Tetapan Dielektrik Bahan

KATA PENGANTAR Puji dan syukur senantiasa kami panjatkan ke hadirat Illahi Rabbi yang telah melimpahkan rahmat, karunia serta hidayahNya, sehingga kami dapat menyusun makalah dengan tema “Sifat Dielektrik dan Optik Bahan” dengan baik sampai akhirnya kami dapat menyelesaikan makalah ini dengan tepat waktu. Makalah ini disusun sebagai syarat kelulusan untuk mata kuliah Fisika Zat Padat Lanjut. Makalah ini berisikan tentang tetapan dilektrik, polarisabilitas, ferroelektrik, piezoelektrik dan tetapan optik Penyusun menyadari bahwa tanpa adanya bimbingan dan pengarahan dari berbagai pihak, makalah ini tidak mungkin akan tersusun baik.Oleh karena itu, pada kesempatan ini diperkenankanlah kami mengucapkan terimakasih yang sebesar-besarnya kepada semua pihak yang telah membantu penyelesaian makalah ini. Ucapan terimakasih terutama kami haturkan kepada Bapak Edi Istiyono, M.Si. selaku dosen pengampu mata kuliah Fisika Zat Padat Lanjut, serta teman-teman Pendidikan Fisika Reguler 2005 yang telah memberikan motivasi sehingga makalah ini dapat tersusun dengan baik. Penulis menyadari bahwasanya makalah yang penulis susun masih jauh dari kesempurnaan, oleh Karen itu, penulis sangat mengharapkan saran dan kritik yang membangun dari semua pihak demi kesempurnaan untuk makalah-makalah selanjutnya. Akhir kata, semoga makalah ini dapat bermanfaat bagi semua pihak.

Yogyakarta, 12 Oktober 2008 Penulis

1

Pendahuluan Dalam sebuah konduktor, elektron terluar dari sebuah atom sangat mudah untuk terpisah dan berpindah dari satu atom ke atom lainnya bila diletakkan dalam medan listrik. Sedangkan pada suatu dielektrik, elektron lebih mudah meloncat atau diam pada posisi setimbang sehingga mereka tidak bisa terpisah jika diletakkan dalam suatu medan listrik. Jadi, medan listrik tidak memproduksi perpindahan muatan dalam suatu dielektrik. Hal ini yang menyebabkan bahan dielektrik merupakan bahan insulator yang baik. Contoh dari bahan dielektrik adalah parafin, kaca, dan mika. Hal-hal yang berkaitan inilah yang akan ita bahas pada bab ini. 1. Tetapan Dielektrik Bahan Salah satu karakterisktik yang penting dari sebuah dielektrik adalah konstanta dielektrik. Sebelum dijelaskan mengenai konstanta dielektrik, terlebih dahulu kita membahas polarisasi. Walaupun di sini tidak ada perpindahan muatan ketika sebuah dielektrik diletakkan dalam suatu medan listrik, namun di sini terjadi sedikit pergeseran dari muatan positif dan negatif dalam atom atau molekul suatu dielektrik sehingga mereka menjadi dipoledipole. Pada keadaan ini, sebuah dielektrik dikatakan terpolarisasi. Jika diasumsikan bahwa sebuah dielektrik terdiri dari banyak pasangan muatan yang saling berlawanan dan masing-masing pasangan tersebut menempati posisi yang sama sehingga bahan dilektrik dikatakan netral. Pengaruh dari medan listrik luar menyebabkan muatan positif bergerak searah dengan medan listrik tersebut dan muatan negatif pada arah

2

berlawanan, sehingga material sekarang terdiri dari banyak dipole. Hal ini dapat digambarkan sebagai berikut : 0100090000037800000002001c00000000000400000003010800050000000b0 200000000050000000c027d02cd08040000002e0118001c000000fb021000070000 000000bc02000000000102022253797374656d0002cd08000080ba11007261ce30 285a16000c020000cd080000040000002d01000004000000020101001c000000fb 029cff0000000000009001000000000440001254696d6573204e657720526f6d616 e0000000000000000000000000000000000040000002d010100050000000902000 000020d000000320a5a0000000100040000000000ca087e0220002d00040000002 d010000030000000000 Gambar 1.1 Polarisasi pada sepotong bahan dielektrik Dari penjelasan di atas maka dapat diketahui bahwa bahan dilektrik  yang ditempatkan dalam suatu medan listrik eksternal E akan mengalami perpindahan listrik :   D = ε0E

(1.1)

Dengan adalah permitivitas vakum. Di samping itu bahan dielektrik menjadi terpolarisasi, sehingga sifat elektromekanikanya berubah melalui ungkapan :    D = ε0E + P

(1.2)

Dengan adalah medan listrik dalam bahan. Gabungan dari kedua persamaan di atas dihasilkan :  1  E = E0 − P ε0

