Fundamentals of Electrodynamics
14 ELECTRIC CURRENT IN SEMICONDUCTORS Basic Concepts and Form ulas
Sem iconductors are m aterials having re sistiv ity betw een th a t of conductors and insulato rs; th eir re s is tiv ity decreases w ith rising tem p eratu re and the presence of im p u rities. T yp ical sem iconductors are elem ents of group IV of the Periodic T able, whose atom s have four valency electrons in the outer shell (like germ anium Ge and silicon Si). At low tem peratures, cry stals of these elem ents do not contain free electrons and are good insu lato rs. The covalent bonds in such cry stals are ru p tu red w ith increasing tem p eratu re, illum inance, or due to strong electric fields. Free electrons appear, and in trin sic electron conduction emerges in (n-type) sem iconductors. In trin sic hole conduction of (p-type) sem i conductors is due to th e displacem ent of holes.
Im p u rity conduction in sem iconductors is due to th e pres ence of “alien” group V elem ents (like arsenic or antim ony) or group I I I elem ents (like boron and alum inium ). In the former case, im p u rity electron conduction is created, and in the la tte r, im p u rity hole conduction sets in. Thus, th e
154 __________Ch. II. Fundam entals of E lectrodynam ics
in tro d u ctio n of im p u rities into pure sem iconductors can destroy th e eq u ilibrium between the p -ty p e and w-type con ductions.
W hen p- and rc-type sem iconductors are brought in con ta c t, a b arrier layer emerges as a resu lt of diffusion through th e p-n ju n ctio n . The ap p licatio n of an ex tern al field to a p-n ju n ctio n m ay change its conduction and create the con d itio n s for u n ila te ra l conduction.
A sem iconductor diode is a sem iconductor w ith a p-n junction . Its advantages over vacuum tu b e diodes include sm all size, re lia b ility , and efficiency.
Questions and Problems
14.1. Figure 58 shows the tem peratu re dependences of resistance for conductors and sem iconductors. W hich of
them corresponds to sem iconduc tors?
14.2. W hat are th e m obile charge carriers in a pure sem iconductor?
14.3. W hat is the ra tio between the num ber of holes and the num ber of free electrons in a pure sem i conductor? Is th is ra tio preserved for im p u rity conduction of sem icon ductors?
14.4. W hat w ill th e ty p e of con duction in germ anium w ith trace im p u rities of phosphorus or alum in ium be?
14.5. How do the c o n d u ctiv ities of germ anium and silicon vary w ith lowering tem p eratu re?
14.6. By w hat factor w ill th e curren t den sity in a sem i conductor change if the v elocity of the electrons increases from 0.5 to 0.75 m/s as a resu lt of a tem p erature increase from 0 to 175°C, w hile the electron num ber d en sity increases
thereby from 1.3 x 1014 to 2.1 X 1018 m~3?
14.7. The velo city of directio n al m otion of free electrons in a sem iconductor is 0.25 m /s for a given tem perature. D eterm ine the m o b ility of th e charges and th eir num ber den sity if the current den sity is 4 X 10“2 A /m 2 for a field stren g th of 100 V/m.
§ 15. E lectrom agnetism 155 14.8. W h at is a therm istor? W hy are th erm istors called nonlinear resistances?
14.9. W hat is the difference between a th erm isto r and a photoresistor?
14.10. W h at is a tran sisto r? W hich regions does the cry stal of a tra n sisto r contain?
14.11. The thickness of th e base in a tra n sisto r is very sm all (1-25 pm ). W hy?
14.12. W hat is the ra tio between the e m itte r, base, and collector currents?
14.13. W h at is the adv an tag e of sem iconductor devices over vacuum tubes in rad io engineering?
§ 15. ELECTROMAGNETISM
Basic Concepts and Form ulas
A m agnetic field is a special case of electrom agnetic field, being characterized by th e action on a m oving charged particle of a force p ro p ortion al to
the charge of th e particle and its velocity.
The shape of a m agnetic field de pends on the shape of th e cu rren t- carrying conductor producing it. For exam ple, th e m agnetic field formed around a stra ig h t cu rren t- carrying conductor is g rap h ic ally represented by m agnetic field lines in the form of concentric rings in the plane p erpendicular to the d i rection of the cu rrent (Fig. 59). The direction of th e m agnetic field in th is case is given by A m pere’s (right- hand screw) rule: ro ta tio n of the head of a screw indicates th e direc
tion of th e m agnetic field lines if the m otion of the screw body coincides w ith th e d irection of th e current.
The m agnetic field of a cu rren t-carry ing coil (solenoid) is sim ilar to the m agnetic field of a perm anent bar m agnet.
The in te rac tio n between m agnetic fields formed by p ar allel current-carry in g conductors is determ ined by the
156 Ch. II. Fundam entals of Electrodynam ics form ula
F = a / l/ a *
r m 2:la '
where I x and I2 are the cu rren ts in the conductors, I is the len gth of wire over which the force is acting, a is the sepa ratio n betw een th e conductors, and |xm is th e absolute per m ea b ility of the m edium characterizin g the dependence of the force of in te rac tio n of cu rren t-carry ing conductors on the properties of the m edium:
M'm = HoH-
Here p 0 = 4jt x 10"7 H /m is th e m agnetic co n stan t, and p is th e re la tiv e p erm eab ility of th e m edium (see T able 21).
A m agnetic field exerts a force F \ (Am pere’s law) on a curren t-carryin g conductor:
FA = B I l sin a .
If the conductor is perpendicular to m agnetic field lines (a = 90°), we have
Fa = B I L
The p ro p o rtio n a lity factor B is called the m agnetic in du ction and is th e force ch aracteristic of th e m agnetic field. M agnetic in du ction is a vector q u a n tity . The SI / * un it' m agnetic in d u ctio n is th e tesla (T). ( X \ ^ an y P °in t *n a uniform m agnetic field, th e v 5 ] m agnetic in d u ctio n has th e sam e m agnitude and direction. Therefore, such a field is g rap h ically represented by p a ra lle l stra ig h t lines w ith uniform density.
Vig. 60 m agnetic flux is equal to th e num ber of m agnetic field lines piercing a surface of area S if th e m agnetic in d uctio n vector coincides w ith the norm al to th is surface:
O = B S .
The SI u n it of m agnetic flux is th e weber (Wb).
The m agnetic properties of a c u rren t loop are characterized by the m agnetic m om ent P mag (Fig. 60):