1 Introduction

As integrated circuits (ICs) continue to advance to smaller semiconductor process nodes, the cut-off frequency (fT) and the maximum oscillation frequency (fmax) of silicon (Si)-based radio frequency (RF) microelectronic devices are now moving into the terahertz (THz) range. Compared to the traditional III-V devices, Si-based high-frequency devices have the technical advantages of low cost, easy mass production, and compatibility with the ULSI technology, gradually attracting attention in the application of THz ICs [1]. As the nuclear devices in RF ICs, silicon–germanium (SiGe) heterojunction bipolar transistors (HBTs) offer the advantages of strain engineering and are compatible with CMOS technology. In order to develop fT of SiGe HBTs in the range of 0.5–0.7 THz for the applications such as space communications and remote sensing, the “DOTFIVE” and “DOTSEVEN” projects [2, 3] have been proposed by STMicroelectronics, Infineon, and other research institutions to give full play to the great potential and technical advantages of SiGe HBTs in the reference circuits and systems. The international semiconductor technology roadmap (ITRS) predicts that the fT/fmax of SiGe HBT will reach 570/610 GHz by 2020 [4]. The improvement of the frequency response of SiGe HBTs is achieved by continuously optimizing the process and scaling the lateral size, which may increase the process cost [5,6,7].

As the characteristic size of microelectronics devices is becoming smaller and smaller, the challenge of size-scaling is becoming more and more significant. Strain engineering has been considered one of the important technologies for high-speed devices [8]. Some attempts have been made to introduce the strain effect in SiGe HBTs [9,10,11,12]. Metal interconnects are stacked near the SiGe HBTs according to the BiCMOS-9 W technologies of STMicroelectronics [9], because of the different thermal expansion coefficients between each layer, the uniaxial stress is generated into the devices, fT and fmax are then increased by 21% and 12%, respectively. A strained-Si (SSi) HBT structure is proposed [10], using a relaxed SiGe virtual substrate as the collector and an SSi layer as the emitter. The current gain is improved by 11% compared to traditional SiGe HBTs, but the self-heating effect is significant which limits the frequency performance. An external SiGe stress film is used to apply uniaxial stress to the base region of Si bipolar transistor (BJT), and TCAD simulation is carried out based on the fluid dynamics model [11], and the simulation results showed that fT and fmax are increased by 5% and 3%, respectively. In addition, the effect of global additional stress on frequency response is investigated by full-band Monte-Carlo simulation [12], but the methods of stress introduction and stress adjustment are not discussed in detail.

In this work, a new NPN SiGe HBT architecture utilizing a Si1−yGey stress raiser in the bulk-Si collector region is proposed. Due to the mismatch of the lattice constants between the Si1−yGey stress raiser and Si substrate, additional compressive stress is applied along the horizontal axis, and tensile stress is induced along the vertical axis, which enhances electron mobility in the collector region. The physical mechanisms affecting the DC and AC performance of the proposed device will be investigated by theoretical calculation and TCAD simulation.

2 Device structure

The proposed structure of NPN SiGe HBT with an embedded stress raiser is shown in Fig. 1. The emitter region consists of a thin monocrystalline silicon cap layer and a thick polysilicon layer. Both the emitter and the base regions have the same lateral width, which is beneficial for reducing the parasitic effect between the cap layer and base layer, thus improving characteristics frequency. To diminish the base intrinsic resistance, the lateral width of the emitter is reduced to less than 100 nm. In the collector region, the stress raiser generates uniaxial compressive stress, which can improve the electron mobility, and reduce the series resistance, longitudinal transit time, as well as BC junction capacitance. In the emitter region, the thin Si cap layer is also subjected to the same uniaxial compressive stress as the collector region, and the current injected from the base region to the emitter region is effectively decreased by the interfacial energy barrier between the polysilicon layer and strained-Si (SSi) cap layer, which is advantageous for improving current gain.

