1778 IEEE TRANSACTIONS ON ELECTRON DEVICES. VOL. 43, NO. I I , NOVEMBER 1996

Theoretical Analysis of the Breakdown Voltage in Pseudomorphic HFET’ s

Kurt W. Eisenbeiser, Member, IEEE, Jack R. East, Member, IEEE, and G. I. Haddad, Fellow, IEEE

Abstract-In this paper a two-dimensional (2-D) model based on a solution to the moments Of the Boltzmann transport equation is used to study breakdown in pseudomorphic Heterojunction Field Effect Transistors (HFET’s). The effects of the energy conservation equation and the space charge effects of generated carriers are studied in the model. The model is then used to

the simulation of the breakdown characteristics of a submicron HFET. After determining the best model for this work, we use i t to study impact ionization effects in pseudomorphic HFET’~, The to show the regions Of the device that dominate impact ionization breakdown. Then the model

is first

study breakdown in GaAs channel and Ino 57Gao 4 i A ~ channel HFET’s. The model shows that impact ionization breakdown in these structures is dominated by generation in two regions: 1) the high field region near the corner of the gate, and 2) the channel near the top heterojunction. Next, the effect of a thin pseudomorphic layer, which has a high threshold energy for impact ionization, is studied. This layer is shown to significantly improve the breakdown voltage of the HFET if used properly. Finally the effects of doping on breakdown voltage of these HFET’s are studied. This study shows that increased doping can improve the maximum estimated output power of these devices.

I. INTRODUCTION

UMERICAL modeling is an important tool to estimate N the effects that material or geometry changes may have on the performance of a device. Several simulations of break- down in GaAs MESFET’s have been reported [1]-[3]. There have also been some simulations of breakdown effects in Heterojunction Field Effect Transistors (HFET’s) reported [4], IS]. This paper will focus on modeling impact ionization breakdown effects in pseudomorphic HFET’s and study ways in which the material properties of the pseudomorphic layers can be used to improve the breakdown voltage of a HFET. The simulations that follow are based on an approximate solution to the Boltzmann transport equation [ 6 ] , [7]. Impact ionization effects are then included in the model. Reported simulations have generally used either a solution to the ionization integral or inclusion of impact ionization generation in the transport equations to model impact ionization breakdown in a FET. We have studied both methods using our model and will compare them to experimental results to quantify the errors in each model. We have also included the energy conservation equation in our model and again compare the simulated results to experiment to quantify the errors in calculated breakdown voltage that arise from neglecting this equation in

Manuscript received April 27, 1995; revised November 20, 1995. The review of‘this paper was arranged by Editor P. M. Solomon. This work was supported by the U.S. Army Research Olfice under the URI Program Contract DAAL-03-92-G-0101.

K. W. Eisenbeiser was with Solid State Electronics Laboratory, The University ofMichigan, Ann Arbor, MI 48109 USA. He is now with Motorola. Tempe, AZ 85284 USA.

J. R. East and G. 1. Haddad are with Solid State Electronics Laboratory, The University of Michigan, Ann Arbor, MI 48109 USA.

Publisher Item Identifier S 00 18-9383(96)07706-4.

is used to design HFET structures that best take advantage of the unique properties of the pseudomorphic material. Finally the model is used to predict the effects of doping variations on the saturation current and breakdown voltage of these HFET’ s.

11. MODEL

This paper will look at two transport models and their effects on the calculated breakdown voltage in FET’s. The two models are an energy model and a drift-diffusion model. The basic form of these models and their derivation are described in [6] and [7]. The equations used for the energy model are

Equation (1) is Poisson’s equation, (2) and (3) are the charge conservation equations for electrons and holes respectively where the electron and hole current densities are given by (4) and (5 ) . Equation (6) is the electron energy conservation equation. In these equations E is the dielectric constant, E is the electric field, q is the electronic charge, p is the hole number, n is the electron number, N o is the ionized donor impurity number, NA is the ionized acceptor impurity number, . I , is the electron current density, G is the generation rate, R is the recombination rate, .J, is the hole current density, /L,, is the electron mobility, E,, is the electric field for electrons, k~ is Boltzmann’s constant, T, is the electron temperature, p p is

0018-9383/96$05.00 0 1996 IEEE

kIStNBEISER P t al ANALYSJS OF BREAKDOWN VOLTAGE IN PSEUDOMOKPHIC HFET', 1779

3

2.5

2

I .5

1

0.5

0

0 0.2 0.4 0.6 0.8 1 1.2

Average Electron Energy (eV)

Fig. 1. Steady state electron cnergy relaxation time and effective field as a function of the avei-age electron energy for a GaAs sample doped at 1 . 0 ~ l O I 7 cm-3.

