Tài liệu Semiconductor MaterialsS. K. Tewksbury Microelectronic Systems Research Center Dept. of Electrical ppt

Semiconductor Materials S K Tewksbury Microelectronic Systems Research Center Dept of Electrical and Computer Engineering West Virginia University Morgantown, WV 26506 (304)293-6371 Sept 21, 1995 Contents Introduction 2 Crystalline Structures 2.1 Basic Semiconductor Materials Groups 2.1.1 Elemental (IV-IV) Semiconductors 2.1.2 Compound III-V Semiconductors 2.1.3 Compound II-VI Semiconductors 2.2 Three-Dimensional Crystal Lattice 2.3 Crystal Directions and Planes 3 6 Energy Bands and Related Semiconductor Parameters 3.1 Conduction and Valence Band 3.2 Direct Gap and Indirect Gap Semiconductors 3.3 Effective Masses of Carriers 3.4 Intrinsic Carrier Densities 3.5 Substitutional Dopants 12 13 14 16 Carrier Transport 4.1 Low Field Mobilities 4.2 Saturated Carrier Velocities 18 19 21 Crystalline Defects 5.1 Point Defects 5.2 Line Defects 5.3 Stacking Faults and Grain Boundaries 5.4 Unintentional Impurities 5.5 Surface Defects: The Reconstructed Surface 23 23 24 26 26 27 Summary 29 Introduction A semiconductor material has a resistivity lying between that of a conductor and that of an insulator However, in contrast to the granular materials used for resistors, a semiconductor establishes its conduction properties through a complex quantum mechanical behavior within a periodic array of semiconductor atoms, i.e., within a crystalline structure For appropriate atomic elements, the crystalline structure leads to a disallowed energy band between the energy level of electrons bound to the crystal’s atoms and the energy level of electrons free to move within the crystalline structure (i.e., not bound to an atom) This “energy gap” fundamentally impacts the mechanisms through which electrons associated with the crystal’s atoms can become free and serve as conduction electrons The resistivity of a semiconductor is proportional to the free carrier density, and that density can be changed over a wide range by replacing a very small portion (about in 106 ) of the base crystal’s atoms with different atomic species (doping atoms) The majority carrier density is largely pinned to the net dopant impurity density By selectively changing the crystalline atoms within small regions of the crystal, a vast number of small regions of the crystal can be given different conductivities In addition, some dopants establish the electron carrier density (free electron density) while others establish the “hole” carrier density (holes are the dual of electrons within semiconductors) In this manner, different types of semiconductor (n-type with much higher electron carrier density than the hole density and p-type with much higher hole carrier density than the electron carrier density) can be located in small but contacting regions within the crystal By applying electric fields appropriately, small regions of the semiconductor can be placed in a state in which all the carriers (electron and hole) have been expelled by the electric field, and that electric field sustained by the exposed dopant ions This allows electric switching between a conducting state (with a settable resistivity) and a non-conducting state (with conductance vanishing as the carriers vanish) This combination of localized regions with precisely controlled resistivity (dominated by electron conduction or by hole conduction) combined with the ability to electronically control the flow of the carriers (electrons and holes) leads to the semiconductors being the foundation for contemporary electronics This foundation is particularly strong because a wide variety of atomic elements (and mixtures of atomic elements) can be used to tailor the semiconductor material to specific needs The dominance of silicon semiconductor material in the electronics area (e.g., the VLSI digital electronics area) contrasts with the rich variety of semiconductor materials widely used in optoelectronics In the latter case, the ability to adjust the bandgap to desired wavelengths of light has stimulated a vast number of optoelectronic components, based on a variety of technologies Electronic components also provide a role for non-silicon semiconductor technologies, particularly for very high bandwidth circuits which can take advantage of the higher speed capabilities of semiconductors using atomic elements similar to those used in optoelectronics This rich interest in non-silicon technologies will undoubtedly continue to grow, due to the rapidly advancing applications of optoelectronics, for the simple reason that silicon is not suitable for producing an efficient optical source This chapter provides an overview of many of the semiconductor materials in use To organize the information, the topic is developed from the perspective of the factors contributing to the electronic behavior of devices created in the semiconductor materials Section discusses the underlying crystalline structure and the semiconductor parameters which result from that structure Section discusses the energy band properties in more detail, extracting the basic semiconductor parameters related to those energy bands Section discusses carrier transport Crystalline defects, which can profoundly impact the behavior of devices created in the semiconductors, are reviewed in Section Crystalline Structures 2.1 Basic Semiconductor Materials Groups Most semiconductor materials are crystals created by atomic bonds through which the valence band of the atoms are filled with electrons through sharing of an electron from each of four nearest neighbor atoms These materials include semiconductors composed of a single atomic species, with the basic atom having four electrons in its valence band (supplemented by covalent bonds to four neighboring atoms to complete the valence band) These elemental semiconductors therefore use atoms from group IV of the atomic chart Other semiconductor materials are composed of two atoms, one from group N (N < 4) and the other from group M (M > 4) with N + M = 8, filling the valence bands with electrons The major categories of semiconductor material are summarized below 2.1.1 Elemental (IV-IV) Semiconductors Elemental semiconductors consist of crystals composed of only a single atomic element from group IV of the periodic chart, i.e., germanium (Ge), silicon (Si), carbon (C), and tin (Sn) Silicon is the most commonly used electronic semiconductor material, and is also the most common element on earth Table summarizes the naturally occurring abundance of some elements used for semiconductors, including non-elemental (compound) semiconductors Table 1: Abundance (fraction of elements occurring on earth) of common elements used for semiconductors Element Abundance Si Ga As Ge Cd In 0.28 1.5 × 10−5 1.8 × 10−6 × 10−6 × 10−7 × 10−7 Figure 1a illustrates the covalent bonding (sharing of outer shell, valence band electrons by two atoms) through which each group IV atom of the crystal is bonded to four neighboring group IV atoms, creating filled outer electron bands of electrons In addition to crystals composed of only a single group IV atomic species, one can also create