Fig. 1
figure 1

Device structure of proposed NPN SiGe HBT with an embedded stress raiser

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The brief process flow is shown in Fig. 2. The proposed device structure selects a P-type (110)-oriented Si substrate. An N+-doped layer and an N−-doped layer are epitaxially formed as buried layer (sub-collector) and collector region, respectively, and the right collector region is N+-doped. The N− collector region is ion implanted to form the P+-doped on both sides as two extrinsic base regions. A SiO2 layer with a thickness of 1–2 μm is deposited on the surface of the device to define the position of an active region. A P-type Si1−xGex layer, an intrinsic SSi cap layer, and an N+-doped polysilicon layer are selective epitaxially formed in the active region. A nitride layer is deposited on the surface of the device, both the nitride layer and SiO2 layer are photoetched, the P+ inner base region is etched, and an embedded Si1−yGey layer is selective epitaxially formed. A polycrystalline Si1−yGey layer is also deposited on the surface of the embedded Si1−yGey layer with the same Ge mole fraction y as a part of the extrinsic base. Two polysilicon electrodes are re-deposited and metal silicide is deposited, to form the electrodes as the emitter, base, and collector.

Fig. 2
figure 2

Brief process flow of proposed NPN SiGe HBT structure

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3 Estimation of strain mechanism

Since the lattice constant of SiGe is greater than that of Si, the embedded Si1−yGey stress raiser generates a longitudinal uniaxial compressive stress σxx in the collector region. The lattices of Si collector are further compressed, and the lattice constant decreases. The conventional biaxially strained Si1−xGex base is superimposed with uniaxial compressive stress to form the uni-biaxially strained base region. The Si cap layer in the emitter region is also affected by the uniaxial compressive stress σxx. Considering the possibility of integrating with uniaxially strained Si pMOSFETs, the additional stress is usually applied along the [110] direction, and the strain tensors of the Si cap layer and bulk-Si collector are then expressed as the same form [12]

$$\varepsilon_{{{\text{Si}}}} = \left[ {\begin{array}{*{20}c} {s_{12} \sigma_{{{\text{xx}}}} } & 0 & 0 \\ 0 & {\tfrac{1}{2}(s_{11} + s_{12} )\sigma_{{{\text{xx}}}} } & {\tfrac{1}{4}s_{44} \sigma_{{{\text{xx}}}} } \\ 0 & {\tfrac{1}{4}s_{44} \sigma_{{{\text{xx}}}} } & {\tfrac{1}{2}(s_{11} + s_{12} )\sigma_{{{\text{xx}}}} } \\ \end{array} } \right],$$
(1)

s11, s12 and s44 are the elastic compliance coefficients, and the longitudinal strain tensor is

$$\varepsilon_{{||,{\text{Si}}}} = \frac{1}{2}(s_{11} + s{}_{12})\sigma_{{{\text{xx}}}} .$$
(2)

Once the biaxially strained SiGe base region is subjected to additional uniaxial stresses from the collector region, the lattice of Si1−xGex will be further compressed and the lattice constant will be reduced. In order to maintain the same strain level as the longitudinal strain tensor ε||,Si in Eq. (2), the longitudinal strain tensor in the uni-biaxially strained base can be equated to

$$\varepsilon_{{\text{||,SiGe}}} = (1 + \varepsilon_{{||{\text{,Si}}}} )\frac{{a_{0} }}{a(x)} - 1,$$
(3)

where a0 and a(x) represent the lattice constants of relaxed Si and relaxed Si1-xGex, respectively. If the longitudinal strain tensor of biaxially strained base is consistent with ε||,SiGe in Eq. (3), the equivalent lattice constant a*(x) of uni-biaxially strained base can be written as:

$$a^{*} (x) = \frac{a(x)}{{\left[ {1 + \frac{1}{2}(s_{11} + s_{12} )\sigma_{{{\text{xx}}}} } \right]}}.$$
(4)