I I n GaAs

GaAs substrate

Fig. 2. Schematic of experimental device

the hole mobility, Ep is the electric field for holes, U, is the hole diffusion constant, E,, is the energy separation between the upper and lower conduction band valleys, F is the fraction of upper valley electrons, To is the lattice temperature, T", is the energy relaxation time and 7) is the average total electron velocity. This velocity is equal to the electron current density divided by both the electron charge and the average electron number.

The electron mobility, pT1, and the energy relaxation time, T,,,, are functions of the average electron energy and are found from Monte Carlo studies. The electron mobility is calculated using the equation

(7)

where p1," is the low field electron mobility, E,* is an effective electric field that relates the mobility to the average total energy instead of the electric field. EnlllaX is the held for peak electron velocity and T I , ~ ~ ~ ~ , is electron saturation velocity. The energy dependence of E,,e and 7 - 1 ~ - are found from Monte Carlo generated data such as that shown in Fig. 1 for ,rj,-GaAs.

The drift-diffusion model uses a simplified form of these equations where the electron velocity and tnobility are as- sumed to be functions of the local electric field. Equation (6) then is not needed in the drift-diffusion model, and the electron temperature is assumed to be equal to the lattice temperature. In both models the equations are discritized and solved on a staggered mesh using a finite difference method.

The modeling of impact ionization effects in a FET can be achieved with several approaches. One approach utilizes the ionization integral, which can be written for electron initiated ionization as

mn(r)exp - (o.(T') - aP(r'))dr' dr = 1 (8)

to calculate breakdown. In this equation a,, is the electron initiated ionization rate and ap is the hole initiated ionization rate. In this approach the potential distribution in the device is calculated from a self-consistent, iterative solution to (1)-(5). This potential distribution is used to determine the breakdown path in the device. The breakdown path is the path that maximizes the ionization integral. The breakdown path starts at the drain side of the gate and ends at the drain. After the maximum breakdown path has been determined, the ionization integral is calculated along this path. If the integral is less than one, the drain bias is increased and the potential profile and integral are calculated again. This process is repeated until the ionization integral is greater than one and the breakdown condition is reached.

Another method to calculate a device's breakdown voltage is to include impact ionization in the generation term in (2) and (3). The total of the generation term minus the recombination term, G-R, is made up of four terms: 1) thermal generation- recombination; 2) impact ionization generation; 3) Auger recombination; and 4) surface recombination. The impact ionization generation term can be written as

. I' pat11 [ 1'. I

Through this term impact ionization effects can be included in the transport model. The ionization coefficients used in (8) and (9) are functions of both the electric field and the lattice temperature. They can be written as 181

1780 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 43, NO. 11, NOVEMBER 1996

2 8

16

14

12

10

8

6

4

/

Breakdown Path Calculation

/ **-IC

.-• Electron Temp Model with Generation

cteristics

0 . 0 0.2 0 . 4 0.6 0.8 Gate-to-Drain Spacing (pm)

Fig. 3. Comparison of modeled results to experimental results

where E is the electric field, Ei is the threshold energy for impact ionization, E, is the optical phonon energy and X is the mean free path for optical phonon scattering for energetic carriers. The parameters in this equation are found from a constrained empirical fit to measured ionization data [9]. For materials such as pseudomorphic materials not studied in [9], theoretical values are used.

Breakdown of the device in this model is determined by first solving the Poisson and conservation equations including the generation terms. The steady state current is then deter- mined from this model as the current at which the real current in the time dependent solution becomes constant and the displacement current approaches zero. The bias in the model starts with a gate bias near threshold and a small drain bias. The drain bias is then increased. As the voltage is increased the current is monitored until breakdown is reached. Breakdown is defined as the voltage at which the drain current reaches 20% of the open channel saturation current.

