High Frequency Silicon-Germanium Heterostructure
Devices: Simulation and Analysis
BRISHBHAN PANWAR, GAGAN KHANDURI
Centre for Applied Research in Electronics
Indian Institute of Technology Delhi
Hauz-Khas, New-Delhi-110016
INDIA
Abstract: - An NPN Si/SiGe/Si double-heterojunction bipolar transistor (DHBT) and NPN Si/SiGe/SiGe single- heterojunction bipolar transistor (SiGe SHBT) structures have been simulated and their performance has been analyzed for high current applications. The performance of both the structures for current gain and cut-off frequency at high collector current density is analyzed using 2-dimensional MEDICI device simulator. A theoretical model is developed for both the structures and the predictions are observed to be in conformity with the simulated results. The comparison of results for current gain and cut-off frequency at high current densities predict better performance for the SiGe SHBT structure in comparison with the SiGe DHBT device. The improved performance of the SHBT structure is attributed to the base-collector homojunction of the structure, which prohibits the formation of retarding potential barrier at base-collector junction. This retarding potential barrier is prevalent in SiGe DHBT devices owing to valence band offset for the holes at base-collector heterojunction and degrades its high current performance.
Keywords: - SiGe, heterojunction, homojunction, retarding potential barrier, collector current density, valence band offset.
1 Introduction
The development in material systems and feasibility of integrating silicon germanium (SiGe) process with silicon (Si) technology has provided an impetus in the advancement of narrow bandgap SiGe base heterojunction structures. This has led to the realization of extremely high cut-off frequency of 30 GHz and maximum frequency of oscillation of 50 GHz in the Si/SiGe/Si NPN double-heterostructure bipolar transistors (DHBTs) [1,2]. However, the NPN Si/SiGe/Si narrow bandgap DHBT structures are observed to exhibit poor frequency response and rapid fall in the current gain at high collector current densities [3]. The degraded performance of SiGe DHBT structures is attributed to the valance band offset for holes at base-collector heterojunction, which gives genesis of retarding potential barrier for minority electrons at base-collector junction. A rapid decrease in the (ft), and current gain () for the collector current densities Jc exceeding the Kirk current density, JK , is predicted by Cottrel and Yu [3]. Therefore, alternate HBT structures without valence band offset for holes at base-collector junction need to be evolved for improving the current gain and cut-off frequencies at high collector currents. An alternative approach is to conceive a HBT structure with base-collector homojunction to inhibit the formation of retarding potential barrier at base-collector junction. In our recent work we have presented a theoretical formulation and simulations for a proposed Si/SiGe/SiGe Graded-Heterojunction transistor for improved current gain and cutoff frequency at high collector current densities [4]. However, the work on SiGe Graded-HBT is under the restrictions of minimum critical thickness limit and maximum Ge at% for SiGe layer.
Nevertheless, the recent advances in the growth of completely dislocation free SiGe bulk crystals having uniform Ge at% with adjustable lattice parameters and band gap has led to the development of completely new possibilities and applications for the use of SiGe heterostructures [5]. Sheng [6], in his recent work suggests the use of these bulk SiGe substrates for the growth of thick, lattice matched and strained SiGe epilayers. The present work uses the simulation and theoretical formulations as a step forward in considering such SiGe base and collector epilayers to avoid the formation of retarding potential barrier at base-collector junction. We have considered a worst case of unstrained (dislocation free) SiGe layer grown on bulk SiGe substrate in the proposed modeling and simulation of SiGe SHBT structure. However, the adaptation of the recent technological advancement relating to the growth of thick, lattice matched and strained SiGe epilayers on dislocation free bulk SiGe substrates need to be investigated for further enhanced performance of this structure.
