Gauss, truang dien tir se la:
t(x) = x^ < X <0
^ ỉ//j(x-xy) 0 <x <XM
(1.23)
Vdi Ep va En la hing so dỉn moi cua ban dan loai p va n.
Vi vecto cam ung phap tuyen D = ẹE phai lien tuc tai x = 0, nen NaXp = NpXn
DQ doc cua the tinh di^n dugrc xac djnh khi biet gia trj am ciia di^n tnrdng, vi di^ trucmg bang gradient ciia the tinh dỉn, va mang dau am.
Neu chon the ning bJng 0 khi x < Xp ta co:
nx) '-^ix^x,? '-^ix^x,? 2B, qK X<,-X^ - x^^x^O 2£, . ] . ' ^ 2£ ^ilXXyf-X^) OSxSXj^^ s x^<x (1.24)
Thi tiip xLic dugc tinh loan blng each su dyng cac gia tri trong khdng gian bl
chieu ciia cac mire Fermi Fn, Fp cac gia trj do dugc d ria viing hoi tri va viing din Ê
Ecn trudc lien kit:
1^0 =
F^-F. , _E„+i^E,-(F,-Ê)-{Ê-F^)
O li him cdng, \i li dg chinh ning lugng gi&a muc chan khdng va muc Fermi
cimg chinhli ning lugng cin thiit di lly mgt difn tu tir ria viing din lin muc chan khdng.
Chiiu dii viing nghio phia p dugc xic dinh niu biit VQ.
2€^ ' 2Ê^N^
(1.26) Niu tiip xiic dugc dat dudi mpt HDT, ta thay VQ blng VQ-V^ :
^P = \ 2s,{V,-Vj <iN,N^{.N^-^^N,) ^D 1 ^^ (1.27) Ria viing nang lugng la:
Eix^^i '"^^^'^ ^'""^^ 5rx^ = (^*^^^"'^» ^ ' " ^ ^
'^ -^E,-qV(x) N-stdt '^ ^ fi,(x) + 5 ^ N-suk ^j jgx
Nhan thIy ring, vdi tiip xuc di thi, do cd su khic nhau vi dp rgng vimg elm da tao ra doan dut gay d vimg dan va viing hda trị Doan dut gay d vimg din lam giim hing rao thi đi vdi difn tu, lam cho difn tu di tir n sang p di di ding ban. Ngugc lai, doan dirt gay d miin hoi trj ting hang rao thi đi vdi Id trdng, lim cho cac Id trdng khd khan horn khi di chuyin tir miin p sang miin n.
1.8J Tiep xuc Ohmic:
Tiip xuc Ohmic la mgt viing cua thiit bi bin din ma dudng die trung Vdn-Ampe la tuyin tinh va đi xirng.
NIU dudng dac trung V-A khdng tuyin tinh va bat đi ximg, thi tiip xiic la tiip xuc Schottkỵ
Muc Fermi, hay ndi chinh xac han la thi hoa hgc ciia hai chat bat ky khi tiep xiic phai blng nhau khi can blng nhift. Su chinh Ifch giua nang lugng Fermi va muc chan khdng dugc ggi la ham cdng. Mgt kim loai tiip xiic va mgt ban dan khi tiip xiic cd the cd ham cdng khac nhau, ky hifu la (p^ va tps. Niu vay, khi tiip xiic, difn tu se chay tir vat lieu cd ham cdng be sang vat lieu cd ham cdng Idn cho tdi khi muc Fermi giua hai viing dugc can bang.
Khi ly, vat lifu cd him cdng be hon si cd mOt lugng difn tich duong, trong kU
vat lieu cd ham cdng Idn hon si cd mgt lugng difn tich am. Khi ly gifta chung si c4
mgt thi iTnh difn nao đ, dugc ggi la thi ngi, ky hifu la Vbị Thi tiip xiic niy xuit hifa khi hai chit rln bit ky tiip xiic, va la nguyin nhin cua hifn tugng chinh luu diod^ hieu img Seebeck. Thi ndi cung la nguyin nhan ciia hifn tugng be cong vung ning lugng d gin chd tiip xiic cua chit ban din. Dang chii y li hifn tugng bi cong viiQg ning lugng khdng xiy ra d phin Idn kim loai vi chiing cd chiiu dii che chin rlt ngin ( nghia la trudng difn tir chi md rfng vdi dg dii ngin d vung giao difn.).