111. COMPARISON OF THE MODELS TO EXPERIMENT

The models described above result in three separate models: the ionization integral model, the drift-diffusion model with an impact ionization generation term and the energy model with an impact ionization generation term. To determine the usefulness of these models as predictors of the breakdown voltage in a submicron FET, the calculated breakdown voltage

as a function of the gate-to-drain spacing for a GaAs MESFET is compared to experimental results. The experimental device is a GaAs MESFET with a 0.2-pm gate, a gate-to-source spacing of 0.15 pm and gate-to-drain spacings ranging from 0.05 pm to 0.65 pm. The gate-to-drain spacing is defined as the distance from the gate to the edge of the drain side ohmic cap since this heavily doped ohmic cap layer effectively pins the edge of the depletion region and prevents further extension of the depletion region toward the drain. Fig. 2 shows a schematic of the experimental device. The dimensions of the experimental device were determined by SEM analysis.

A comparison of the modeled results to experimental results is shown in Fig. 3. This figure shows that the ion- ization integral or breakdown path method does not provide quantitatively accurate results. This method neglects the space charge effects from generated carriers which can result in large errors. As the impact ionization in the device becomes large, the number of generated carriers becomes comparable to the number of carriers already present in some regions of the device. The generated carriers can significantly alter the potential distribution in some regions of the device and lead to a lower breakdown voltage. This inaccuracy results in a large overestimation of the breakdown voltage using the breakdown path model.

The drift-diffusion model with impact ionization included in the generation term provides more accurate results. Fig. 3 shows that the drift-diffusion model with the generation term

EISENBEISER ef al.: ANALYSIS OF BREAKDOWN VOLTAGE IN PSEUDOMORPHIC HFET’s 1781

g a t e

I

Electric Field

d r a i n s o u r c e

I Fig. 4. Modeled electric field near the edge of the depletion region. Solid curve is drift-diffusion model, dashed curve is energy model

g a t e

I

Fig. 5. Modeled electron velocity near the edge of the depletion region. Solid curve is drift-diffusion model, dashed curve is energy model.

provides quantitatively more accurate results but still has significant errors. The drift-diffusion model errors arise largely from inaccuracies in the drift-diffusion transport model for submicron devices. Fig. 4 shows the modeled electric field near the edge of the depletion region for the drift-diffusion and energy models for a 0.2-pm gate length device with a 0.8-pm gate-to-drain spacing. This figure shows that the drift- diffusion model overestimates the electric field in the FET. At small gate-to-drain spacings the large electric field in the depletion region dominates the impact ionization breakdown of the device. Since the drift-diffusion model overestimates this field, it overestimates the impact ionization generation in the device and underestimates the breakdown voltage of the device at small gate-to-drain spacings. This can be seen in Fig. 3. At larger gate-to-drain spacings the electric fields in the depletion region become smaller and the overestimation of electric field by the drift-diffusion model is less significant. In this case the inaccuracy in the drift-diffusion model can be explained by the current density predicted by the model. Fig. 5 shows the electron velocity in the channel of a 0.2-pm gate length FET with a 0.8-pm gate-to-drain spacing as modeled by the drift-diffusion and energy models. This figure shows that the drift-diffusion model significantly underestimates the electron velocity in a submicron FET. This leads to an under- estimation of the current density in the device. The saturation current calculated by the energy model is within 15% of the measured current but the saturation current calculated by the drift-diffusion model is much less. The drift-diffusion model typically predicts saturation current densities that are only about 20% to 30% of the measured current density. The

smaller current density in the drift-diffusion model leads to an underestimation of the impact ionization generation rate. This result can be seen in the overestimation of breakdown voltage by the drift-diffusion model at large gate-to-drain spacings.

The energy model does a much better job of predicting the experimental results. Over most of the gate-to-drain spacings the model is within 10% of the experimental values. The model does an especially good job of qualitatively predicting the effects of changing gate-to-drain spacing on breakdown voltage. In the high breakdown voltage region there is larger error in the energy model, but it is still qualitatively reflective of the experimental results.