For compressive stress, σxx < 0, and conversely, σxx > 0. It is clear that a*(x) > a(x) in Eq. (4), which corresponds to the fact that the uniaxial compressive stress applied in the collector is equivalent to an increase in Ge mole fraction of Si1−xGex base while maintaining the same level of strain as in a biaxially strained base, which leads to a decrease in the band-gap and an increase in the intrinsic carrier concentration of Si1−xGex base and SSi cap layer. ft is usually considered to represent the characteristic frequency. In the small-signal model, the expressions of ft and fmax are as follows [13]:

$$f_{{\text{T}}} = \frac{1}{{2\pi \left[ {\tau_{{\text{F}}} + \frac{kT}{{qI_{{\text{C}}} }}(C_{{{\text{BE}}}} + C_{{{\text{BC}}}} ) + (R_{{\text{E}}} + R_{{\text{C}}} )C_{{{\text{BC}}}} } \right]}},$$
(5)

and

$$f_{{{\text{max}}}} = \sqrt {\frac{{f_{{\text{T}}} }}{{8\pi R_{{\text{B}}} C_{{{\text{BC}}}} }}} ,$$
(6)

where kT/qIC is the BE junction dynamic resistance, IC is the collector current, CBC and CBE are the BC junction capacitance and BE junction capacitance, and RE and RC the emitter resistance and collector resistance, respectively. The forward transit time is approximately expressed as [14]

$$\tau_{{\text{F}}} \approx \frac{1}{\beta }\left( {\frac{{W_{{\text{E}}} }}{{S_{{{\text{pE}}}} }} + \frac{{W_{{\text{E}}}^{2} }}{{2D_{{{\text{pE}}}} }}} \right) + \frac{{W_{{\text{B}}}^{2} }}{{2D_{{{\text{nB}}}} }}.$$
(7)

In order to reflect the effect of stress on the characteristic frequency, this work only considers the Ge mole fraction of the Si1-xGex base as a constant, and uniform doping in the base region. In Eq. (7), We and Wb are the emitter region thickness and base region thickness, respectively. β is the current gain, and DpE and DnE are the minority carrier diffusion coefficients in the emitter region and base region, respectively. As shown in Fig. 3, an extremely thin oxide-like (SiOr) layer is formed at the interface between the polysilicon and SSi cap layer, SpE represents the holes recombination velocity at the interface, and d is the thickness of the oxide-like layer. χe and χh represent the barrier heights for electrons and holes, respectively. For electrons injected from the emitter into the base, the transport properties are virtually unaffected by the SiOr layer and are transparent to the electrons due to small χe [15]. The holes from the base are injected into the polysilicon layer through the SiOr layer in the form of quantum tunneling. Vj is the voltage across Si/SiGe heterojunction, and the applied voltage is VBE = Vj + ΔVn. ΔVp (> > kT/q) is the difference between quasi-Fermi energy levels Efp1 and Efp2. Using the Boltzmann distribution, the tunneling current can be written as [16]

$$J_{{\text{P}}} = J_{{{\text{PT}}}} = \frac{{4q\pi m_{{\text{h}}}^{*} (kT)^{2} P_{{\text{T}}} }}{{h^{3} }}\exp \left( { - \frac{{q\Delta V_{{\text{p}}} - E_{{{\text{fp}}1}} }}{kT}} \right),$$
(8)

where h is the Planck constant, \(m_{{\text{h}}}^{*}\) is the effective mass of holes,

$$P_{{\text{T,Si}}} = \exp ( - d\sqrt {\chi_{{\text{h}}} } )$$
Fig. 3
figure 3

Energy-band system of poly-Si/oxide-like layer/SSi cap layer

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is the tunneling probability of holes. The SSi cap layer is very thin and is uniformly doped with the concentration of Nd. χh increases ΔEV,SSi due to the upward shift of the valence band under the action of stress, and the tunneling probability becomes

$$P_{{\text{T,SSi}}} \approx \exp ( - d\sqrt {\chi_{{\text{h}}} + \Delta E_{{\text{V,SSi}}} } ).$$
(9)

