POINT-CONTACT TRANSISTOR SURFACE EFFECTS 771 



where /c and le are the collector and emitter currents. The a can be con- 

 sidered as the product of three terms, that is: 



a = aSy (2) 



where 7 and /i represent the injection efficiency and transport factor 

 respectively for minority carriers. The term a^- is the "intrinsic" current 

 multiplication of the collector itself. As mentioned above, there are 

 theoretical reasons to account for an ai as large as (1 -f h), where h is 

 the ratio tin/y^p of the mobilities of electrons and holes, and thus the 

 term ai may be roughly as large as 3.1. The average current gain, a, 

 taken over a large interval of emitter current, is seldom found to be 

 greater than this value, and is usually about 2.5. However, the small 

 signal a at low emitter current usually is found to be considerably larger 

 than 3.1. 



Several mechanisms have been proposed to account for this excess 

 current gain at low emitter bias in formed transistors. The most generally 

 known of these are the p-n hook hypothesis and the trapping model. ' 



The experiments to be described in this section will be concerned pri- 

 marily with the characteristics of formed points as transistor collectors, 

 and thus with the transport factor /S. The subject of the origin of the 

 intrinsic «»■ will be discussed further in a later section. 



The experiment of Valdes indicates that the properties of a formed 

 point contact depend on the physical properties of a small region of ger- 

 manium near the point, produced by impurity diffusion from the point 

 or imperfections introduced during the formmg pulse. A highly idealized 

 representation of the physical situation is shown in Fig. 1 . This is a radial 

 model of a formed point contact on a semi-infinite block of n-germanium 

 (respectively p) , with a hemispherical p-layer (radius c:^ ro) . The electron 

 and hole concentrations in the formed layer near the junction are desig- 

 nated as Up and p. If a reverse bias Vc is applied to the point, a potential 

 difference F(ri) — F(r2) = Vj results from the resistance of the junction 

 at ro . For r ^ ro , at distances well outside ?'o , the potential V{r) and 

 the magnitude of the field E(r) are given by 



where / is the total current through the point. For 



I Fo - V(n) I « 1 F^ I, V{r2) ^V,-Vj, 