(1.3)

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Tampak bahwa polarisasi bahan menyebabkan terjadinya induksi medan. Hal ini dapat dijelaskan dari gambar berikut :   +

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 1 E Gambar 1.2 Medan E melawan medan luar 0 , resultan medan  E internal adalah Polarisasi

menyebabkan

terjadinya

muatan

terpolarisasi

pada

permukaan bahan , yakni muatan positif di sebelah kanan dan muatan negatif  di sebelah kiri. Muatan ini menimbulkan medan listrik E yang arahnya ke kiri   E melawan medan luar 0 , akibatnya medan internal resultan yakni E lebih  E kecil dari pada 0 . Pada umumnya ada hubungan fungsional antara polarisasi dan medan

listrik,

  P ( E ) atau Px = Px ( E x , E y , E z )

 dan selanjutnya jika E = 0 maka ada

   P = 0 atau P ≠ 0 P kemungkinan nilai dari . Jika (0) ≠ 0 maka bahan

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dipolarisasikan rata dalam ketidakadaan medan. Hal ini dapat dijelaskan  bahwa bahan memiliki polarisasi permanen, selanjutnya P (0) = 0 maka ada kemungkinan yang diharapkan ketika berbicara tentang polarisasi yang dihasilkan oleh medan. Secara umum bahan dielektrik dapat dibagi menjadi : a. Dielektrik Non Linear  P (0) = 0 adalah masih dengan memungkinkan Daerah dengan   P dan E hubungan antara tetapi sulit untuk sebagian besar bahan, bagaimanapun juga membutuhkan keadaan/ kondisi, seperti medan yang sangat besar/ panjang, atau temperatur rendah atau keduanya. Oleh  karena itu pencarian tersebut cukup memberikan P sebagai deret  pangkat dalam komponen E yaitu : Pi = ∑ α ij E j + ∑∑ β ijk E j E k + .... j

j

(1.4)

k

Dimana indeks i, j, k mengambil nilai x, y, z. Bentuk tersebut memiliki  α , β ,.... P asumsi bahwa (0) = 0 . Nilai khusus dari koefisien ij ijk akan tergantung keadaan yang meliputi dielektrik khusus. Jika orde kedua atau suku-suku tinggi dalam komponen

 E

dibutuhkan untuk

menggambarkan atau merincikan bahan, maka dielektrik tersebut non linear.

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b. Dielektrik Linear  P Dalam kasus ini, secara umum hubungan komponen terhadap komponen  E dapat dituliskan dalam bentuk : Px = ε 0 ( χ xx E x + χ xy E y + χ xz E z ) Py = ε 0 ( χ yx E x + χ yy E y + χ yz E z ) Pz = ε 0 ( χ zx E x + χ zy E y + χ zz E z )  χ xx χ xy χ xz  E x   Px        Py  = ε 0  χ yx χ yy χ yz  E y       χ χ χ  E   Pz   zx zy zz  z 

  P = ε 0 χE

Dengan faktor keseimbangan

χ ij

disebut komponen dari tensor

χ suseptibilitas listrik. Telah diperkenalkan faktor ε 0 sehingga ij akan tidak berdimensi. Pada umumnya

χ ij

merupakan fungsi dari posisi dalam bahan.

tidak konstan, tapi dapat

χ ij

tidak dapat bergantung

sebab akan membawa kembali ke masalah non linear (persamaa1.4).  Dari bentuk tersebut dapat dilihat bahwa hubungan P tidak akan paralel

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  dengan E dalam dielektrik. Sedangkan hubungan D akan paralel  terhadap E . c. Dielektrik Isotropik Linear Diasumsikan bahwa pada suatu bahan yang diberikan memiliki  kelistrikan dari dielektrik tidak tergantung arah E . Kemudian keadaan tersebut diketahui sebagai isotropik. Sejak itu satu arah adalah  kelengkapan ekuivalensi terhadap yang lain. P harus paralel terhadap E , jika

χ ij = 0 jika i ≠ 0 dan χ xx = χ yy = χ zz

, sehingga persamaan (1.5) dapat

ditulis sebagai berikut :  χ xx 0 0  1 0 0       P = ε 0  0 χ yy 0  E = ε 0 χ  0 1 0  E    0 0 1    0 0 χ zz 

  P = χ eε 0 E

(1.5)

Dengan adalah suseptibilitas listrik sehingga perpindahan listrik dapat dijelaskan dengan :    D = ε 0E + ε 0χe E   D = ε 0 (1 + χ e ) E   D = ε 0Ke E

Besarnya dan menunjukkan karakteristik sifat kelistrikan dari bahan yang ditentukan dengan eksperimen, dan nilai –nilai tersebut dapat dicari