Neglecting the recombination in the cap layer, the tunneling current is rewritten as

$$J_{{\text{P}}} = \frac{{qn_{{\text{i,SSi}}}^{2} P_{{\text{T,SSi}}} }}{{N_{{\text{D}}} }}\sqrt {\frac{kT}{{2\pi m_{{\text{h}}}^{*} }}} \exp \left( {\frac{{qV_{{\text{j}}} }}{kT}} \right) = \frac{{qn_{{\text{i,Si}}}^{2} }}{{G_{{\text{E,SSi}}} }}\exp \left( {\frac{{qV_{{{\text{BE}}}} }}{kT}} \right),$$
(10)

where ni,Si and ni,SSi are the intrinsic carrier concentrations of relaxed Si and SSi, respectively. The stress applied to the Si cap layer yields the downward shift of the conduction band, ΔVn is then increased by ΔEC,SSi/q, and the internal junction voltage is decreased by ΔVj = ΔEC,SSi/q. For the uniform doping base with a constant of Ge mole fraction, the Gummel number of the emitter region and the collector current density are as follows:

$$G_{{\text{E,SSi}}} = \frac{{N_{{\text{D}}} }}{{S_{{{\text{pE}}}} }}\frac{{n_{{{\text{i,}}\;{\text{Si}}}}^{2} }}{{n_{{{\text{i,}}\;{\text{SSi}}}}^{{2}} }}\exp \left( {\frac{{q\Delta V_{{\text{n}}} + \Delta E_{{\text{C,SSi}}} }}{kT}} \right),$$
(11)
$$J_{{\text{C}}} = \frac{{q\exp \left( {\frac{{qV_{{{\text{BE}}}} }}{kT}} \right)}}{{\left[ {\int_{0}^{{W_{{\text{B}}} }} {\frac{{N_{{\text{B}}} }}{{D_{{\text{B}}}^{*} (n_{{\text{i,SiGe}}}^{*} )^{2} }}{\text{d}}x} } \right]}} = \frac{{q(n_{{{\text{i}},{\text{SiGe}}}} )^{2} }}{{G_{{{\text{B}},{\text{SSi}}}} }}\exp \left( {\frac{{qV_{{{\text{BE}}}} }}{kT}} \right).$$
(12)

The recombination velocity is expressed as \(S_{{{\text{pE}}}} = P_{{\text{T,SSi}}} \sqrt {kT/2\pi m_{{\text{h}}}^{*} } .\) As discussed earlier, the additional stress leads to an increase in the intrinsic carrier concentration, i.e. \(n_{{\text{i,SiGe}}}^{*} > n_{{{\text{i}},{\text{SiGe}}}} .\) The minority carrier diffusion coefficient also increases in accordance with \(D_{{{\text{pE}}}}^{*} \propto \mu_{{{\text{nB}}}} = (1 + 3x)\mu_{{{\text{n0}}}}\)[17], where μn0 is the electron mobility of relaxed Si. It follows that because the additional stress makes the Ge fraction of Si1-xGex base increase equivalently, leading to an increase in \(D_{{\text{B}}}^{*}\). The Gummel number of the base region can be derived directly from Eq. (12) as

$$G_{{\text{B,SSi}}} = \frac{{(n_{{\text{i,SiGe}}} )^{2} }}{{(n_{{\text{i,SiGe}}}^{*} )^{2} }}\frac{{W_{{\text{B}}} N_{{\text{B}}} }}{{D_{{\text{B}}}^{*} }}\exp \left( {\frac{{q\Delta V_{{\text{n}}} + \Delta E_{{\text{C,SSi}}} }}{kT}} \right).$$
(13)

