PRINCIPLES OF TRANSISTOR ACTION 273 



The increased conductivity caused by hole emission accounts not only 

 for the large forward currents, but also for the relatively small dependence 

 of spreading resistance on contact area. At a small distance from the con- 

 tact, the concentrations and voltages are independent of contact area. The 

 voltage drop within this small distance is a small part of the total and does 

 not vary rapidly with current. 



We have assumed that the electron current, !«, at the contact is negligi- 

 ble compared with the hole current, Ih. An estimate of the electron cur- 

 rent can be obtained as follows: From the diode theory, 



le = (enebVaAc/-i) exp (—{fb — eVb)/kT), (4.34) 



since the electron concentration at the semi-conductor boundary of the 

 space-charge layer is Ueb and the height of the barrier with the voltage 

 applied is (fb — eVb- For simplicity we assume that both neb and Hkb are 

 large compared wdth Ueo so that w^e may replace Ueb by Uhb without appre- 

 ciable error. The latter can be obtained from the value of xj/ at the contact: 



lA = Ih/ia (4.35) 



Expressing ip in terms of fihb, we find 



Hhb = Ih/SkTfXha (4.36) 



Using (4.33) for Vb, and (3.5b) for Uko we find after some reduction, 



/. = Ih'/Icrit, (4.37) 



where 



_ 256 Ch (kTnh) T , ,, V f . 



Icrit = exp { — <Phm/kT) (4.38) 



■n-eva 



The energy difference iphm is the difference between the Fermi level and the 

 filled band at the metal-semi-conductor interface. Evaluated for german- 

 ium at room temperature, (4.38) gives 



Icrit = 0.07 e\T^{—(pkJkT) amps, 



which is a fairly large current if iphm is not too large compared with kT. 

 If Ih is small compared with Icrit, the electron current will be negligible. 



V — Theoretical Considerations about Transistor Action 



In this section we discuss some of the problems connected with transistor 

 action, such as: 



(1) fields produced by the collector current, 



(2) transit times for the holes to flow from emitter to collector, 



(3) current multiplication in collector, 



(4) feedback resistance. 



