Simulating Boron Diffusion in Silicon Germanium

 

Introduction

The silicon germanium heterojunction bipolar transistor (SiGe HBT) is a promising technology for combining the operating speed of compound material devices with the production capability of bulk silicon. The presence of a narrower-bandgap material in the base region where most of the bandgap offset occurs in the valence band, creates an energy well for holes. With the lower energy barrier, a lower hole current density can be obtained for a given electron current density increasing the transistor’s gain [1]. Thus the base can then be highly doped, greatly increasing high frequency performance whilst still retaining a reasonable gain. For this reason, the diffusion of boron in SiGe is of great interest.

The incorporation of high boron levels in the base region along with the Ge-induced effects makes prediction of boron diffusion through the SiGe layer difficult. Published experimental data has shown that boron diffusion in SiGe differs from that in bulk silicon. Specifically, experimental evidence indicates that the boron diffusivity in SiGe is dependent on the concentration of germanium with boron diffusivity decreasing as the germanium content increases [2, 3]. To account for such effects, a diffusion model has been implemented in SSuprem4 for the diffusion of boron in SiGe.

Boron Diffusion in SiGe

In the new diffusion model, silicon germanium is treated as highly-Ge-doped silicon. The model takes into account two effects discussed in published works: 1) boron diffusivity decreases exponentially with Ge content [2] and 2) intrinsic carrier concentration increases linearly with Ge content [3]. Strain effects are considered negligible in this model. To account for the exponential variation of boron diffusivity with Ge content, the boron diffusivity term associated with the neutral boron-interstitial pair is modeled as:

where DIX.0 and DIX.E are the prefactor and activation energy for the diffusivity of a neutral boron-interstitial pair in silicon, x is the Ge fraction of the SiGe layer, k is the Boltzman constant, T is temperature, and EAFACT.SIGE is a calibration parameter. Similarly, the linear variation of intrinsic carrier concentration with Ge content is modeled as:

where NIFACT.SIGE is a calibration parameter and nSii is the intrinsic carrier concentration of silicon calculated as:

where NI.0, NI.E, and NI.POW are additional calibration parameters. The user-defined calibration parameters EAFACT.SIGE and NIFACT.SIGE have default values of 1.5 and 100, respectively. The value of these calibration parameters as well as the value of NI.0, NI.E, or NI.POW can be set on the MATERIAL statement. The diffusion model for boron diffusion in silicon germanium is activated with the MODEL.SIGE parameter on the METHOD statement.

Because SiGe layers are treated as Ge-doped silicon in the new diffusion model, adding SiGe layers to existing ATHENA structures is handled a little differently. Silicon germanium layers are added to a structure using the DEPOSIT statement, however they are added as silicon rather than SiGe. The Ge concentration in the deposited layer is set using the C.GERMANIUM parameter and should be calculated as:

where Nsi is the atomic density of undoped silicon (5x1022 atoms/cm3). Specifying a germanium concentration in the above manner will create a SiGe layer with uniform Ge content. To create a layer with a graded composition profile, a second parameter, GE.FINAL, must be specified on the DEPOSIT statement. When GE.FINAL is used, C.GERMANIUM specifies the initial germanium concentration and GE.FINAL specifies the final germanium concentration. For example, the following DEPOSIT statement defines a 0.1 micron thick SiGe layer with a graded Ge profile starting at x = 0.002 at the lower boundary and increasing linearly to x = 0.2 at the upper boundary:

DEPOSIT SILICON THICK=0.1 DIV=10 \
C.GERMANIUM=1E20 GE.FINAL=1E22

With the new diffusion model, ATHENA treats SiGe as Ge-doped silicon. This however is not the case for ATLAS. Before exporting a structure to the device simulator, Ge-doped silicon regions must be converted to silicon germanium. To convert those regions include the SIGE.CONV parameter on the STRUCTURE statement. When the SIGE.CONV parameter is specified, all silicon material nodes with a germanium concentration above 5x1019 cm-3 are converted to silicon germanium material nodes. The composition fraction at the converted nodes is calculated as:

Simultaneously, all Ge, active Ge, and donor or acceptor concentrations associated with the Ge content are removed from the structure. This conversion only works for 2D structures.

 

Simulation Results

To evaluate the general performance of the new model for boron diffusion in silicon germanium, a test structure similar to that proposed by R. Lever et al. [3] was created using SSuprem4. The structure consists of a uniformly-doped silicon epilayer sandwiched between two thin layers of SiGe. Beneath the SiGe/Si/SiGe stack is a 10 micron silicon substrate. Above the SiGe/Si/SiGe stack is a 0.25 micron silicon layer and a 0.25 micron oxide cap. The base doping level of the silicon epilayer was 6x1018 cm-3. The SiGe layers were initially given a uniform composition fraction of 10%. The Fully-Coupled diffusion model was used for all of the simulations.

The most outstanding feature of the simulation results is the pileup of boron at the Si/SiGe interface. As reported by R. Lever et al. [3], this occurs because boron has a higher activation energy in silicon than in silicon germanium. Figure 1 shows the boron profiles following a 12 hour, 850°C anneal for initial doping concentrations of 3x1018 cm-3, 6x1018 cm-3, 9x1018 cm-3, and 12x1018 cm-3. As can be seen, the boron pileup increases with concentration, and the boron diffusivity in SiGe is significantly lower than it is in silicon. The results also show that the doping dependence of the boron pileup begins to saturate for concentrations above 1x1018 cm-3.

 

Figure 1. Comparison of boron profiles for varying initial
doping concentrations; structure annealed for
12 hours at 850°C; uniform Ge fraction of 10%.