DC current gain is defined as β = GE,SSi/GB,SSi [16]; from Eqs. (12) and (13), we then have the following relationship:

$$\beta = \left( {\frac{1}{{S_{{{\text{pE}}}} }}} \right)\left( {\frac{{n_{{{\text{i,}}\;{\text{Si}}}}^{2} }}{{n_{{{\text{i,}}\;{\text{SSi}}}}^{{2}} }}} \right)\frac{{(n_{{\text{i,SiGe}}}^{*} )^{2} }}{{(n_{{\text{i,SiGe}}} )^{2} }}\left( {\frac{{D_{{\text{B}}}^{*} N_{{\text{D}}} }}{{W_{{\text{B}}} N_{{\text{B}}} }}} \right).$$
(14)

The product of RC and CBC in Eq. (5) represents the charge and discharge time of BC junction barrier capacitance, which has a significant effect on the frequency. There is a large amount of mobile charge in the BC junction barrier region. The width of the barrier region is related to JC. If only the effect of VBE on JC is considered, CBC can be approximated as

$$C_{{{\text{BC}}}} = \frac{{\text{d}}}{{{\text{d}}V_{{{\text{CB}}}} }}\left[ {\left( {qN_{{\text{C}}} - \frac{{J_{{\text{C}}} }}{{v_{{\text{S}}} }}} \right)W_{{{\text{BC}}}} } \right] \approx \left( {qN_{{\text{C}}} - \frac{{J_{{\text{C}}} }}{{v_{{\text{S}}} }}} \right)\frac{{{\text{d}}W_{{{\text{BC}}}} }}{{{\text{d}}V_{{{\text{CB}}}} }},$$
(15)

where vS is the electron saturation velocity in the collector region, WBC is the width of the depletion region of the BC junction, and it is also related to Jc, i.e.

$$W_{{{\text{BC}}}} = \sqrt {2\varepsilon_{{{\text{Si}}}} (V_{{{\text{bi}}}} + V_{{{\text{CB}}}} )/(qN_{{\text{C}}} - J_{{\text{C}}} /v_{{\text{S}}} )} .$$
(16)

The uniaxial stress in the collector region will narrow the band-gap of the collector region, hence, the built-in potential Vbi in the depletion region of the BC junction decreases and CBC increases, but JC is also affected by the stress. If the Ge mole fraction y of the stress raiser is very small, then the effect of stress on CBC is negligible [11]. In addition, considering that the stress of embedded Si1-yGey stress raiser increases with increasing values of y, dislocations can be introduced within the collector region. The dislocations in Si and Ge are mainly prismatic ones that can form suspended chains, and act as donors or acceptors, resulting in a compensation effect on the charge concentration. The dislocations can be considered as scattering centers and affect the mobility and resistivity, which will also affect the frequency characteristics under the action of larger stress.

4 Results and analysis

The physical models used for simulation are the concentration-dependent mobility model, the Auger recombination model, the stress model, the parallel electric field-dependent model, the band-gap narrowing model, the energy balance transport model, the Shockley–Read–Hall recombination model, and the Fermi–Dirac statistical model. After these models have been deployed, numerical methods such as Newton iteration and Gummel iteration are used to calculate the parameters of each grid to obtain the characteristics. In this section, the proposed structure is simulated using the ATHENA module of the SILVACO TCAD tools according to the process steps in Fig. 2, and the device structure file generated by the ATHENA module is imported into the ATLAS module for simulation. Based on the device architecture shown in Fig. 1, the parameters for simulation are listed in Table 1.

Table 1 Structural and process parameters for simulations
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Figure 4 shows the variation of the additional uniaxial stress in the collector region along the transport direction (longitudinal) for different Ge mole fractions of the stress raiser. It is clear that the stress raiser can effectively introduce stress within the collector region and that the generated stress increases significantly as the Ge fraction of the stress raiser increases.