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dalam beberapa tabel. Untuk semua bahan, dengan , positif untuk medan statis, maka. Dari persamaan (1.6) dapat diketahui bahwa dan paralel dalam keadaan itu. Konstanta dielektrik untuk beberapa bahan bisa dilihat pada tabel di bawah ini. Jika medan listrik dalam suatu dielektrik dibuat sangat kuat, maka medan listrik tersebut akan memulai menarik elektron sama sekali keluar dari molekulnya, sehingga bahan menjadi penghantar. Medan listrik maksimum yang bisa dilawan oleh dielektrik tanpa bocor disebut kuat dielektrik. Tabel. Konstanta dielektrik bahan untuk medan tetap. No. 1. 2. 3. 4. 5. 6. 7. 8. 9. 10. 11. 12. 13. 14. 15. 16. 17. 18. 19. 20. 21. 22. 23. 24 25.

Medium Vakum Udara Styrofram Parafin Plywood Polystyrene Amber Karet Kayu Plexiglas Tanah pasir kering Nylon Sulfur Quartz Bakelit Formica Lead glass Mika Marmer Kaca flinta Amonia (cair) Gliserin Air (destilat) TiO2 BaTiO2

Konstanta Dielektrik 1 1.0006 1.03 2.1 2.1 2.7 3 3 3 3.4 3.4 3.8 4 5 5 6 6 6 8 10 22 50 81 89-173 1200

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2. Polarisabilitas Polarisasi bahan yaitu pensejajaran momen dipole molekul yang terjadi karena medan listrik. Oleh karena itu, diambil asumsi bahwa molekul p sebanding dengan medan listrik lokal ε x pada molekul yang bersangkutan : p = αε x

……………………….

(2.1) Dengan α adalah polarisabilitas molekul. Sehubungan dengan proses polarisasi bahan, struktur molekul atau atom yang membangun suatu bahan dapat dikelompokkan menjadi : a. Molekul polar, yaitu molekul yang mempunyai resultan momen dipole permanent tidak sama dengan nol. Contoh : H2O b. Molekul Non Polar, yaitu molekul yang mempunyai resultan momen dipole permanent sama dengan nol. Contoh : CO2. c. Molekul Ionik, yaitu molekul yang berikatan ionik. Contoh : NaCl d. Atom kristal kovalen bersifat nonpolar dan nonionik. Contoh :Si dan Ge Berdasarakan jenis molekul atau atom di atas dan perilakunya saat dikenakan medan, maka polarisabilitas bahan dapat dikelompokkan dalam beberapa jenis berikut: a. Polarisabilitas Polar/Orientasimal (

αp

)

Momen dipole permanent bahan terdistribusi secara acak sehingga

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polarisasi sama dengan nol. Saat dikenakan medan listrik momen dipole cenderung mensejajarkan diri terhadap arah medan, sehingga polarisasi tidak sama

dengan nol. Polarisabilitas polar dibedakan menjadi

polarisabilitas polar static dan polarisabilitas polar bolak-balik. b. Polarisabilitas Ionik ( α i ) Medan menyebabkan ion positif bergerak searah medan dan ion negatif bergerak berlawanan arah medan sehingga panjang ikatan antar ion menjadi longgar. Perpindahan relatif ion bermuatan ini menghasilkan momen dipole dalam satuan yang sebelumnya tidak ada. c. Polarisabilitas Elektronik ( α e ) Masing-masing ion atau atom dalam molekul terdiri dari inti (nukleus) dan elektron. Bila dikenakan medan, maka ion atau atom individual tersebut menjadi terpolarisasi karena elektron mengalami perpindahan relatif terhadap inti kearah yang berlawanan dengan arah medan. Hal yang sama juga terjadi pada atom netral. Polarisabilitas ini juga terdiri dari polarisibilitas elektronik statis dan polarisabilitas elektronik bolakbalik. Dari uraian diatas, umumnya polarisabilitas total suatu bahan dapat ditulis

α = αe + αi + α p

…2.2

Bentuk α e terjadi pada semua jenis bahan. Sedangkan bentuk α i hanya terjadi pada bahan ionik. Pada bahan polar dapat terjadi proses

