Chapter 6. Silicon-Germanium Technologies

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1 Chapter 6 licon-germanium Technologies 6.0 Introduction The design of bipolar transistors requires trade-offs between a number of parameters. To achieve a fast base transit time, hence achieving a high value of cut-off frequency, the base width W of the transistor needs to be very small as shown in the base transit time τ equation τ W 2D nb, where D nb is the electron diffusion coefficient in the base. However, there is a limit that the base width can be reduced. Otherwise punch-through of the base would occur when the emitter-base depletion region intersects the collector-base depletion region in the base. Thinner depletion regions can be achieved by increasing the base doping concentration, and hence one strategy for improving the performance of silicon bipolar transistors would be to increase the base doping concentration, so that narrower base width could be achieved without encountering punchthrough. The problem with this strategy is that increasing the base doping, degrades emitter efficiency γ e, encourage more recombination in the base meaning higher base current. Hence, the β value of the transistor as shown by equation DnbWE N β W N Ab De becomes smaller, where W E is the emitter width, N De is the donor doping concentration in the emitter, N Ab is the acceptor doping concentration in the base. This trade-off between gain and base transit time has remained as the main issue that limits the maximum achievable cut-off frequency of a silicon bipolar transistor. In practice, it is technologically difficult to obtain cut-off frequencies much higher than 50GHz in silicon bipolar transistors. In the 1990s a revolution in bipolar transistor design occurred with the emergence of silicon-germanium Ge Heterojunction ipolar Transistors HTs. Previously, heterojunction bipolar transistors had only been available limited the use of compound semiconductor technologies, such as AlGaAs/GaAs heterojunction because for effective heterojunction formation, it requires two semiconductors without mismatch lattice constant, as it is the situation for AlGaAs and GaAs. The lattice mismatch between silicon and germanium Ge is relatively large at 4.2% and hence it is very difficult to form a heterojunction between and Ge without the generation of mismatch

2 6 licon Germanium Technologies dislocations at the interface. However, materials research carried out earlier showed that a good heterojunction could be obtained if the Ge layer was thin and the Ge content is relatively low as low as 30% or less in silicon. In these circumstances, although the Ge layer is grown under strain but it fits perfectly onto the silicon lattice without the generation of mismatch dislocations. One must give credit to the epitaxial growth process that able to reproduce strained or pseudomorphic Ge layers that was the vital technology breakthrough leading to the emergence of the Ge HT. Figure 6.1 shows a cross-section of a typical Ge heterojunction bipolar transistor. The p + Ge base layer is grown after oxide isolation formation and is followed in the same growth step by the growth of a p-type cap. nglecrystal material is formed where the silicon collector is exposed and polycrystalline material over the oxide isolation. The boundary between these two types of material is shown by the dotted lines shown in Fig The polycrystalline material is heavily p + doped using an extrinsic base implant and then used to contact the base in a similar way to that employed in the double polysilicon bipolar transistor. The emitter is formed by diffusing arsenic from the polysilicon emitter to over-dope the cap n-type. The isolation is deep trench type refilled silicon dioxide. Ge HT has been produced with values of maximum frequency f max of over 300GHz, and with extremely low values of noise figure. Their main applications are in wireless communication systems and optical fiber communication systems. Ge HT is generally integrated with MOS transistors in a icmos technology, so that the HTs can be used in the radio frequency RF application. Figure 6.1: Cross-sectional view of a silicon-germanium heterojunction bipolar transistor

3 6.1 Material Properties of licon-germanium 6 licon Germanium Technologies Let discuss two most important material properties of silicon-germanium 1- xge x materials. They are the properties of pseudomorphic silicon-germanium that should be formed so that it would not have lattice mismatch when form a heterojunction with silicon crystal. The second property is to determine the critical thickness of 1-x Ge x that should have in order does not form strained mismatch junction with silicon. Other properties such as physical properties will not be discussed here Pseudomorphic licon-germanium 1-x Ge x has a diamond-like lattice structure and the lattice constant is given by Vegard s rule. a Ge a + x(a Ge a (6.1 x x 1 where x is the germanium fraction and a is the lattice constant. The lattice constant of silicon a is A, the lattice constant of germanium a Ge is A and the lattice mismatch is 4.2%. When a 1 x Ge x layer is grown on a silicon substrate, the lattice mismatch at the interface between the 1-x Ge x and the silicon has to be accommodated. This can either be done by compression of the 1-x Ge x layer so that it fits to the silicon lattice or by the creation of mismatch dislocations at the interface. These two possibilities are illustrated schematically in Fig In the former case, the 1-x Ge x layer adopts the silicon lattice spacing in the plane of the growth and hence the normally cubic 1-x Ge x crystal is distorted. When 1-x Ge x growth occurs in this way, the 1-x Ge x layer is under compressive strain and the layer is described as pseudomorphic layer. In the latter case, the 1-x Ge x layer is unstrained, or relaxed, and the lattice mismatch at the interface is accommodated by the formation of misfit dislocations. These mismatch dislocations generally lie in the plane of the interface, as shown in Fig. 6.2 but dislocations can also thread vertically through the 1-x Ge x layer

