _i−1 )} / dt
= F (τ, Q _DC (t _i ), q (t _i ))
Or
{Dq (t _i ) −dq (t _i−1 )} / dt
= F (τ, Q _DC (t _i ), q (t _i-1 ))
As a result, it is possible to calculate the temporal change dq (t) / dt of the transient charge q (t) that follows the time delay τ.

As described above, in the present embodiment, the IDC in the quasi-static state is obtained, and a transient current dq (t) / dt is obtained separately from the IDC, and added to obtain the current I (t) = I _DC. + Dq (t) / dt is obtained.

  A conventional IGBT physical model (Hefner Model) is an approximate solution of a time-dependent excess carrier diffusion equation which is one of the basic equations.

  On the other hand, in this embodiment, the current in the quasi-static state (steady state) is analytically obtained from the diffusion equation of excess carriers that does not depend on time, and is calculated by a method of adding a transient change in time to the steady current. . That is, instead of directly calculating the transient “excess carrier distribution” inside the device, “charge (the result of integrating the excess carrier distribution)” is used. As a result, since the number of parameters can be reduced as compared with the conventional model, parameter extraction becomes easy.

  In addition, the element model of the present embodiment is a physical model, and is not a behavior model (behavior model) including many fitting parameters. Therefore, since the element characteristics of a single element can be calculated when the element structure is determined, the element structure and circuit design can be optimized.

Here, FIG. 3 shows the hole distribution in the base at the time of turn-off. The vertical axis represents the hole density, and the horizontal axis represents the distance from the collector base boundary. A portion indicated by a triangle indicated by a broken line in the drawing is a hole distribution in the above-described quasi-static state (steady state). In an example of steady approximation, the distribution of holes in the base portion at turn-off (or turn-on) is an amount (Q (t _i )) determined by a triangular area indicated by a broken line.

  On the other hand, at the time of turn-off, transient carrier accumulation occurs. It is theoretically possible to solve this transient carrier simultaneously with the current flowing through the IGBT using the carrier diffusion equation, but in that case, an infinite series expansion is required, which is not practical. Moreover, if approximated, a sufficient solution cannot be obtained as in the conventional example described above.

In the present embodiment, this time change of q (t) is separated from the static state, and a tracking delay time τ is given to the static accumulated charge Q (t) and the transient accumulated charge q (t). The temporal change dq (t) / dt of the transient accumulated charge is determined by the corresponding function f (τ, Q _DC (t _i ), q (t _i )). Therefore, an accurate current can be obtained by a simple calculation as compared with the case of solving the diffusion equation.

FIG. 4 shows a flowchart of static characteristic calculation processing in the present embodiment. First, the electrode potential of each electrode is set (S11). The power supply voltage (Vanode) and gate voltage (Vg) to which the emitter electrode is connected are set to 500 V, 15 V, etc., for example. The collector voltage is usually 0V. In the above formula, various conditions for necessary elements are also set here. Next, an initial value of the element internal potential (V _EB ) is set (S12). For example, a value such as 0.6V is set.

Then, the element internal current component is calculated under the set conditions (S13). That is, the eq. Based on 1, 2, 5, I _E , I _C , and I _Drain are calculated. Next, Kirchhoff's law is verified by the law (S14), and it is determined whether the error is within an allowable range (S15). That is, it is determined whether I _E -I _C -I _{Drain is} substantially zero or not.

If it is determined in S15 that the error is not within the allowable range, the element internal potential VEB is updated, the process returns to S13, and this is repeated until the determination in S15 becomes Yes. If the determination in S15 is Yes, the value of the main current _IE is output. In this way, the operation of the IGBT according to the input conditions is simulated.

FIG. 5 shows a flowchart of the transient characteristic calculation process. First, a stored charge amount Q _DC (t = 0) in a steady state with respect to the gate voltages V _g (t = 0) and V _Anode (t = 0) at time t = 0 is obtained (S21). Here, Q _DC (t = 0) is the charge (carrier) distribution P _Baseneutral in the base neutral region (the neutral region is expressed as neutral) and the charge Q _C (t = 0 in the collector-base depletion layer). ), Q _B (t = 0).

Here, the accumulated charge amount Q _DC in the neutral base region in the steady state is expressed as follows as a function of V _EB .

Q _DC = AP _B L _B {exp (qV _EB / kT) −2} tanh (W / 2L _B )
here,
A: active region area D _{B of} element: base region minority carrier diffusion coefficient L _B : base region minority carrier diffusion length k: Boltzmann constant P _B : base region impurity concentration q: elementary charge W: neutral base region width.

Here, the derivation of the accumulated charge amount Q _DC will be briefly described. The accumulated charge amount Q _DC is obtained by integrating the steady state excess carrier distribution in the neutral base region. When P (x) is an excess carrier concentration, P (x) in a steady state is expressed as follows.

Since the accumulated charge amount Q _DC is obtained by integrating this excess carrier concentration in the neutral base region, it is expressed by the following equation.

Then, t = t _i in _{V g (t = t i)} , enter the _{V Anode (t = t i)} , in this condition, determine the charge distribution p steady state (x) (S22). This charge distribution is the same as the method for _obtaining P _Baseneutral described above.

Then, the integral in the base neutral region of the hole distribution is calculated to obtain the steady state hole charge amount Q _p (t _i ) in the base neutral region (S23).

Q _p (t _i ) = ∫p _DC (x) dx [Base neutral region]
Next, Q _C (t _i ) and Q _B (t _i ) at time t _i are obtained (S24), and from these sums, Q _DC (t _i ) = Q _C (t _i ) + Q _B (t _i ) + Q _p (t _i ) is obtained (S25).