semiconductor crystals consisting of two or more atoms, all from group IV For example, silicon carbide (SiC) has been investigated for high temperature applications Six Ge1−x semiconductors are under present study to achieve bandgap engineering within the silicon system In this case, a fraction x (0 < x < 1) of the atoms in an otherwise silicon crystal are silicon while a fraction − x have been replaced by germanium This ability to replace a single atomic element with a combination of two atomic elements from the same column of the periodic chart appears in the other categories of semiconductor described below (and is particularly important for optoelectronic devices) Group IV Group III Group V Group II Group VI Si Ga As Cd Se IV IV IV IV III V III V II VI II VI IV IV IV IV V III V III VI II VI II IV IV IV IV III V III V II VI II VI IV IV IV IV V III V III VI II VI II (a) (b) (c) Figure 1: Bonding arrangements of atoms in semiconductor crystals (a) Elemental semiconductor such as silicon (b) Compound III-V semiconductor such as GaAs (c) Compound II-VI semiconductor such as CdS 2.1.2 Compound III-V Semiconductors The III-V semiconductors are prominent (and will gain in importance) for applications of optoelectronics In addition, III-V semiconductors have a potential for higher speed operation than silicon semiconductors in electronics applications, with particular importance for areas such as wireless communications The compound semiconductors have a crystal lattice constructed from atomic elements in different groups of the periodic chart The III-V semiconductors are based on an atomic element A from Group III and an atomic element B from Group V Each Group III atom is bound to four Group V atoms, and each Group V atom is bound to four Group III atoms, giving the general arrangement shown in Figure 1b The bonds are produced by sharing of electrons such that each atom has a filled (8 electron) valence band The bonding is largely covalent, though the shift of valence charge from the Group V atoms to the Group III atoms induces a component of ionic bonding to the crystal (in contrast to the elemental semiconductors which have purely covalent bonds) Representative III-V compound semiconductors are GaP, GaAs, GaSb, InP, InAs, and InSb GaAs is probably the most familiar example of III-V compound semiconductors, used for both high speed electronics and for optoelectronic devices Optoelectronics has taken advantage of ternary and quaternary III-V semiconductors to establish optical wavelengths and to achieve a variety of novel device structures The ternary semiconductors have the general form (Ax , A1−x )B (with two group III atoms used to fill the group III atom positions in the lattice) or A(Bx , B1−x ) (using two group V atoms in the Group V atomic positions in the lattice) The quaternary semiconductors use two Group III atomic elements and two Group V atomic elements, yielding the general form (Ax , A1−x )(By , B1−y ) In such constructions, ≤ x ≤ Such ternary and quaternary versions are important since the mixing factors (x and y) allow the bandgap to be adjusted to lie between the bandgaps of the simple compound crystals with only one type of Group III and one type of Group V atomic element The adjustment of wavelength allows the material to be tailored for particular optical wavelengths, since the wavelength λ of light is related to energy (in this case the gap energy Eg ) by λ = hc/Eg , where h is Plank’s constant and c is the speed of light Table provides examples of semiconductor laser materials and a representative optical wavelength for each, providing a hint of the vast range of combinations which are available for optoelectronic applications Table 3, on the other hand, illustrates the change in wavelength (here corresponding to color in the visible spectrum) by adjusting the mixture of a ternary semiconductor Table 2: Semiconductor optical sources and representative wavelengths Material layers used ZnS AlGaInP/GaAs AlGaAs/GaAs GaInAsP/InP InGaAsSb/GaSb AlGaSb/InAsSb/GaSb PbSnTe/PbTe wavelength 454 580 680 1580 2200 3900 6000 nm nm nm nm nm nm nm Table 3: Variation of x to adjust wavelength in GaAsx P1−x semiconductors Ternary Compound GaAs0.14 P0.86 GaAs0.35 P0.65 GaAs0.6 P0.4 Color Yellow Orange Red In contrast to single element elemental semiconductors (for which the positioning of each atom on a lattice site is not relevant), III-V semiconductors require very good control of stoichiometry (i.e., the ratio of the two atomic species) during crystal growth For example, each Ga atom must reside on a Ga (and not an As) site and vice versa For these and other reasons, large III-V crystals of high quality are generally more difficult to grow than a large crystal of an elemental semiconductor such as Si 2.1.3 Compound II-VI Semiconductors These semiconductors are based on one atomic element from Group II and one atomic element from Group VI, each type being bonded to four nearest neighbors of the other type as shown in Figure 1c The increased amount of charge from Group VI to Group II atoms tends to cause the bonding to be more ionic than in the case of III-V semiconductors II-VI semiconductors can be created in ternary and quaternary forms, much like the III-V semiconductors Although less common than the III-V semiconductors, the II-VI semiconductors have served the needs of several important applications Representative II-VI semiconductors are ZnS, ZnSe,and ZnTe (which form in the zinc blende lattice structure discussed below); CdS and CdSe, (which can form in either the zinc blende or the wurtzite lattice structure) and CdTe which forms in the wurtzite lattice structure 2.2 Three-Dimensional Crystal Lattice The two-dimensional views illustrated in the previous section provide a simple view of the sharing of valence band electrons and the bonds between atoms However, the full 3-D lattice structure is considerably more complex than this simple 2-D illustration Fortunately, most semiconductor crystals share a common basic structure, developed below FCC Lattice A FCC Lattice B (a) (b) (c) Figure 2: Three-dimensional crystal lattice structure (a) Basic cubic lattice (c) Facecentered cubic (fcc) lattice (c) Two interpenetrating fcc lattices In this figure, the dashed lines between atoms are not atomic bonds but instead are used merely to show the basic outline of the cube The crystal structure begins with a cubic arrangement of atoms as shown in Figure 2a This cubic lattice is extended to a face-centered cubic (fcc) lattice, shown in 2b, by adding an atom to the center of each face of the cube (leading to a lattice with 14 atoms) The lattice constant is the side dimension of this cube The full lattice structure combines two of these fcc lattices, one lattice interpenetrating the other (i.e., the corner of one cube is positioned within the interior of the other cube, with the faces remaining parallel), as illustrated in Figure 2c For the III-V and II-VI semiconductors with this fcc lattice foundation, one fcc lattice is constructed from one type of element (e.g., type III) and the second fcc lattice is constructed from the other type of element (e.g., group