4 6 licon Germanium Technologies licon substrate Pseudomorphic Mismatch dislocation Figure 6.2: Illustration of pesudomorphic 1-x Ge x growth and mismatch dislocation formation Critical Thickness The question asked, what is a maximum thickness of 1-x Ge x that can be grown before relaxation of the strain occurs through the formation of mismatch dislocations? This is the critical thickness of the 1-x Ge x layer depends strongly on the germanium content as shown in Fig The original calculations of critical layer thickness were made by Matthews and lakeslee on the basis of the mechanical equilibrium of an existing threading dislocation. However, measurements of dislocation densities in 1-x Ge x showed, in many cases, no evidence of mismatch dislocations for 1-x Ge x layers considerably thicker than the Matthews-lakeslee limit. These results were explained by People and ean who calculated the critical thickness. From the figure, for a 30% germanium content, the critical thickness of the pseudomorphic 1-x Ge x is approximately 15nm using the original calculation by Matthews and lakeslee

5 6 licon Germanium Technologies Figure 6.3: Critical 1-x Ge x thickness as a function of germanium percentage 6.3 and-gap Engineering A Ge HT is produced by sandwiching a Ge base between a silicon collector and a silicon emitter. To understand the physical behavior of Ge heterojunction bipolar transistor HT, the band diagrams of a Ge heterojunction bipolar transistor and a bipolar transistor JT are compared in Fig The energy band diagram of the Ge HT is indicated by the solid line and that for the JT by the dashed line. In the valence band, the bandgap difference is seen as discontinuities at the emitter/base and collector/base heterojunctions, while in the conduction band it is seen as spikes. The majority of the band-gap difference between Ge and occurs in the valence band, so the valence band discontinuity is much bigger than the conduction band spike. For most practical purposes the conduction band spike is small that it has little effect on the electrical behavior of Ge heterojunction bipolar transistor. A comparison of the band diagrams in Fig. 6.4 shows that the barrier height to electron flow from emitter to base E b in conduction band is much smaller in the Ge HT than the JT. This means that the collector current at a given base-to-emitter voltage V E will be larger in a Ge heterojunction bipolar transistor than in a silicon bipolar transistor. The barrier height for the hole flows from the base to the emitter in valence band is approximately the same in the Ge heterojunction bipolar transistor and the silicon bipolar transistor,

6 6 licon Germanium Technologies which means that the base currents of the two types of device will be approximately the same. Figure 6.4: Energy band diagrams of -Ge heterojunction bipolar transistor (solid line and homojunction bipolar transistor (dashed line The Gummel plots of a comparable Ge HT and JT are shown in Fig It can be seen that the gain of the Ge HT is much higher than that of the JT and that this increased gain is due to an increased collector current. The increased collector current of a Ge HT can be thought of in another way. When Ge HT is used in circuit, the circuit is usually designed to operate at a given current. If a Ge HT and JT are compared at a given current, the Ge HT requires lower base-to-emitter V E as illustrated in Fig Lower V E in Ge HT circuit means lower power consumption

7 6 licon Germanium Technologies Figure 6.5: Comparison of Gummel plots of a Ge HT and a bipolar transistor showing the lower V E for the Ge heterojunction bipolar transistor 6.4 Electrical Parameters of Ge HT nce conduction band spike in the a Ge HT is very small, by including the effects of doping induced band-gap narrowing and germanium induced bandgap narrowing the collector current I C of a Ge HT is I C qa D 2 ( ( n ( W ( N b nb Ab i qv exp kt E ( NCN V ( N N C V Ge E exp kt G (6.2 where N C and N V are the effective density of state in conduction and valence bands respectively. nce the barrier height for the hole flows from the base to the emitter in valence band is approximately the same in the Ge HT and the JT then the base current I is equal to I qad n 2 2L W qv exp kt nb bo b E (6.3 b where n bo is the minority carrier concentration in base

8 6 licon Germanium Technologies nce the base current I is the same for both Ge HT and JT, the ratio of the current gain β Ge of the Ge HT and current gain β is taken as equal to the ratio of Ge HT collector current and JT collector current, which is equal to ( N N Ge C V Ge E G exp (6.4 ( N N kt β β C The base transit time τ of Ge HT is equal to V 2 W ( D b nb τ ( τ (6.5 2( Dnb ( D nb Ge Ge 6.5 Graded ase Ge HT One will find that the pseudomorphic Ge HT has large gain then JT and the cut-off frequency f T is has no changed much. An additional band-gap engineering concept can be applied to further reduce the base transit time and increase the cut-off frequency f T. This is done by graded base by increasing the content of Ge atom in emitter end to collector from zero mole to a value of not more than 0.3 mole. The graded profile and the energy band diagram of the base graded Ge HT is illustrated in Fig The band-gap at the collector is lower than that at the emitter. This gives a gradient on the conduction band, which acts as a built-in electric field E bi that would accelerate electrons as they move from the emitter to the collector. Figure 6.6: Profiles and energy band diagram of a Ge HT with a germanium graded base