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ketiga polarisasi diatas. Terdapat ciri khusus yang membedakan satu sama lain dari ketiga polarisasi diatas, yaitu : a. Polarisasi polar menunjukkan kebergantungan kuat terhadap suhu, sedangkan dua polarisasi yang lain tidak. Konstanta dielektrik bahan polar mengalami penurunan seiring dengan kenaikan suhu. b. Perilaku polarisabilitas bolak-balok yaitu saat bahan dikenakan medan listrik bolak-balik. 3. Piezoelektrik Piezoelektrik adalah kemampuan untuk membangkitkan tenaga listrik jika dikenai gaya mekanik, atau membangkitkan gaya mekanik apabila dikenai tegangan listrik, misalnya yang terjadi pada kristal piezoelektrik. Kristan piezoelektrik adalah kristal yang memperlihatkan adanya efek piezoelektrik pada dirinya. Efek piezoelektrik yaitu tmbulnya beda potensial antara sisi-sisi yang berhadapan pada kristal non konduktor tertentu ( kristal piezoelektrik ) akibat pemberian tegangan mekanik antara kedua sisi tersebut. Efek langsung piezoelektrik menunjukkan bahwa pada kristal terjadi regangan, maka akan terjadi pula medan listrik. Sedangkan pada efek balik, pemakaian medan listriklah yang menghasilkan regangan. Dengan demikian gejala piezoelektrik dapat digunakan untuk mengkonversikan energi listrik menjadi energi mekanik atau sebaliknya seperti yang terjadi pada tranduser. Gejala Piezoelektrik hanya terjadi pada bahan non sentrosimetri

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karena distorsi yang terjadi menyebabkan perpindahan muatan ionik dalam kristal yang semula berhimpit karena adanya tekanan, seperti gambar berikut : 0100090000037800000002001c00000000000400000003010800050000000b0200 000000050000000c027d02cd08040000002e0118001c000000fb021000070000000 000bc02000000000102022253797374656d0002cd08000080ba11007261ce30285 a16000c020000cd080000040000002d01000004000000020101001c000000fb029c ff0000000000009001000000000440001254696d6573204e657720526f6d616e000 0000000000000000000000000000000040000002d0101000500000009020000000 20d000000320a5a0000000100040000000000ca087e0220002d00040000002d010 000030000000000 P = χ eε 0 ε + d T Keterangan : P = polarisasi

χ 0 = suseptibilitas listrik ε = medan listrik ε 0 = permitivitas vakum T = tetapan mekanik 4. Ferroelektrik Umumnya suseptibilitas ionik tidak tergantung pada suhu. Tetapi pada bahan ferroelektrik konstanta dielektrik berubah terhadap suhu melalui hubungan hukum Curie – Weiss. C ∈ r = T − Tc

….

( 4.1 )

Dengan C adalah konstanta Curie dan TC adalah suhu Curie. Hal ini

12

ditunjukkan oleh gambar 4.1 berikut :

Dalam fasa ferroelektrik pusat muatan positif, kristal tidak berimpit dengan pusat muatan negatif. Gejala ferroelektrik hanya terjadi pada kelas nonsentrosimetri polar. Arah polarisasi spontan ferroelektrik tidak sama dalam keseluruhan bagian bahan. Oleh karena itu bahan terdiri dari sejumlah domain, yakni daerah dimana polarisasinya konstan. Domain berbeda mempunyai polarisasi berbeda pula sehingga polarisasi total bahan menjadi nol saat setimbang. Pensejajaran domain terjadi bila dikenakan medan listrik eksternal, yakni domain yang polarisasinya searah medan bertambah banyak dan sebaliknya. Dengan demikian bahan ferroelektrik menunjukkan loop histerisis. Contoh bahan ferroelektrik adalah jenis sperovskit misalnya Barium ( BaTiO3 ). Diatas suhu Curie ( Tc = 180°C ) BaTiO3 berstruktur kubik, tetapi dibawah suhu − Curie strukturnya berubah menjadi tetragonal. Dalam fasa ini ion Ti4+ dan O2

bergeser terhadap ion Ba2+. Akibatnya terjadilah pemisahan pusat muatan positif dan negatif sejauh 0,012 mm, sehingga terjadi polarisasi spontan.

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5. Konstanta Optik Ingat

permitivitas

bahwa

konstanta

oleh

perambatan

berhubungan

dengan

atau

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itu digunakan oleh

.

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Hubungan itu sering ditulis :

………………………

(5.1)

Dimana n dan k adalah bilangan real dan imajiner, berturut-turut dari 010009000003de0500000000bd05000000000400000003010800050000000b0200 000000050000000c022b002a00030000001e00bd050000410b2000cc002a002900 000000002a0029000000000028000000290000002a000000010008000000000000 0000000000000000000000000000000000000000000000ffffff00fefefe00eafefe00 0072ba00d4fefe009b009b00fefed400baeafe00ba727200fefeea009bd4fe00d49b00 0072baea00eaba7200fed49b00009bd4007272ba00feeaba0000009b00ba720000ba 729b0072009b00720072009b00720000007200d49b72007200000000727200729b d4009b000000d4fed400baba720000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000000000

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Bagian imajiner dari konstanta perambatan dapat diukur langsung jika zat padat tembus cahaya dengan cukup. Irisan dari ketebalan z dapat dikatakan diterangi dengan cahaya monokromatik. Jika I0 adalah intensitas sebelum keluar dalam sisi lain, kemudian dalam koefisien pemadaman. Refleksitas dari suatu sampel merupakan konstanta optik lain yang menarik. Anggap radiasi datang secara normal pada permukaan sampel seperti pada gambar di bawah ini. Sumbu z sepanjang garis normal dengan z=0 pada batas. Gelombang datang mempunyai perambatan

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R

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) sampel merupakan perbandingan dari intensitas yang

direfleksikan dari intensitas yang datang.