V) In the case of ternary and quaternary semiconductors, elements from the same atomic group are placed on the same fcc lattice All bonds between atoms occur between atoms in different fcc lattices For example, all Ga atoms in the GaAs crystal are located on one of the fcc lattices and are bonded to As atoms, all of which appear on the second fcc lattice The interatomic distances between neighboring atoms is therefore less than the lattice constant For example, the interatomic spacing of Si atoms is 2.35 ˚ but A the lattice constant of Si is 5.43 ˚ A If the two fcc lattices contain elements from different groups of the periodic chart, the overall crystal structure is called the zinc blende lattice In the case of an elemental semiconductor such as silicon, silicon atoms appear in both fcc lattices and the overall crystal structure is called the diamond lattice (carbon crystallizes into a diamond lattice creating true diamonds, and carbon is a group IV element) As in the discussion regarding III-V semiconductors above, the bonds between silicon atoms in the silicon crystal extend between fcc sublattices Although the common semiconductor materials share this basic diamond/zinc blende lattice structure, some semiconductor crystals are based on a hexagonal close-packed (hcp) lattice Examples are CdS and CdSe In this example, all the Cd atoms are located on one hcp lattice while the other atom (S or Se) is located on a second hcp lattice In the spirit of the diamond and zinc blende lattices above, the complete lattice is constructed by interpenetrating these two hcp lattices The overall crystal structure is called a wurtzite lattice Type IV-VI semiconductors (PbS, PbSe, PbTe, and SnTe) exhibit a narrow band gap and have been used for infrared detectors The lattice structure of these example IV-VI semiconductors is the simple cubic lattice (also called an NaCl lattice) 2.3 Crystal Directions and Planes Crystallographic directions and planes are important in both the characteristics and the applications of semiconductor materials since different crystallographic planes can exhibit significantly different physical properties For example, the surface density of atoms (atoms/cm2 ) can differ substantially on different crystal planes A standardized notation (the so-called Miller indices) is used to define the crystallographic planes and directions normal to those planes The general crystal lattice defines a set of unit vectors (a,b, and c) such that an entire crystal can be developed by copying the unit cell of the crystal and duplicating it at integer offsets along the unit vectors, i.e., replicating the basis cell at positions na a + nb b + nc c, where na , nb , and nc are integers The unit vectors need not be orthogonal in general For the cubic foundation of the diamond and zinc blende structures, however, the unit vectors are in the orthogonal x, y, and z directions Figure shows a cubic crystal, with basis vectors in the x,y, and z directions Superimposed on this lattice are three planes (Figures 3a, b and c) The planes are defined relative to the crystal axes by a set of three integers (h, k, l) where h corresponds to the plane’s intercept with the x-axis, k corresponds to the plane’s intercept with the y-axis and l corresponds to the plane’s intercept with the z-axis Since parallel planes are equivalent planes, the intercept integers are reduced to the set of the three smallest integers having the same ratios as the above intercepts The (100), (010) and (001) planes correspond to the faces of the cube The (111) plane is tilted with respect to the cube faces, intercepting the x, y, and z axes at 1, 1, and 1, respectively In the case of a negative axis intercept, the corresponding Miller index is given as an integer and a bar over the integer,e.g., (¯ 100), i.e., similar to (100) plane but intersecting x-axis at -1 z y x (a) (b) (c) Figure 3: Examples of crystallographic planes within a cubic lattice organized semiconductor crystal (a) (010) plane (b) (110) plane (c) (111) plane Additional notation is used to represent sets of planes with equivalent symmetry and to represent directions For example, {100} represents the set of equivalent planes (100), (¯ 100) ¯ (001), and (00¯ The direction normal to the (hkl) plane is designated [hkl] (010), (010), 1) The different planes exhibit different behavior during device fabrication and impact electrical device performance differently One difference is due to the different reconstructions of the crystal lattice near a surface to minimize energy Another is the different surface density of atoms on different crystallographic planes For example, in Si the (100), (110), and (111) planes have surface atom densities (atoms per cm2 ) of 6.78×1014 , 9.59×1014 , and 7.83×1014 , respectively Energy Bands and Related Semiconductor Parameters A semiconductor crystal establishes a periodic arrangement of atoms, leading to a periodic spatial variation of the potential energy throughout the crystal Since that potential energy varies significantly over interatomic distances, quantum mechanics must be used as the basis for allowed energy levels and other properties related to the semiconductor Different semiconductor crystals (with their different atomic elements and different inter-atomic spacings) lead to different characteristics However, the periodicity of the potential variations leads to several powerful general results applicable to all semiconductor crystals Given these general characteristics, the different semiconductor materials exhibit properties related to the variables associated with these general results A coherent discussion of these quantum mechanical results is beyond the scope of this chapter and we therefore take those general results as given In the case of materials which are semiconductors, a central result is the energymomentum functions defining the state of the electronic charge carriers In addition to the familiar electrons, semiconductors also provide holes (i.e positively charged particles) which behave similarly to the electrons Two energy levels are important: one is the energy level (conduction band) corresponding to electrons which are not bound to crystal atoms and which can move through the crystal and the other energy level (valence band) corresponds to holes which can move through the crystal Between these two energy levels, there is a region of “forbidden” energies (i.e., energies for which a free carrier can not exist) The separation between the conduction and valence band minima is called the energy gap or band gap The energy bands and the energy gap are fundamentally important features of the semiconductor material and are reviewed below 3.1 Conduction and Valence Band In quantum mechanics, a “particle” is represented by a collection of plane waves (ej(ωt−k·x) ) where the frequency ω is related to the energy E according to E = hω and the momentum ¯ p is related to the wave vector by p = hk In the case of a classical particle with mass m ¯ moving in free space, the energy and momentum are related by E = p2 /(2m) which, using the relationship between momentum and wave vector, can be expressed as E = (¯ k)2 /(2m) h In the case of the semiconductor, we are interested in the energy/momentum relationship for a free electron (or hole) moving in the semiconductor, rather than moving in free space In general, this E-k relationship will be quite complex and there will be a multiplicity of E-k “states” resulting from the quantum mechanical effects One consequence of the periodicity of the crystal’s atom sites is a periodicity in the wave vector k, requiring that we consider only values of k over a limited range (with the E-k relationship periodic in k) Figure illustrates a simple example (not a real case) of a conduction band and a valence band in the energy-momentum plane (i.e., the E vs k plane) The E vs k relationship of the conduction band will exhibit a minimum energy value and, under equilibrium conditions, the electrons will favor being in that minimum energy state Electron energy levels above this minimum (Ec ) exist, with a corresponding value of momentum The E vs k relationship for the valence band corresponds to the energy-momentum relationship for holes In this case, the energy values increase in the direction toward the bottom of the page and the “minimum” valence band energy level Ev is the maximum value in Figure When an electron bound to an atom is provided with sufficient energy to become a free electron, a Energy E Conduction band minimum (free electrons) Ec Energy gap Eg Ev Valence band minimum (free holes) L [111] direction Γ Κ [100] direction k k Figure 4: General structure of conduction and valence bands hole is left behind Therefore, the energy gap Eg = Ec − Ev represents the minimum energy necessary to generate an electron-hole pair (higher energies will initially produce electrons with energy greater than Ec , but such electrons will generally lose energy and fall into the potential minimum) The details of the energy bands and the bandgap depend on the detailed quantum mechanical solutions for the semiconductor crystal structure Changes in that structure (even for a given semiconductor crystal such as Si) can therefore lead to changes in the energy band results Since the thermal coefficient of expansion of semiconductors is nonzero, the band gap depends on temperature due to changes in atomic spacing with changing temperature Changes in pressure also lead to changes in atomic spacing Though these changes are small, the are observable in the value of the energy gap Table gives the room temperature value of the energy gap Eg for several common semiconductors, along with the rate of change of Eg with temperature (T ) and pressure (P ) at room temperature The temperature dependence, though small, can have a significant impact on carrier densities A heuristic model of the temperature dependence of Eg is Eg (T ) = Eg (0o K) − αT /(T + β) Values for the parameters in this equation are provided in Table Between 0K and 1000K, the values predicted by this equation for the energy gap of GaAs are accurate to about × 10−3 eV (electron volts) 10 Group IV Semiconductor Si Group IV III Acceptor Substitutes Group IV Accepts electron to mimic Si V Donor Forfeits electron to mimic Si (a) Group III-V Semiconductor Ga Group III II Acceptor Substitutes Group V Substitutes Group III Accepts electron to mimic Ga As Group V IV Acceptor IV Donor Forfeits electron to mimic Ga Accepts electron to mimic As VI Donor Forfeits electron to mimic As (b) Figure 6: Substitution of dopant atoms for crystal atoms (a) IV-IV semiconductors (e.g., silicon) (b) III-V semiconductors (e.g., GaAs) Carrier Transport Currents in semiconductors arise both due to movement of free carriers in the presence of an electric field and due to diffusion of carriers from high, carrier density regions into lower, carrier density regions Currents due to electric fields are considered first In earlier discussions, it was noted that the motion of an electron in a perfect crystal can be represented by a free electron with an effective mass m∗ somewhat different than the e 18 real mass me of an electron In this model, once the effective mass has been determined, the atoms of the perfect crystal can be discarded and the electron viewed as moving within free space If the crystal is not perfect, however, those deviations from perfection remain after the perfect crystal lattice has been discarded and act as scattering sites within the “free space” seen by the electron in the crystal Substitution of a dopant for an element of the perfect crystal leads to a distortion of the perfect lattice from which electrons can scatter If that substitutional dopant is ionized, the electric field of that ion adds to the scattering Impurities located at interstitial sites (i.e., between atoms in the normal lattice sites) also disrupt the perfect crystal and lead to scattering sites Crystal defects (e.g., a missing atom) disrupt the perfect crystal and appears as a scattering site in the “free space” seen by the electron In useful semiconductor crystals, the density of such scattering sites is small relative to the density of silicon atoms As a result, removal of the silicon atoms through use of the effective mass leaves a somewhat sparsely populated space of scattering sites The perfect crystal corresponds to all atomic elements at the lattice positions and not moving, a condition which can occur only at 0K At temperatures above absolute zero, the atoms have thermal energy which causes them to move away from their ideal site As the atom moves away from the nominal, equilibrium site, forces act to return it to that site, establishing the conditions for a classical oscillator problem (with the atom oscillating about its equilibrium location) Such oscillations of an atom can transfer to a neighboring atom (by energy exchange), leading to the oscillation propagating through space This wave-like disturbance is called a phonon and serves as a scattering site (phonon scattering, also called lattice scattering) which can appear anywhere in the crystal 4.1 Low Field Mobilities The dominant scattering mechanisms in silicon are ionized impurity scattering and phonon scattering, though other mechanisms such as mentioned above contribute Within this “free space” contaminated by scattering centers, the free electron moves at a high velocity (the thermal velocity vtherm ) set by the thermal energy (kB T ) of the electron, with 2kB T /3 = 0.5m∗ vtherm and therefore vtherm = 4kB T /3m∗ At room temperature in Si, the thermal e e velocity is about 1.5 × 107 cm/sec, substantially higher than most velocities which will be induced by applied electric fields or by diffusion Thermal velocities depend reciprocally on effective mass, with semiconductors having lower effective masses displaying higher thermal velocities than semiconductors with higher effective masses At these high thermal velocities, the electron will have an average mean time τn between collisions with the scattering centers during which it is moving as a free electron in free space It is during this period between collisions that an external field acts on the electron, creating a slight displacement of the orbit of the free electron Upon colliding, the process starts