Fig. 4
figure 4

Simulation result of longitudinal stress distribution in collector region

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The variation of the current gain with different stress raiser Ge mole fractions is represented in Fig. 5. When y is between 0 and 5%, the current gain decreases with increasing stress, after which it increases with increasing y values, but the increase is slight, which can be explained according to Eq. (14): The Si1−yGey stress raiser with Ge fraction between 0 and 5% produces very small stress (< 0.1 GPa), and with such small uniaxial compressive stress, the increase in the equivalent Ge mole fraction of the Si1-xGex base is negligible, ΔEg,SSi and ΔEV,SSi are also insignificant. Since χh is usually about 1 eV [15], the tunneling probability PT in Eq. (8) has little effect, which approximately yields \(\beta \propto \sqrt {m_{{\text{h}}}^{*} }\). The theoretical calculations show that the average effective mass of valence band decreases significantly for stress in the range 0 to 0.2 GPa, thus resulting in a slight decrease in β. When the stress is greater than 0.2 GPa, the magnitude of the band-gap shift increases with enhancing stress. As a result, the accumulation of holes, at the interface between the SSi cap layer and SiOr layer, is significantly diminished, then χh plays an important role in sustainably increasing β. In general, the first and second terms to the right of the equal sign in Eq. (14) decrease as stress increases, while the remaining terms increase as stress increases. When the Ge mole fraction y is small, term 1 causes β to decrease; on the contrary, terms 3 and 4 become the main factors that make β increase.

Fig. 5
figure 5

Variation of current gain with Ge mole fraction in stress raiser

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It is necessary to point that there are many factors affecting the characteristic frequency. The previous theoretical analysis is to provide relevant physical basis for analyzing the influence of applied uniaxial stress on the frequency performance and explain the physical mechanism behind in combination with the simulation results, rather than establish an accurate physical model. The distribution of the applied stress σxx along the x-direction is not uniform. By fitting the curve of Fig. 4 to σxx(x), the average stress magnitude over the transverse collector length, in the range of 0 to L, can be calculated as

$$< \sigma_{{{\text{xx}}}} > = \frac{1}{L}\int\limits_{0}^{L} {\sigma_{{{\text{xx}}}} (x){\text{d}}x} .$$
(17)

By substituting the calculation results of Eq. (17) into Eq. (4), the Ge mole fraction of the uni-biaxially strained base region under additional uniaxial stress conditions can be obtained according to the relationship between the Si1-xGex lattice constant and the Ge mole fraction x. The intrinsic carrier concentration of the base region and the diffusion coefficient can then be calculated, and the intrinsic carrier concentration of the SSi cap layer in the emitter region can likewise be obtained [18]. A comparison of the calculated results from Eq. (14) with the simulation results is also exhibited in Fig. 5. It can be found that the theoretical calculation results are basically consistent with the simulation results, which can illustrate the accuracy of the previous theoretical derivation. The reasons for the difference between the two are: (1) the thickness of the cap layer is so thin that, for the convenience of the analysis, it is approximated that no minority carriers are recombined in this layer and the effect of the thickness of the layer is ignored, (2) the interface states and recombination rate in the oxide-like layer are determined by the specific surface cleaning process, and more detailed physical modeling is dependent on the specific fabrication process, (3) to establish a more complete and accurate physical model of current gain, we also need to solve more complex device equations to calculate the distribution of minority carriers and various microscopic currents in the emitter region, which are beyond the scope of this work, and (4) the band-gap narrowing (BGN) effect has been ignored in the previous derivation for convenience, while the BGN model has been employed in the TCAD simulation.