…………………(5.8) Reflektifitas bernilai dari 0 sampai 1.

dan tidak terjadi refleksi jika

n=1 dan k=0. Reflektifitas mendekati 1 jika n atau k menjadi besar. 6. Konduktifitas Optik Sebuah

gambaran

untuk

frekuensi

yang

tergantung

pada

konduktivitas yang diperoleh dari persamaan tetapan Boltzman. Dengan menganggap elektron dalam pengikat tunggal dan digunakan saat relaksasi yang dapat ditulis

……(6.1) Dirac dan

adalah waktu relaksasi. Meskipun kita asumsikan pada gradien

temperatur hilang, kita harus menggolongkan dua istilah karena medan listrik

189

tetapi gayanya kecil dapat mengabaikannya. Untuk

merupakan sebuah medan lemah, sepanjang.

sumbu x dan diasumsikan

di mana bentuk kedua lebih

kecil disbanding yang pertama. Substitusi bentuk persamaan (6.1) dan

abaikan hasil

. Juga substitusi

.

Kemudian selesaikanlah untuk f10. Hasilnya :

…………(6.2) Perbandingan merupakan perbandingan kecil mendekati. Jadi istilah selanjutnya dalam dominator dapat diabaikan. Kemudian komponen x dalam rapat arus adalah : …………(6.3) Dimana penjumlahan tersebut berhubungan dengan semua keadaan dalam pengikat. Faktor pengali

adalah konduktivitas : ……….(6.4)

Jika waktu relaksasi (pelemahan) tidak tergantungoleh k,

dapat

difaktorkan dari penjumlahan dn persamaan (6.4) dapat dituliskan sebagai berikut : ……………. (6.5) Dimana

adalah konduktivitas dari

= 0. Bagian real dan imajiner dari ó

190

menunjukkan kejelasan dalam kedua penggambaran. Persamaan (6.5) memberikan alasan genap jika waktu relaksasi tergantung pada k, menentukan dapat digantikan oleh rata-rata yang berpadanan. Untuk luas

bagian real pada ó adalah berbanding dengan

.N

Keduanya sangat kecil dan kita tentukan free carries adalah terpenting untuk

melengkapi optik jika frekuensi temperature ruang

angular

atau lebih kecil. Dalam

sekitar 10-12 atas atas yang mempengaruhi free carriers

adalah pada bagian gelombang mikro atau infrared dalam spektrum. Sehubungan dengan hasil frekuensi free carriers sangat penting wujud permeabilitas statik dan

adalah

hilang untuk sebagian besar material

kecuali apabila terjadi jika dalam keadaan padat dari sebagian semi konduktor ionik. 7. Permitivitas Efektif Kita belajar tentang free carriar contribution ke sinyal optis kaitannya dengan permitivitas efektif ∈eff = ∈ + (i σ / ω ) dengan bagian riil ∈’eff = ∈’

σ 0 t (1 + ω 2 t 2 ) dan bagian imaginer ∈’’ = σ 0 / ω (1 + ω 2 t 2 ) dimana kita eff mengambil ∈’’ menjadi 0 mengasumsikan pita parabolic dan menggunakan

σ 0 = ne 2 t / m 2 dengan m adalah massa efektif.

ne 2 t 2

(

2 2 ∈’eff = ∈- m ∗ 1 + ω t

)

 ω p2 t 2  1 −   1+ ω2t2   = ∈’ 

…….(7.1)

191

ne 2 t 2

(

∈ ω p2 t 2

∈’’eff = ∈- m ∗ 1 + ω t Dimana

2

ω p ne 2 / m ∗

2

) = ∈’’+ ωt (1 + ω t ) 2 2

…….(7.2)

disebut frekuensi polar plasma. Ini adalah suatu

parameter penting untuk penentuan pada determination of free carrier contribution ke serat optis. Kalau kita lihat, ini juga merupakan frekuensi alami osilasi dari sistem free carrier. Untuk semi konduktor intrinsik pada suhu ruangan adalah antara 1015 carrier/m3 dan 1020 carrier/m3 bersesuaian dengan frekuensi plasma sekitar 109rad/s. pada gelombang radio sekitar 1012 rad/s. pada gelombang mikro, frekuensi plasma lebih kecil pada temperatur rendah frekuensi plasma. Sangat baik pada tepi fundamental absorbtion dan dengan mudah semi konduktor pada semua suhu. Karena kekhasan dari semi konduktor

ω pt

kurang dari 1 dan ∈’eff adalah

positif untuk semua frekuensi. Gambar 10 – 19 menunjukkan perbandingan

ω t ∈’eff / ∈’ sebagai fungsi dari ω untuk p = 0,5 untuk frekuensi rendah dari frekuensi plasma free carrier’s untuk mengurangi permeabilitas efektif

persamaan 7.1 ∈’eff = ∈’

(1 − ω t ) pada frekuensi tinggi ∈’ 2 p

2

eff

hampir sama

dengan ∈’.