again, producing again a slight displacement in the orbit of the free electron This displacement divided by the mean free time τn between collisions represents the velocity component induced by the external electric field In the absence of such an electric field, the electron would be scattered in random directions and display no net displacement in time With then applied electric field, the 19 electron has a net drift in the direction set by the field For this reason, the induced velocity component is called the drift velocity and the thermal velocities can be ignored By using the standard force equation F = eE = m∗ dv/dt with velocity v = at time e t = and with an acceleration time τn , the final velocity vf after time τn is then simply vf = eτn E/m∗ and, letting vdrif t = vf /2, vdrif t = eτn E/(2m∗ ) e e The drift velocity vdrif t in an external field E is seen above to vary as vdrif t = µn E, where the electron’s low field mobility µn is given approximately by µn ≈ eτn /(2m∗ ) Similarly, e holes are characterized by a low field mobility µp ≈ eτp /(2m∗ ), where τp is the mean time h between colisions for holes This simplified mobility model yields a mobility which is inversely proportional to the effective mass The effective electron masses in GaAs and Si are 0.09me and 0.26me , respectively, suggesting a higher electron mobility in GaAs than in Si (in fact, the electron mobility in GaAs is about times greater than that in Si) The electron and hole effective masses in Si are 0.26me and 0.38me , respectively, suggesting a higher electron mobility than hole mobility in Si (in Si, µn ≈ 1400 cm2 /V · sec and µp ≈ 500 cm2 /V · sec) The simplified model for µn and µp above is based on the highly simplified model of the scattering conditions encountered by carriers moving with thermal energy Far more complex analysis is necessary to obtain theoretical values of these mobilities For this reason, the approximate model should be regarded as a guide to mobility variations among semiconductors and not as a predictive model Table 8: Conductivity effective masses for common semiconductors Ge m∗ e m∗ h Si GaAs 0.12 m0 0.23 m0 0.26 m0 0.38 m0 0.063 m0 0.53 Table 9: Mobility and temperature dependence at 300K Mobility is in cm2 /V · sec Adapted from [11] Ge µn Mobility Temperature dependence Si µp µn µp GaAs µn µp 3900 T −1.66 1900 T −2.33 1400 T −2.5 470 T −2.7 8000 340 – T −2.3 The linear dependence of the mobility µn (µp ) on τn (τp ), suggested by the simplified development above, also provides a qualitative understanding of the mobility dependence on impurity doping and on temperature As noted earlier, phonon scattering and ionized impurity scattering are the dominant mechanisms controlling the scattering of carriers in most semiconductors At room temperature and for normally used impurity doping concentrations, phonon scattering typically dominates ionized impurity scattering As the temperature decreases, the thermal energy of the crystal atoms decreases, leading to a decrease 20 in the phonon scattering and an increase in the mean free time between phonon scattering events The result is a mobility µphonon which increases with decreasing temperature according to µphonon ≈ B1 T −α where α is typically between 1.6 and 2.8 at 300K Table gives the room temperature mobility and temperature dependence of mobility at 300K for Ge, Si, and GaAs In the case of ionized impurity scattering, the lower temperature leads to a lower thermal velocity, with the electrons passing ionized impurity sites more slowly and suffering a stronger scattering effect As a result, the mobility µion decreases with decreasing temperature Starting at a sufficiently high temperature that phonon scattering dominates, the overall mobility will initially increase with decreasing temperature until the ionized impurity scattering becomes dominant, leading to subsequent decreases in the overall mobility with decreasing temperature In Si, Ge, and GaAs, for example, the mobility increases by a factor of roughly at 77K relative to the value at room temperature, illustrating the dominant role of phonon scattering in these semiconductors under normal doping conditions Since scattering probabilities for different mechanisms add to yield the net scattering probability which, in turn, defines the overall mean free time between collisions, mobilities (e.g., phonon scattering mobility and lattice scattering mobility) due to different mechanisms −1 are combined as µ−1 = µ−1 phonon + µion , i.e., the smallest mobility dominates The mobility due to lattice scattering depends on the density of ionized impurity sites, with higher impurity densities leading to shorter distances between scattering sites and smaller mean free times between collisions For this reason, the mobility shows a strong dependence on impurity doping levels at temperatures for which such scattering is dominant As the ionized impurity density increases, the temperature at which the overall mobility becomes dominated by impurity scattering increases In Si at room temperature, for example, µe ≈ 1400 and µp ≈ 500 for dopant concentrations below ≈ 1015 cm3 , decreasing to approximately 300 and 100, respectively, for concentrations > 1018 cm3 These qualitative statements above can be made substantially more quantitative by providing detailed plots of mobility vs temperature and vs impurity density for the various semiconductor materials Examples of such plots are provided in several references (e.g., [1]-[10]) Diffusion results from a gradient in the carrier density For example, the flux of electrons due to diffusion is given by Fe = −Dn dn/dx, with Fp = −Dp dp/dx for holes The diffusion constants Dn and Dp are related to the mobilities above by Dn = µn (kb T /e)µe and Dp = (kB T /e)µp , the so-called Einstein relations In particular, the mean time between collisions tcol determines both the mobility and the diffusion constant 4.2 Saturated Carrier Velocities The mobilities discussed above are called “low field” mobilities since they apply only for sufficiently small electric fields The low field mobilities represent the scattering from distortions of the perfect lattice, with the electron gaining energy from the electric field between collisions at such distortion sites At sufficiently high electric fields, the electron gains sufficient energy to encounter inelastic collisions with the elemental atoms of the perfect crystal 21 Since the density of such atoms is very high (i.e., compared to the density of scattering sites), this new mechanism dominates the carrier velocity at sufficiently high fields and causes the velocity to become independent of the field (i.e., regardless of the electric field strength, the electron accelerates to a peak velocity at which the inelastic collisions appear and the energy of the electron is lost) The electric field at which velocities become saturated is referred to as the critical field Ecr Table 10 summarizes the saturated velocities and critical fields for electrons and holes in Si The saturated velocities in GaAs and Ge are about × 106 cm/sec, slightly lower than the saturated velocity in Si Table 10: Saturated velocity