  Next, the delay time τ is calculated (S26).

  The delay time τ is not a mere constant but a function of the PNP emitter-base potential VEB, and is calculated by the following equation.

W (V _EB ) = W _B −W _depletion = √ (Dτ)
That is,
τ = [W (VEB)] ² / D
It is. Here, W: neutral base region width, W _depletion : depletion layer width, W _B : PNP base width, D: excess carrier diffusion coefficient in the neutral base region.

Then, using this delay time τ, a transient charge amount q (t _i ) is obtained using a recurrence formula. That is, dq (t) / dt = (1 / τ) (Q (t) −q (t _i )) is expressed by a recurrence formula,
q (t _i ) = {q (t _i-1 ) + ((t _i -t _i-1 ) / τ) Q (t _i )} / (1+ (t _i -t _i-1 ) / τ)
Thus, the charge amount q (t _i ) at time t _i is obtained (S26).

After S26, it is determined whether the time t _i is smaller than the predetermined time T (S27). If Yes, the process returns to S22, the time is advanced, and NO is determined in S27. The calculation is performed until the time reaches T.

As a result, q (t _i ) at each time is obtained, and from this change dq (t) / dt, the current in the transient state is obtained, and therefore I (t) = I _DC (t) including the transient characteristics. + Dq (t) / dt is obtained.

  As described above, the present embodiment employs a method in which a steady solution is obtained as an analytically exact solution by a diffusion equation that does not depend on time, and a transient carrier time change is added to the steady solution. Furthermore, since the temporal change of the transient charge is expressed as a function of the delay τ, the charge QDC in the steady state assuming a quasi-static state, and the transient charge q (t), a significant change from the quasi-stationary approximation Dynamic response can be calculated. As a result, high-precision calculation is possible without sacrificing calculation speed.

It is an equivalent circuit diagram of IGBT. It is a figure which shows the structure of IGBT typically. It is a figure which shows the hole accumulation | storage state in IGBT. It is a flowchart of the calculation process of a static characteristic. It is a flowchart of the calculation process of a transient characteristic.

Explanation of symbols

  10 cathode, 12 P + region, 14 N + region, 16 P− region, 18 N− region, 20 P + region, 22 anode, 24 gate insulating film, 26 gate electrode.

Claims (4)

A field effect transistor having a source region, a channel region, and a drain region, the drain current of which is controlled by an input signal to the gate electrode; and an emitter region, a base region, and a collector region, the drain current of the field effect transistor being a base A bipolar transistor that is input to the region and whose collector current is controlled, a cathode is connected to the source region and the collector region, an anode is connected to the emitter region, and a current between the anode and cathode is controlled by the input signal In an IGBT simulation apparatus for simulating the operation of an insulated gate bipolar transistor (IGBT) which is a three-terminal semiconductor element,
A hole current I _E to be discharged to the cathode of the IGBT, the hole current I _C flowing from the anode, the drain flowing through the channel region connected to the gate electrode through the gate oxide film from the cathode toward the base region current I _Drain, for the three current, together represented by the function _{V EB} is regarded as being determined by the potential difference _{V EB} between said emitter region and said base region, while changing the potential difference _{V EB, I E = I C} + I _For the Kirchhoff's law called _Drain, the potential difference V _EB is calculated so that the error in the calculation result is less than or equal to a predetermined value . Using the obtained potential difference V _EB , each current in a quasi-static state that does not depend on time An IGBT simulation apparatus characterized in that: The IGBT simulation apparatus according to claim 1,
The transient current flowing through the device during IGBT switching is expressed as a function of the accumulated charge Q _DC (t) and the transient accumulated charge q (t) in the steady state assuming a time delay τ and a quasi-static state. Is calculated as a time change dq (t) / dt of the charge amount q (t) accumulated in the element determined using f (τ, Q _DC (t), q (t)). Each of the obtained transient currents is added to the current in the quasi-static state to obtain each current;
The IGBT simulation apparatus characterized by expressing the time delay τ by using the potential difference V _EB . The IGBT simulation apparatus according to claim 2,
The time delay τ is expressed by τ = W ² / D.
Here, W is the width of the neutral base region of the IGBT, and D is the excess carrier diffusion coefficient in the neutral base region. A field effect transistor having a source region, a channel region, and a drain region, the drain current of which is controlled by an input signal to the gate electrode, and an emitter region, a base region, and a collector region, and a drain of the field effect transistor A bipolar transistor in which a current is input to a base region and a collector current is controlled; a cathode is connected to the source region and the collector region; an anode is connected to the emitter region; and a current between the anode and the cathode by the input signal In an IGBT simulation program for simulating the operation of an insulated gate bipolar transistor (IGBT), which is a three-terminal semiconductor element,
A hole current I _E to be discharged to the cathode of the IGBT, the hole current I _C flowing from the anode, the drain flowing through the channel region connected to the gate electrode through the gate oxide film from the cathode toward the base region current I _Drain, for the three current, together represented by a function of _{V EB} is regarded as being determined by the potential difference _{V EB} between said emitter region and said base region, while changing the potential difference _{V EB, I E = I C} + I _For the Kirchhoff's law called _Drain, the potential difference V _EB is calculated so that the error in the calculation result is less than or equal to a predetermined value . Using the obtained potential difference V _EB , each current in a quasi-static state that does not depend on time An IGBT simulation program characterized in that