192

(

)

2 ( ) Gambar 7.1 : Penyerapan free carrier : 2 / σ 0 ε 0 dW / dt ave sebgai fungsi ωt

dimana ω adalah frekuensi putar dan t adalah waktu relaksasi. Penyerapan tinggi untuk frekuensi putar dibawah 1/t. tetapi cenderung kearah nol ketika frekuensi menjadi besar. Sebagian besar semi konduktor dan isolator pada suhu kamar 1/t dengan orde 1012 rad/s.

[ω Pada frekuensi rendah n = K =

2 p

t / 2ω

]

1 2

. Ketika n dan K keduanya

sangat besar dari 1 maka reflektivitasnya 1. Gelombang itu masuk, contoh dari

severely attenuated pada frekuensi tinggi n = ∈' / ∈0

∈' / ∈0

dan K =

(ω

2 p

/ 2ω 2 t

)

freee carrier sudah cukup berpengaruh pada frekuensi tinggi indeks

khas dari refleksi dan pemadaman berkurang. Sebagian besar campuran semi konduktor terbatas. Untuk ωt >> 1 tidak

193

selalu terlihat secara eksperimen ketika frekuensi bergantung pada t menjadi frekuensi tinggi. Meskipun demikian koefisien attenuation untuk radiasi infra −s merah sering dinyatakan sebagai Cω di mana C dan S adaalah konstanta

empiris. Eksponen S antara 2,5 dan 4,5 kita berpikir tentang pita tunggal. Bagaimanapun semua elektron valensi carrier dan konduksi pita berkontribusi untuk konstanta optik dan kontribusi berbagai pita harus dijumlahkan untuk mencari permitivitas efektif total. Persamaan (7.1) dan (7.2) pegangan untuk masing-masing pita dengan nilai σ 0 dan t bergantung pita.

Gambar 7.2 kontruksi free carrier pada bagian riil dari permitivitas efektif. ' ' Untuk ωpt = 0.5 dengan catatan lebih kecil dari ∈ tetapi ∈ cenderung

frekuensinya lebih besar

DAFTAR PUSTAKA Derziel, Alder Van. 1957. Solid State Physical Electronics. Japan : Prentice HallInc

194

Suyoso.2000. Listrik Magnet. Yogyakarta: FMIPA Universitas Negeri Yogyakarta. CONTOH SOAL Dua buah plat kapasitor dengan masing-masing kerapatan permukaannya 0100090000034a0300000000290300000000040000000301080005000000 0b0200000000050000000c0217001700030000001e0029030000410b2000 cc0016001600000000001600160000000000280000001600000016000000 010008000000000000000000000000000000000000000000000000000000 0000ffffff00fefefe00489cdf00df9c48000074bf0048000000fedf9c00bffefe0 000007400bf7400009cdffe009c484800fefedf00dffefe0000489c009c48000 0480074004800480000004800febf740074bffe0074000000fefebf0000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000

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Penyelesaian : Medan listrik pada permukaan dengan kerapatan σ adalah 010009000003220300000000010300000000040000000301080005000000 0b0200000000050000000c021d000f00030000001e0001030000410b2000 cc001c000e00000000001c000e0000000000280000000e0000001c0000000 100080000000000000000000000000000000000000000000000000000000 000ffffff00fefefe00489cdf0074000000fefebf00dffefe0000489c00bf740000 febf740074bffe009c480000fefedf00df9c48009cdffe00000048009c484800 bffefe000000740074489c009c487400bf74480048007400fedf9c00000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000 000000000000000000000000000000000000000000000000000000000000

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dengan arah dari positif ke negative. Polarisasi

dari kedua plat adalah besarnya sama yaitu negatif sehingga medan listrik yang timbul adalah

pada plat dari plat

negative ke plat positif.

201

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c.