The present paper proposes an NPN Si/SiGe/SiGe single-heterojunction bipolar transistor (SHBT) structure with uniform 20% germanium mole fraction in the unstrained base and collector regions. The SHBT structure compromises on the strain induced bandgap narrowing in unstrained SiGe base, but the selection of < 25 % Ge mole fraction in the base ensures that the loss in band gap narrowing effect is minimum [7]. The SiGe SHBT structure is simulated using two-dimensional MEDICI device simulator, known for its authenticated results at the device level for SiGe HBT structures [8], and its performance is compared with SiGe DHBT. The proposed SHBT structure shows significant improvement in current gain and cutoff frequency roll-off at high collector current densities.
2 Theory
In NPN silicon BJT, an expression relating the electron density nc with the collector current density Jc for constant drift velocity dsat condition is given as [9]:
(1)
At sufficiently high collector current density, the base-collector junction shifts into the collector space-charge region resulting in the vertical widening of the effective neutral base region width, and is known as Kirk phenomenon [9]. At the onset of Kirk phenomenon, (at Kirk current density Jk), the electron density in base-collector space charge region, nc (= nk, electron density at start of Kirk effect), is related with the device parameters by the expression:
(2)
Where the total voltage across base-collector junction (Vbctot) is the sum of built-in potential barrier at base-collector junction (Vbi) and the terminal base-collector voltage (Vbct). Nc is the collector-doping concentration, is the dielectric constant for Si, q is the electronic charge and Wc is the collector width as now whole collector width corresponds to space charge region.
In Si BJT, at the onset of Kirk phenomenon, holes are injected into the collector from the base to compensate the electron charge in collector, resulting in the formation of the current induced base. However, for SiGe DHBTs having a sizable alloy mole fraction, there is a valence band discontinuity for holes at base-collector junction. This valence band discontinuity suppresses injection of holes into the collector as ncexceeds nk. Eventually, there will be an accumulation of mobile electrons in collector due to velocity saturation and an accumulation of holes in base due to valence band offset at base-collector junction. The combination of these mobile electrons together with localized holes form a dipole layer, which in turn give rise to an electric field E0 at the base-collector junction. Any further increase in the collector current density will consequently increase the dipole strength and increases the electric field E0. The presence of the electric field E0 at base-collector heterojunction gives rise to a retarding potential barrier(Vbp) in conduction band, which opposes the flow of electrons from emitter to collector through the base. An increased electron density in the base at base-collector junction n(Wb) is now required to support and maintain the electron density nc and collector current density Jc. The electron density nc in base-collector space charge region for collector density Jc, in SiGe DHBT derived from the basic Poisson’s equation is:
(3)
The electron density in base at base-collector junction n(Wb)formaintaining nc inside base-collector space charge region is simply given by using current continuity and Boltzmann statistics across the retarding potential barrier Vbp :
(4)
where KT/q = VT is the thermal voltage.
The retarding potential barrier Vbp for electrons can be expressed as:
(5)
Where Ev is the valence band discontinuity for holes and Nbis the neutral base width. Solving Eq. (3), (4) and (5) for a uniformly doped base gives the effect of bias dependent retarding potential barrier Vbp and base-emitter biasing Vbeon the collector current density Jc as:
Jc = (6)
Where, ni0 is the intrinsic carrier concentration.
Eq. (4) predicts that an increased electron concentration n(Wb)in the base at base-collector junctionis required to maintain the electron concentration nc in base-collector space charge region. A corresponding increase in the number of electrons in the base at base-emitter junction is required to support electron diffusion across the base. The modified value of electron density in base at emitter-base junction n(0) is expressed as:
(7)
Where [nc (dsat Wb) / Dnb] is the electron density in the base at the base-emitter junction corresponding to the electron density in base-collector space-charge region nc. The second term in Eq. (7), [nc {exp (qVbp / KT)}] is the electron density in base at the base-emitter junction as a result of increased electron concentration in base at base-collector junction because of the retarding potential barrier at base-collector junction.