Figure 6 gives the variation of the collector current JC with the BE junction voltage VBE and the Ge mole fraction y. It can be seen that the uniaxial additional stress does increase JC. According to Eq. (12), it is mainly because of the increase in minority carriers diffusion coefficient and the equivalent Ge mole fraction x in the base region caused by the stress raiser, but there is no change in the order of magnitude. This is due to the fact that the effective voltage Vj falling on the Si/SiGe heterojunction decreases as ΔEC,SSi increases. JC is generally enhanced by increasing y. In the collector region, the recombination rate of Si/SiGe interface caused by edge dislocation is enhanced as y increases; hence, the variation of JC with y is not significant, which is consistent with the experimental conclusion reported in [11]. Moreover, the theoretical results of JC, also exhibited in Fig. 6, are closer to the simulation results, which is because the electron current injected into the base region is little affected by the barrier height and surface states of the oxide-like layer [15], but mainly depends on the band shift.

Fig. 6
figure 6

Variation of collector current with Ge mole fraction in stress raiser

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Under the small-signal condition, once the common emitter current gain H21 and unidirectional transmission power gain U are reduced to 0 dB, the characteristic frequency at a certain collector current can be obtained according to the definitions of fT and fmax. For example, the variation of these two parameters with frequency f is simulated at different VBE conditions for y = 0.1, as shown in Fig. 7. By extracting the data from the curves, the frequency characteristic curves for different y can be obtained, as shown in Figs. 8 and 9. It is clear that fT and fmax are significantly increased compared to the case without the stress raiser (y = 0), by about 29.1% and 71.5%, respectively. The peak values of fT and fmax reached 507.7 GHz and 730.7 GHz for y = 0.15 and y = 0.1, respectively, entering the "half-THz" frequency band. According to the earlier analysis, the favorable factors leading to an increase in the characteristic frequency as additional stress increases are the increase in current gain, collector current, and interfacial recombination rate. In the base region, the additional uniaxial stress equivalently increases the Ge mole fraction x, resulting an increase in minority carrier diffusion coefficient and a simultaneous decrease in the resistance of the working base region, and in the emitter and collector regions, the stress increases the carrier mobility and reduces the series resistances.

Fig. 7
figure 7

a Variation of small-signal current gain H21, and b variation of power gain U, with frequency in unidirectional transmission

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Fig. 8
figure 8

Cut-off frequency response with different Ge mole fractions in stress raiser

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Fig. 9
figure 9

Maximum oscillation frequency response with different Ge mole fraction in stress raiser

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In Fig. 8, it should be mentioned that fT increases as y increases from 0 to 0.15 but decreases when y is between 0.15 and 0.3, which is mainly due to the influence of the edge dislocations in the collector region, as described above, on the product RC × CBC in Eq. (5). On the one hand, the barrier capacitance CBC is increased because part of mobile charge (JC/qvs) is counteracted by dislocations. On the other hand, the distorted lattices become the scattering centers. In the N−-doped collector region, the dislocations as the acceptor centers have anisotropic scattering effect on the carrier, reduces the electron mobility and increases the collector resistance. Therefore, the product RC × CBC in Eq. (5) is increases, resulting in a decrease in cut-off frequency.

Figure 9 depicts the variation of the maximum oscillation frequency with collector current for different Ge fraction y. From Eq. (6), the trend is similar to that of the cut-off frequency. At higher strain levels, CBC increases, but fT and fmax increase and then decrease as y increases. Note the change in fmax is greater than that in fT. In addition to the influence of CBC, the base resistance RB is also another factor. Qualitatively, this is most likely due to the thin base layer, where the dislocations at the Si/Si1-xGex interface act as a deep energy level, enhancing the recombination in the base region and reducing the concentration holes. The dislocations scattering mentioned above also has a negative effect on the mobility of holes. The impurity compensation and dislocations scattering effect lead to the increase in RB, which is greater than that of fT, thus worsening the fmax.

For more visual analysis of the frequency performance, the maximum variation of fT and fmax for different Ge mole fractions of the stress raiser is provided in Fig. 10. Obviously, the Ge fractions corresponding to the maximum of the two are different. When measuring the comprehensive performance of transistors, in fact, the product of some specific parameters is defined as the figure-of-merit (FoM) considering the correlation or restriction relationship of the parameters. The product fT × fmax is then used here to define the frequency FoM of the proposed SiGe HBT, so as to determine the fraction in the stress raiser when the best frequency performance is achieved. Also, it is clear that the product fT × fmax reaches its maximum value at y = 0.1, which represents the best frequency characteristics.