Soal dan Pembahasan 1. Apa ciri khusus yang membedakan antara polarisabilitas ionik dan elektronik? ( Ragil Pri T / 05302241023 ). Jawab : Bentuk polarisabilitas elektronik terjadi pada semua jenis bahan, sedangkan

bentuk polarisabilitas ionik hanya terjadi pada bahan ionik

2. a.) Bagaimana cara membuktikan resultan momen dipole permanent suatu molekul polar tidak sama dengan nol? Jawab : yaitu dengan mengetahui jumlah elektron valensi setiap unsur yang dimiliki setiap unsur, apabila elektron valensi yang ada digunakan untuk bergabung, atau dengan kata lain elektron digunakan bersama, sehingga untuk memenuhi oktaf elektron digunakan dari dua elektron dari dua unsur. Keadaan demikian yang menimbulkan momen dipole (gaya tarik menarik) unsur-unsur di dalamnya tidak sama dengan nol. Contoh :

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molekul polar, yaitu H2O, atom O mempunyai elektron valensi = 6, sedangkan H elektron valensi = 2. 0100090000037800000002001c0000000000040000000301080005000000 0b0200000000050000000c027d02cd08040000002e0118001c000000fb021 000070000000000bc02000000000102022253797374656d0002cd0800008 0ba11007261ce30285a16000c020000cd080000040000002d01000004000 000020101001c000000fb029cff0000000000009001000000000440001254 696d6573204e657720526f6d616e00000000000000000000000000000000 00040000002d010100050000000902000000020d000000320a5a00000001 00040000000000ca087e0220002d00040000002d010000030000000000 b.) Bagaimana piezoelektrik itu terjadi? Sebutkan contoh piezoelektrik! ( Isnaini Nurul Hidayati / 05302241010 ). Jawab : Gejala piezoelektrik hanya terjadi pada bahan non sentrosimetri karena distorsi yang terjadi menyebabkan perpindahan muatan ionik dalam kristal yang semula berhimpit karena adanya tekanan. Piezoelektrisitas adalah kemampuan dari suatu benda (pada umumnya kristal dan keramik) untuk menghasilkan potensial listrik sebagai response terhadap tekanan mekanik yang diberikan. Efek piezoelektrik adalah suatu efek yang reversible,

dimana

terdapat

efek

piezoelektrik

langsung

(direct

piezoelectric effect) dan efek piezoelektrik balikan (converse piezoelectric effect). Efek piezoelektrik langsung adalah produksi potensial listrik akibat adanya tekanan mekanik. Sedangkan efek piezoelektrik balikan adalah produksi tekanan akibat pemberian tegangan listrik, contohnya adalah kristal lead zirconate titanate yang akan mengalami perubahan dimensi sampai maksimal 0.1 % jika diberi tegangan listrik. Contoh penggunaan piezoelektrik adalah untuk memecah batu ginjal tanpa pembedahan. 3. Piezoelektrik termasuk polarisasi yang mana? (ken utami / 05302241034 ) J jawab :Struktur kristal bisa dibagi menjadi 32 kelompok, berdasarkan pada jumlah sumbu putar dan bidang pantulan pada kristal yang membuat struktur kristal tidak berubah. Dari 32 kelompok kristal tersebut, 21 di antaranya

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adalah non-centrosymmetric (tidak memiliki sebuah pusat simetri). Dari 21 kelompok tadi, 20 di antaranya menunjukkan sifat piezoelektrik yang langsung, sedang 1 kelompok tetap berada di kelompok kubus 432. Sepuluh dari 20 kelompok piezoelektrik memiliki sifat polar (berkutub)—mereka memiliki polarisasi yang spontan, memiliki sebuah dipol dalam sel satuan mereka, dan menunjukkan piroelektrisitas. Jika dipol ini bisa dibalikkan dengan menerapkan medan listrik, maka berarti bahan itu bersifat feroelektrik. Setiap bahan dielektrik mengembangkan polarisasi dielektrik saat sebuah medan listrik diterapkan, namun substansi yang memiliki pemisahan muatan secara alami biarpun tidak ada medan listrik disebut sebagai bahan polar. Polar tidaknya sebuah bahan ditentukan oleh struktur kristalnya. Hanya 10 dari 32 kelompok struktur kristal yang berkutub. Semua kristal polar merupakan piroelektrik, jadi 10 kelompok kristal polar terkadang dianggap sebagai kelompok-kelompok piroelektrik. 4. Sebutkan karakteristik masing-masing bahan dielektrik! ( Erna Puspitasari / 05302241029 ) Jawab : d. Dielektrik Non Linear  P Daerah dengan (0) = 0 adalah masih dengan memungkinkan   P dan E hubungan antara tetapi sulit untuk sebagian besar bahan, bagaimanapun juga membutuhkan keadaan/ kondisi, seperti medan yang sangat besar/ panjang, atau temperatur rendah atau keduanya. e. Dielektrik Linear   hubungan P tidak akan paralel dengan E dalam dielektrik.   Sedangkan hubungan D akan paralel terhadap E . f. Dielektrik Isotropik Linear Diasumsikan bahwa pada suatu bahan yang diberikan memiliki  kelistrikan dari dielektrik tidak tergantung arah E . Kemudian keadaan tersebut diketahui sebagai isotropik.