and critical field for Si at room temperature Adapted from [1] Saturated velocity Critical electric field Electrons Holes 1.1 × 107 cm/sec 9.5 × 106 cm/sec × 103 V/cm 1.95 × 104 V/cm Figure shows representative velocity vs electric field characteristics for electrons in silicon and in GaAs The linear dependence at small fields illustrates the low field mobility, with GaAs having a larger low field mobility than silicon However, the saturated velocities vsat not exhibit such a large difference between Si and GaAs Also, the saturated velocities not exhibit as strong a temperature dependence as the low field mobilities (since the saturated velocities are induced by large electric fields, rather than being perturbations on thermal velocities) Figure also exhibits an interesting feature in the case of GaAs With increasing electric field, the velocity initially increases beyond the saturated velocity value, falling at higher electric fields to the saturated velocity This negative differential mobility region has been discussed extensively as a potential means of achieving device speeds higher than would be obtained with fully saturated velocities Table 11 summarizes the peak velocities for various semiconductors Table 11: Saturated velocity and critical field for various semiconductors Semiconductor Peak velocity (cm/sec) × 106 × 106 1.2 × 107 × 107 1.7 × 107 × 107 × 107 AsAs AlSb GaP GaAs PbTe InP InSb As device dimensions have decreased, the saturated velocities have become a more severe limitation With critical fields in silicon about 104 V/cm, one volt across one micron leads to 22 10 Carrier drift velocity (cm/sec) GaAs (electrons) Si (electrons) 10 Si (holes) 10 10 10 10 10 10 Electric field (V/cm) 10 Figure 7: Velocity versus electric field for silicon and GaAs semiconductors Adapted from [4] saturated velocities Rather than achieving a current proportional to applied voltage (as in the case of the low field mobility condition), currents become largely independent of voltage under saturated velocity conditions In addition, the emergence of saturated velocities also compromises the speed advantages implied by high mobilities for some semiconductors (e.g., GaAs vs Si) In particular, although higher low field velocities generally lead to higher device speeds under low field conditions, the saturated velocities give similar speed performance at high electric fields Crystalline Defects A variety of defects occur in semiconductor crystals, many of which lead to degradations in performance and require careful growth and fabrication conditions to minimize their occurrence Other defects are relatively benign This section summarizes several of the defect types 5.1 Point Defects The point defects correspond to a lattice atom missing from its position Two distinct cases appear, as shown in Figure Schottky defects, shown in Figure 8a, result when an atom is missing from a lattice site Typically the atom is assumed to have migrated to the surface (during crystal growth) where it takes a normal position at a surface lattice site An 23 energy Es is required to move a lattice atom to the crystal surface, that energy serving as an activation energy for Schottky defects At temperature T , the equilibrium concentration Nsd of Schottky defects is given by Nsd = NL exp(−Esd /kT ), where NL is the density of lattice atoms, and there is necessarily some non-zero concentration of such defects appearing while the crystal is at the high temperatures seen during growth The high temperature defect densities are “frozen” into the lattice as the crystal cools (a) (b) Figure 8: Point defects in semiconductors (a) Schottky defects (b) Frenkle defects Frenkle defects result when an atom moves away from a lattice site and assumes a position between lattice sites (i.e., takes an interstitial position), as shown in Figure 8b The Frenkle defect therefore corresponds to a pair of defects, namely the empty lattice site and the extra interstitially positioned atom The activation energy Ef d required for formation of this defect pair again establishes a non-zero equilibrium concentration Nf d of Frenkle defects √ given by Nf d = NL NI exp(−Ef d /kT ) Again, the Frenkle defects tend to form during crystal growth and are “frozen” into the lattice as the crystal crystallizes These point defects significantly impact semiconductor crystals formed mainly through ionic bonding However, the covalent bonds of Group IV and the largely covalent bonds of Group III-V semiconductors are much stronger than ionic bonds, leading to much higher activation energies for point defects and a correspondingly lower defect density in semiconductors with fully or largely covalent bonds For this reason, the Schottky and Frenkle defects are not of primary importance in the electronic behavior of typical IV-IV and III-V semiconductors 5.2 Line Defects Three major types of line defects (edge dislocations, screw dislocations, and antiphase defects) are summarized here The line defects are generally important factors in the electrical behavior of semiconductor devices since their influence (as trapping centers, scattering sites, etc.) extends over distances substantially larger than atomic spacings Edge dislocations correspond to an extra plane inserted orthogonal to the growth direction of a crystal, as illustrated in Figure 8a The crystalline lattice is disrupted in the region near where the extra plane starts, leaving behind a line of dangling bonds, as shown The dangling bonds can lead to a variety of effects The atoms at the start of the dislocation 24 (a) Ga (b) As Defect plane Normal Crystal Crystal with antiphase defect plane (c) Figure 9: Line defects (a) Edge dislocation (b) Screw dislocation (c) Antiphase defect are missing a shared electron in their outer band, suggesting that they may act as traps, producing a linear chain of trap sites with interatomic spacings (vastly smaller than normally encountered between intentionally introduced acceptor impurities In addition to their impact on the electrical performance, such defects can compromise the mechanical strength of the crystal Screw dislocations result from an extra plane of atoms appearing at the surface In this case (illustrated in Figure 8b), the growth process leads to a spiral structure growing vertically (from the edge of the extra plane The change in lattice structure over an extended region as the crystal grows can introduce a variety of changes in the etching properties of the crystal, degraded junctions, etc In addition, the dangling bonds act as traps, impacting electrical characteristics Antiphase defects occur in compound semiconductors Figure 8c illustrates a section of a III-V semiconductor crystal in which the layers of alternating Ga and As atoms on the right side is one layer out of phase relative to the layers on the left side This phase error leads to bonding defects in the plane joining the two sides, impacting the electrical performance of devices Such defects require precision engineering of the growth of large diameter crystals to ensure that entire planes form simultaneously 25 Defect plane Crys allite tallit (a) Cryst eA B (b) Figure 