/> « JL \CTlO\S l.\ SKMICO.XDl CTORS 469 



tlow easily into I'^ since the i)otential distribulioii there favors their en- 

 trance. Since, however, A is open-circuited this hole How biases J2 in the 

 forward (Hrection; since J-i is high resistance, an a|)preciable bias is developed 

 before the counter current equals the inward hole llow and a steady state is 

 reached. Xo similar effect occurs in the branch X^ ; consequently P2 will be 

 found to be floating (open-circuited) at a more positive jxjtential than Xo . 



Parts (b) to (e) describe this reasoning in more comj^lete terms. We 

 suppose that the /^-regions are more highly conducting than the ;'-regions 

 so that the current across Ji , shown in (b), is mainly holes. The [)otentials 

 s?p and ip„ along the .v-axis will be similar to those of Figs. 5 and 6; (c) shows 

 this situation and indicates that the difTusion length for electrons in the 

 /^-region is less than for holes in the ^-region. Along the y axis (f,, and (fn 

 vary as shown in (e), the reasoning being as follows: At the origin of coordi- 

 nates ipp and (fn have the same values as for (c). The transverse hole current 

 (d) has a small positive component at y = since, as mentioned above, P» 

 tends to absorb holes and thus increase difTusion along the plus y-axis. Since 

 the net transverse current is zero, /„ = —Ip in (d). The <p curves of (e) 

 have been drawn to conform to the currents in (d); </?„ is nearly constant 

 in the //-region and tpp is nearly constant in the /(-region. As concluded in 

 connection with Figs. 5 and 6, <p„ and ipp are also nearly constant across the 

 transition region. These conclusions lead to the shape of ifn and (pp for y > 

 in (e). For y < 0, the reasoning is the same as that used in Sections 3 and 4 

 and we conclude that (f,, is essentially constant. Hence, a difference in the 

 Fermi levels at 7^2 and X2 will result. 



In Fig. 10 we show a structure for which we can make quantitative calcu- 

 lations of the variations of tpp and tp,, ■ We assume for this case that the 

 forward current from Pi to .V does not {produce an apj^reciable voltage drop, 

 i.e. change in \j/ and s?„ , in region T. This will be a good approximation if the 

 dimensions are suitably proportioned. We shall next solve for the steady- 

 state distribution of p subject to the indicated boundary conditions assuming 

 that p is a function of .v only. As we have discussed in Section 4.1, when p is 

 small compared to ;/ in the //-region, we can write 



In keeping with the treatment in the next section of this structure as a 

 transistor, the terminals are designated emitter, collector and base, the po- 

 tentials with respect to the base being ^p^ and s^, . The contact to .V or the 

 base is such that <pb — <Pn in this region. Hence, the boundary conditions at 

 /i and J2 are 



Pi = pnc"'^"^ X = -u> (5.2) 



p.=^Pnc'"'"' x=-Viv (5.3) 



