The discussion about p-n junctions in the semiconductor device is fundamental both

Transcription

1 CHAPTER II MATERIALS JUNCTIONS 2.1 p-n Junctions Homojunction The discussion about p-n junctions in the semiconductor device is fundamental both in modern electronic applications and in understanding other semiconductor devices. Almost semiconductor devices are built in this structure. The p-n junction theory also serves the foundation of the physics of semiconductor devices. When an intrinsic semiconductor is doped with donor impurities, it becomes n-type semiconductor. Otherwise when it is doped with acceptor impurities becomes p-type semiconductor. If these two type semiconductor are connected, then a p-n junction would form. At the interface of this junction a depletion region also with electrical field appears. The appearance of depletion region also with electrical field contributes to the certain potential profile of the junction. From the Gauss law and the Poisson equation we get 6

2 7, (2.1.1), (2.1.2) or, (2.1.3) where in the is dielectric constant while E and V are electrical and potential field, respectively. In the case of abrupt junction, with donor impurities and acceptor impurities, the carrier densities on this semiconductor is. (2.1.4) Inside the depletion region and assuming complete ionization,, for (2.1.5a), for. (2.1.5b) The electric field is then obtained by integrating Eq. (2.1.5) with respect to z., for (2.1.6a), for. (2.1.6a)

3 8 Figure 2.1 Abrupt p-n junction in thermal equilibrium. (a) Space-charge distribution. Dashed lines indicate corrections to depletion approximation. (b) Electric-field distribution.(c) Potential distribution where is the built-in potential. (c) Energy-band diagram. (Sze [12])

4 9 At, the magnitude of electric field in the p-type and n-type are equal and maximum, so that. (2.1.7) To get the potential profile we integrate again Eq. (2.1.6) with respect to z., for (2.1.8a), for (2.1.8b) where refer to potential at. The built in potential at the interface can be writen as, (2.1.9) where and are the built in potential on the n and p-type side., (2.1.10a). (2.1.10b) Then the maximum potential field in the Eq. (2.1.7) can be expressed as. (2.1.11)

5 10 At the boundary, the electric field must be continous and the total negative charge per unit area in p-side must be precisely equal to the total positive charge per unit area in the n side., (2.1.12). (2.1.13) By using Eqs. (2.1.12) and (2.1.13) we can get the depletion width both in p and n- type side., (2.1.14a). (2.1.14b) Heterojuntion There is a little bit different between pn-homojunction and pn-heterojunction semiconductor. This difference is on the potential profile which will produce according to this junction. This difference appears because of the discontinuity at conduction band and valence band. The potential profile of pn-heterojunction with p- type semiconductor bandgap narrower than n-type semiconductor bandgap is shown in Fig. 1.2.

6 11 a Figure 2.2 Energy-band diagrams for (a) two isolated semiconductors of opposite types and different Eg and (b) their idealized anisotype heterojunction at thermal equilibrium. b In the pn-heterojunction, the electric displacement must be continuous at the interface. (2.1.15) By using boundary condition above, we will get the depletion region in the pnheterojunction as, (2.1.16a). (2.1.16a)

7 Metal-Semiconductor Contacts At least there are two metal semiconductor contacts in HBT, i.e. at the emitter and collector. This contact requires the existence of a particular potential profile at both ends of the HBT potential. The metal material is chosen selectively to provide an ohmic contact betwen metal and semiconductor. The aim is to make a good connection between metal and semiconductor so it does not disturb any performance of this devices. The potential variation within the depletion layer is similar to that in one side of a p-n junction(sze) or junction. The depletion width in the pn homojunction semiconductor are, (2.2.1a). (2.2.1b) The total depletion width is the sum of both equations above.. (2.2.2) For p + -n junction,, then Eq. (2.2.2) becomes

8 Figure 2.3 (a) A schematic of a metal-semiconductor junction. (b) The various important energy levels in the metal and the semiconductor with respect to the vacuum level. (c) The junction potential produced when the metal and semiconductor are brought together. Due to the built-in potential at the junction, a depletion region of width W is created. (Singh [3]) 13

9 14. (2.2.3) The electric field and potential profile of this connection are expressed as, (2.2.4), (2.2.5) where is the potential barrier height which formed at the metal-semiconductor boundary. This barrier height is written as, (2.2.6) where and are metal work function and electron affinity of the semiconductor respectively.