Errors in the energy model arise from several sources. The first limitation in the model is the assumption that the breakdown voltage of the device is limited by impact ioniza- tion. There are several other forms of gate breakdown that can limit a device’s high voltage performance. One form of breakdown is thermionic emission over the gate barrier. The emitted carriers can contribute directly to the leakage current of the device or they can gain energy in the depletion region and contribute to impact ionization generation. To study these effects, thermionic emission was included in the model described above. At reasonable gate barrier heights the thermionic emission did increase the gate current but (did not significantly change the calculated breakdown voltage. At smaller gate barrier heights, less that about 0.3 eV, the emitted carriers did significantly change the device properties near breakdown. When the number of emitted electrons becomes comparable to the number of generated carriers in the depletion region near breakdown, the thermionic emission mechanism

1782

gate

i-AlGaAs

IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 43, NO. 11, NOVEMBER 1996

drain

source

n++

gate_ i-AlGaAs

i-GaAs

i-AlGaAs

drain

n++

Fig. 6. 1 x 1oz5 cmp.'spl

Impact ionization generation rate. Gate-to-drain spacing is 0.2 bm. The peak rate is 1.3 x l oz6 cmP3sp1 and the contour step size is

iource

n++

i-GaAs

i-AlGaAs

n++

Fig. 7. 1 x i oz5 cmp3s-'.

Impact ionization generation rate. Gate-to-drain spacing is 0.7 bm. The peak rate is 1.1 x loz6 cmP3s-' and the contour step size is

plays an important role in FET breakdown. The simulation results presented in this study do not include thermionic emission since most of the barrier heights for the material systems studied can be made large enough so that thermionic emission does not have a significant effect on the breakdown of the device.

Tunneling of carriers through the gate barrier, including thermionic-field emission, can also contribute to FET break- down. The tunneling breakdown can take two forms. One

form is tunneling from the gate to the semiconductor under it. This form of tunneling is not included in the model and may cause of some of the quantitative errors present in the model. We have tried to minimize these errors by including at least a 50-A undoped wide bandgap layer in all of the simulated devices that follow. The other form of tunneling breakdown is tunneling from the gate to the surface of the semiconductor. This form of tunneling has been suggested as a breakdown mechanism by Trew and Mishra [lo]. This

EISENBEISER ef al.: ANALYSIS OF BREAKDOWN VOLTAGE IN PSEUDOMORPHIC HFET’s 1783

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2 2

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Strained AlGaAs

Strained GaAs

_ _ _ _ _ - - - - - - - - - * * * - -

.*

0 0 . 2 0 . 4 0.6 0 . 8 2 Gate-to-Drain Spacing (pm)

Fig. 8. Effects of pseudomorphic layers on breakdown voltage in AlGaAs/GaAs FET’s.

breakdown mechanism is heavily dependent upon the surface properties of the device. These surface properties depend not only on the material but also on the processing of the FET which makes modeling difficult. This form of tunneling breakdown was not included in the model.

Another limitation in the model arises from the assumptions in the Boltzmann transport equation. This model is a semi- classical model in which quantum effects are not included. The devices modeled in this study have abrupt heterojunctions and in some cases quantum well channels. Both of these cause errors in the semi-classical model. To reduce the inaccuracies from the quantum effects in the modeled devices, the minimum channel thickness was 400 A and all heterojunctions are assumed to be linearly graded over at least 25 A.

Another area that causes errors in the model is its ability to model imperfections in the device. High electric fields are produced at regions of the gate, drain and source where the metal edge is not smooth. Small imperfections can always be seen in actual fabricated devices. These imperfections lead to electric fields that vary along the width of the gate. These variations are not modeled in the two-dimensional (2- D) model used in this study. The localized high fields can, however, play a significant role in the breakdown of the

device. These variations are very much process dependent which also makes them difficult to model. The result of these imperfections is to lower the breakdown voltage in the device. This is one reason that the models above almost always predict a higher breakdown voltage than is observed experimentally.

IV. RESULTS

In this section, the energy model with impact ionization generation is used to study breakdown in pseudomorphic HFET’s. Pseudomorphic layers have been shown theoretically [ 1 11 and experimentally [ 121 to have a higher threshold energy for impact ionization than lattice matched layers of the same bandgap. The drawback to the pseudomorphic layers is Ithat their thickness is limited to a value less than their critical thickness. This leads to a trade-off. Pseudomorphic layers with more strain have higher threshold energies for impact ionization but smaller critical thicknesses. The very hig;hly strained materials can only be used in thin regions of the device.