The effective valence band offset Ev (= Ev - Vbp) at emitter-base junction provides higher emitter injection efficiency of SiGe HBTs. It can be considered as the effective valence band offset accounting for the high current barrier effects, in terms of valence band discontinuityEv, and conduction band retarding potential barrier Vbp. The relation of the effective band offset Ev with electron density in the base at base-emitter junction n(0) and applied base emitter bias Vbe ( for a specific Jc) is expressed as:
(8)
Eqs. (7) and (8) show the effect of retarding potential barrier Vbp on electron density in the base at emitter-base junction n(0) and applied base-emitter voltage Vbe to sustain the collector current density Jc. The substitution of the expression for n(0) from the Eq. (7) in Eq. (8) predicts the necessity for an increase in Vbe to account for the increase in n(0) required to sustain the collector current density Jc. This requirement of increase in Vbe for a given collector current density Jc will be reflected as a fall in the current gain of the DHBT structure. This prediction is consistent with the discussion of Eq. (6) where an increase in retarding potential barrier Vbp at high collector current density predicts a fall in the DHBT collector current density Jc and current gain.
The term [nc {exp (qVbp / KT)}] on R.H.S. in Eq. (7) has been inducted to compensate for the retarding potential barrier for electrons, in order to sustain the Jc. This leads to increased charge storage in the base and the cutoff frequency ftDHBT for SiGe DHBT after taking into account the excess electronic charge stored in the base assumes the form:
(9)
Where ftSiGeis the peak cutoff frequency for SiGe HBT (without retarding potential barrier) and the additional term shows the degradation in the SiGe DHBT cut off frequency ftDHBT as a consequence of excess base charge.
The analysis of SiGe DHBT illustrates the formation of retarding potential barrier at base-collector junction due to valence band offset for holes. The theory also predicts a fall in the current gain and cut-off frequency at high collector current density as a consequence of this retarding potential Vbp.Whereas, in the proposed SiGe SHBT, there is absence of valence band offset for holes at base collector homojunction. Consequently, the SHBT structure does not give rise to the formation of retarding potential barrier for electrons at base-collector junction and promises higher current gain and cut-off frequency at high collector current density in comparison with SiGe DHBT structure.
3 Simulation Results for SiGe DHBT and SHBT Structures
The physical dimension and doping profiles for the different regions of NPN Si/SiGe/Si DHBT and Si/SiGe/SiGe SHBT structure are identical. The surface emitter doping of 5 × 1019 cm-3and its thickness We1 of 0.2 m are chosen to provide an ohmic contact in both the structures. The emitter doping of 6 × 1018 cm-3 and its thickness We2 of 0.1 m are selected to obtain lower emitter-base capacitance for improved frequency performance of the heterostructures under consideration. The collector doping of 2 × 1016 cm-3 and thickness Wc of 1.6 m has been chosen in both the structures. The SHBT structure possesses uniform 20 at% of germanium in collector in addition to 20 at% of germanium in the base of both SHBT and DHBT structures. The base thickness Wb of 0.1 and uniform base doping of 6.0 × 1017 cm-3 is chosen in the SiGe DHBT and SHBT structures.
The variation in the electron energy in the DHBT and SHBT structures at base-emitter voltage Vbe of 0.9 Volts and collector-emitter voltage Vce of 5.0 Volts is shown in Fig. 1.
Fig.1 Conduction band electron energy EC and valence band electron energy EV for SiGe DHBT and SiGe SHBT. Wbis the base width.
The SiGe DHBT structure operating at the collector current density Jc of 1.85 × 105 A-cm-2 predict a retarding potential barrier Vbp of approx. 0.0625 eV at the base-collector heterojunction for conduction band electrons. This potential barrier is a consequence of valence band offset for holes at base-collector junction as described earlier. The simulation results in Fig. 1 for the SHBT structure (for Jc of 2.79 × 105 A-cm-2) do not show any retarding potential barrier for electrons at base-collector homojunction, as there is no valence band offset for holes at base-collector junction.