 

Boron diffusion in SiGe behaves similarly to that in silicon for varying diffusion times and temperatures. Figure 2 shows the boron profiles following diffusions of 12, 24, 36, and 48 hours at 850, 900, and 950°C. Again it can be seen that the boron pileup is dependent on the initial boron concentration. It is not dependent on the initial diffusion conditions. As expected, the boron profile extends further out from the central silicon epilayer as either the diffusion time or temperature is increased. Figure 3 shows the boron profiles for a Ge content of 1, 5, 10, and 15%. Both boron pileup and diffusivity are significantly affected by the Ge content. At 1%, the resulting boron profile shows very little pileup and essentially no reduction in diffusivity. However at 15%, significant pileup occurs and the diffusivity is low enough that little boron diffuses through the SiGe boundary layers. As will be shown, the influence of Ge content on the diffusion behavior of boron over such a narrow content range can have profound effects on the boron profile in graded SiGe regions.

 

Figure 2. Comparison of boron profiles for varying
diffusion conditions; initial boron concentration of
6x10
18 cm-3; uniform Ge fraction of 10%

 

Figure 3. Comparison of boron profiles for varying Ge
composition fractions; initial boron concentration of
6x1018 cm
-3; structure annealed for 12 hours at 850°C.

Most practical devices do not use uniform germanium content in the base, as this results in impractically thin base region before strain related defects occur. To reduce strain and increase base width, most devices have base regions with “graded” germanium profiles. It is important therefore to examine how well the new diffusion model handles graded profiles. Figure 4 shows the boron profiles from three separate test structures. The first structure included SiGe boundary layers with a graded Ge profile. The Ge content of the graded SiGe regions varied linearly from 10% at the outside edge of the SiGe boundary region to 1% at the inside edge. The second structure includes SiGe boundary layers with uniform Ge content of 10%. In the final structure, the SiGe boundary layers were replaced with undoped silicon. The central silicon epilayer for all three structures was initially doped at 6x1018 cm-3. All three structures were annealed at 850°C for 12 hours in an inert ambient.

 

Figure 4. A) Boron profiles for graded Ge-profile structure,
uniform Ge-profile structure, and silicon structure.
B) Ge profiles for graded and uniform structures.

 

The boron profile for the structure with the uniform SiGe regions is very similar to those profiles presented in Figures 1-3. A moderate amount of boron pileup is observed at the Si/SiGe interface and the diffusivity of boron is noticeably reduced within the SiGe boundary layers. The boron profile in the graded structure differs significantly. Very little pileup is seen at the SiGe interface due to the low Ge content at that boundary. The boron diffusivity at the inner Si/SiGe interface is close to that in the silicon structure. It decreases across the graded SiGe layer reaching a minimum at the outer interface. As can be seen from these results, properly modeling boron diffusion across the SiGe base region of a HBT device is key when simulating technologies with graded base regions. If the device designer were to assume a uniform Ge profile or silicon-like diffusion properties, the simulated junction depth would be significantly different than that of the actual device.

As with any simulation, some level of model calibration is generally needed to match experimental results. To this end, the new diffusion model for boron in SiGe provides two calibration parameters: EAFACT.SIGE and NIFACT.SIGE. Figures 5 and 6 show the boron profiles for differing values of NIFACT.SIGE and EAFACT.SIGE, respectively. For both sets of simulations, the initial boron concentration in the central silicon epilayer is 6x1018 cm-3. The structures were annealed at 850°C for 12 hours in an inert ambient. Variations in NIFACT.SIGE directly affect the amount of boron pileup at the Si/SiGe interface. Variations in NIFACT.SIGE do not significantly affect boron diffusivity in the SiGe layers. It should also be noted that a significant deviation from the default value was necessary to see any significant change in the profile. The performance of the new diffusion model for boron in SiGe does not appear to be sensitive to variations in NIFACT.SIGE under these conditions. The new diffusion model was much more sensitive to variations in EAFACT.SIGE. The value of EAFACT.SIGE does not appear to alter the amount of pileup at the Si/SiGe interface much, but it has a significant affect on the amount of diffusivity reduction in the SiGe regions. This is expected due to the nature of Equation 1.

Figure 5. Comparison of boron profiles for varying values of
NIFACT.SIGE; initial boron concentration of 6x10 cm
-3;
structure annealed for 12 hours at 850°C.

 

Figure 6. Comparison of boron profiles for varying values of
EAFACT.SIGE;
initial boron concentration of 6x10
18 cm-3;
structure annealed for 12 hours at 850°C.

 

Summary

Following the work of [2] and [3], a new model for the diffusion of boron in silicon germanium has been implemented in SSuprem4. This new diffusion model treats SiGe as highly-Ge-doped silicon and accounts for two effects: 1) boron diffusivity decreases exponentially as the Ge content increases and 2) the intrinsic carrier concentration increases linearly as the Ge content increases. To evaluate the general behavior of the new model, a simple test structure was created with which various doping and diffusion conditions were studied. The most outstanding feature of the new model is the resulting boron pileup at the Si/SiGe interface. It was also shown that the diffused profiles in layers with uniform and graded Ge profiles differ significantly.

 

References

  1. D. Vook et al., "Double-Diffused Graded SiGe Base Bipolar Transistors," IEEE Transactions on Electron Devices, vol. 41, pp. 1013-1018, June 1994.
  2. K. Rajendran et al., "Simulation of Boron Diffusion in Strained Si1-xGex Epitaxial Layers," SYSPAD-2000, pp. 206-209.
  3. R. Lever et al., "Boron Diffusion Across Silicon-Silicon Germanium Boundaries," Journal of Applied Physics, vol. 83, pp. 1988-1994, February 15, 1998.