The model described above serves as a very good tool to determine the regions of high-impact ionization generation in HFET’s. Once these regions have been identified, the

1784 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 43, NO. 11, NOVEMBER 1996

source

n++

drain r---

n-InAlAs ~ n++

i-InAlAs 1

Fig. 9. Impact ionization generation rate. The peak rate is 1.0 x 10" cmp3sp1 and the contour step size is 1 x 10" ~ m - ~ s - .

model can be used to study the effects of placing thin, highly strained layers in these critical regions. In this way the optimal use of the pseudomorphic layers in terms of higher device breakdown voltage can be determined. The pseudomorphic layer is simulated simply by changing the threshold energy for electron initiated impact ionization in the pseudomorphic layer. Electron transport in the direct bandgap pseudomorphic layer should be similar to that in the corresponding lattice matched layer with the same bandgap [ 111.

The first device simulated is an Alo.25Gao.75As/GaAs HEMT. Figs. 6 and 7 show contour plots of the impact ionization generation rate in a device with a small gate-to-drain spacing and a larger gate-to-drain spacing respectively. These contour plots show contours of equal generation rate. The outer contour is always the contour of lowest generation rate and is shown with a light gray curve. The contours become darker for higher generation rates. The center of each set of closed contour lines represents a peak in the generation rate. The relative height of these peaks can be determined by the number of contour lines around the peak. The higher peaks have more contour lines around them. The relative slope of the region leading up to the peak can be determined from the spacing between contour lines. Contour lines that are closer together represent a steeper slope.

Fig. 6 shows that most of the significant generation in the small gate-to-drain spacing device takes place in the AlGaAs layer. There is a secondary generation peak in the channel but this peak is much less than the peak in the AlGaAs. As the gate-to-drain spacing is increased, the peak electric field in the

depletion region is reduced. This causes the generation rate in the high field region in the AlGaAs to decrease. The generation rate around the peak in the channel is much less sensitive to changes in the gate-to-drain spacing, so near breakdown this peak is comparable to the AlGaAs peak in the long gate-to- drain spacing device. Fig. 7 shows the generation rate in this long gate-to-drain spacing device.

After these two regions of high-impact ionization genera- tion have been determined, the use of pseudomorphic layers to reduce this generation was considered. The simplest approach would be to replace the entire high-generation area shown in Figs. 6 and 7 with high threshold pseudomorphic material. The problem with this approach is that the high generation regions total 500 8, to 600 8, in thickness. A 500 8, pseudomorphic layer can only have a small amount of strain. Since the impact ionization threshold energy is directly related to the amount of strain in the layer, the 500-A pseudomorphic layer will have a threshold energy that is only slightly higher than a lattice matched layer, and the breakdown voltage of such a device shows only a small improvement over the lattice matched device. A better approach is to use a highly strained layer. This limits the critical thickness of the layer but greatly improves its threshold energy. The limited critical thickness means that the highly strained pseudomorphic layer can be used either in place of the AlGaAs Schottky, donor and spacer layers where one peak in the generation rate occurs, or in place of the GaAs channel where the other generation rate peak occurs but not in both regions. The model was used to determine which of these uses is better.

EISENBEISER et al.: ANALYSIS OF BREAKDOWN VOLTAGE IN PSEUDOMORPHIC HFET's 1785

Strained InGaAs

e e'

e Strainel e In IAs

Lattice Matched

0.2 0.2 0.3 0.4 0.5 0.6 0.7 Gate-to-Drain Spacing (pm)

Fig. 10. Effects of pseudomorphic layers on breakdown voltage in InAlAshGaAs FET's

Fig. 8 shows the results of these simulations. The solid curve shows the breakdown voltage as a function of gate-to- drain spacing for a lattice matched device. If the channel in this device is replaced by a pseudomorphic layer with 1.4% bulk lattice mismatch, breakdown characteristics shown by the dotted curve result. This curve shows that at small gate-to- drain spacing the pseudomorphic channel does not improve the breakdown voltage of the device very much since most of the impact ionization generation occurs in the AlGaAs layers. As the gate-to-drain spacing is increased, the secondary generation peak in the channel becomes significant and the pseudomorphic channel does improve the breakdown voltage of the device. If instead of using a pseudomorphic channel, the AlGaAs layers are replaced by pseudomorphic layers of the same bandgap but with 1.4% bulk lattice mismatch, a larger improvement is seen in the breakdown voltage for all gate-to-drain spacings. This is shown by the dashed curve in Fig. 8. This means that for all gate-to-drain spacings the impact ionization generation peak in the AlGaAs layer makes a significant contribution to the breakdown voltage of the device. The best use of the pseudomorphic layer then is in place of the surface AlGaAs layers. The predicted improvement in breakdown voltage that occurs when the surface AlGaAs layers are replaced by pseudomorphic layers of the same bandgap has been verified experimentally [ 131.