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5. Bagaimana efek piezoelektrik terjadi? Apa maksud dari pemberian tegangan mekanik? ( Reval D/ 05302241024 ) Jawab : Piezoelektrisitas adalah kemampuan dari suatu benda (pada umumnya kristal dan keramik) untuk menghasilkan potensial listrik sebagai response terhadap tekanan mekanik yang diberikan. Efek piezoelektrik adalah suatu efek yang reversible, dimana terdapat efek piezoelektrik langsung (direct piezoelectric effect) dan efek piezoelektrik balikan (converse piezoelectric effect). Efek piezoelektrik langsung adalah produksi potensial listrik akibat adanya tekanan mekanik. Sedangkan efek piezoelektrik balikan adalah produksi tekanan akibat pemberian tegangan listrik, contohnya adalah kristal lead zirconate titanate yang akan mengalami perubahan dimensi sampai maksimal 0.1 % jika diberi tegangan listrik Masing-masing sisi membentuk kutub listrik. Dan ketika suatu tekanan mekanik diterima oleh kristal piezoelektrik bentuk simetris dari tiap-tiap muatan listrik tersebut berubah menjadi tidak simetris yang akan menghasilkan tegangan listrik. Sebagai contoh, 1 cm kubik kristal quartz dengan tekanan mekanik sebesar 2000 Newton akan menghasilkan tegangan listrik sebesar 12500 Volt. Berdasarkan arah datangnya tekanan, terdapat tiga operasi yang dapat dilakukan yaitu transverse effect, longitudinal effect, dan shear effect. 6. Dari Hukum Currie- Weiss, apa yang terjadi jika t < TC ? ( M Minan Chusni/ 05302241019 ) Jawab: pada kelompok bahan ferroelektrik konstanta dielektrik berubah

terhadap suhu melalui hubungan hukum Currie- Weiss ∈r =

C T − Tc bila t < .

TC , bahan menjadi terpolarisasi secara spontan ( fase ferroelektrik) 7. Pada grafik konstanta Currie, akan stabil pada suhu berapa dan akan turun pada suhu berapa? ( Arinal Muna/ 05302241039 ) Jawab : pada kelompok bahan ferroelektrik konstanta dielektrik berubah

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C terhadap suhu melalui hubungan hukum Currie- Weiss ∈r = T − Tc . bila t < TC , bahan menjadi terpolarisasi secara spontan ( fase ferroelektrik). bila t > TC , polarisasi hanya dapat terjadi jika pada bahan dikenakan medan eksternal dan polarisasinya lenyap bila medan dihilangkan ( fase paraelektrik ) 8. Apa arti dari koefisien pemadaman? ( Ragil Pri T/ 05302241023 ) Jawab :

istilah yang tepat sebenarnya adalah koefisien pelemahan yang

menunjukkan adanya pelemahan dari berkas cahaya yang dipengaruhi oleh frekuensi. 9. Nilai tetapan Currie itu berapa? Diperoleh dari mana? n + ik menunjukkan apa? ( Ika Sarti W/ 05302241018 ) Jawab : Tetapan Currie sesuai dengan suhu curie yaitu 180 K. Diperoleh dari percobaan. Adapun keterangan untuk n, I, dan k yaitu : n = indeks bias riil i = imajiner k = koefisien pelemahan 10. Dari Hukum Currie- Weiss, apa yang terjadi jika t > TC ? ( Warsito/ 05302241019 ) Jawab: pada kelompok bahan ferroelektrik konstanta dielektrik berubah

terhadap suhu melalui hubungan hukum Currie- Weiss ∈r =

C T − Tc bila t > TC .

, polarisasi hanya dapat terjadi jika pada bahan dikenakan medan eksternal dan polarisasinya lenyap bila medan dihilangkan ( fase paraelektrik ) 11. Apa hubungan dielektrik dengan frekuensi plasma? ( Ken Utami/ 05302241034 ) Jawab : dielektrik tidak ada hubungan dengan frekuensi plasma karena frekuensi plasma berhubungan dengan permitivitas efektif. frekuensi polar plasma adalah suatu parameter penting untuk penentuan pada determination of free carrier contribution ke serat optis. Kalau kita lihat, ini

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juga merupakan frekuensi alami osilasi dari sistem free carrier. Untuk semi konduktor intrinsik pada suhu ruangan adalah antara 1015 carrier/m3 dan 1020 carrier/m3 bersesuaian dengan frekuensi plasma sekitar 109rad/s. pada gelombang radio sekitar 1012 rad/s. pada gelombang mikro, frekuensi plasma lebih kecil pada temperatur rendah frekuensi plasma.

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