10: (a) Stacking faults and (b) grain boundary defects 5.3 Stacking Faults and Grain Boundaries Stacking faults result when an extra, small area plane (platelet) of atoms occurs within the larger crystal The result is that normal planes are distorted to extend over that platelet (as illustrated in Figure 10a Here, a “stack” of defects appears above the location of the platelet Electrical properties are impacted due to traps and other effects Grain boundaries appear when two growing microcrystals with different crystallographic orientations merge, leaving a line of defects along the plane separating the two crystalline lattices as shown in Figure 10b As illustrated, the region between the two misoriented crystal lattices is filled from each of the lattices, leaving a plane of defects Grain boundaries present barriers to conduction at the boundary and produce traps and other electrical effects In the case of polysilicon (small grains of silicon crystal in the polysilicon area), the behavior includes the effect of the silicon crystal seen within the grains as well as the effects of grain boundary regions (i.e., acts as an interconnected network of crystallites) 5.4 Unintentional Impurities Chemicals and environments encountered during crystal growth and during device microfabrication contain small amounts of impurities which an be incorporated into the semiconductor crystal lattice Some unintentional impurities replace atoms at lattice sites and are called substitutional impurities Others take positions between lattice sites and are called interstitial impurities Some impurities are benign in the sense of not strongly impacting the behavior of devices Others are beneficial, improving device performance Examples include hydrogen which can compensate dangling bonds and elements which give rise to deep energy trapping levels (i.e., energy levels near the center of the band gap) Such deep level trapping levels are important in indirect gap semiconductors in establishing recombination time constants In fact, gold was deliberately incorporated in earlier silicon bipolar transistors to increase the recombination rate and achieve faster transistors Finally, other impurities are 26 detrimental to the device performance Table 12: Trap states (with energy Et ) in GaAs Adapted from [3] Type Ec − Et Shallow donor ≈ 5.8 meV Oxygen donor 0.82 eV Chromium acceptor 0.61 eV Deep acceptor 0.58 eV Electron trap 0.90 eV Electron trap 0.41 eV Name Type Et − Ev Shallow acceptor ≈ 10 meV Tin acceptor 0.17 eV Copper acceptor 0.42 eV Hole trap 0.71 eV Hole trap 0.29 eV Hole trap 0.15 eV EL2 EL1 EL3 EB3 EB6 Name HB2 HB6 HC1 Optoelectronic devices are often more sensitive to unintentionally occurring impurities A variety of characteristic trap levels are associated with several of the defects encountered Table 12 summarizes several established trap levels in GaAs, some caused by unintentional impurities and others caused by defects The strategy for semiconductor material growth and microfabrication is therefore a complex strategy, carefully minimizing those unintentional impurities (e.g., sodium in the gate oxides of silicon MOS transistors), selectively adding impurities at appropriate levels to advantage, and maintaining a reasonable strategy regarding unintentional impurities which are benign 5.5 Surface Defects: The Reconstructed Surface If one imagines slicing a single crystal along a crystallographic plane, a very high density of atomic bonds are broken between the two halves Such dangling bonds would represent the surface of the crystal, if the crystal structure extended fully to the surface However, the atomic lattice and broken bonds implied by the above slicing not represent a minimum energy state for the surface As a result, there is a reordering of bonds and atomic sites at the surface to achieve a minimum energy structure The process is called surface reconstruction and leads to a substantially different “lattice” structure at the surface This surface reconstruction will be highly sensitive to a variety of conditions, making the surface structure in real semiconductor crystals quite complex Particularly important are any surface layers (e.g., the native oxide on Si semiconductors) which can incorporate atoms different from the semiconductors basis atoms The importance of surfaces is clearly seen in Si MOS transistors, where surface interfaces with low defect densities are now readily achieved The reconstructed surface can significantly impact electrical properties of several devices For example, mobilities of carriers moving in the surface region can be substantially reduced compared to bulk mobilities In addition, MOS devices are sensitive to fixed charge and trap sites which can moderate the voltage appearing at the semiconductor surface relative to the applied gate voltage Surface reconstruction is a very complex and detailed topic and is not considered further here Typically, microfabrication techniques have carefully evolved to achieve high quality 27 Table 13: Properties of GaAs and Si semiconductors at room temperature (300K) CdS and CdSe both can appear in either zinc blende or wurtzite lattice forms Indirect and direct bands are indicated by (I) and (D) in the energy gap column Adapted from [8] Lattice Lattice constant (˚) A Energy gap (eV) Electron effective mass Hole effective mass Dielectric constant Electron mobility /V -sec) (cm Hole mobility /V -sec) (cm C Si Diamond Diamond 3.5668 5.4310 5.47 (I) 1.11 (I) 1,800 1,350 1,200 480 Diamond 5.6461 0.67 (I) 0.25 ml : 0.16 mh : 0.5 ml : 0.04 mh : 0.3 5.7 11.7 Ge 16.3 3,900 1,900 AlP AlAs Zinc blende Zinc blende 5.4625 5.6605 2.43 2.16 (I) 0.2 0.98 0.19 1.58 0.08 0.13 0.5 9.8 12.0 80 1,000 180 AlSb GaN GaP GaAs Zinc blende Wurtzite Zinc blende Zinc blende 6.1355 3.189 5.4506 5.6535 1.52 (I) 3.4 2.26 (I) 1.43 (D) 0.11 0.2 0.13 0.067 11 12 10 12.5 900 300 300 8,500 400 GaSb InAs InSb InP Zinc Zinc Zinc Zinc blende blende blende blende 6.0954 6.0584 6.4788 5.8687 0.72 0.36 0.18 1.35 (D) (D) (D) (D) 0.045 0.028 0.013 0.077 15.0 12.5 18 12.1 5,000 22,600 100,000 4,000 1,000 200 1,700 600 CdS CdSe CdTe PbS PbSe Zinc blende Zinc blende Zinc blende NaCl NaCl 5.83 6.05 6.4816 5.936 6.147 2.42 (D) 1.73 (D) 1.50 (D) 0.37 (I) 0.26 (I) 5.4 10.0 10.2 17.0 23.6 340 800 1,050 500 1,800 50 100 600 930 PbTe NaCl 6.45 0.29 (I) 0.2 0.13 0.11 0.1 ml : 0.07 mt : 0.039 ml : 0.24 mt : 0.02 30 6,000 4,100 ml : mt : ml : mt : 28 ml : 0.49 mh : 1.06 ml : 0.39 0.8 0.67 ml : 0.12 mh : 0.5 0.39 0.33 0.18 ml : 0.12 mh : 0.60 0.7 0.4 0.35 0.1 ml : 0.06 mh : 0.03 ml : 0.3 mh : 0.02 150 400 surfaces Summary A rich diversity of semiconductor materials, led by the extraordinarily advanced device technologies for silicon microelectronics and III-V optoelectronics, has been explored for a wide range of applications Much of the computing, information, and consumer electronics revolutions expected over the next decade will rest of the foundation of these important crystalline materials As established semiconductor materials such as silicon continue to define the frontier for advanced fabrication of very small devices, new materials are emerging or being