The In~.~~Alo.4sAs/Ino.53Gao,47As system is another system that has been studied with the model. The situation in this system is significantly different from the AlGaAdGaAs system. The Ino.~2Alo.48A~/Ino,~~Ga~,4~As system has a larger conduction band discontinuity than Alo.~5Gao.~5As/GaAs, 0.45 eV compared to 0.25 eV, and the Ino.53Gao.47As channel has a much lower threshold energy for impact ionization than the Ino.52Alo.48As layers. Fig. 9 shows that in this system impact ionization generation in the channel is much more important. There is still a peak in the generation rate in the Ino,52Al0.48As, but in this case it is much smaller than the peak channel generation rate for all gate-to-drain spacings. This result is supported by experimental evidence which shows that impact ionization in the channel dominates breakdown in this type of device [ 141.

Once again the model was used to simulate the effects of a pseudomorphic layer in place of either the Ino.52Alo.48As Schottky, donor and spacer layers or the Ino.53Gao.47As chan- nel. These results are shown in Fig. 10 and can be explained by the generation rate contours. The dashed curve shows tlhat some improvement in breakdown voltage can be obtained when the In0.52A10.48As layers are replaced by a pseudo- morphic layer of the same bandgap. This shows the effect of the secondary peak in the impact ionization generation in .the Ino.52A10.48As layers. When the Ino.53Gao.47As channel is re-

1786 IEEE TRANSACTIONS ON ELECTRON DEVICES, VOL. 43, NO. 1 I , NOVEMBER 1996

Doped InGaAs

Doped InGaAs a n d InAlAs ......................... l . , . . . I . . . . . , , , , / . , , . * I . .

I I I I I I 0.2 0.2 0.3 0.4 0 .5 0.6 0.7

Gate-to-Drain Spacing (pm) Fig. 11. Effects of doping on breakdown voltage in InAlAslInCaAs FET's.

placed by a pseudomorphic layer of the same bandgap such as Ino.73Gao.12Alo 15As, even more improvement in breakdown voltage can be achieved for all gate-to-drain spacings. Large improvements in breakdown voltage then can be achieved by replacing the Ino,53Gao.47As channel with a pseudomorphic layer of the same bandgap. This result has been verified experimentally [ 151.

Another parameter that was studied with the model is the relation between doping and breakdown voltage. A simple analysis of a homogeneous FET shows that [16]

where Vbr is the breakdown voltage, N(y) is the doping distribution, and a is the channel thickness. As the doping is increased, the current in the device is increased but the breakdown voltage of the device decreases. There is not much change in the breakdown voltage-saturation current product with doping in this case. The situation in a HFET is more complicated due to the fact that there are several regions where impact ionization generation is important to breakdown. Fig. 11 shows the effects of doping on the breakdown voltage in a In0 52A10 4sAs/Ino 53Gao 47As HFET. Two devices, a HEMT and a doped channel device, are compared by the

dashed and dotted curves respectively. These devices are exactly the same except the HEMT has a doped In0.52A10.48As layer and the doped channel device has a doped Ino.53Gao.47As layer. The total doping in these devices is the same so the saturation current in the devices is similar. This figure shows that doping the In0.52A10.48As results in a higher breakdown voltage than doping the Ino.53Gao.47As. This result can be explained by Fig. 9 which shows that breakdown in this device is caused mainly by generation in the channel. The doped In0.52A10.48As layer, which results in increased generation in this layer, causes less degradation in the breakdown voltage than the doped Ino.53Gao.47As layer.

The solid curve in Fig. 11 shows the breakdown character- istics of a device with doping in both the In0.52A10.48As and Ino.53Gao.47As layers. This device has twice as much doping as either of the other devices. The simulation results for this device show that is will have worse breakdown voltage than either of the other devices. The breakdown voltage of these devices, however, is at most 25% less than the best breakdown voltage. Meanwhile the saturation current of these devices is almost 100% higher than the other devices due to the increased doping. The tradeoff for the increased doping then is favorable in terms of the breakdown voltage-saturation current product

EISENBEISER et al.: ANALYSIS OF BREAKDOWN VOLTAGE IN PSEUDOMORPHIC HFET’s 1187

of these devices. A device where both the wide bandgap donor layer and the channel are doped then may provide higher maximum output power than a HEMT or a doped channel device. This doping scheme can be used to further improve the power performance of the pseudomorphic devices.