The simulated results in Fig. 2 show net carrier concentration of approx. 4 1018 cm-3 and 5.14 1018 cm-3 in the base at emitter-base and base-collector junction in the DHBT structure for the collector current density Jc of 1.85 × 105 A-cm-2. This corresponds to an electron concentration n(0)of 9.82 1018 cm-3 and n(Wb) of 2.34 1018 cm-3 and a hole concentration of approx. 13.85 1018 cm-3 and 7.49 1018 cm-3 in the base at emitter-base and base-collector junction in the DHBT structure. On the other hand, a considerably lower net carrier concentration of approx. 2.4 1018 cm-3 and 3.6 1017 cm-3 is observed in the base at emitter-base and base-collector junction in the SHBT structure for an even higher collector current density of Jc of 2.79 × 105 A-cm-2 is observed.
Fig.2 Net carrier concentration in SiGe SHBT and SiGe DHBT at collector-emitter voltage Vce of 5 Volts and base-emitter voltage Vbe of 0.9 Volts.
This corresponds to an electron concentration n(0)of 5.34 1018 cm-3 and n(Wb) of 7.67 1017 cm-3 and a hole concentration of approx. 2.93 1018 cm-3 and 11.2 1017 cm-3 in the base at emitter-base and base-collector junction in the SHBT structure. Therefore, the simulation results predict a higher electron concentration in base at the emitter-base and base-collector junction in the DHBT structure in comparison with SHBT structure. This is consistent with the expression in Eq. (4) and Eq. (7), which predict an increase in electron concentration n(Wb) and n(0)in the DHBT structure with an increase in Vbp, in order to sustain the value of collector current density Jc.
The increase in net carrier concentration in the base at base-emitter and base-collector junctions in DHBT structure shown in Fig. 2 reflects the requirement of a concurrent increase in base-emitter biasing voltage Vbe. The expressions in Eq. (7) and (8) forecast the requirement of Vbe of approx. 0.9 volts in DHBT in comparison with Vbe of 0.845 volts in SHBT structure to sustain the current density Jc of 1.85 × 105 A-cm-2. This is confirmed by the Gummel plots showing the dependence of collector current density Jc and base current density Jb on the base-emitter bias voltage Vbe for DHBT and SHBT structures in Fig. 3. This requirement of a higher base-emitter biasing voltage Vbe to sustain the collector current density Jc will be reflected as a fall in the current gain (at high Jc)in the DHBT structure. The dependence of current gain on the collector current density for both the structures is shown in Fig. 4. The current gain of 40 in case of SHBT
Fig.3 Gummel plots for SiGe SHBT and SiGe DHBT.
structure and virtually zero in the DHBT structure is predicted by the simulation results for the collector current density of approx. 1.8 × 105 A-cm-2. Therefore, the SHBT structure achieves better current gain performance in comparison with DHBT at high collector current densities.
Fig.4 Current gain Vs. Collector current density plot for SiGe SHBT and SiGe DHBT.
At high collector current densities, the higher net carrier concentration in base at base-collector and base-emitter junction (Fig. 2), leads to minority charge storage in the base region of DHBT structure. The increase in the charge storage in the base of the DHBT structure due to retarding potential barrier, will lead to the fall in its cutoff frequency, as predicted by Eq. (9).
Fig.5 Cut-off frequency Vs. Collector current density plot for SiGe SHBT and SiGe DHBT.
Therefore, the SiGe SHBT promises to have a higher cutoff frequency in comparison with SiGe DHBT structure, as there is no retarding potential barrier and associated charge accumulation. The simulation results in Fig. 5 predict an order high cut-off frequency in the SHBT structure in comparison with DHBT structure at the collector current density of approx. 1.8 × 105 A-cm-2.
4 Conclusion
We have investigated, studied and simulated a SiGe DHBT along with a proposed NPN SiGe SHBT structure to obtain improved current gain and cut-off frequency performance at high collector current densities. A theoretical formulation is provided to supplement the simulation results predicting a higher current gain and improved cut-off frequency performance of the SHBT structure. The DHBT structure is found to suffer from the drawback of genesis of retarding potential barrier owing to valence band offset at base-collector heterojunction. The superior performance of the SiGe SHBT structure at high collector current density is attributed to the base-collector homojunction, which prohibits the formation of retarding potential barrier for minority electrons.