9 6 licon Germanium Technologies Assuming uniform doping profile and linerly graded germanium profile across the base, the collector current is shown in equation (6.6. I C qadnbn W N exp( E 1 exp A 2 io G(0 qv exp kt / kt ( E / kt G(grade E E exp kt gb (NCN V (N VN C Ge E kt G(grad (6.6 where E G(0 is the germanium-induced band-gap narrowing at emitter end of the base, E G(W is the germanium-induced band-gap narrowing at collector end of the base, and E G(grade E G(0 - E G(W is the grading of germanium Ge across the base. D nb is the average diffusivity of electron in the graded Ge base. The gain equation follows eqation (6.7, which is β β (N E CN V Dnb Ge (N CN VDnb kt E 1 exp kt G(grade G(grade E exp kt Ge (6.7 The gain equation indicates that the enhancement varies exponentially with germanium concentration at emitter end of the base E G(0, whereas it varies linearly with grading E G(grade. This means that if the germanium content is graded from zero at the emitter end, a relative small gain enhancement wii be obtained. A trapezoidal germanium profile instead of triangular profile is needed for large gain enhancement as shown in Fig G(0 Figure 6.7: Options for germanium profiles in Ge HTs with graded germanium

10 6 licon Germanium Technologies The base transit time for the graded base Ge HT follows equation (6.8. τ W D kt E kt 1 E ( 1 exp( E / kt 2 G(grade (6.8 nb G(grade G(grde The ratio of base transit time for a grade base Ge HT compared with JT is shown in equation (5.9. τ τ 2kT E ( D kt 1 E ( exp( E / kt Ge nb G(grade (6.9 G(grade ( Dnb Ge G(grade The equation shows that the ratio is less than one for finite grading. This shall mean that graded base Ge HT improves the cut-off frequency. It has been shown that for a grading across the base of 100meV, the transit time improves by half. For collector design, it is necessary to consider the transit time and breakdown voltage. A thick collector layer results longer transit time. A thick collector layer means also lower electric field resulting lower drift velocity. It is possible to have lower electric field and high velocity by mean of adding an undoped layer collector with a p + pulse doped layer near the sub-collector for an npn HT transistor as shown in Fig Electron entering the collector layer can maintain its higher mobility of lower valley during most of the collector transit time. Such device is called ballistic collector transistor. This transistor has a better cut-off frequency response than the conventional Ge HT over a narrow range of bias voltages such as the collector base voltage. This device is being used for switching application and microwave power amplifications. Figure 6.8: allistic collector transistor

11 6 licon Germanium Technologies Exercises 6.1. State the reason why there is a limit that the base width can be reduced Describe how the transit time of carrier in the base affects the gain value of the bipolar transistor State the reason why pseudomorphic Ge- heterojunction bipolar transistor design has a higher gain than silicon bipolar junction transistor Calculate the lattice constant of 0.7 Ge 0.3 and percentage of lattice mismatch when it forms a heterojunction with silicon Assuming that the effective density of states in conduction band and valence are the same for both Ge HT and bipolar transistors, calculate the percentage gain in β value of Ge heterojunction HT over the silicon bipolar transistor design How the cut-off frequency of the pseudomorphic Ge HT be improved?

12 6 licon Germanium Technologies ibliography 1. Jasprit ngh, "Semiconductor Device", McGraw Hill Inc S. M. Sze, Semiconductor Devices: Physics and Technology, 2 nd Edition, John Wiley & Sons, Inc Peter Ashburn, Ge Heterojunction ipolar Transistors, John wiley,

13 6 licon Germanium Technologies allistic collector transistor...12 and-gap engineering...7 E Emitter efficiency...3 G Graded base Ge HT...10 Gummel plot...8 M Matthews and lakeslee...6 P Pseudomorphic silicon-germanium...4, 5 S Semiconductor Germanium...11 Ge...3 Ge... See Semiconductor Ge heterojunction bipolar transistor...4 licon germanium...3 V Vegard s rule

CONTENTS. 2.2 Schrodinger's Wave Equation 31. PART I Semiconductor Material Properties. 2.3 Applications of Schrodinger's Wave Equation 34

CONTENTS. 2.2 Schrodinger's Wave Equation 31. PART I Semiconductor Material Properties. 2.3 Applications of Schrodinger's Wave Equation 34 CONTENTS Preface x Prologue Semiconductors and the Integrated Circuit xvii PART I Semiconductor Material Properties CHAPTER 1 The Crystal Structure of Solids 1 1.0 Preview 1 1.1 Semiconductor Materials