reconsidered as possible additional capabilities for higher speed, lower power, and other advantages This chapter has provided a broad overview of semiconductor materials Many fine and highly readable books, listed in the references, provide the additional depth which could not be provided in this brief chapter Tables of various properties are provided throughout the chapter, with much of the relevant information provided in Table 13 Defining Terms • Elemental semiconductors: semiconductor crystals composed of a single atomic element • Compound semiconducuctors: semiconductor crystals composed of two or more atomic elements from different groups of the periodic chart • Ternary semiconductors: compound semiconductors with two atomic elements from one group and one atomic element from a second group of the periodic chart • Quaternary semiconductors: compound semiconductors with two atomic elements from one group and two atomic elements from a second group of the periodic chart • Conduction band: energy level for free electrons at rest in the semiconductor crystal • Valence band: energy for bound electrons and for free holes at rest in the semiconductor crystal • Band gap: energy difference between the conduction band and the valence band • Indirect gap semiconductor: semiconductor whose conduction band minimum and valence band minimum appear at different wave vectors (different momenta) • Direct gap semiconductor: semiconductor whose conduction band minumum and valance band minimum appear at the same wave vector (same momenta) Important for optical sources • Effective mass: value of carrier mass used to represent motion of a carrier in the semiconductor as though the motion were in free space 29 • Intrinsic semiconductors: semiconductors with no intentional or non-intentional impurities (dopants) • Amphoteric impurities: doping impurities which may act as either a donor or an acceptor • Shallow energy level dopants: doping impurities whose energy level lies very close to the conduction (valence) band for donors (acceptors) • Deep energy level impurities: doping impurities or other impurities whose energy level lies toward the center of the bandgap Important for carrier recombination in indirect gap semiconductors • Ambipolar semiconductors: semiconductors which can be selectively doped to achieve either n-type or p-type material • Unipolar semiconductors: semconductors which can be selectively doped to achieve only n-type or only p-type material • Low field mobility: proportionality constant between carrier velocity and electric field • Saturated velocities: maximum carrier velocity induced by electric field (due to onset of inelastic scattering) • substitutional impurities: impurities which replace the crystal’s base atom at that base atom’s lattice position Further Information The list of references focusses on books which have become popular in the field The reader is advised to refer to such books for additional detail on semiconductor materials.The Institute for Electrical and Electronics Engineers (IEEE, Piscataway, NJ) publishes several journals which provide information on recent advances in materials and their uses in devices Examples include the IEEE Trans Electron Devices, the IEEE Solid State Circuits Journal, the IEEE Journal on Quantum Electronics, and the IEEE Journal on Lightwave Technology The American Physical Society also publishes several journals focussing on semiconductor materials One providing continuing studies of materials is the Journal of Applied Physics The Optical Society of America (OSA, Washington, DC) publishes Applied Optics, a journal covering many practical issues as well as new directions The Society of Photo-Optical Instrumentation Engineers (SPIE, Bellingham, WA) sponsors a broad range of conferences, with an emphasis on optoelectronic materials but also covering other materials The SPIE can be contacted directly for a list of its extensive set of conference proceedings 30 References [1] Tyagi, M.S., Introduction to Semiconductor Materials, John Wiley & Sons, New York, 1991 [2] Nicollian, E.H and Brews, J.R., MOS Physics and Technology, John Wiley & Sons, New York, 1982 [3] Shur, M., GaAs Devices and Circuits, Plenum Press, New York, 1987 [4] Sze, S.M., Physics of Semiconductor Devices, 2nd edition, Wiley Interscience, New York, 1981 [5] Băer, K.W., Survey of Semiconductor Physics, Vol 1: Electrons and Other Particles o in Bulk Semiconductors, Van Nostrand, New York, 1990 [6] Băer, K.W., Survey of Semiconductor Physics, Vol 2: Barriers, Junctions, Surfaces, o and Devices, Van Nostrand, New York, 1992 [7] Haug, A., Theoretical Solid State Physics, Volumes and 2, Pergamon Press, Oxford, 1975 [8] Wolfe, C.M., Holonyak, N., and Stillman, G.E., Physical Properties of Semiconductors, Prentice Hall, New York, 1989 [9] Smith, R.A., Semiconductors, Cambridge Univ Press, London, 1978 [10] Howes, M.J and Morgan, D.V., Gallium Arsenide: Materials, Devices, and Circuits, John Wiley & Sons, New York, 1985 [11] Wang, S., Fundamentals of Semiconductor Theory and Device Physics, Prentice Hall, Englewood Cliffs, 1989 [12] Moss,T.S and Paul, W., Handbook on Semiconductors, Vol 1: Band Theory and Transport Properties, North Holland, Amsterdam, 1982 [13] Moss, T.S and Balkanski, M (eds), Handbook on Semiconductors, Vol 2: Optical Properties of Solids, North Holland Publ Co., Amsterdam, 1980 [14] Moss, T.S and Keller, S.P (eds), Handbook on Semiconductors, Vol 3: Material Properties and Preparation, North Holland Publ Co., Amsterdam, 1980 [15] Loewrro, M.H (ed), Dislocations and Properties of Real Materials, Inst of Metals, London, 1985 [16] Lannoo, M and Bourgoin, J., Point Defects in Semiconductors, Springer-Verlag, Berlin, 1981 31 [17] Capasso, F and Margaritondo, G (eds), Heterojunction and Band Discontinuities, North Holland, Amsterdam, 1987 [18] Wilmsen, C.W (ed), Physics and Chemistry of III-V Compound Semiconductor Interfaces, Plenum Press, New York, 1985 [19] Willardson, A.K and Beer, A.C (eds), Semiconductors and Semimetals, Vol 22, Academic Press, New York, 1985 [20] Pantelides, S.T., Deep Centers in Semiconductors, Gordon & Breach Sci Publ., New York, 1986 [21] Wilmsen, C.W (ed), Physics and Chemistry of III-V Compounds, Plenum Press, New York, 1985 [22] Irvine, S.J.C., Lum, B., Mullin, J.B., and Woods, J (eds), II-VI Compounds 1982, North Holland, Amsterdam, 1982 [23] Beadle, W.E., Tsai, J.C.C., and Plummer, R.D (eds), Quick Reference Manual for Silicon Integrated Circuit Technology, John Wiley & Sons, New York, 1985 32 ... tions), knowledge of the density of one of the carrier types (e.g., of p) allows direct determination of the density of the other (e.g., n = n2 /p) Values of ni vary considerably among i semiconductor. .. categories of semiconductor material are summarized below 2.1.1 Elemental (IV-IV) Semiconductors Elemental semiconductors consist of crystals composed of only a single atomic element from group IV of. .. densities of states are fundamental parameters used in evaluating the electrical characteristics of semiconductors The equations above for n and p apply both to intrinsic semiconductors (i.e., semiconductors