Fig. 10
figure 10

Defined frequency figure-of-merit with different Ge mole fractions in stress raiser

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As mentioned earlier, the SiGe HBT structure designed in this paper is similar to that of a 90-nm SSi pMOS transistor. In the pMOS transistors, since SiGe stress raiser is embedded in the source and drain, transverse compressive stress is then induced in the channel, improving the mobility of carriers and enhancing the channel current. Spontaneously, a real-time application of this work is the integration with 90-nm SSi CMOS transistors to form a BiCMOS inverter, which includes one pMOS transistor, two SiGe HBTs and three nMOS transistors, as given in Fig. 11. We now use ATHENA module in TCAD tools to construct the BiCMOS structure, the device-circuit hybrid simulation is carried out by using ATLAS module, and the influence of Ge mole fraction y on the delay time of the proposed SiGe HBT BiCMOS inverter is then explored. Figure 12a shows that the logic function of the inverter is correct, and Fig. 12b shows that the delay time in the falling edge of output signal decreases with the increase in Ge mole fraction of stress raiser used in the proposed SiGe HBT.

Fig. 11
figure 11

Circuit of BiCMOS inverter used in TCAD simulation

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Fig. 12
figure 12

a Timing sequence response and b delay time of proposed SiGe HBT BiCMOS inverter

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As mentioned in Sect. 1, the additional stresses are currently introduced in a variety of ways, and for the purpose of summary and comparison, Table 2 shows the effect of different stress types and different stress raisers on frequency performance in some previous works with similar device structures. The global additional stress used in [12] has the most obvious effect on the improvement of cut-off frequency, because the stress is as high as—1GPa, and it can be predicted that the greater the stress is, the more significant the enhancement may be, which is consistent with the simulated results of this work, but it is not necessarily that the greater the stress is, the better. The reasons are also analyzed before. The additional stresses in the other two references are actually fixed, which depend on the device process parameters. It should be pointed that, however, it is really difficult to estimate which has a better impact on the frequency performance because the device structures and process parameters even simulation methods are quite different. From these data available, it seems that embedding a stress raiser inside gives better frequency performance, as the stress acts over a larger scope, and it is believed that, by further improving the manufacturing process, we can obtain even better frequency performance.

Table 2 Improvements of fT and fmax with different stress types and different stress raisers
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5 Conclusion

In this work, a device structure for a scaled SiGe HBT with embedded Si1−yGey stress raiser in the collector region is designed. With the additional stress, the theoretical analysis shows that the improvement of the frequency characteristics is mainly due to the change of the strained Si/SiGe band structure, as well as the improvement of the physical parameters such as the current gain, the interface recombination rate and the RC × CBC product, while the effect of the dislocation scattering caused by the stress on the relevant physical parameters is also taken into account. The simulation results show that the additional stresses can significantly improve the frequency performance, and the Ge mole fraction in the stress raiser can be flexibly adjusted to achieve the enhancement of the characteristic frequency with different degrees. In particular, the proposed frequency FoM reaches a maximum at a Ge fraction of 0.1, which is similar to that of the SiGe source/drain in an SSi pMOS transistor fabricated with conventional 90-nm technology. The device structure proposed in this work has potential compatibility with Si-base CMOS technology, resulting in a BiCMOS device structure with a smaller size or layout size and better performance. It should be pointed that different additional stress introduction methods have been mentioned in this paper; however, it is really difficult to estimate which has a better impact on the frequency characteristics since the device structures and process parameters with these methods are quite different. It is believed that, by further improving the manufacturing process or device structures of, we can obtain even better frequency performance.