Chpter 1 STRUCTURAL ISSUES IN SEMICONDUCTORS Most semiconductor devices re mde from crystlline mterils. The following gures provide n overview of importnt crystlline properties of semiconductors, like Si, GAs, etc.
SEMICONDUCTORS: STRUCTURAL ISSUES Different sttes of mtter nd clssifiction bsed on the order present in the mteril. MATTER SOLID LIQUID GASEOUS LIQUID CRYSTAL Crystlline: Long-rnge order. Polycrystlline: Long-rnge order over severl microns. Amorphous/Glsses: Good short-rnge order, but no longrnge order. No short- or long-rnge order. Mtter cn "flow" nd tke the shpe of the continer. No short- or long-rnge order. Long-rnge order nd flow of toms/molecules. Semiconductors used in most technologies re high qulity crystlline mterils (some exceptions re morphous silicon, used for thin film trnsistor nd solr cells). Prof. Jsprit Singh www.eecs.umich.edu/~singh
CRYSTALLINE MATERIALS: SOME DEFINITIONS BRAVAIS LATTICE: Collection of points tht fill up spce. Every point hs the sme environment round it. TRANSLATION VECTORS: A trnsltion of the crystl by vector T tht tkes point R to R+T nd leves the entire crystl invrint. PRIMITIVE TRANSLATION VECTORS: Strting t ny prticulr lttice point, we cn construct 3 vectors tht tke us to 3 nerest neighbors points (non-coplnr). The smllest such vectors re clled primitive vectors 1,, 3. BASIS: A crystl is produced by ttching bsis to every lttice point. The bsis consists of one or more toms. Prof. Jsprit Singh www.eecs.umich.edu/~singh
PRIMITIVE CELL: The primitive vectors define prllelopiped of volume 1,, 3 which is clled the primitive cell. There re mny different wys of selecting primitive cell. Alterntive primitive cell for D lttices. The shpe of the primitive cell cn be defined by set of prmeters 1 = 1 ; = ; 3 = 3 1 α 3 3 1 = cos 1 ; α = cos 1 ; α 3 1 3 = cos 1 1 3 1 Prof. Jsprit Singh www.eecs.umich.edu/~singh
Nottion for primitive cell. α 1 α α 3 1 Brvis lttices cn be formed only if α = 0; π or 5π ; π or 3π ; π or π ; π 3 3 3 3 Number of Restrictions on conventionl System lttices cell xes nd singles Triclinic 1 1 3 α β γ Monoclinic 1 3 α = γ = 90 β Orthorhombic 1 3 α = β = γ = 90 Tetrgonl 1 = 3 α = β = γ = 90 Cubic 3 1 = = 3 α = β = γ = 90 Trigonl 1 1 = = 3 α = β = γ < 10, 90 Hexgonl 1 1 = 3 α = β = 90 γ = 10 Prof. Jsprit Singh www.eecs.umich.edu/~singh
c β α γ b c α b triclinic monoclinic bse-centered c b orthorhombic bse-centered body-centered fce-centered c b tetrgonl body-centered α α α rhomboherdrl c π/3 hexgonl cubic body-cubic fce-centered cubic Prof. Jsprit Singh www.eecs.umich.edu/~singh
Most semiconductors hve n underlying lttice tht is either fce-centered cubic (fcc) or hexgonl closed pck (hcp). FACE CENTERED CUBIC: The lttice sites t the edges of cube nd t the center of tis fces. The edge of the cube is clled the lttice constnt. z 3 1 y x Primitive bsis vectors for the fce-centered cubic lttice. 1 = (y + z), = (z + x), 3 = (x + y) Prof. Jsprit Singh www.eecs.umich.edu/~singh
DIAMOND AND ZINC BLENDE STRUCTURES The zinc blende crystl structure. The structure consists of the interpenetrting fcc lttices, one displced from the other by distnce ( ) long the body digonl. The underlying Brvis lttice is fcc with two-tom bsis. The positions of the two toms is (000) nd. Positions of the toms A = (n1,n 1,n 3 ), (n 1 +,n + 1,n 3 + 1 ), 1 1 3 3 1 (n 1 +,n +,n 3 ),(n 1 +,n +,n 3 + ), 1 1 3 1 3 (n 1 +,n,n 3 + ),(n 1 +,n +,n 3 + ), 1 1 1 3 3 (n 1,n +,n 3 + ),(n 1 +,n +,n 3 + ) 1 1 (0,, ) 1 1 (,,,) 1 ( ) 1 1 (,0, ) 1 1 (0,0,0) (,,0) Tetrhedrl bonding Nture of chemicl bonds in dimond or zinc blende structure Prof. Jsprit Singh www.eecs.umich.edu/~singh
FCC AND HCP STRUCTURES + Spheres on the strting lyer Centers of spheres on the second lyer Centers of spheres on the third lyer fcc + + + + + + + + hcp () + + + + + + + + + + c-xis hcp lttice positions 3 (b) 1 () A schemtic of how the fcc nd hcp lttices re formed by closepcking of spheres. (b) Arrngement of lttice points on n hcp lttice. Zinc Blende underlying lttice is fcc Wurtzite underlying lttice is hcp G As Cd S GAs CdS Prof. Jsprit Singh www.eecs.umich.edu/~singh
ZINC BLENDE AND WURTZITE c-xis B A [1,1,1] xis B A () (b) Orienttions of djcent tomic tetrhedr in wurtzite () nd zinc blende (b). The A nd B refer to the two different species of tom. SEMICONDUCTORS Elements commonly found in semiconductor compounds I II III IV V VI VII Be B C N O F Mg Al Si P S Cl Cu Zn G Ge As Se Br Ag Cd In Sn Sb Te I Hg Tl Pb Bi Prof. Jsprit Singh www.eecs.umich.edu/~singh
IMPORTANT PLANES IN ZINC BLENDE OR DIAMOND STRUCTURES ATOMS ON THE (110) PLANE Ech tom hs bonds: bonds in the (110) plne 1 bond connects ech tom to djcent (110) plnes Cleving djcent plnes requires breking 1 bond per tom. ATOMS ON THE (001) PLANE bonds connect ech tom to djcent (001) plne. Atoms re either G or As in GAs crystl. Cleving djcent plnes requires breking bonds per tom. ATOMS ON THE (111) PLANE Could be either G or As. 1 bond connecting n djcent plne on one side. 3 bonds connecting n djcent plne on the other side. Some importnt plnes in the cubic system with their Miller indices. This figure lso shows how mny bonds connect djcent plnes. This number determines how esy or difficult it is to cleve the crystl long these plnes by cutting the bonds joining the djcent plnes. Prof. Jsprit Singh www.eecs.umich.edu/~singh