Trong vat ly cd diin, di vugt qua hang rao thi, h^t tii trong bin din phii tfch trt dii ning lugng di nhiy tir muc Fermi lin dinh ciia viing din. Ning lugng cin thilt dJ vugt qua hang rao thi OB la tdng ciia thi ngi va ria ciia muc Fermi va vung din. Vdi
ban din loai n, (pB = <PM -yJfs, vdi sZ li ai lyc difn td cua chit bin din, dugc dinh
nghia la hifu gii^a muc chin khdng va muc din.
Vdi bin dan lôi p, (pe = Eg - ((PM -XS ), Eg li dg rOng viing elm.
Niu kich thich di hat tii vugt qua hing rao thi li kich thich nhift, thi qui trinh dugc gpi li buc xa nhift. Mpt qui trinh can blng quan trpng trong cic tilp xiic thyc li hien tugng xuyin him lugng tụ Gin diing WKK, cho chiing ta hue tranh don giin nhlt cau qua trinh xuyin ham, trong đ xic suit xuyin qua hang rio thi phy thuOc vio dO
cao hang rao the va chieu day theo kiiu him mu,
Trong trudng hgp tiip xuc, chiiu diy dugc cho bdi dg rgng viing nghio h?t tii, no vao cd ma trudng ndi xuyin sau vao chat ban din. Dg rgng vimg nghio W dugc tinh loan blng each giai phuang trinh Poisson va xem xet sy cd mit cua cic t^p chit
trong ban dan.
e (1.29)
Trong đ p la mat dg difn tich. £ la hang sd diin mdị
Chung ta chi xet theo mgt chi6u, vi tiep xiic dugc coi la mit phing. Tich phan
phuong trinh tren, vai gii thik mat do dien tich la hing s6 trong vung ngheo hat tai, ta
co:
dV px ^
dx € (1.30)
Hang sd tich phan e vi do rgng vimg ngheo dugc djnh nghia la chiiu dai ma trong đ giao difn dugc che chin toan bd. Khi đ:
2£ e (1.31) V(0)= Vbi dugc su dung de phii hgp vdi hlng sd tich phan.
Dg rpng vimg ngheo dugc xac dinh blng each dat V(W)= 0, diiu nay din tdi
V P (1.32)
Vdi 0 < x < W, p = eNdopant ' i m^t dp dien tich idn hoa ciia donor hay acceptor trong ban dan bi lam ngheo toan bd, e la difn tich ciia difn tu, p va Vbi cd gia tri duong vdi cac ban dan loai n va dau am vdi ban dan loai p.
Chii y vdi each suy diin dan gian rang chieu cao hang rao thi (dua tren ai luc dien tu va trudng ndi), va dp day hang rao thi (dua trin trudng ndi, hang sd dien mdi ban din va mat dp tap), chi bj dieu chinh bang each thay đi kim loai hoac thay doi mat dp tap. Trong ky thuat, chpn kim loai tiep xiic la dan, khdng phan iing va can bang nhift, can blng dien va it bien dang, sau do se tang nhiet dp pha tap, chd tiep xiic de thu hep dp rpng viing hang rao thẹ Viing pha tap nhieu dugc ky hieu n^ va p"^ tuy thupc vao kiiu hat taị Vi he sd truyen qua trong hieu ung xuyin ham phu thupc kiiu ham e mu đi vdi khdi lugng hat, chat ban din vdi khdi lugng hieu dung be han se de tham gia vao tiip xiic. Ngoai ra, ban din vdi khe nang lugng be han ciing de dang tham gia vao tiip xuc vi ai luc dien tu (va do vay chieu cao hang rao the) se be han.