V. CONCLUSION

In this paper a model based on the solution to the moments of the Boltzmann transport equation has been expanded to include impact ionization generation effects. This model has been shown to qualitatively agree with experimental results for the breakdown voltage in a GaAs MESFET. This model is used to show that for an Alo z5Gao 75As/GaAs HEMT the optimum use of a high-impact ionization threshold energy pseudomor- phic layer is in place of the Alo zjGao 75As layer under the gate. This will result in a significant improvement in the breakdown voltage of the device. In the In0 52A10 48As/Ino 53

Gao 47As system a HEMT with the pseudomorphic layer used as a channel material is the most effective use of the pseudomorphic layers’ high threshold energy. Finally the effect of three doping schemes on the breakdown voltage of a HFET was studied. This study showed that a device with doping in both the channel and the wide bandgap donor layer will have a higher breakdown voltage-saturation current product than a device with doping in only one of these regions.

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[I] Y. Wada and M. Tomizawa, “Drain avalanche breakdown in gallium arsenide MESFET’s,” lEEE Trans. Electron Devices, vol. 35, no. 1 I , pp. 1765-1770, Nov. 1988.

[2] H. Mizuta, K. Yamaguchi, and S. Takahashi, “Surface potential effect on gate-drain avalanche breakdown in GaAs MESFET’s,” IEEE Trans. Electron Devices, vol. ED-34, no. 10, pp. 2027-2033, Oct. 1987.

131 J. Ashworth and P. Lindorfer, “Analysis of the breakdown phenom- ena in GaAs MESFET’s,” presented at Int. Symp. GaAs and Related . .

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[7] D. Teeter, J. East, R. Mains, and G. Haddad, “Large signal characteriza- tion and numerical modeling of the GaAdAlGaAs HBT,” IEEE MjT-S Dig., pp. 651-654, 1991.

[ 8 ] Y. Okuto and C. Crowell, “Energy-conservation considerations in the characterization of impact ionization in semiconductors,” Phys. Rev. B , vol. 6, no. 8, pp. 3076-3081, Oct. 15, 1972.

[9] H.-F. Chau, “Doping profile studies for HBT’s and HEMT’s ‘with improved breakdown and speed characteristics,” Ph.D. dissertation, The University of Michigan, Ann Arbor, 1992.

[ 101 R. Trew and U. Mishra, “Gate breakdown in MESFET’s and HEMT’s,” IEEE Electron Device Lett., vol. 12, no. 10, pp. 524-526, Oct. 1991.

[ 1 11 J. Singh, “The tailoring of impact ionization phenomenon using pseu- domorphic structures-Application to InGaAlAs on GaAs and InP substrates,” Semicond. Sci. Technol., vol. 7, pp. B509-B511, 1992.

[ 12) J. David, M. Morley, A. Wolstenholme, R. Grey, M. Pate, G. Hill, G. Rees, and P. Robson, “Enhanced breakdown voltages in strained In- GaAs/GaAs structures,” Appl. Phys. Lett., vol. 61, no. 7, pp. 2042-2044, Oct. 26, 1992.

1131 K. Eisenbeiser, J. East, J. Singh, W. Li, and G. Haddad, “Bri-ak- down voltage improvement in strained InGaAlAs/GaAs FET’s,” IEEE Electron Device Lett., vol. 13, no. 8, pp. 421423, Aug. 1992.

[14] A. Moolji, S. Bahl, and J. del Alamo, “Impact ionization in In- AlAs/InGaAs HFET’s,” IEEE Electron Device Lett., vol. 15, no. 8, pp. 313-315, Aug. 1994.

[ 151 K. Eisenbeiser, J. East, G. Haddad, and T. Brock, “Breakdown voltage improvement in pseudomorphic FET’s,” to he published.

[ 161 W. Frensley, “Power-limiting breakdown effects in GaAs MESFET’s,” IEEE Trans. Electron Devices, vol. ED-28, no. 8, pp. 962-970, iiug. 1981.

Kurt W. Eisenbeiser (S’91-M’95), photograph and biography not available at the time of publication.

Jack R. East (S’70-M’72), photograph and biography not available at the time of publication.

G. I. Haddad (S’57-M’61-SM’66-F’72), photograph and biography not available at the time of publication.